******************************************************************************** * GENERAL UTILITY LATTICE PROGRAM * * Julian Gale * * Curtin Institute for Computation * * School of Molecular and Life Sciences * * Curtin University, Western Australia * ******************************************************************************** * Version = 5.2.0 * Last modified = 28th July 2019 * ******************************************************************************** * optimise - perform optimisation run * * ocell - use cell parameters as the optimisation variables * * phonon - calculate phonons for final geometry * * nomodcoord - do not mod input coordinates * * rfo - optimisation step to be determined by RFO method * ******************************************************************************** Job Started at 15:46.05 28th July 2019 Number of CPUs = 1 Host name = M-A0034725 Total number of configurations input = 1 ******************************************************************************** * Input for Configuration = 1 * ******************************************************************************** Formula = Mg8O8 Number of irreducible atoms/shells = 16 Total number atoms/shells = 16 Dimensionality = 3 : Bulk Cartesian lattice vectors (Angstroms) : 4.225106 0.000000 0.000000 0.000000 4.225106 0.000000 0.000000 0.000000 8.500000 Cell parameters (Angstroms/Degrees): a = 4.2251 alpha = 90.0000 b = 4.2251 beta = 90.0000 c = 8.5000 gamma = 90.0000 Initial cell volume = 151.737926 Angs**3 Temperature of configuration = 0.00 K Pressure of configuration = 0.000 GPa Fractional coordinates of asymmetric unit : -------------------------------------------------------------------------------- No. Atomic x y z Charge Occupancy Label (Frac) (Frac) (Frac) (e) (Frac) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 2.00000 1.000000 2 Mg c 0.000000 * 0.000000 * 0.500000 * 2.00000 1.000000 3 Mg c 0.000000 * 0.500000 * 0.250000 * 2.00000 1.000000 4 Mg c 0.000000 * 0.500000 * 0.750000 * 2.00000 1.000000 5 Mg c 0.500000 * 0.000000 * 0.250000 * 2.00000 1.000000 6 Mg c 0.500000 * 0.000000 * 0.750000 * 2.00000 1.000000 7 Mg c 0.500000 * 0.500000 * 0.000000 * 2.00000 1.000000 8 Mg c 0.500000 * 0.500000 * 0.500000 * 2.00000 1.000000 9 O c 0.500000 * 0.500000 * 0.250000 * -2.00000 1.000000 10 O c 0.500000 * 0.500000 * 0.750000 * -2.00000 1.000000 11 O c 0.500000 * 0.000000 * 0.000000 * -2.00000 1.000000 12 O c 0.500000 * 0.000000 * 0.500000 * -2.00000 1.000000 13 O c 0.000000 * 0.500000 * 0.000000 * -2.00000 1.000000 14 O c 0.000000 * 0.500000 * 0.500000 * -2.00000 1.000000 15 O c 0.000000 * 0.000000 * 0.250000 * -2.00000 1.000000 16 O c 0.000000 * 0.000000 * 0.750000 * -2.00000 1.000000 -------------------------------------------------------------------------------- Brillouin zone sampling points : -------------------------------------------------------------------------------- Point number x y z Weight -------------------------------------------------------------------------------- 1 0.000000 0.000000 0.000000 1.00000000 -------------------------------------------------------------------------------- ******************************************************************************** * General input information * ******************************************************************************** Species output for all configurations : -------------------------------------------------------------------------------- Species Type Atomic Atomic Charge Radii (Angs) Library Number Mass (e) Cova Ionic VDW Symbol -------------------------------------------------------------------------------- Mg Core 12 24.31 2.000000 1.100 0.000 1.640 O Core 8 16.00 -2.000000 0.730 0.000 1.360 -------------------------------------------------------------------------------- Lattice summation method = Ewald (3-D) = Parry (2-D) = Saunders et al (1-D) Accuracy factor for lattice sums = 12.000 Analytic derivatives to be used Time limit = Infinity Maximum range for interatomic potentials = 100000.000000 Angstroms General interatomic potentials : -------------------------------------------------------------------------------- Atom Types Potential Parameter Value Units Cutoffs(Ang) 1 2 Min / Max -------------------------------------------------------------------------------- O c Mg c Buckingham Buckingham A 1346.6000 eV 0.000 8.000 Buckingham rho 0.29840000 Ang Buckingham C 0.0000000 eV*Ang^6 -------------------------------------------------------------------------------- O c O c Buckingham Buckingham A 22764.300 eV 0.000 8.000 Buckingham rho 0.14900000 Ang Buckingham C 20.370000 eV*Ang^6 -------------------------------------------------------------------------------- ******************************************************************************** * Output for configuration 1 * ******************************************************************************** Repeat cell scan for 41 points Scan vector for cell parameters: a = 0.000000 b = 0.000000 c = 0.000000 alpha = 20.000000 beta = 20.000000 gamma = 0.000000 ################################################################################ # Output for cell point 0 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.51578835 eV Monopole - monopole (real) = -162.80688474 eV Monopole - monopole (recip)= -217.63469762 eV Monopole - monopole (total)= -380.44158236 eV -------------------------------------------------------------------------------- Total lattice energy = -327.92579402 eV -------------------------------------------------------------------------------- Total lattice energy = -31639.8263 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.925794 Gnorm: 0.007951 CPU: 0.008 ** Hessian has required structure Cycle: 1 Energy: -327.931717 Gnorm: 0.000093 CPU: 0.012 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.93171735 eV Final Gnorm = 0.00000159 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24874979 eV Monopole - monopole (real) = -163.11927212 eV Monopole - monopole (recip)= -218.06119502 eV Monopole - monopole (total)= -381.18046714 eV -------------------------------------------------------------------------------- Total lattice energy = -327.93171735 eV -------------------------------------------------------------------------------- Total lattice energy = -31640.3978 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.225103 0.000000 0.000000 0.000000 4.225103 0.000000 0.000000 0.000000 8.450234 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.225103 Angstrom dE/a 0.000001 eV/Ang b 4.225103 Angstrom dE/b 0.000001 eV/Ang c 8.450234 Angstrom dE/c 0.000076 eV/Ang alpha 90.000000 Degrees dE/alpha 0.000000 eV/Deg beta 90.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.849312 Angs**3 Density of cell = 3.549895 g/cm**3 Non-primitive cell volume = 150.849312 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.000000 0.000000 -0.000000 0.000000 3 Mg c 0.000000 0.000000 0.000000 0.000000 4 Mg c 0.000000 -0.000000 0.000000 0.000000 5 Mg c -0.000000 0.000000 0.000000 0.000000 6 Mg c -0.000000 0.000000 -0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c -0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c -0.000000 0.000000 -0.000000 0.000000 12 O c -0.000000 -0.000000 -0.000000 0.000000 13 O c 0.000000 -0.000000 -0.000000 0.000000 14 O c 0.000000 -0.000000 -0.000000 0.000000 15 O c 0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 370.7364 163.0620 163.0602 0.0000 0.0000 0.0000 2 163.0620 370.7364 163.0602 -0.0000 -0.0000 0.0000 3 163.0602 163.0602 370.7269 0.0000 -0.0000 -0.0000 4 0.0000 -0.0000 0.0000 163.0606 -0.0000 -0.0000 5 0.0000 -0.0000 -0.0000 -0.0000 163.0606 -0.0000 6 0.0000 0.0000 -0.0000 -0.0000 -0.0000 163.0620 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003688 -0.001127 -0.001127 -0.000000 -0.000000 -0.000000 2 -0.001127 0.003688 -0.001127 0.000000 0.000000 -0.000000 3 -0.001127 -0.001127 0.003689 -0.000000 0.000000 0.000000 4 -0.000000 0.000000 -0.000000 0.006133 0.000000 0.000000 5 -0.000000 0.000000 0.000000 0.000000 0.006133 0.000000 6 -0.000000 -0.000000 0.000000 0.000000 0.000000 0.006133 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 232.28496 232.28496 232.28496 Shear Modulus (GPa) = 132.76997 139.37112 136.07054 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.11564 6.26583 6.19119 Velocity P-wave (km/s) = 10.73790 10.85273 10.79547 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00430506 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 271.11363 271.11363 271.10639 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30547 0.30547 Poissons Ratio (y) = 0.30547 0.30547 Poissons Ratio (z) = 0.30548 0.30548 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 y 0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 y 0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.78965 0.00000 0.00000 y 0.00000 7.78965 0.00000 z 0.00000 0.00000 7.79003 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.79099 2 = 2.79099 3 = 2.79106 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 243.50 243.50 243.50 243.50 344.62 344.62 344.62 344.62 344.63 344.63 355.68 355.68 390.53 390.53 399.15 399.16 399.16 426.15 426.15 426.15 426.15 453.36 453.36 453.36 453.36 457.33 457.33 457.34 457.34 457.34 457.34 475.31 475.31 488.92 488.92 488.92 609.76 609.76 609.76 609.76 798.99 798.99 799.00 968.16 968.16 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.313211 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.0248 seconds ################################################################################ # Output for cell point 1 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24888884 eV Monopole - monopole (real) = -163.10237401 eV Monopole - monopole (recip)= -218.06654048 eV Monopole - monopole (total)= -381.16891449 eV -------------------------------------------------------------------------------- Total lattice energy = -327.92002565 eV -------------------------------------------------------------------------------- Total lattice energy = -31639.2698 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.920026 Gnorm: 0.000043 CPU: 0.028 **** Optimisation achieved **** Final energy = -327.92002565 eV Final Gnorm = 0.00004259 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24888884 eV Monopole - monopole (real) = -163.10237401 eV Monopole - monopole (recip)= -218.06654048 eV Monopole - monopole (total)= -381.16891449 eV -------------------------------------------------------------------------------- Total lattice energy = -327.92002565 eV -------------------------------------------------------------------------------- Total lattice energy = -31639.2698 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.225103 0.000000 0.000000 0.000000 4.225103 0.000000 -0.073741 -0.073741 8.449590 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.225103 Angstrom dE/a 0.000284 eV/Ang b 4.225103 Angstrom dE/b 0.000284 eV/Ang c 8.450234 Angstrom dE/c -0.002004 eV/Ang alpha 90.500000 Degrees dE/alpha 0.000000 eV/Deg beta 90.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.837824 Angs**3 Density of cell = 3.550165 g/cm**3 Non-primitive cell volume = 150.837824 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c 0.000000 0.000000 0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 0.000000 0.000000 0.000000 6 Mg c 0.000000 0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c -0.000000 -0.000000 -0.000000 0.000000 9 O c 0.000000 0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 0.000000 0.000000 11 O c -0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 -0.000000 0.000000 0.000000 13 O c -0.000000 -0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 0.000000 0.000000 15 O c 0.000000 0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 370.7527 163.1425 163.0691 -3.8527 -0.7067 0.0619 2 163.1425 370.7527 163.0691 -0.7067 -3.8527 0.0619 3 163.0691 163.0691 370.7171 0.3271 0.3271 -0.1003 4 -3.8527 -0.7067 0.3271 163.0546 -0.0773 -4.5640 5 -0.7067 -3.8527 0.3271 -0.0773 163.0546 -4.5640 6 0.0619 0.0619 -0.1003 -4.5640 -4.5640 163.1562 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003690 -0.001128 -0.001127 0.000085 -0.000008 0.000000 2 -0.001128 0.003690 -0.001127 -0.000008 0.000085 0.000000 3 -0.001127 -0.001127 0.003689 -0.000039 -0.000039 0.000001 4 0.000085 -0.000008 -0.000039 0.006140 0.000008 0.000172 5 -0.000008 0.000085 -0.000039 0.000008 0.006140 0.000172 6 0.000000 0.000000 0.000001 0.000172 0.000172 0.006139 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 232.28486 232.30932 232.29709 Shear Modulus (GPa) = 132.67140 139.38250 136.02695 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.11314 6.26585 6.18997 Velocity P-wave (km/s) = 10.73576 10.85283 10.79446 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00430506 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 270.99100 270.99100 271.06740 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30567 0.30552 Poissons Ratio (y) = 0.30567 0.30552 Poissons Ratio (z) = 0.30544 0.30544 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 y 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 z -0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 0.00000 0.00000 -0.00000 0.00000 y 0.00000 -0.00000 0.00000 -0.00000 0.00000 0.00000 z -0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.79105 0.00118 0.03667 y 0.00118 7.79105 0.03667 z 0.03667 0.03667 7.79228 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.78216 2 = 2.79103 3 = 2.80073 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 243.36 243.36 243.56 243.56 340.76 340.76 344.36 344.71 348.35 348.35 355.75 355.75 390.54 390.54 397.58 399.17 400.63 426.06 426.06 426.19 426.19 453.33 453.33 453.33 453.33 455.28 455.28 457.15 457.41 459.34 459.34 475.37 475.37 488.99 488.99 489.08 609.72 609.72 609.78 609.78 799.02 799.02 799.04 968.19 968.19 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.313186 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.0359 seconds ################################################################################ # Output for cell point 2 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24930931 eV Monopole - monopole (real) = -163.05167806 eV Monopole - monopole (recip)= -218.08257982 eV Monopole - monopole (total)= -381.13425789 eV -------------------------------------------------------------------------------- Total lattice energy = -327.88494858 eV -------------------------------------------------------------------------------- Total lattice energy = -31635.8854 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.884949 Gnorm: 0.000175 CPU: 0.039 **** Optimisation achieved **** Final energy = -327.88494858 eV Final Gnorm = 0.00017512 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24930931 eV Monopole - monopole (real) = -163.05167806 eV Monopole - monopole (recip)= -218.08257982 eV Monopole - monopole (total)= -381.13425789 eV -------------------------------------------------------------------------------- Total lattice energy = -327.88494858 eV -------------------------------------------------------------------------------- Total lattice energy = -31635.8854 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.225103 0.000000 0.000000 0.000000 4.225103 0.000000 -0.147477 -0.147477 8.447659 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.225103 Angstrom dE/a 0.001134 eV/Ang b 4.225103 Angstrom dE/b 0.001134 eV/Ang c 8.450234 Angstrom dE/c -0.008251 eV/Ang alpha 91.000000 Degrees dE/alpha 0.000000 eV/Deg beta 91.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.803358 Angs**3 Density of cell = 3.550976 g/cm**3 Non-primitive cell volume = 150.803358 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.000000 -0.000000 -0.000000 0.000000 3 Mg c 0.000000 -0.000000 0.000000 0.000000 4 Mg c 0.000000 -0.000000 0.000000 0.000000 5 Mg c -0.000000 -0.000000 0.000000 0.000000 6 Mg c -0.000000 -0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c -0.000000 0.000000 -0.000000 0.000000 12 O c -0.000000 0.000000 -0.000000 0.000000 13 O c 0.000000 -0.000000 -0.000000 0.000000 14 O c 0.000000 0.000000 -0.000000 0.000000 15 O c 0.000000 0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 370.8014 163.3842 163.0958 -7.7041 -1.4136 0.2475 2 163.3842 370.8014 163.0958 -1.4136 -7.7041 0.2475 3 163.0958 163.0958 370.6876 0.6546 0.6546 -0.4015 4 -7.7041 -1.4136 0.6546 163.0365 -0.3094 -9.1260 5 -1.4136 -7.7041 0.6546 -0.3094 163.0365 -9.1260 6 0.2475 0.2475 -0.4015 -9.1260 -9.1260 163.4389 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003695 -0.001132 -0.001128 0.000169 -0.000016 0.000002 2 -0.001132 0.003695 -0.001128 -0.000016 0.000169 0.000002 3 -0.001128 -0.001128 0.003691 -0.000078 -0.000078 0.000004 4 0.000169 -0.000016 -0.000078 0.006161 0.000032 0.000345 5 -0.000016 0.000169 -0.000078 0.000032 0.006161 0.000345 6 0.000002 0.000002 0.000004 0.000345 0.000345 0.006157 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 232.28412 232.38244 232.33328 Shear Modulus (GPa) = 132.37500 139.41669 135.89584 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.10561 6.26590 6.18627 Velocity P-wave (km/s) = 10.72934 10.85313 10.79142 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00430507 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 270.62309 270.62309 270.95026 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30625 0.30568 Poissons Ratio (y) = 0.30625 0.30568 Poissons Ratio (z) = 0.30531 0.30531 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 0.00000 0.00000 -0.00000 0.00000 y -0.00000 0.00000 0.00000 -0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.79524 0.00474 0.07355 y 0.00474 7.79524 0.07355 z 0.07355 0.07355 7.79903 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.77407 2 = 2.79115 3 = 2.81132 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 -0.00 242.91 242.91 243.74 243.74 336.77 336.77 343.59 344.95 351.94 351.94 355.95 355.95 390.58 390.58 395.91 399.19 402.02 425.82 425.82 426.30 426.30 453.18 453.18 453.25 453.25 453.26 453.26 456.59 457.61 461.29 461.29 475.55 475.55 489.20 489.20 489.57 609.61 609.61 609.87 609.87 799.10 799.10 799.18 968.25 968.25 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.313110 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.0463 seconds ################################################################################ # Output for cell point 3 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.25245420 eV Monopole - monopole (real) = -162.96717943 eV Monopole - monopole (recip)= -218.10932197 eV Monopole - monopole (total)= -381.07650139 eV -------------------------------------------------------------------------------- Total lattice energy = -327.82404720 eV -------------------------------------------------------------------------------- Total lattice energy = -31630.0093 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.824047 Gnorm: 0.000409 CPU: 0.049 ** Hessian has required structure Cycle: 1 Energy: -327.824103 Gnorm: 0.000001 CPU: 0.053 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.82410344 eV Final Gnorm = 0.00000000 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.22330444 eV Monopole - monopole (real) = -162.95488389 eV Monopole - monopole (recip)= -218.09252399 eV Monopole - monopole (total)= -381.04740788 eV -------------------------------------------------------------------------------- Total lattice energy = -327.82410344 eV -------------------------------------------------------------------------------- Total lattice energy = -31630.0147 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.224185 0.000000 0.000000 0.000000 4.224185 0.000000 -0.221349 -0.221349 8.450065 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.224185 Angstrom dE/a 0.000000 eV/Ang b 4.224185 Angstrom dE/b 0.000000 eV/Ang c 8.455861 Angstrom dE/c -0.000000 eV/Ang alpha 91.500000 Degrees dE/alpha 0.000000 eV/Deg beta 91.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.780747 Angs**3 Density of cell = 3.551509 g/cm**3 Non-primitive cell volume = 150.780747 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.000000 0.000000 -0.000000 0.000000 3 Mg c 0.000000 -0.000000 0.000000 0.000000 4 Mg c 0.000000 -0.000000 0.000000 0.000000 5 Mg c -0.000000 0.000000 0.000000 0.000000 6 Mg c -0.000000 -0.000000 0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c -0.000000 0.000000 0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c -0.000000 0.000000 -0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c 0.000000 0.000000 -0.000000 0.000000 14 O c 0.000000 0.000000 0.000000 0.000000 15 O c 0.000000 0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 371.3813 164.0466 162.9422 -11.5530 -2.1459 0.5618 2 164.0466 371.3813 162.9422 -2.1459 -11.5530 0.5618 3 162.9422 162.9422 368.5888 1.0390 1.0390 -0.8970 4 -11.5530 -2.1459 1.0390 162.8865 -0.6912 -13.6808 5 -2.1459 -11.5530 1.0390 -0.6912 162.8865 -13.6808 6 0.5618 0.5618 -0.8970 -13.6808 -13.6808 164.1581 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003700 -0.001136 -0.001134 0.000255 -0.000023 0.000004 2 -0.001136 0.003700 -0.001134 -0.000023 0.000255 0.000004 3 -0.001134 -0.001134 0.003716 -0.000119 -0.000119 0.000008 4 0.000255 -0.000023 -0.000119 0.006202 0.000073 0.000521 5 -0.000023 0.000255 -0.000119 0.000073 0.006202 0.000521 6 0.000004 0.000004 0.000008 0.000521 0.000521 0.006179 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 232.13242 232.35706 232.24474 Shear Modulus (GPa) = 131.77904 139.41424 135.59664 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.09139 6.26538 6.17900 Velocity P-wave (km/s) = 10.71611 10.85195 10.78424 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00430789 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 270.28713 270.28713 269.07917 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30704 0.30514 Poissons Ratio (y) = 0.30704 0.30514 Poissons Ratio (z) = 0.30651 0.30651 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 -0.00000 0.00000 y 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 -0.00000 0.00000 y 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.77457 0.01062 0.10961 y 0.01062 7.77457 0.10961 z 0.10961 0.10961 7.88565 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.76992 2 = 2.78639 3 = 2.82814 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 241.99 241.99 243.86 243.86 332.75 332.75 342.06 345.13 355.04 355.04 355.45 355.45 389.55 389.55 393.25 400.01 402.74 425.97 425.97 427.06 427.06 450.40 450.40 453.67 453.67 453.68 453.68 455.99 458.28 462.82 462.82 474.52 474.52 488.72 489.99 489.99 609.56 609.56 610.14 610.14 798.98 798.98 799.76 968.01 968.01 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.312555 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.0641 seconds ################################################################################ # Output for cell point 4 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.22549564 eV Monopole - monopole (real) = -162.83666517 eV Monopole - monopole (recip)= -218.12998174 eV Monopole - monopole (total)= -380.96664692 eV -------------------------------------------------------------------------------- Total lattice energy = -327.74115128 eV -------------------------------------------------------------------------------- Total lattice energy = -31622.0111 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.741151 Gnorm: 0.000309 CPU: 0.069 ** Hessian has required structure Cycle: 1 Energy: -327.741184 Gnorm: 0.000000 CPU: 0.073 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.74118372 eV Final Gnorm = 0.00000000 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.20359230 eV Monopole - monopole (real) = -162.82758011 eV Monopole - monopole (recip)= -218.11719591 eV Monopole - monopole (total)= -380.94477602 eV -------------------------------------------------------------------------------- Total lattice energy = -327.74118372 eV -------------------------------------------------------------------------------- Total lattice energy = -31622.0142 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.223484 0.000000 0.000000 0.000000 4.223484 0.000000 -0.295255 -0.295255 8.449844 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.223484 Angstrom dE/a -0.000000 eV/Ang b 4.223484 Angstrom dE/b -0.000000 eV/Ang c 8.460154 Angstrom dE/c -0.000000 eV/Ang alpha 92.000000 Degrees dE/alpha 0.000000 eV/Deg beta 92.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.726795 Angs**3 Density of cell = 3.552780 g/cm**3 Non-primitive cell volume = 150.726795 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 0.000000 0.000000 0.000000 3 Mg c -0.000000 -0.000000 0.000000 0.000000 4 Mg c 0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 0.000000 0.000000 0.000000 6 Mg c 0.000000 0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c 0.000000 -0.000000 0.000000 0.000000 9 O c 0.000000 -0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 -0.000000 0.000000 12 O c 0.000000 -0.000000 0.000000 0.000000 13 O c -0.000000 -0.000000 -0.000000 0.000000 14 O c -0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 371.8811 164.8185 162.8403 -15.3930 -2.8795 1.0068 2 164.8185 371.8811 162.8403 -2.8795 -15.3930 1.0068 3 162.8403 162.8403 366.9624 1.4616 1.4616 -1.6057 4 -15.3930 -2.8795 1.4616 162.7413 -1.2403 -18.2257 5 -2.8795 -15.3930 1.4616 -1.2403 162.7413 -18.2257 6 1.0068 1.0068 -1.6057 -18.2257 -18.2257 165.0164 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003709 -0.001143 -0.001140 0.000341 -0.000029 0.000008 2 -0.001143 0.003709 -0.001140 -0.000029 0.000341 0.000008 3 -0.001140 -0.001140 0.003738 -0.000161 -0.000161 0.000015 4 0.000341 -0.000029 -0.000161 0.006258 0.000131 0.000702 5 -0.000029 0.000341 -0.000161 0.000131 0.006258 0.000702 6 0.000008 0.000008 0.000015 0.000702 0.000702 0.006215 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 232.00888 232.41360 232.21124 Shear Modulus (GPa) = 131.00327 139.44816 135.22571 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.07235 6.26502 6.16944 Velocity P-wave (km/s) = 10.69898 10.85133 10.77542 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00431018 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 269.64257 269.64257 267.53486 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30826 0.30489 Poissons Ratio (y) = 0.30826 0.30489 Poissons Ratio (z) = 0.30729 0.30729 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y 0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 z -0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.76334 0.01883 0.14585 y 0.01883 7.76334 0.14585 z 0.14585 0.14585 7.96004 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.76523 2 = 2.78290 3 = 2.84530 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: 0.00 0.00 0.00 240.80 240.80 244.13 244.13 328.59 328.59 340.05 345.53 354.58 354.58 358.77 358.77 388.81 388.81 390.61 400.65 403.60 425.83 425.83 427.77 427.77 447.66 447.66 453.87 453.87 453.93 453.93 454.96 459.01 464.43 464.43 473.97 473.97 488.58 490.83 490.83 609.40 609.40 610.43 610.43 798.96 798.96 800.35 967.89 967.89 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.312051 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.0853 seconds ################################################################################ # Output for cell point 5 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.20609731 eV Monopole - monopole (real) = -162.67565531 eV Monopole - monopole (recip)= -218.16538966 eV Monopole - monopole (total)= -380.84104498 eV -------------------------------------------------------------------------------- Total lattice energy = -327.63494767 eV -------------------------------------------------------------------------------- Total lattice energy = -31611.7641 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.634948 Gnorm: 0.000405 CPU: 0.089 ** Hessian has required structure Cycle: 1 Energy: -327.635004 Gnorm: 0.000000 CPU: 0.093 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.63500423 eV Final Gnorm = 0.00000000 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.17839176 eV Monopole - monopole (real) = -162.66441270 eV Monopole - monopole (recip)= -218.14898329 eV Monopole - monopole (total)= -380.81339599 eV -------------------------------------------------------------------------------- Total lattice energy = -327.63500423 eV -------------------------------------------------------------------------------- Total lattice energy = -31611.7695 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.222540 0.000000 0.000000 0.000000 4.222540 0.000000 -0.369275 -0.369275 8.449725 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.222540 Angstrom dE/a -0.000000 eV/Ang b 4.222540 Angstrom dE/b -0.000000 eV/Ang c 8.465848 Angstrom dE/c -0.000000 eV/Ang alpha 92.500000 Degrees dE/alpha 0.000000 eV/Deg beta 92.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.657303 Angs**3 Density of cell = 3.554419 g/cm**3 Non-primitive cell volume = 150.657303 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c 0.000000 0.000000 0.000000 0.000000 4 Mg c 0.000000 0.000000 0.000000 0.000000 5 Mg c -0.000000 -0.000000 0.000000 0.000000 6 Mg c -0.000000 -0.000000 0.000000 0.000000 7 Mg c -0.000000 0.000000 0.000000 0.000000 8 Mg c -0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 0.000000 -0.000000 0.000000 10 O c 0.000000 -0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 -0.000000 0.000000 0.000000 13 O c 0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 0.000000 -0.000000 0.000000 15 O c 0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 372.5551 165.8109 162.7015 -19.2139 -3.6317 1.5663 2 165.8109 372.5551 162.7015 -3.6317 -19.2139 1.5663 3 162.7015 162.7015 364.8388 1.9452 1.9452 -2.5297 4 -19.2139 -3.6317 1.9452 162.5471 -1.9560 -22.7477 5 -3.6317 -19.2139 1.9452 -1.9560 162.5471 -22.7477 6 1.5663 1.5663 -2.5297 -22.7477 -22.7477 166.1198 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003720 -0.001152 -0.001147 0.000429 -0.000032 0.000013 2 -0.001152 0.003720 -0.001147 -0.000032 0.000429 0.000013 3 -0.001147 -0.001147 0.003766 -0.000206 -0.000206 0.000023 4 0.000429 -0.000032 -0.000206 0.006331 0.000209 0.000889 5 -0.000032 0.000429 -0.000206 0.000209 0.006331 0.000889 6 0.000013 0.000013 0.000023 0.000889 0.000889 0.006263 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 231.84255 232.48633 232.16444 Shear Modulus (GPa) = 129.99985 139.49180 134.74582 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.04766 6.26455 6.15706 Velocity P-wave (km/s) = 10.67671 10.85052 10.76397 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00431327 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 268.84623 268.84623 265.51051 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30973 0.30455 Poissons Ratio (y) = 0.30973 0.30455 Poissons Ratio (z) = 0.30837 0.30837 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 0.00000 y -0.00000 -0.00000 -0.00000 0.00000 -0.00000 0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 y 0.00000 0.00000 -0.00000 0.00000 -0.00000 0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.74786 0.02933 0.18178 y 0.02933 7.74786 0.18178 z 0.18178 0.18178 8.05969 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.76136 2 = 2.77822 3 = 2.86562 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 239.24 239.24 244.48 244.48 324.35 324.35 337.44 346.04 353.96 353.96 361.95 361.95 387.55 387.83 387.83 401.52 404.34 425.67 425.67 428.70 428.70 444.65 444.65 453.67 454.11 454.11 454.26 454.26 459.97 465.98 465.98 473.27 473.27 488.35 491.96 491.96 609.20 609.20 610.82 610.82 798.94 798.94 801.12 967.74 967.74 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.311401 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.1039 seconds ################################################################################ # Output for cell point 6 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.18125253 eV Monopole - monopole (real) = -162.47884506 eV Monopole - monopole (recip)= -218.20793856 eV Monopole - monopole (total)= -380.68678363 eV -------------------------------------------------------------------------------- Total lattice energy = -327.50553109 eV -------------------------------------------------------------------------------- Total lattice energy = -31599.2774 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.505531 Gnorm: 0.000505 CPU: 0.107 ** Hessian has required structure Cycle: 1 Energy: -327.505621 Gnorm: 0.000000 CPU: 0.111 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.50562077 eV Final Gnorm = 0.00000000 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.14778066 eV Monopole - monopole (real) = -162.46567124 eV Monopole - monopole (recip)= -218.18773019 eV Monopole - monopole (total)= -380.65340143 eV -------------------------------------------------------------------------------- Total lattice energy = -327.50562077 eV -------------------------------------------------------------------------------- Total lattice energy = -31599.2860 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.221330 0.000000 0.000000 0.000000 4.221330 0.000000 -0.443446 -0.443446 8.449820 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.221330 Angstrom dE/a -0.000000 eV/Ang b 4.221330 Angstrom dE/b -0.000000 eV/Ang c 8.473060 Angstrom dE/c -0.000000 eV/Ang alpha 93.000000 Degrees dE/alpha 0.000000 eV/Deg beta 93.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.572605 Angs**3 Density of cell = 3.556418 g/cm**3 Non-primitive cell volume = 150.572605 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 0.000000 0.000000 0.000000 3 Mg c -0.000000 0.000000 0.000000 0.000000 4 Mg c -0.000000 0.000000 -0.000000 0.000000 5 Mg c 0.000000 -0.000000 0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 0.000000 0.000000 9 O c 0.000000 0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c -0.000000 -0.000000 -0.000000 0.000000 12 O c 0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 -0.000000 0.000000 14 O c 0.000000 0.000000 0.000000 0.000000 15 O c 0.000000 0.000000 0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 373.4135 167.0394 162.5138 -23.0193 -4.3989 2.2570 2 167.0394 373.4135 162.5138 -4.3989 -23.0193 2.2570 3 162.5138 162.5138 362.2102 2.5071 2.5071 -3.6703 4 -23.0193 -4.3989 2.5071 162.2918 -2.8423 -27.2490 5 -4.3989 -23.0193 2.5071 -2.8423 162.2918 -27.2490 6 2.2570 2.2570 -3.6703 -27.2490 -27.2490 167.4834 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003733 -0.001163 -0.001156 0.000518 -0.000034 0.000019 2 -0.001163 0.003733 -0.001156 -0.000034 0.000518 0.000019 3 -0.001156 -0.001156 0.003802 -0.000253 -0.000253 0.000032 4 0.000518 -0.000034 -0.000253 0.006426 0.000308 0.001083 5 -0.000034 0.000518 -0.000253 0.000308 0.006426 0.001083 6 0.000019 0.000019 0.000032 0.001083 0.001083 0.006323 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 231.62671 232.57460 232.10065 Shear Modulus (GPa) = 128.75992 139.54476 134.15234 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.01705 6.26398 6.14176 Velocity P-wave (km/s) = 10.64906 10.84953 10.74976 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00431729 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 267.89839 267.89839 263.00062 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31146 0.30411 Poissons Ratio (y) = 0.31146 0.30411 Poissons Ratio (z) = 0.30978 0.30978 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.72758 0.04204 0.21725 y 0.04204 7.72758 0.21725 z 0.21725 0.21725 8.18763 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.75808 2 = 2.77228 3 = 2.88967 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 237.29 237.29 244.90 244.90 320.03 320.03 334.19 346.64 353.17 353.17 364.95 364.95 383.99 386.60 386.60 402.62 405.01 425.50 425.50 429.88 429.88 441.33 441.33 452.16 454.33 454.33 454.69 454.69 461.16 467.47 467.47 472.48 472.48 488.00 493.39 493.39 608.96 608.96 611.30 611.30 798.89 798.89 802.07 967.55 967.55 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.310600 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.1221 seconds ################################################################################ # Output for cell point 7 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.14979789 eV Monopole - monopole (real) = -162.24654657 eV Monopole - monopole (recip)= -218.25747842 eV Monopole - monopole (total)= -380.50402499 eV -------------------------------------------------------------------------------- Total lattice energy = -327.35422710 eV -------------------------------------------------------------------------------- Total lattice energy = -31584.6788 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.354227 Gnorm: 0.000591 CPU: 0.125 ** Hessian has required structure Cycle: 1 Energy: -327.354352 Gnorm: 0.000001 CPU: 0.129 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.35435181 eV Final Gnorm = 0.00000000 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.11203982 eV Monopole - monopole (real) = -162.23228986 eV Monopole - monopole (recip)= -218.23410178 eV Monopole - monopole (total)= -380.46639163 eV -------------------------------------------------------------------------------- Total lattice energy = -327.35435181 eV -------------------------------------------------------------------------------- Total lattice energy = -31584.6909 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.219876 0.000000 0.000000 0.000000 4.219876 0.000000 -0.517791 -0.517791 8.449956 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.219876 Angstrom dE/a -0.000000 eV/Ang b 4.219876 Angstrom dE/b -0.000000 eV/Ang c 8.481626 Angstrom dE/c -0.000000 eV/Ang alpha 93.500000 Degrees dE/alpha 0.000000 eV/Deg beta 93.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.471335 Angs**3 Density of cell = 3.558812 g/cm**3 Non-primitive cell volume = 150.471335 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.000000 0.000000 3 Mg c -0.000000 0.000000 0.000000 0.000000 4 Mg c -0.000000 0.000000 -0.000000 0.000000 5 Mg c 0.000000 -0.000000 0.000000 0.000000 6 Mg c 0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 0.000000 0.000000 9 O c 0.000000 0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 -0.000000 0.000000 12 O c 0.000000 -0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 -0.000000 0.000000 14 O c -0.000000 0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 374.4565 168.4997 162.2697 -26.8054 -5.1849 3.0789 2 168.4997 374.4565 162.2697 -5.1849 -26.8054 3.0789 3 162.2697 162.2697 359.1315 3.1651 3.1651 -5.0270 4 -26.8054 -5.1849 3.1651 161.9682 -3.8989 -31.7254 5 -5.1849 -26.8054 3.1651 -3.8989 161.9682 -31.7254 6 3.0789 3.0789 -5.0270 -31.7254 -31.7254 169.1026 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003748 -0.001175 -0.001167 0.000610 -0.000032 0.000027 2 -0.001175 0.003748 -0.001167 -0.000032 0.000610 0.000027 3 -0.001167 -0.001167 0.003845 -0.000305 -0.000305 0.000042 4 0.000610 -0.000032 -0.000305 0.006543 0.000430 0.001289 5 -0.000032 0.000610 -0.000305 0.000430 0.006543 0.001289 6 0.000027 0.000027 0.000042 0.001289 0.001289 0.006397 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 231.35620 232.68027 232.01824 Shear Modulus (GPa) = 127.27700 139.60816 133.44258 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.98029 6.26330 6.12343 Velocity P-wave (km/s) = 10.61577 10.84835 10.73269 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00432234 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 266.80489 266.80489 260.04573 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31341 0.30360 Poissons Ratio (y) = 0.31341 0.30360 Poissons Ratio (z) = 0.31149 0.31149 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.70336 0.05690 0.25223 y 0.05690 7.70336 0.25223 z 0.25223 0.25223 8.34340 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.75520 2 = 2.76522 3 = 2.91763 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 234.94 234.94 245.38 245.38 315.63 315.63 330.31 347.35 352.26 352.26 367.76 367.76 379.94 385.16 385.16 403.94 405.63 425.32 425.32 431.28 431.28 437.74 437.74 450.43 454.44 454.44 455.20 455.20 462.57 468.93 468.93 471.70 471.70 487.57 495.12 495.12 608.68 608.68 611.88 611.88 798.83 798.83 803.19 967.34 967.34 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.309661 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.1401 seconds ################################################################################ # Output for cell point 8 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.11452016 eV Monopole - monopole (real) = -161.97971037 eV Monopole - monopole (recip)= -218.31468063 eV Monopole - monopole (total)= -380.29439100 eV -------------------------------------------------------------------------------- Total lattice energy = -327.17987085 eV -------------------------------------------------------------------------------- Total lattice energy = -31567.8561 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.179871 Gnorm: 0.000689 CPU: 0.143 ** Hessian has required structure Cycle: 1 Energy: -327.180043 Gnorm: 0.000001 CPU: 0.147 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.18004345 eV Final Gnorm = 0.00000001 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.07109883 eV Monopole - monopole (real) = -161.96413163 eV Monopole - monopole (recip)= -218.28701065 eV Monopole - monopole (total)= -380.25114228 eV -------------------------------------------------------------------------------- Total lattice energy = -327.18004345 eV -------------------------------------------------------------------------------- Total lattice energy = -31567.8728 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.218151 0.000000 0.000000 0.000000 4.218151 0.000000 -0.592358 -0.592358 8.450373 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.218151 Angstrom dE/a -0.000000 eV/Ang b 4.218151 Angstrom dE/b -0.000000 eV/Ang c 8.491794 Angstrom dE/c -0.000000 eV/Ang alpha 94.000000 Degrees dE/alpha 0.000000 eV/Deg beta 94.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.355762 Angs**3 Density of cell = 3.561547 g/cm**3 Non-primitive cell volume = 150.355762 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 0.000000 0.000000 6 Mg c 0.000000 0.000000 0.000000 0.000000 7 Mg c 0.000000 -0.000000 -0.000000 0.000000 8 Mg c -0.000000 -0.000000 -0.000000 0.000000 9 O c 0.000000 0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 -0.000000 0.000000 12 O c 0.000000 -0.000000 -0.000000 0.000000 13 O c -0.000000 0.000000 -0.000000 0.000000 14 O c -0.000000 -0.000000 -0.000000 0.000000 15 O c -0.000000 0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 375.6993 170.2036 161.9591 -30.5653 -5.9970 4.0341 2 170.2036 375.6993 161.9591 -5.9970 -30.5653 4.0341 3 161.9591 161.9591 355.5557 3.9349 3.9349 -6.6129 4 -30.5653 -5.9970 3.9349 161.5663 -5.1383 -36.1679 5 -5.9970 -30.5653 3.9349 -5.1383 161.5663 -36.1679 6 4.0341 4.0341 -6.6129 -36.1679 -36.1679 170.9890 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003766 -0.001188 -0.001181 0.000705 -0.000026 0.000037 2 -0.001188 0.003766 -0.001181 -0.000026 0.000705 0.000037 3 -0.001181 -0.001181 0.003897 -0.000362 -0.000362 0.000053 4 0.000705 -0.000026 -0.000362 0.006686 0.000580 0.001507 5 -0.000026 0.000705 -0.000362 0.000580 0.006686 0.001507 6 0.000037 0.000037 0.000053 0.001507 0.001507 0.006486 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 231.01695 232.79975 231.90835 Shear Modulus (GPa) = 125.53445 139.67985 132.60715 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.93693 6.26250 6.10189 Velocity P-wave (km/s) = 10.57641 10.84696 10.71254 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00432869 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 265.56884 265.56884 256.58812 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31551 0.30300 Poissons Ratio (y) = 0.31551 0.30300 Poissons Ratio (z) = 0.31360 0.31360 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 z 0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 z 0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.67446 0.07382 0.28649 y 0.07382 7.67446 0.28649 z 0.28649 0.28649 8.53290 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.75257 2 = 2.75693 3 = 2.95035 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 232.14 232.14 245.93 245.93 311.15 311.15 325.75 348.14 351.20 351.20 370.33 370.33 375.32 383.48 383.48 405.50 406.24 425.14 425.14 432.92 432.92 433.83 433.83 448.50 454.32 454.32 455.80 455.80 464.22 470.37 470.37 471.04 471.04 486.99 497.18 497.18 608.36 608.36 612.56 612.56 798.75 798.75 804.50 967.09 967.09 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.308558 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.1597 seconds ################################################################################ # Output for cell point 9 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.07410167 eV Monopole - monopole (real) = -161.67823111 eV Monopole - monopole (recip)= -218.37846380 eV Monopole - monopole (total)= -380.05669491 eV -------------------------------------------------------------------------------- Total lattice energy = -326.98259324 eV -------------------------------------------------------------------------------- Total lattice energy = -31548.8219 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -326.982593 Gnorm: 0.000791 CPU: 0.163 ** Hessian has required structure Cycle: 1 Energy: -326.982825 Gnorm: 0.000003 CPU: 0.168 ** Hessian has required structure **** Optimisation achieved **** Final energy = -326.98282510 eV Final Gnorm = 0.00000002 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.02512387 eV Monopole - monopole (real) = -161.66180555 eV Monopole - monopole (recip)= -218.34614342 eV Monopole - monopole (total)= -380.00794897 eV -------------------------------------------------------------------------------- Total lattice energy = -326.98282510 eV -------------------------------------------------------------------------------- Total lattice energy = -31548.8442 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.216133 0.000000 0.000000 0.000000 4.216133 0.000000 -0.667193 -0.667193 8.451196 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.216133 Angstrom dE/a -0.000000 eV/Ang b 4.216133 Angstrom dE/b -0.000000 eV/Ang c 8.503706 Angstrom dE/c -0.000000 eV/Ang alpha 94.500000 Degrees dE/alpha 0.000000 eV/Deg beta 94.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.226548 Angs**3 Density of cell = 3.564611 g/cm**3 Non-primitive cell volume = 150.226548 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.000000 0.000000 -0.000000 0.000000 3 Mg c 0.000000 -0.000000 0.000000 0.000000 4 Mg c 0.000000 0.000000 0.000000 0.000000 5 Mg c -0.000000 0.000000 0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c 0.000000 -0.000000 -0.000000 0.000000 8 Mg c 0.000000 -0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c -0.000000 -0.000000 -0.000000 0.000000 12 O c 0.000000 0.000000 -0.000000 0.000000 13 O c -0.000000 -0.000000 -0.000000 0.000000 14 O c 0.000000 0.000000 -0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c -0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 377.1606 172.1598 161.5682 -34.2922 -6.8390 5.1257 2 172.1598 377.1606 161.5682 -6.8390 -34.2922 5.1257 3 161.5682 161.5682 351.4715 4.8339 4.8339 -8.4374 4 -34.2922 -6.8390 4.8339 161.0727 -6.5699 -40.5683 5 -6.8390 -34.2922 4.8339 -6.5699 161.0727 -40.5683 6 5.1257 5.1257 -8.4374 -40.5683 -40.5683 173.1508 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003785 -0.001202 -0.001197 0.000803 -0.000014 0.000050 2 -0.001202 0.003785 -0.001197 -0.000014 0.000803 0.000050 3 -0.001197 -0.001197 0.003959 -0.000426 -0.000426 0.000064 4 0.000803 -0.000014 -0.000426 0.006861 0.000763 0.001742 5 -0.000014 0.000803 -0.000426 0.000763 0.006861 0.001742 6 0.000050 0.000050 0.000064 0.001742 0.001742 0.006592 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 230.59507 232.93170 231.76338 Shear Modulus (GPa) = 123.51480 139.75902 131.63691 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.88645 6.26158 6.07691 Velocity P-wave (km/s) = 10.53046 10.84537 10.68907 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00433661 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 264.20101 264.20101 252.60282 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31768 0.30232 Poissons Ratio (y) = 0.31768 0.30232 Poissons Ratio (z) = 0.31621 0.31621 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 0.00000 y -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.64043 0.09268 0.31982 y 0.09268 7.64043 0.31982 z 0.31982 0.31982 8.76153 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.74732 2 = 2.75000 3 = 2.98867 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 228.87 228.87 246.53 246.53 306.61 306.61 320.45 349.02 349.97 349.97 370.06 372.62 372.62 381.53 381.53 406.85 407.31 424.96 424.96 429.61 429.61 434.81 434.81 446.42 453.82 453.82 456.49 456.49 466.11 470.63 470.63 471.84 471.84 486.24 499.56 499.56 608.00 608.00 613.35 613.35 798.62 798.62 805.99 966.81 966.81 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.307281 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.1794 seconds ################################################################################ # Output for cell point 10 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.02871889 eV Monopole - monopole (real) = -161.34275169 eV Monopole - monopole (recip)= -218.44852092 eV Monopole - monopole (total)= -379.79127261 eV -------------------------------------------------------------------------------- Total lattice energy = -326.76255372 eV -------------------------------------------------------------------------------- Total lattice energy = -31527.5914 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -326.762554 Gnorm: 0.000896 CPU: 0.184 ** Hessian has required structure Cycle: 1 Energy: -326.762859 Gnorm: 0.000004 CPU: 0.191 ** Hessian has required structure **** Optimisation achieved **** Final energy = -326.76285854 eV Final Gnorm = 0.00000002 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.97433219 eV Monopole - monopole (real) = -161.32609667 eV Monopole - monopole (recip)= -218.41109406 eV Monopole - monopole (total)= -379.73719073 eV -------------------------------------------------------------------------------- Total lattice energy = -326.76285854 eV -------------------------------------------------------------------------------- Total lattice energy = -31527.6208 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.213794 0.000000 0.000000 0.000000 4.213794 0.000000 -0.742352 -0.742352 8.452583 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.213794 Angstrom dE/a -0.000001 eV/Ang b 4.213794 Angstrom dE/b -0.000001 eV/Ang c 8.517530 Angstrom dE/c -0.000001 eV/Ang alpha 95.000000 Degrees dE/alpha 0.000000 eV/Deg beta 95.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.084549 Angs**3 Density of cell = 3.567983 g/cm**3 Non-primitive cell volume = 150.084549 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 0.000000 -0.000000 0.000000 3 Mg c 0.000000 -0.000000 0.000000 0.000000 4 Mg c 0.000000 0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 0.000000 0.000000 6 Mg c 0.000000 0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c -0.000000 -0.000000 0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 0.000000 0.000000 11 O c -0.000000 -0.000000 -0.000000 0.000000 12 O c -0.000000 0.000000 -0.000000 0.000000 13 O c -0.000000 -0.000000 -0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c 0.000000 0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 378.8629 174.3785 161.0803 -37.9780 -7.7145 6.3570 2 174.3785 378.8629 161.0803 -7.7145 -37.9780 6.3570 3 161.0803 161.0803 346.8645 5.8803 5.8803 -10.5112 4 -37.9780 -7.7145 5.8803 160.4709 -8.2045 -44.9169 5 -7.7145 -37.9780 5.8803 -8.2045 160.4709 -44.9169 6 6.3570 6.3570 -10.5112 -44.9169 -44.9169 175.5973 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003806 -0.001217 -0.001216 0.000906 0.000004 0.000066 2 -0.001217 0.003806 -0.001216 0.000004 0.000906 0.000066 3 -0.001216 -0.001216 0.004031 -0.000499 -0.000499 0.000074 4 0.000906 0.000004 -0.000499 0.007074 0.000984 0.001998 5 0.000004 0.000906 -0.000499 0.000984 0.007074 0.001998 6 0.000066 0.000066 0.000074 0.001998 0.001998 0.006717 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 230.07314 233.07432 231.57373 Shear Modulus (GPa) = 121.19476 139.84459 130.51967 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.82815 6.26053 6.04821 Velocity P-wave (km/s) = 10.47723 10.84356 10.66197 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00434644 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 262.71284 262.71284 248.05771 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31980 0.30158 Poissons Ratio (y) = 0.31980 0.30158 Poissons Ratio (z) = 0.31940 0.31940 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 y -0.00000 -0.00000 -0.00000 0.00000 0.00000 0.00000 z -0.00000 -0.00000 0.00000 -0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 y 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 z -0.00000 -0.00000 0.00000 -0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.60074 0.11333 0.35194 y 0.11333 7.60074 0.35194 z 0.35194 0.35194 9.03646 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.73631 2 = 2.74730 3 = 3.03362 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 225.08 225.08 247.17 247.17 302.00 302.00 314.38 348.56 348.56 349.96 364.07 374.53 374.53 379.30 379.30 407.50 409.39 424.81 424.81 425.15 425.15 436.97 436.97 444.21 452.77 452.77 457.29 457.29 468.25 470.62 470.62 473.35 473.35 485.28 502.28 502.28 607.60 607.60 614.24 614.24 798.45 798.45 807.68 966.48 966.48 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.305816 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.2071 seconds ################################################################################ # Output for cell point 11 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.97860028 eV Monopole - monopole (real) = -160.97409844 eV Monopole - monopole (recip)= -218.52445263 eV Monopole - monopole (total)= -379.49855108 eV -------------------------------------------------------------------------------- Total lattice energy = -326.51995080 eV -------------------------------------------------------------------------------- Total lattice energy = -31504.1839 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -326.519951 Gnorm: 0.001006 CPU: 0.212 ** Hessian has required structure Cycle: 1 Energy: -326.520345 Gnorm: 0.000006 CPU: 0.219 ** Hessian has required structure **** Optimisation achieved **** Final energy = -326.52034525 eV Final Gnorm = 0.00000004 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.91900748 eV Monopole - monopole (real) = -160.95801652 eV Monopole - monopole (recip)= -218.48133621 eV Monopole - monopole (total)= -379.43935273 eV -------------------------------------------------------------------------------- Total lattice energy = -326.52034525 eV -------------------------------------------------------------------------------- Total lattice energy = -31504.2220 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.211103 0.000000 0.000000 0.000000 4.211103 0.000000 -0.817898 -0.817898 8.454724 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.211103 Angstrom dE/a -0.000001 eV/Ang b 4.211103 Angstrom dE/b -0.000001 eV/Ang c 8.533479 Angstrom dE/c -0.000001 eV/Ang alpha 95.500000 Degrees dE/alpha 0.000000 eV/Deg beta 95.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 149.930870 Angs**3 Density of cell = 3.571640 g/cm**3 Non-primitive cell volume = 149.930870 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c 0.000000 0.000000 0.000000 0.000000 4 Mg c 0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c -0.000000 -0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 -0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 380.8330 176.8715 160.4752 -41.6130 -8.6271 7.7319 2 176.8715 380.8330 160.4752 -8.6271 -41.6130 7.7319 3 160.4752 160.4752 341.7176 7.0932 7.0932 -12.8468 4 -41.6130 -8.6271 7.0932 159.7410 -10.0547 -49.2018 5 -8.6271 -41.6130 7.0932 -10.0547 159.7410 -49.2018 6 7.7319 7.7319 -12.8468 -49.2018 -49.2018 178.3397 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003830 -0.001232 -0.001238 0.001015 0.000031 0.000087 2 -0.001232 0.003830 -0.001238 0.000031 0.001015 0.000087 3 -0.001238 -0.001238 0.004117 -0.000584 -0.000584 0.000082 4 0.001015 0.000031 -0.000584 0.007334 0.001253 0.002282 5 0.000031 0.001015 -0.000584 0.001253 0.007334 0.002282 6 0.000087 0.000087 0.000082 0.002282 0.002282 0.006865 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 229.42935 233.22526 231.32730 Shear Modulus (GPa) = 118.54311 139.93515 129.23913 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.76109 6.25935 6.01538 Velocity P-wave (km/s) = 10.41585 10.84152 10.63081 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00435864 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 261.11560 261.11560 242.91097 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.32175 0.30079 Poissons Ratio (y) = 0.32175 0.30079 Poissons Ratio (z) = 0.32334 0.32334 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.55479 0.13559 0.38247 y 0.13559 7.55479 0.38247 z 0.38247 0.38247 9.36735 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.72382 2 = 2.74428 3 = 3.08653 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 220.71 220.71 247.85 247.85 297.34 297.34 307.44 346.97 346.97 350.96 357.28 375.87 375.87 376.78 376.78 408.23 411.77 420.56 420.56 424.71 424.71 439.42 439.42 441.90 451.06 451.06 458.19 458.19 470.65 471.14 471.14 474.96 474.96 484.08 505.34 505.34 607.16 607.16 615.26 615.26 798.22 798.22 809.58 966.12 966.12 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.304147 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.2356 seconds ################################################################################ # Output for cell point 12 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.92404180 eV Monopole - monopole (real) = -160.57333354 eV Monopole - monopole (recip)= -218.60573952 eV Monopole - monopole (total)= -379.17907306 eV -------------------------------------------------------------------------------- Total lattice energy = -326.25503126 eV -------------------------------------------------------------------------------- Total lattice energy = -31478.6233 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -326.255031 Gnorm: 0.001121 CPU: 0.241 ** Hessian has required structure Cycle: 1 Energy: -326.255536 Gnorm: 0.000008 CPU: 0.248 ** Hessian has required structure **** Optimisation achieved **** Final energy = -326.25553592 eV Final Gnorm = 0.00000006 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.85952097 eV Monopole - monopole (real) = -160.55887138 eV Monopole - monopole (recip)= -218.55618551 eV Monopole - monopole (total)= -379.11505689 eV -------------------------------------------------------------------------------- Total lattice energy = -326.25553592 eV -------------------------------------------------------------------------------- Total lattice energy = -31478.6719 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.208021 0.000000 0.000000 0.000000 4.208021 0.000000 -0.893908 -0.893908 8.457855 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.208021 Angstrom dE/a -0.000002 eV/Ang b 4.208021 Angstrom dE/b -0.000002 eV/Ang c 8.551810 Angstrom dE/c -0.000001 eV/Ang alpha 96.000000 Degrees dE/alpha 0.000000 eV/Deg beta 96.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 149.766938 Angs**3 Density of cell = 3.575550 g/cm**3 Non-primitive cell volume = 149.766938 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.000000 0.000000 0.000000 0.000000 3 Mg c 0.000000 -0.000000 0.000000 0.000000 4 Mg c 0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 -0.000000 -0.000000 0.000000 8 Mg c -0.000000 -0.000000 0.000000 0.000000 9 O c 0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 -0.000000 0.000000 12 O c 0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 -0.000000 0.000000 0.000000 14 O c -0.000000 0.000000 0.000000 0.000000 15 O c -0.000000 0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 383.1027 179.6522 159.7284 -45.1849 -9.5800 9.2545 2 179.6522 383.1027 159.7284 -9.5800 -45.1849 9.2545 3 159.7284 159.7284 336.0093 8.4923 8.4923 -15.4583 4 -45.1849 -9.5800 8.4923 158.8592 -12.1351 -53.4086 5 -9.5800 -45.1849 8.4923 -12.1351 158.8592 -53.4086 6 9.2545 9.2545 -15.4583 -53.4086 -53.4086 181.3906 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003855 -0.001246 -0.001265 0.001132 0.000070 0.000113 2 -0.001246 0.003855 -0.001265 0.000070 0.001132 0.000113 3 -0.001265 -0.001265 0.004217 -0.000685 -0.000685 0.000085 4 0.001132 0.000070 -0.000685 0.007653 0.001584 0.002600 5 0.000070 0.001132 -0.000685 0.001584 0.007653 0.002600 6 0.000113 0.000113 0.000085 0.002600 0.002600 0.007040 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 228.63641 233.38141 231.00891 Shear Modulus (GPa) = 115.51739 140.02884 127.77312 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.68398 6.25803 5.97790 Velocity P-wave (km/s) = 10.34510 10.83922 10.59504 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00437376 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 259.41877 259.41877 237.10730 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.32332 0.29998 Poissons Ratio (y) = 0.32332 0.29998 Poissons Ratio (z) = 0.32821 0.32821 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 -0.00000 -0.00000 0.00000 -0.00000 0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z 0.00000 -0.00000 0.00000 -0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.50187 0.15922 0.41096 y 0.15922 7.50187 0.41096 z 0.41096 0.41096 9.76736 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.70973 2 = 2.74069 3 = 3.14914 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: 0.00 0.00 0.00 215.70 215.70 248.55 248.55 292.61 292.61 299.56 345.16 345.16 349.56 352.00 373.93 373.93 376.33 376.33 409.07 414.47 416.11 416.11 424.67 424.67 439.55 442.16 442.16 448.64 448.64 459.21 459.21 472.20 472.20 473.31 476.72 476.72 482.61 508.73 508.73 606.69 606.69 616.40 616.40 797.90 797.90 811.68 965.72 965.72 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.302255 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.2642 seconds ################################################################################ # Output for cell point 13 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.86542852 eV Monopole - monopole (real) = -160.14182575 eV Monopole - monopole (recip)= -218.69170456 eV Monopole - monopole (total)= -378.83353031 eV -------------------------------------------------------------------------------- Total lattice energy = -325.96810179 eV -------------------------------------------------------------------------------- Total lattice energy = -31450.9389 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -325.968102 Gnorm: 0.001242 CPU: 0.269 ** Hessian has required structure Cycle: 1 Energy: -325.968742 Gnorm: 0.000011 CPU: 0.276 ** Hessian has required structure **** Optimisation achieved **** Final energy = -325.96874232 eV Final Gnorm = 0.00000009 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.79635848 eV Monopole - monopole (real) = -160.13035462 eV Monopole - monopole (recip)= -218.63474617 eV Monopole - monopole (total)= -378.76510079 eV -------------------------------------------------------------------------------- Total lattice energy = -325.96874232 eV -------------------------------------------------------------------------------- Total lattice energy = -31451.0007 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.204502 0.000000 0.000000 0.000000 4.204502 0.000000 -0.970473 -0.970473 8.462268 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.204502 Angstrom dE/a -0.000003 eV/Ang b 4.204502 Angstrom dE/b -0.000003 eV/Ang c 8.572842 Angstrom dE/c -0.000002 eV/Ang alpha 96.500000 Degrees dE/alpha 0.000000 eV/Deg beta 96.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 149.594617 Angs**3 Density of cell = 3.579669 g/cm**3 Non-primitive cell volume = 149.594617 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.000000 0.000000 3 Mg c -0.000000 -0.000000 0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 0.000000 0.000000 6 Mg c 0.000000 0.000000 -0.000000 0.000000 7 Mg c 0.000000 -0.000000 -0.000000 0.000000 8 Mg c 0.000000 -0.000000 -0.000000 0.000000 9 O c 0.000000 0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 0.000000 0.000000 11 O c 0.000000 0.000000 0.000000 0.000000 12 O c 0.000000 -0.000000 -0.000000 0.000000 13 O c -0.000000 0.000000 -0.000000 0.000000 14 O c -0.000000 -0.000000 -0.000000 0.000000 15 O c -0.000000 0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 385.7097 182.7364 158.8105 -48.6787 -10.5765 10.9294 2 182.7364 385.7097 158.8105 -10.5765 -48.6787 10.9294 3 158.8105 158.8105 329.7135 10.0981 10.0981 -18.3620 4 -48.6787 -10.5765 10.0981 157.7966 -14.4622 -57.5197 5 -10.5765 -48.6787 10.0981 -14.4622 157.7966 -57.5197 6 10.9294 10.9294 -18.3620 -57.5197 -57.5197 184.7642 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003882 -0.001259 -0.001298 0.001261 0.000124 0.000147 2 -0.001259 0.003882 -0.001298 0.000124 0.001261 0.000147 3 -0.001298 -0.001298 0.004337 -0.000810 -0.000810 0.000080 4 0.001261 0.000124 -0.000810 0.008049 0.001993 0.002964 5 0.000124 0.001261 -0.000810 0.001993 0.008049 0.002964 6 0.000147 0.000147 0.000080 0.002964 0.002964 0.007248 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 227.66023 233.53862 230.59942 Shear Modulus (GPa) = 112.05905 140.12316 126.09111 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.59503 6.25653 5.93500 Velocity P-wave (km/s) = 10.26339 10.83663 10.55390 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00439251 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 257.62695 257.62695 230.57194 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.32425 0.29919 Poissons Ratio (y) = 0.32425 0.29919 Poissons Ratio (z) = 0.33430 0.33430 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.44115 0.18395 0.43675 y 0.18395 7.44115 0.43675 z 0.43675 0.43675 10.25486 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.69392 2 = 2.73628 3 = 3.22377 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: 0.00 0.00 0.00 209.95 209.95 249.25 249.25 287.83 287.83 290.62 340.79 343.13 343.13 353.05 370.73 370.73 375.38 375.38 410.06 412.27 412.27 417.53 424.73 424.73 437.21 445.24 445.24 445.52 445.52 460.36 460.36 473.77 473.77 476.26 478.66 478.66 480.81 512.45 512.45 606.18 606.18 617.67 617.67 797.49 797.49 814.02 965.27 965.27 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.300115 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.2912 seconds ################################################################################ # Output for cell point 14 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.80326155 eV Monopole - monopole (real) = -159.68134624 eV Monopole - monopole (recip)= -218.78145975 eV Monopole - monopole (total)= -378.46280599 eV -------------------------------------------------------------------------------- Total lattice energy = -325.65954445 eV -------------------------------------------------------------------------------- Total lattice energy = -31421.1679 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -325.659544 Gnorm: 0.001369 CPU: 0.297 ** Hessian has required structure Cycle: 1 Energy: -325.660353 Gnorm: 0.000014 CPU: 0.304 ** Hessian has required structure **** Optimisation achieved **** Final energy = -325.66035317 eV Final Gnorm = 0.00000014 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.73015970 eV Monopole - monopole (real) = -159.67467480 eV Monopole - monopole (recip)= -218.71583808 eV Monopole - monopole (total)= -378.39051287 eV -------------------------------------------------------------------------------- Total lattice energy = -325.66035317 eV -------------------------------------------------------------------------------- Total lattice energy = -31421.2459 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.200493 0.000000 0.000000 0.000000 4.200493 0.000000 -1.047707 -1.047707 8.468325 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.200493 Angstrom dE/a -0.000004 eV/Ang b 4.200493 Angstrom dE/b -0.000004 eV/Ang c 8.596970 Angstrom dE/c -0.000002 eV/Ang alpha 97.000000 Degrees dE/alpha 0.000000 eV/Deg beta 97.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 149.416350 Angs**3 Density of cell = 3.583939 g/cm**3 Non-primitive cell volume = 149.416350 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 0.000000 0.000000 4 Mg c 0.000000 -0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 0.000000 0.000000 6 Mg c 0.000000 0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c -0.000000 -0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c -0.000000 -0.000000 0.000000 0.000000 12 O c 0.000000 0.000000 -0.000000 0.000000 13 O c -0.000000 -0.000000 0.000000 0.000000 14 O c 0.000000 0.000000 -0.000000 0.000000 15 O c 0.000000 0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 388.6990 186.1416 157.6858 -52.0758 -11.6193 12.7613 2 186.1416 388.6990 157.6858 -11.6193 -52.0758 12.7613 3 157.6858 157.6858 322.7978 11.9322 11.9322 -21.5757 4 -52.0758 -11.6193 11.9322 156.5182 -17.0550 -61.5131 5 -11.6193 -52.0758 11.9322 -17.0550 156.5182 -61.5131 6 12.7613 12.7613 -21.5757 -61.5131 -61.5131 188.4768 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003910 -0.001268 -0.001337 0.001406 0.000199 0.000192 2 -0.001268 0.003910 -0.001337 0.000199 0.001406 0.000192 3 -0.001337 -0.001337 0.004480 -0.000966 -0.000966 0.000063 4 0.001406 0.000199 -0.000966 0.008551 0.002508 0.003390 5 0.000199 0.001406 -0.000966 0.002508 0.008551 0.003390 6 0.000192 0.000192 0.000063 0.003390 0.003390 0.007500 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 226.45806 233.69139 230.07472 Shear Modulus (GPa) = 108.08560 140.21482 124.15021 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.49166 6.25485 5.88564 Velocity P-wave (km/s) = 10.16848 10.83371 10.50636 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00441583 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 255.73404 255.73404 223.20062 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.32417 0.29852 Poissons Ratio (y) = 0.32417 0.29852 Poissons Ratio (z) = 0.34204 0.34204 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.37168 0.20945 0.45902 y 0.20945 7.37168 0.45902 z 0.45902 0.45902 10.85615 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.67623 2 = 2.73078 3 = 3.31363 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 203.35 203.35 249.94 249.94 280.47 282.99 282.99 330.81 340.85 340.85 354.08 367.14 367.14 372.34 372.34 409.64 409.64 411.26 420.99 424.92 424.92 434.92 441.70 441.70 448.66 448.66 461.66 461.66 475.84 475.84 478.64 479.50 480.88 480.88 516.51 516.51 605.64 605.64 619.10 619.10 796.94 796.94 816.60 964.78 964.78 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.297691 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.3199 seconds ################################################################################ # Output for cell point 15 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.73819718 eV Monopole - monopole (real) = -159.19420098 eV Monopole - monopole (recip)= -218.87383330 eV Monopole - monopole (total)= -378.06803428 eV -------------------------------------------------------------------------------- Total lattice energy = -325.32983711 eV -------------------------------------------------------------------------------- Total lattice energy = -31389.3562 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -325.329837 Gnorm: 0.001504 CPU: 0.324 ** Hessian has required structure Cycle: 1 Energy: -325.330855 Gnorm: 0.000017 CPU: 0.332 ** Hessian has required structure **** Optimisation achieved **** Final energy = -325.33085526 eV Final Gnorm = 0.00000020 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.66177376 eV Monopole - monopole (real) = -159.19473577 eV Monopole - monopole (recip)= -218.79789326 eV Monopole - monopole (total)= -377.99262902 eV -------------------------------------------------------------------------------- Total lattice energy = -325.33085526 eV -------------------------------------------------------------------------------- Total lattice energy = -31389.4544 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.195930 0.000000 0.000000 0.000000 4.195930 0.000000 -1.125748 -1.125748 8.476477 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.195930 Angstrom dE/a -0.000006 eV/Ang b 4.195930 Angstrom dE/b -0.000006 eV/Ang c 8.624690 Angstrom dE/c -0.000004 eV/Ang alpha 97.500000 Degrees dE/alpha 0.000000 eV/Deg beta 97.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 149.235373 Angs**3 Density of cell = 3.588286 g/cm**3 Non-primitive cell volume = 149.235373 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 0.000000 0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c -0.000000 0.000000 0.000000 0.000000 8 Mg c -0.000000 -0.000000 -0.000000 0.000000 9 O c -0.000000 0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 0.000000 0.000000 11 O c -0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 -0.000000 -0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 0.000000 -0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 392.1240 189.8883 156.3109 -55.3527 -12.7106 14.7550 2 189.8883 392.1240 156.3109 -12.7106 -55.3527 14.7550 3 156.3109 156.3109 315.2220 14.0166 14.0166 -25.1197 4 -55.3527 -12.7106 14.0166 154.9816 -19.9351 -65.3615 5 -12.7106 -55.3527 14.0166 -19.9351 154.9816 -65.3615 6 14.7550 14.7550 -25.1197 -65.3615 -65.3615 192.5468 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003941 -0.001271 -0.001388 0.001574 0.000303 0.000252 2 -0.001271 0.003941 -0.001388 0.000303 0.001574 0.000252 3 -0.001388 -0.001388 0.004655 -0.001170 -0.001170 0.000026 4 0.001574 0.000303 -0.001170 0.009200 0.003173 0.003903 5 0.000303 0.001574 -0.001170 0.003173 0.009200 0.003903 6 0.000252 0.000252 0.000026 0.003903 0.003903 0.007808 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 224.97626 233.83225 229.40425 Shear Modulus (GPa) = 103.47817 140.29933 121.88875 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.37008 6.25294 5.82825 Velocity P-wave (km/s) = 10.05723 10.83041 10.45097 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00444491 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 253.71179 253.71179 214.84259 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.32252 0.29811 Poissons Ratio (y) = 0.32252 0.29811 Poissons Ratio (z) = 0.35204 0.35204 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 y 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 y 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.29239 0.23532 0.47657 y 0.23532 7.29239 0.47657 z 0.47657 0.47657 11.61018 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.65651 2 = 2.72384 3 = 3.42324 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 195.78 195.78 250.59 250.59 268.93 278.09 278.09 319.40 338.29 338.29 355.06 363.11 363.11 366.75 366.75 408.58 408.58 412.72 424.89 425.29 425.29 432.75 437.18 437.18 452.48 452.48 463.13 463.13 476.05 478.37 478.37 483.07 483.42 483.42 520.89 520.89 605.08 605.08 620.69 620.69 796.24 796.24 819.46 964.23 964.23 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.294942 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.3480 seconds ################################################################################ # Output for cell point 16 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.67110386 eV Monopole - monopole (real) = -158.68341694 eV Monopole - monopole (recip)= -218.96726621 eV Monopole - monopole (total)= -377.65068315 eV -------------------------------------------------------------------------------- Total lattice energy = -324.97957929 eV -------------------------------------------------------------------------------- Total lattice energy = -31355.5616 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -324.979579 Gnorm: 0.001647 CPU: 0.353 ** Hessian has required structure Cycle: 1 Energy: -324.980860 Gnorm: 0.000020 CPU: 0.360 ** Hessian has required structure **** Optimisation achieved **** Final energy = -324.98086010 eV Final Gnorm = 0.00000029 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.59233247 eV Monopole - monopole (real) = -158.69439034 eV Monopole - monopole (recip)= -218.87880223 eV Monopole - monopole (total)= -377.57319257 eV -------------------------------------------------------------------------------- Total lattice energy = -324.98086010 eV -------------------------------------------------------------------------------- Total lattice energy = -31355.6852 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.190733 0.000000 0.000000 0.000000 4.190733 0.000000 -1.204770 -1.204770 8.487300 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.190733 Angstrom dE/a -0.000009 eV/Ang b 4.190733 Angstrom dE/b -0.000009 eV/Ang c 8.656628 Angstrom dE/c -0.000005 eV/Ang alpha 98.000000 Degrees dE/alpha 0.000000 eV/Deg beta 98.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 149.056029 Angs**3 Density of cell = 3.592603 g/cm**3 Non-primitive cell volume = 149.056029 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 0.000000 0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 0.000000 0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 0.000000 -0.000000 0.000000 10 O c 0.000000 -0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c 0.000000 -0.000000 -0.000000 0.000000 13 O c -0.000000 -0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 -0.000000 0.000000 15 O c -0.000000 0.000000 0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 396.0484 193.9992 154.6322 -58.4799 -13.8516 16.9153 2 193.9992 396.0484 154.6322 -13.8516 -58.4799 16.9153 3 154.6322 154.6322 306.9358 16.3741 16.3741 -29.0160 4 -58.4799 -13.8516 16.3741 153.1346 -23.1264 -69.0303 5 -13.8516 -58.4799 16.3741 -23.1264 153.1346 -69.0303 6 16.9153 16.9153 -29.0160 -69.0303 -69.0303 196.9944 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003976 -0.001266 -0.001453 0.001778 0.000451 0.000334 2 -0.001266 0.003976 -0.001453 0.000451 0.001778 0.000334 3 -0.001453 -0.001453 0.004872 -0.001447 -0.001447 -0.000047 4 0.001778 0.000451 -0.001447 0.010066 0.004056 0.004544 5 0.000451 0.001778 -0.001447 0.004056 0.010066 0.004544 6 0.000334 0.000334 -0.000047 0.004544 0.004544 0.008197 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 223.14729 233.95111 228.54920 Shear Modulus (GPa) = 98.06033 140.37064 119.21549 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.22447 6.25077 5.76052 Velocity P-wave (km/s) = 9.92504 10.82665 10.38563 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00448134 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 251.48639 251.48639 205.26923 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31841 0.29819 Poissons Ratio (y) = 0.31841 0.29819 Poissons Ratio (z) = 0.36533 0.36533 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 0.00000 0.00000 -0.00000 0.00000 y 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.20203 0.26109 0.48772 y 0.26109 7.20203 0.48772 z 0.48772 0.48772 12.57704 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.63457 2 = 2.71509 3 = 3.55927 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 187.04 187.04 251.16 251.16 255.74 273.11 273.11 306.31 335.39 335.39 355.94 358.58 358.58 358.58 358.58 409.05 409.05 414.51 425.89 425.89 429.28 430.79 431.92 431.92 456.71 456.71 464.79 464.79 472.96 481.37 481.37 486.39 486.39 486.98 525.59 525.59 604.49 604.49 622.46 622.46 795.34 795.34 822.61 963.64 963.64 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.291807 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.3753 seconds ################################################################################ # Output for cell point 17 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.60373919 eV Monopole - monopole (real) = -158.15300384 eV Monopole - monopole (recip)= -219.05965877 eV Monopole - monopole (total)= -377.21266260 eV -------------------------------------------------------------------------------- Total lattice energy = -324.60892342 eV -------------------------------------------------------------------------------- Total lattice energy = -31319.7990 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -324.608923 Gnorm: 0.001800 CPU: 0.381 ** Hessian has required structure Cycle: 1 Energy: -324.610539 Gnorm: 0.000023 CPU: 0.388 ** Hessian has required structure **** Optimisation achieved **** Final energy = -324.61053912 eV Final Gnorm = 0.00000042 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.52328291 eV Monopole - monopole (real) = -158.17856028 eV Monopole - monopole (recip)= -218.95526176 eV Monopole - monopole (total)= -377.13382204 eV -------------------------------------------------------------------------------- Total lattice energy = -324.61053912 eV -------------------------------------------------------------------------------- Total lattice energy = -31319.9549 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.184813 0.000000 0.000000 0.000000 4.184813 0.000000 -1.285000 -1.285000 8.501568 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.184813 Angstrom dE/a -0.000013 eV/Ang b 4.184813 Angstrom dE/b -0.000013 eV/Ang c 8.693625 Angstrom dE/c -0.000008 eV/Ang alpha 98.500000 Degrees dE/alpha 0.000000 eV/Deg beta 98.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 148.885097 Angs**3 Density of cell = 3.596728 g/cm**3 Non-primitive cell volume = 148.885097 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.000000 0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 0.000000 0.000000 4 Mg c 0.000000 -0.000000 0.000000 0.000000 5 Mg c -0.000000 -0.000000 0.000000 0.000000 6 Mg c -0.000000 -0.000000 0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 -0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 -0.000000 0.000000 15 O c 0.000000 -0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 400.5433 198.5036 152.5842 -61.4224 -15.0450 19.2485 2 198.5036 400.5433 152.5842 -15.0450 -61.4224 19.2485 3 152.5842 152.5842 297.8639 19.0272 19.0272 -33.2853 4 -61.4224 -15.0450 19.0272 150.9131 -26.6535 -72.4778 5 -15.0450 -61.4224 19.0272 -26.6535 150.9131 -72.4778 6 19.2485 19.2485 -33.2853 -72.4778 -72.4778 201.8455 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004018 -0.001247 -0.001542 0.002041 0.000665 0.000453 2 -0.001247 0.004018 -0.001542 0.000665 0.002041 0.000453 3 -0.001542 -0.001542 0.005152 -0.001842 -0.001842 -0.000179 4 0.002041 0.000665 -0.001842 0.011274 0.005283 0.005383 5 0.000665 0.002041 -0.001842 0.005283 0.011274 0.005383 6 0.000453 0.000453 -0.000179 0.005383 0.005383 0.008704 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 220.88325 234.03273 227.45799 Shear Modulus (GPa) = 91.55729 140.41960 115.98844 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.04537 6.24827 5.67876 Velocity P-wave (km/s) = 9.76490 10.82233 10.30718 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00452728 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 248.87476 248.87476 194.09769 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31037 0.29924 Poissons Ratio (y) = 0.31037 0.29924 Poissons Ratio (z) = 0.38369 0.38369 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 -0.00000 0.00000 0.00000 -0.00000 -0.00000 y 0.00000 -0.00000 0.00000 0.00000 0.00000 -0.00000 z -0.00000 -0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 y 0.00000 -0.00000 0.00000 0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.09921 0.28621 0.48985 y 0.28621 7.09921 0.48985 z 0.48985 0.48985 13.85534 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.61017 2 = 2.70409 3 = 3.73212 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 176.90 176.90 240.55 251.61 251.61 268.02 268.02 291.16 332.10 332.10 348.01 348.01 353.48 353.48 356.65 410.71 410.71 416.70 425.85 425.85 426.79 426.79 429.11 434.22 461.42 461.42 466.67 466.67 469.31 484.87 484.87 489.87 489.87 491.27 530.62 530.62 603.89 603.89 624.44 624.44 794.18 794.18 826.09 962.98 962.98 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.288196 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.4040 seconds ################################################################################ # Output for cell point 18 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.53574175 eV Monopole - monopole (real) = -157.60808866 eV Monopole - monopole (recip)= -219.14771808 eV Monopole - monopole (total)= -376.75580674 eV -------------------------------------------------------------------------------- Total lattice energy = -324.22006499 eV -------------------------------------------------------------------------------- Total lattice energy = -31282.2801 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -324.220065 Gnorm: 0.001963 CPU: 0.408 ** Hessian has required structure Cycle: 1 Energy: -324.222103 Gnorm: 0.000022 CPU: 0.416 ** Hessian has required structure **** Optimisation achieved **** Final energy = -324.22210310 eV Final Gnorm = 0.00000071 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.45688017 eV Monopole - monopole (real) = -157.65482545 eV Monopole - monopole (recip)= -219.02415783 eV Monopole - monopole (total)= -376.67898328 eV -------------------------------------------------------------------------------- Total lattice energy = -324.22210310 eV -------------------------------------------------------------------------------- Total lattice energy = -31282.4768 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.178047 0.000000 0.000000 0.000000 4.178047 0.000000 -1.366716 -1.366716 8.520183 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.178047 Angstrom dE/a -0.000022 eV/Ang b 4.178047 Angstrom dE/b -0.000022 eV/Ang c 8.736667 Angstrom dE/c -0.000013 eV/Ang alpha 99.000000 Degrees dE/alpha 0.000000 eV/Deg beta 99.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 148.728975 Angs**3 Density of cell = 3.600503 g/cm**3 Non-primitive cell volume = 148.728975 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.000000 0.000000 3 Mg c -0.000000 0.000000 0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 -0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 -0.000000 0.000000 11 O c 0.000000 0.000000 0.000000 0.000000 12 O c 0.000000 -0.000000 -0.000000 0.000000 13 O c 0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 0.000000 -0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 405.7119 203.4233 150.0816 -64.1253 -16.2834 21.7521 2 203.4233 405.7119 150.0816 -16.2834 -64.1253 21.7521 3 150.0816 150.0816 287.9482 21.9976 21.9976 -37.9584 4 -64.1253 -16.2834 21.9976 148.2341 -30.5501 -75.6424 5 -16.2834 -64.1253 21.9976 -30.5501 148.2341 -75.6424 6 21.7521 21.7521 -37.9584 -75.6424 -75.6424 207.1181 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004073 -0.001204 -0.001671 0.002406 0.000994 0.000634 2 -0.001204 0.004073 -0.001671 0.000994 0.002406 0.000634 3 -0.001671 -0.001671 0.005534 -0.002448 -0.002448 -0.000423 4 0.002406 0.000994 -0.002448 0.013070 0.007099 0.006560 5 0.000994 0.002406 -0.002448 0.007099 0.013070 0.006560 6 0.000634 0.000634 -0.000423 0.006560 0.006560 0.009409 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 218.08085 234.06058 226.07072 Shear Modulus (GPa) = 83.53877 140.43628 111.98753 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 4.81684 6.24537 5.57703 Velocity P-wave (km/s) = 9.56585 10.81730 10.21076 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00458546 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 245.50996 245.50996 180.71725 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.29566 0.30206 Poissons Ratio (y) = 0.29566 0.30206 Poissons Ratio (z) = 0.41036 0.41036 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 y 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 0.00000 0.00000 y -0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 6.98221 0.31005 0.47891 y 0.31005 6.98221 0.47891 z 0.47891 0.47891 15.61310 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.58305 2 = 2.69026 3 = 3.95827 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 165.03 165.03 222.87 251.89 251.89 262.77 262.77 273.50 328.37 328.37 335.18 335.18 347.72 347.72 357.12 413.31 413.31 418.87 418.87 419.41 427.80 428.09 428.09 439.81 465.02 466.66 466.66 468.82 468.82 488.90 488.90 493.99 493.99 495.96 535.97 535.97 603.27 603.27 626.64 626.64 792.70 792.70 829.96 962.26 962.26 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.284009 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.4315 seconds ################################################################################ # Output for cell point 19 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.47124306 eV Monopole - monopole (real) = -157.05651001 eV Monopole - monopole (recip)= -219.22834261 eV Monopole - monopole (total)= -376.28485262 eV -------------------------------------------------------------------------------- Total lattice energy = -323.81360956 eV -------------------------------------------------------------------------------- Total lattice energy = -31243.0634 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -323.813610 Gnorm: 0.002138 CPU: 0.436 ** Hessian has required structure Cycle: 1 Energy: -323.816198 Gnorm: 0.000018 CPU: 0.443 ** Hessian has required structure **** Optimisation achieved **** Final energy = -323.81619766 eV Final Gnorm = 0.00000113 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.39591038 eV Monopole - monopole (real) = -157.13268236 eV Monopole - monopole (recip)= -219.07942568 eV Monopole - monopole (total)= -376.21210804 eV -------------------------------------------------------------------------------- Total lattice energy = -323.81619766 eV -------------------------------------------------------------------------------- Total lattice energy = -31243.3131 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c 0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c 0.000000 0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.170296 0.000000 0.000000 0.000000 4.170296 0.000000 -1.450306 -1.450306 8.544473 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.170296 Angstrom dE/a -0.000037 eV/Ang b 4.170296 Angstrom dE/b -0.000037 eV/Ang c 8.787195 Angstrom dE/c -0.000016 eV/Ang alpha 99.500000 Degrees dE/alpha 0.000000 eV/Deg beta 99.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 148.600101 Angs**3 Density of cell = 3.603626 g/cm**3 Non-primitive cell volume = 148.600101 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.000000 0.000000 3 Mg c -0.000000 0.000000 -0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 -0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 0.000000 0.000000 9 O c 0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 0.000000 0.000000 0.000000 12 O c 0.000000 0.000000 -0.000000 0.000000 13 O c -0.000000 -0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c 0.000000 0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 411.6596 208.7936 147.0190 -66.5278 -17.5644 24.4284 2 208.7936 411.6596 147.0190 -17.5644 -66.5278 24.4284 3 147.0190 147.0190 277.0708 25.3042 25.3042 -43.0565 4 -66.5278 -17.5644 25.3042 144.9949 -34.8447 -78.4519 5 -17.5644 -66.5278 25.3042 -34.8447 144.9949 -78.4519 6 24.4284 24.4284 -43.0565 -78.4519 -78.4519 212.8414 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004159 -0.001117 -0.001882 0.002979 0.001543 0.000937 2 -0.001117 0.004159 -0.001882 0.001543 0.002979 0.000937 3 -0.001882 -0.001882 0.006102 -0.003478 -0.003478 -0.000897 4 0.002979 0.001543 -0.003478 0.016016 0.010065 0.008391 5 0.001543 0.002979 -0.003478 0.010065 0.016016 0.008391 6 0.000937 0.000937 -0.000897 0.008391 0.008391 0.010487 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 214.59901 234.00593 224.30247 Shear Modulus (GPa) = 73.25496 140.40346 106.82921 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 4.50867 6.24193 5.44472 Velocity P-wave (km/s) = 9.30887 10.81135 10.08812 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00465985 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 240.42014 240.42014 163.87764 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.26847 0.30840 Poissons Ratio (y) = 0.26847 0.30840 Poissons Ratio (z) = 0.45245 0.45245 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 y 0.00000 -0.00000 0.00000 0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 y 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 6.84923 0.33192 0.44746 y 0.33192 6.84923 0.44746 z 0.44746 0.44746 18.17390 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.55290 2 = 2.67298 3 = 4.26734 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 150.91 150.91 201.96 251.91 251.91 252.60 257.20 257.20 320.07 320.07 324.07 324.07 341.19 341.19 357.23 410.85 410.85 416.74 416.74 422.74 426.95 429.90 429.90 446.14 460.03 471.26 471.26 472.50 472.50 493.53 493.53 498.88 498.88 501.11 541.65 541.65 602.67 602.67 629.12 629.12 790.82 790.82 834.26 961.47 961.47 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.279060 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.4593 seconds ################################################################################ # Output for cell point 20 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.41243409 eV Monopole - monopole (real) = -156.50811721 eV Monopole - monopole (recip)= -219.29548034 eV Monopole - monopole (total)= -375.80359755 eV -------------------------------------------------------------------------------- Total lattice energy = -323.39116346 eV -------------------------------------------------------------------------------- Total lattice energy = -31202.3038 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -323.391163 Gnorm: 0.002325 CPU: 0.464 ** Hessian has required structure Cycle: 1 Energy: -323.394474 Gnorm: 0.000014 CPU: 0.471 ** Hessian has required structure **** Optimisation achieved **** Final energy = -323.39447413 eV Final Gnorm = 0.00000122 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.34439084 eV Monopole - monopole (real) = -156.62595500 eV Monopole - monopole (recip)= -219.11290996 eV Monopole - monopole (total)= -375.73886497 eV -------------------------------------------------------------------------------- Total lattice energy = -323.39447413 eV -------------------------------------------------------------------------------- Total lattice energy = -31202.6232 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c 0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c 0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c 0.000000 0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.161383 0.000000 0.000000 0.000000 4.161383 0.000000 -1.536289 -1.536289 8.576215 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.161383 Angstrom dE/a -0.000040 eV/Ang b 4.161383 Angstrom dE/b -0.000040 eV/Ang c 8.847137 Angstrom dE/c -0.000012 eV/Ang alpha 100.000000 Degrees dE/alpha 0.000000 eV/Deg beta 100.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 148.515222 Angs**3 Density of cell = 3.605685 g/cm**3 Non-primitive cell volume = 148.515222 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.000000 0.000000 3 Mg c -0.000000 0.000000 -0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 -0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 -0.000000 0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 0.000000 0.000000 11 O c -0.000000 0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 -0.000000 0.000000 13 O c 0.000000 -0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 -0.000000 0.000000 15 O c 0.000000 0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 418.5212 214.6485 143.2580 -68.5442 -18.8777 27.2724 2 214.6485 418.5212 143.2580 -18.8777 -68.5442 27.2724 3 143.2580 143.2580 265.0911 28.9598 28.9598 -48.6008 4 -68.5442 -18.8777 28.9598 141.0612 -39.5684 -80.8067 5 -18.8777 -68.5442 28.9598 -39.5684 141.0612 -80.8067 6 27.2724 27.2724 -48.6008 -80.8067 -80.8067 219.0415 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004331 -0.000926 -0.002289 0.004063 0.002617 0.001532 2 -0.000926 0.004331 -0.002289 0.002617 0.004063 0.001532 3 -0.002289 -0.002289 0.007102 -0.005550 -0.005550 -0.001949 4 0.004063 0.002617 -0.005550 0.021738 0.015804 0.011787 5 0.002617 0.004063 -0.005550 0.015804 0.021738 0.011787 6 0.001532 0.001532 -0.001949 0.011787 0.011787 0.012448 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 210.25709 233.82914 222.04311 Shear Modulus (GPa) = 59.32480 140.29739 99.81110 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 4.05625 6.23779 5.26133 Velocity P-wave (km/s) = 8.95825 10.80417 9.92422 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00475608 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 230.87624 230.87624 140.81097 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.21376 0.32234 Poissons Ratio (y) = 0.21376 0.32234 Poissons Ratio (z) = 0.52851 0.52851 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 y 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 y 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 6.69823 0.35117 0.38031 y 0.35117 6.69823 0.38031 z 0.38031 0.38031 22.23510 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.51934 2 = 2.65149 3 = 4.71743 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 133.76 133.76 176.56 227.37 250.92 250.92 251.57 251.57 302.70 302.70 319.08 319.08 333.72 333.72 356.82 401.60 401.60 420.99 420.99 426.51 426.86 432.38 432.38 453.31 454.38 474.06 474.06 479.03 479.03 498.82 498.82 504.72 504.72 506.77 547.66 547.66 602.10 602.10 631.90 631.90 788.41 788.41 839.07 960.59 960.59 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.273058 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.4861 seconds ################################################################################ # Output for cell point 21 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.36336115 eV Monopole - monopole (real) = -155.97720744 eV Monopole - monopole (recip)= -219.34099035 eV Monopole - monopole (total)= -375.31819780 eV -------------------------------------------------------------------------------- Total lattice energy = -322.95483665 eV -------------------------------------------------------------------------------- Total lattice energy = -31160.2049 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -322.954837 Gnorm: 0.002527 CPU: 0.491 ** Hessian has required structure Cycle: 1 Energy: -322.959114 Gnorm: 0.000034 CPU: 0.499 ** Hessian has required structure **** Optimisation achieved **** Final energy = -322.95911422 eV Final Gnorm = 0.00000008 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.30809160 eV Monopole - monopole (real) = -156.15474051 eV Monopole - monopole (recip)= -219.11246532 eV Monopole - monopole (total)= -375.26720583 eV -------------------------------------------------------------------------------- Total lattice energy = -322.95911422 eV -------------------------------------------------------------------------------- Total lattice energy = -31160.6176 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c 0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c 0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c 0.000000 0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.151079 0.000000 0.000000 0.000000 4.151079 0.000000 -1.625398 -1.625398 8.617923 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.151079 Angstrom dE/a 0.000003 eV/Ang b 4.151079 Angstrom dE/b 0.000003 eV/Ang c 8.919217 Angstrom dE/c 0.000001 eV/Ang alpha 100.500000 Degrees dE/alpha 0.000000 eV/Deg beta 100.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 148.499341 Angs**3 Density of cell = 3.606071 g/cm**3 Non-primitive cell volume = 148.499341 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 0.000000 -0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 -0.000000 -0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 0.000000 0.000000 8 Mg c -0.000000 -0.000000 0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 0.000000 -0.000000 0.000000 11 O c -0.000000 0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 -0.000000 0.000000 13 O c 0.000000 -0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 -0.000000 0.000000 15 O c 0.000000 0.000000 0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 426.4602 221.0221 138.6147 -70.0579 -20.2048 30.2697 2 221.0221 426.4602 138.6147 -20.2048 -70.0579 30.2697 3 138.6147 138.6147 251.8191 32.9649 32.9649 -54.6033 4 -70.0579 -20.2048 32.9649 136.2548 -44.7478 -82.5707 5 -20.2048 -70.0579 32.9649 -44.7478 136.2548 -82.5707 6 30.2697 30.2697 -54.6033 -82.5707 -82.5707 225.7421 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004849 -0.000367 -0.003432 0.007060 0.005623 0.003208 2 -0.000367 0.004849 -0.003432 0.005623 0.007060 0.003208 3 -0.003432 -0.003432 0.009646 -0.011546 -0.011546 -0.005193 4 0.007060 0.005623 -0.011546 0.037749 0.031828 0.020956 5 0.005623 0.007060 -0.011546 0.031828 0.037749 0.020956 6 0.003208 0.003208 -0.005193 0.020956 0.020956 0.017644 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 204.80164 233.47142 219.13653 Shear Modulus (GPa) = 38.88787 140.08286 89.48536 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 3.28390 6.23269 4.98149 Velocity P-wave (km/s) = 8.43636 10.79533 9.68792 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00488277 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 206.22114 206.22114 103.66822 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.07571 0.35578 Poissons Ratio (y) = 0.07571 0.35578 Poissons Ratio (z) = 0.70772 0.70772 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 y 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 y 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 6.52718 0.36744 0.23904 y 0.36744 6.52718 0.23904 z 0.23904 0.23904 29.62972 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.48188 2 = 2.62480 3 = 5.44378 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 112.10 112.10 144.23 195.90 242.72 242.72 250.72 250.72 283.59 283.59 313.20 313.20 325.13 325.13 355.69 390.87 390.87 426.05 426.14 426.14 431.95 435.73 435.73 448.49 461.49 477.27 477.27 486.36 486.36 504.85 504.85 511.71 511.71 513.02 554.02 554.02 601.61 601.61 635.07 635.07 785.32 785.32 844.49 959.62 959.62 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.265474 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.5151 seconds ################################################################################ # Output for cell point 22 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.32982161 eV Monopole - monopole (real) = -155.48453165 eV Monopole - monopole (recip)= -219.35274303 eV Monopole - monopole (total)= -374.83727468 eV -------------------------------------------------------------------------------- Total lattice energy = -322.50745307 eV -------------------------------------------------------------------------------- Total lattice energy = -31117.0392 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -322.507453 Gnorm: 0.002743 CPU: 0.520 ** Hessian has required structure Cycle: 1 Energy: -322.513055 Gnorm: 0.000090 CPU: 0.528 ** Hessian has required structure **** Optimisation achieved **** Final energy = -322.51305548 eV Final Gnorm = 0.00000365 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.29561869 eV Monopole - monopole (real) = -155.74932752 eV Monopole - monopole (recip)= -219.05934665 eV Monopole - monopole (total)= -374.80867417 eV -------------------------------------------------------------------------------- Total lattice energy = -322.51305548 eV -------------------------------------------------------------------------------- Total lattice energy = -31117.5798 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c 0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c 0.000000 0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.139084 0.000000 0.000000 0.000000 4.139084 0.000000 -1.718702 -1.718702 8.673306 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.139084 Angstrom dE/a 0.000124 eV/Ang b 4.139084 Angstrom dE/b 0.000124 eV/Ang c 9.007448 Angstrom dE/c 0.000008 eV/Ang alpha 101.000000 Degrees dE/alpha 0.000000 eV/Deg beta 101.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 148.591221 Angs**3 Density of cell = 3.603841 g/cm**3 Non-primitive cell volume = 148.591221 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c 0.000000 0.000000 -0.000000 0.000000 4 Mg c -0.000000 0.000000 0.000000 0.000000 5 Mg c 0.000000 0.000000 -0.000000 0.000000 6 Mg c 0.000000 -0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 0.000000 0.000000 9 O c -0.000000 -0.000000 0.000000 0.000000 10 O c 0.000000 0.000000 -0.000000 0.000000 11 O c -0.000000 0.000000 0.000000 0.000000 12 O c -0.000000 -0.000000 -0.000000 0.000000 13 O c 0.000000 -0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 -0.000000 0.000000 15 O c 0.000000 0.000000 0.000000 0.000000 16 O c -0.000000 -0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 435.6771 227.9455 132.8383 -70.9055 -21.5134 33.3897 2 227.9455 435.6771 132.8383 -21.5134 -70.9055 33.3897 3 132.8383 132.8383 236.9896 37.2964 37.2964 -61.0562 4 -70.9055 -21.5134 37.2964 130.3324 -50.3980 -83.5529 5 -21.5134 -70.9055 37.2964 -50.3980 130.3324 -83.5529 6 33.3897 33.3897 -61.0562 -83.5529 -83.5529 232.9585 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.016117 0.010969 -0.026677 0.067605 0.066198 0.037115 2 0.010969 0.016117 -0.026677 0.066198 0.067605 0.037115 3 -0.026677 -0.026677 0.057619 -0.135687 -0.135687 -0.074582 4 0.067605 0.066198 -0.135687 0.361448 0.355530 0.202411 5 0.066198 0.067605 -0.135687 0.355530 0.361448 0.202411 6 0.037115 0.037115 -0.074582 0.202411 0.202411 0.119300 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 196.79931 232.84313 214.82122 Shear Modulus (GPa) = 4.90911 139.70612 72.30761 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 1.16713 6.22623 4.47929 Velocity P-wave (km/s) = 7.51162 10.78413 9.29306 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00508132 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 62.04542 62.04542 17.35535 ------------------------------------------------------------------------------- Poissons Ratio (x) = -0.68056 0.46300 Poissons Ratio (y) = -0.68056 0.46300 Poissons Ratio (z) = 1.65521 1.65521 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 y 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 y 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 6.33540 0.38224 -0.11664 y 0.38224 6.33540 -0.11664 z -0.11664 -0.11664 47.20723 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.43991 2 = 2.59171 3 = 6.87080 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 82.39 82.39 98.28 154.16 228.70 228.70 249.15 249.15 265.49 265.49 306.16 306.16 315.12 315.12 353.51 378.32 378.32 423.64 432.35 432.35 438.29 440.25 440.25 444.23 470.87 480.97 480.97 494.63 494.63 511.72 511.72 519.94 520.10 520.10 560.75 560.75 601.29 601.29 638.69 638.69 781.32 781.32 850.65 958.53 958.53 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.255065 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.5430 seconds ################################################################################ # Output for cell point 23 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.32044104 eV Monopole - monopole (real) = -155.06130951 eV Monopole - monopole (recip)= -219.31200972 eV Monopole - monopole (total)= -374.37331923 eV -------------------------------------------------------------------------------- Total lattice energy = -322.05287819 eV -------------------------------------------------------------------------------- Total lattice energy = -31073.1797 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -322.052878 Gnorm: 0.002975 CPU: 0.548 ** Hessian has required structure Cycle: 1 Energy: -322.060350 Gnorm: 0.000204 CPU: 0.555 ** Hessian has required structure **** Optimisation achieved **** Final energy = -322.06035302 eV Final Gnorm = 0.00001107 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.32021555 eV Monopole - monopole (real) = -155.45753301 eV Monopole - monopole (recip)= -218.92303556 eV Monopole - monopole (total)= -374.38056856 eV -------------------------------------------------------------------------------- Total lattice energy = -322.06035302 eV -------------------------------------------------------------------------------- Total lattice energy = -31073.9009 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.500000 0.000000 3 Mg c -0.000000 0.500000 0.250000 0.000000 4 Mg c -0.000000 0.500000 0.750000 0.000000 5 Mg c 0.500000 -0.000000 0.250000 0.000000 6 Mg c 0.500000 -0.000000 0.750000 0.000000 7 Mg c 0.500000 0.500000 0.000000 0.000000 8 Mg c 0.500000 0.500000 0.500000 0.000000 9 O c 0.500000 0.500000 0.250000 0.000000 10 O c 0.500000 0.500000 0.750000 0.000000 11 O c 0.500000 -0.000000 0.000000 0.000000 12 O c 0.500000 -0.000000 0.500000 0.000000 13 O c -0.000000 0.500000 0.000000 0.000000 14 O c -0.000000 0.500000 0.500000 0.000000 15 O c -0.000000 -0.000000 0.250000 0.000000 16 O c -0.000000 -0.000000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.124987 0.000000 0.000000 0.000000 4.124987 0.000000 -1.817853 -1.817853 8.748155 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.124987 Angstrom dE/a 0.000376 eV/Ang b 4.124987 Angstrom dE/b 0.000376 eV/Ang c 9.118081 Angstrom dE/c -0.000005 eV/Ang alpha 101.500000 Degrees dE/alpha 0.000000 eV/Deg beta 101.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 148.854422 Angs**3 Density of cell = 3.597469 g/cm**3 Non-primitive cell volume = 148.854422 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 0.000000 0.000000 3 Mg c -0.000000 0.000000 -0.000000 0.000000 4 Mg c -0.000000 0.000000 -0.000000 0.000000 5 Mg c -0.000000 -0.000000 -0.000000 0.000000 6 Mg c 0.000000 -0.000000 -0.000000 0.000000 7 Mg c -0.000000 -0.000000 0.000000 0.000000 8 Mg c -0.000000 -0.000000 0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c 0.000000 0.000000 -0.000000 0.000000 11 O c -0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 -0.000000 -0.000000 0.000000 13 O c -0.000000 -0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 -0.000000 0.000000 15 O c 0.000000 0.000000 -0.000000 0.000000 16 O c -0.000000 -0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 446.4153 235.4372 125.5715 -70.8488 -22.7469 36.5706 2 235.4372 446.4153 125.5715 -22.7469 -70.8488 36.5706 3 125.5715 125.5715 220.2140 41.8845 41.8845 -67.9077 4 -70.8488 -22.7469 41.8845 122.9488 -56.5036 -83.4738 5 -22.7469 -70.8488 41.8845 -56.5036 122.9488 -83.4738 6 36.5706 36.5706 -67.9077 -83.4738 -83.4738 240.6857 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.002099 -0.002949 0.001961 -0.006925 -0.008279 -0.004590 2 -0.002949 0.002099 0.001961 -0.008279 -0.006925 -0.004590 3 0.001961 0.001961 -0.000875 0.017536 0.017536 0.011320 4 -0.006925 -0.008279 0.017536 -0.036840 -0.042775 -0.020354 5 -0.008279 -0.006925 0.017536 -0.042775 -0.036840 -0.020354 6 -0.004590 -0.004590 0.011320 -0.020354 -0.020354 -0.005374 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 189.80491 231.80055 210.80273 Shear Modulus (GPa) = -65.85898 139.08098 36.61100 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = -4.27867 6.21778 3.19012 Velocity P-wave (km/s) = 5.32459 10.76950 8.49510 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00526857 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 476.41011 476.41011 -1142.76122 ------------------------------------------------------------------------------- Poissons Ratio (x) = 1.40509 2.24102 Poissons Ratio (y) = 1.40509 2.24102 Poissons Ratio (z) = -0.93427 -0.93427 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 0.00000 -0.00000 0.00000 0.00000 y 0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 z 0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 y 0.00000 0.00000 -0.00000 0.00000 0.00000 0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 6.14534 0.42101 -2.02207 y 0.42101 6.14534 -2.02207 z -2.02207 -2.02207 140.83072 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.39256 2 = 2.55058 3 = 11.86978 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -47.10 -0.00 0.00 0.00 24.01 24.01 88.52 202.20 202.20 246.50 246.50 253.00 253.00 297.51 297.51 303.29 303.29 349.80 363.45 363.45 415.95 439.86 439.86 444.84 446.23 446.34 446.34 481.71 485.27 485.27 504.04 504.04 519.49 519.49 527.68 530.25 530.25 567.89 567.89 601.33 601.33 642.91 642.91 776.11 776.11 857.74 957.29 957.29 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.235755 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.5702 seconds ################################################################################ # Output for cell point 24 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.34846068 eV Monopole - monopole (real) = -154.75673937 eV Monopole - monopole (recip)= -219.18828715 eV Monopole - monopole (total)= -373.94502652 eV -------------------------------------------------------------------------------- Total lattice energy = -321.59656584 eV -------------------------------------------------------------------------------- Total lattice energy = -31029.1525 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -321.596566 Gnorm: 0.003222 CPU: 0.575 ** Hessian has wrong structure ** Imaginary eigenvectors = 3 ** Hessian has wrong structure ** Imaginary eigenvectors = 2 Cycle: 1 Energy: -322.010035 Gnorm: 0.407387 CPU: 0.595 ** Hessian has wrong structure ** Imaginary eigenvectors = 1 ** Hessian has wrong structure ** Imaginary eigenvectors = 2 Cycle: 2 Energy: -322.398673 Gnorm: 0.846783 CPU: 0.609 ** Hessian has wrong structure ** Imaginary eigenvectors = 1 ** Hessian has wrong structure ** Imaginary eigenvectors = 1 Cycle: 3 Energy: -324.134316 Gnorm: 0.778038 CPU: 0.627 ** Hessian has required structure Cycle: 4 Energy: -327.142381 Gnorm: 0.420128 CPU: 0.635 ** Hessian has required structure Cycle: 5 Energy: -327.707253 Gnorm: 0.170600 CPU: 0.642 ** Hessian has required structure Cycle: 6 Energy: -327.776813 Gnorm: 0.092144 CPU: 0.649 ** Hessian has required structure Cycle: 7 Energy: -327.782328 Gnorm: 0.076801 CPU: 0.656 ** Hessian has required structure Cycle: 8 Energy: -327.785390 Gnorm: 0.026826 CPU: 0.663 ** Hessian has required structure Cycle: 9 Energy: -327.787022 Gnorm: 0.019212 CPU: 0.668 ** Hessian has required structure Cycle: 10 Energy: -327.787680 Gnorm: 0.025386 CPU: 0.674 ** Hessian has required structure Cycle: 11 Energy: -327.787796 Gnorm: 0.012786 CPU: 0.682 ** Hessian has required structure Cycle: 12 Energy: -327.787809 Gnorm: 0.012173 CPU: 0.694 ** Hessian has required structure Cycle: 13 Energy: -327.789080 Gnorm: 0.002123 CPU: 0.706 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.78908550 eV Final Gnorm = 0.00000897 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.23565933 eV Monopole - monopole (real) = -162.96381743 eV Monopole - monopole (recip)= -218.06092740 eV Monopole - monopole (total)= -381.02474483 eV -------------------------------------------------------------------------------- Total lattice energy = -327.78908550 eV -------------------------------------------------------------------------------- Total lattice energy = -31626.6360 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.201177 0.000000 0.000000 0.000000 4.201177 0.000000 -1.859112 -1.859112 8.546567 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.201177 Angstrom dE/a -0.000083 eV/Ang b 4.201177 Angstrom dE/b -0.000083 eV/Ang c 8.941834 Angstrom dE/c -0.000111 eV/Ang alpha 102.000000 Degrees dE/alpha 0.000000 eV/Deg beta 102.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.845949 Angs**3 Density of cell = 3.549974 g/cm**3 Non-primitive cell volume = 150.845949 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000007 -0.000007 0.000002 0.000000 3 Mg c -0.000008 -0.000009 0.000069 0.000000 4 Mg c 0.000008 0.000003 0.000055 0.000000 5 Mg c -0.000009 -0.000008 0.000069 0.000000 6 Mg c 0.000003 0.000008 0.000055 0.000000 7 Mg c -0.000022 -0.000022 -0.000021 0.000000 8 Mg c 0.000013 0.000013 0.000070 0.000000 9 O c -0.000009 -0.000009 0.000006 0.000000 10 O c -0.000007 -0.000007 -0.000051 0.000000 11 O c 0.000012 -0.000028 -0.000172 0.000000 12 O c 0.000003 0.000009 -0.000098 0.000000 13 O c -0.000028 0.000012 -0.000172 0.000000 14 O c 0.000009 0.000003 -0.000098 0.000000 15 O c 0.000009 0.000009 0.000066 0.000000 16 O c 0.000032 0.000032 0.000215 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000032 0.000032 0.000215 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 387.3078 169.9629 159.6887 12.3523 2.6242 0.6709 2 169.9629 387.3078 159.6887 2.6242 12.3523 0.6709 3 159.6887 159.6887 336.2782 -2.3575 -2.3575 -1.1091 4 12.3523 2.6242 -2.3575 160.1841 -0.8713 14.6334 5 2.6242 12.3523 -2.3575 -0.8713 160.1841 14.6334 6 0.6709 0.6709 -1.1091 14.6334 14.6334 168.9702 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003545 -0.001068 -0.001178 -0.000274 0.000005 0.000006 2 -0.001068 0.003545 -0.001178 0.000005 -0.000274 0.000006 3 -0.001178 -0.001178 0.004095 0.000171 0.000171 0.000007 4 -0.000274 0.000005 0.000171 0.006317 0.000091 -0.000553 5 0.000005 -0.000274 0.000171 0.000091 0.006317 -0.000553 6 0.000006 0.000006 0.000007 -0.000553 -0.000553 0.006014 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 230.60241 232.17492 231.38867 Shear Modulus (GPa) = 131.13670 139.30459 135.22065 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.07784 6.26427 6.17176 Velocity P-wave (km/s) = 10.68702 10.85003 10.76884 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00433647 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 282.07690 282.07690 244.20218 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30135 0.28768 Poissons Ratio (y) = 0.30135 0.28768 Poissons Ratio (z) = 0.33229 0.33229 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00003 0.00000 0.00001 -0.00000 -0.00003 0.00000 y 0.00000 -0.00003 0.00001 -0.00003 -0.00000 0.00000 z -0.00002 -0.00002 0.00032 0.00002 0.00002 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00001 0.00000 0.00001 0.00000 -0.00002 0.00000 y 0.00000 -0.00001 0.00001 -0.00002 0.00000 0.00000 z -0.00004 -0.00004 0.00013 0.00002 0.00002 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.18916 0.01042 -0.09422 y 0.01042 7.18916 -0.09422 z -0.09422 -0.09422 9.46813 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.67932 2 = 2.68175 3 = 3.07830 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: 0.00 0.00 0.00 237.91 237.91 240.37 240.37 334.76 334.77 336.77 340.85 353.40 353.40 353.40 353.40 357.26 409.40 409.40 409.40 409.40 417.99 418.43 438.25 438.25 438.25 438.26 440.84 440.84 442.08 442.08 460.56 467.98 468.96 494.04 494.04 494.04 494.04 503.31 503.31 503.31 503.31 741.88 741.88 741.88 741.88 807.83 963.94 963.94 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.311612 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.7215 seconds ################################################################################ # Output for cell point 25 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.75935877 eV Monopole - monopole (real) = -163.26836168 eV Monopole - monopole (recip)= -218.35120660 eV Monopole - monopole (total)= -381.61956828 eV -------------------------------------------------------------------------------- Total lattice energy = -327.86020951 eV -------------------------------------------------------------------------------- Total lattice energy = -31633.4984 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.860210 Gnorm: 0.007180 CPU: 0.727 ** Hessian has required structure Cycle: 1 Energy: -327.862113 Gnorm: 0.000007 CPU: 0.734 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.86211261 eV Final Gnorm = 0.00000000 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24194093 eV Monopole - monopole (real) = -163.04240377 eV Monopole - monopole (recip)= -218.06164978 eV Monopole - monopole (total)= -381.10405355 eV -------------------------------------------------------------------------------- Total lattice energy = -327.86211261 eV -------------------------------------------------------------------------------- Total lattice energy = -31633.6820 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.208507 0.000000 0.000000 0.000000 4.208507 0.000000 -1.936323 -1.936323 8.516849 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.208507 Angstrom dE/a 0.000000 eV/Ang b 4.208507 Angstrom dE/b 0.000000 eV/Ang c 8.946251 Angstrom dE/c 0.000000 eV/Ang alpha 102.500000 Degrees dE/alpha 0.000000 eV/Deg beta 102.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.846451 Angs**3 Density of cell = 3.549962 g/cm**3 Non-primitive cell volume = 150.846451 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c 0.000000 -0.000000 0.000000 0.000000 5 Mg c -0.000000 -0.000000 -0.000000 0.000000 6 Mg c -0.000000 0.000000 0.000000 0.000000 7 Mg c -0.000000 -0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 0.000000 0.000000 9 O c -0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 0.000000 0.000000 11 O c 0.000000 -0.000000 -0.000000 0.000000 12 O c 0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 -0.000000 0.000000 14 O c 0.000000 0.000000 0.000000 0.000000 15 O c 0.000000 0.000000 0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 382.2014 167.6456 160.8211 8.6530 1.7575 0.3228 2 167.6456 382.2014 160.8211 1.7575 8.6530 0.3228 3 160.8211 160.8211 347.1275 -1.3608 -1.3608 -0.5290 4 8.6530 1.7575 -1.3608 161.1845 -0.4127 10.2513 5 1.7575 8.6530 -1.3608 -0.4127 161.1845 10.2513 6 0.3228 0.3228 -0.5290 10.2513 10.2513 166.9189 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003584 -0.001084 -0.001159 -0.000191 0.000009 0.000003 2 -0.001084 0.003584 -0.001159 0.000009 -0.000191 0.000003 3 -0.001159 -0.001159 0.003956 0.000108 0.000108 0.000004 4 -0.000191 0.000009 0.000108 0.006240 0.000043 -0.000385 5 0.000009 -0.000191 0.000108 0.000043 0.006240 -0.000385 6 0.000003 0.000003 0.000004 -0.000385 -0.000385 0.006038 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 231.49237 232.23400 231.86318 Shear Modulus (GPa) = 131.98372 139.34040 135.66206 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.09745 6.26508 6.18183 Velocity P-wave (km/s) = 10.71362 10.85144 10.78275 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00431980 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 279.04565 279.04565 252.81058 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30236 0.29300 Poissons Ratio (y) = 0.30236 0.29300 Poissons Ratio (z) = 0.32341 0.32341 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 0.00000 -0.00000 -0.00000 0.00000 y 0.00000 -0.00000 0.00000 -0.00000 -0.00000 0.00000 z -0.00000 -0.00000 0.00000 0.00000 0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x -0.00000 0.00000 0.00000 0.00000 -0.00000 0.00000 y 0.00000 -0.00000 0.00000 -0.00000 0.00000 0.00000 z -0.00000 -0.00000 0.00000 0.00000 0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.36210 0.00534 -0.07104 y 0.00534 7.36210 -0.07104 z -0.07104 -0.07104 8.86454 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.71233 2 = 2.71307 3 = 2.97846 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 240.14 240.14 241.29 241.29 340.08 341.19 341.19 341.98 358.23 358.23 358.23 358.23 370.72 406.56 406.56 406.56 406.56 412.40 412.53 436.52 436.52 437.13 437.13 447.07 447.07 447.07 447.07 463.49 465.22 470.68 489.60 489.60 489.60 489.60 498.13 498.13 498.13 498.13 742.55 742.55 742.55 742.55 804.96 965.23 965.23 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.312605 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.7503 seconds ################################################################################ # Output for cell point 26 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.78315207 eV Monopole - monopole (real) = -163.32616239 eV Monopole - monopole (recip)= -218.36507212 eV Monopole - monopole (total)= -381.69123452 eV -------------------------------------------------------------------------------- Total lattice energy = -327.90808245 eV -------------------------------------------------------------------------------- Total lattice energy = -31638.1174 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.908082 Gnorm: 0.007295 CPU: 0.755 ** Hessian has required structure Cycle: 1 Energy: -327.910095 Gnorm: 0.000009 CPU: 0.762 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.91009550 eV Final Gnorm = 0.00000000 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24664059 eV Monopole - monopole (real) = -163.09487547 eV Monopole - monopole (recip)= -218.06186062 eV Monopole - monopole (total)= -381.15673609 eV -------------------------------------------------------------------------------- Total lattice energy = -327.91009550 eV -------------------------------------------------------------------------------- Total lattice energy = -31638.3117 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.215838 0.000000 0.000000 0.000000 4.215838 0.000000 -2.013853 -2.013853 8.487304 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.215838 Angstrom dE/a 0.000000 eV/Ang b 4.215838 Angstrom dE/b 0.000000 eV/Ang c 8.952404 Angstrom dE/c 0.000000 eV/Ang alpha 103.000000 Degrees dE/alpha 0.000000 eV/Deg beta 103.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.847322 Angs**3 Density of cell = 3.549941 g/cm**3 Non-primitive cell volume = 150.847322 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 -0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 -0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 0.000000 0.000000 16 O c -0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 377.1271 165.5053 161.8587 4.8781 0.9473 0.1009 2 165.5053 377.1271 161.8587 0.9473 4.8781 0.1009 3 161.8587 161.8587 357.7407 -0.6123 -0.6123 -0.1658 4 4.8781 0.9473 -0.6123 162.0726 -0.1288 5.7797 5 0.9473 4.8781 -0.6123 -0.1288 162.0726 5.7797 6 0.1009 0.1009 -0.1658 5.7797 5.7797 165.0775 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003627 -0.001101 -0.001143 -0.000107 0.000008 0.000001 2 -0.001101 0.003627 -0.001143 0.000008 -0.000107 0.000001 3 -0.001143 -0.001143 0.003830 0.000056 0.000056 0.000001 4 -0.000107 0.000008 0.000056 0.006181 0.000013 -0.000217 5 0.000008 -0.000107 0.000056 0.000013 0.006181 -0.000217 6 0.000001 0.000001 0.000001 -0.000217 -0.000217 0.006073 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 232.04442 232.27116 232.15779 Shear Modulus (GPa) = 132.52576 139.36269 135.94423 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.10998 6.26560 6.18828 Velocity P-wave (km/s) = 10.73040 10.85234 10.79154 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00430952 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 275.73556 275.73556 261.11265 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30355 0.29844 Poissons Ratio (y) = 0.30355 0.29844 Poissons Ratio (z) = 0.31515 0.31515 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.54450 0.00178 -0.04286 y 0.00178 7.54450 -0.04286 z -0.04286 -0.04286 8.34562 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.74622 2 = 2.74640 3 = 2.88967 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 241.89 241.89 242.24 242.24 342.56 343.14 347.62 347.62 362.67 362.67 362.67 362.67 383.64 403.42 403.42 403.42 403.42 406.62 406.65 432.04 432.04 432.23 432.23 456.01 456.01 456.01 456.01 461.20 461.63 478.48 485.15 485.15 485.15 485.15 493.03 493.03 493.03 493.03 743.19 743.19 743.19 743.19 802.22 966.52 966.52 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.313321 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.7776 seconds ################################################################################ # Output for cell point 27 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.80648795 eV Monopole - monopole (real) = -163.35645089 eV Monopole - monopole (recip)= -218.37864215 eV Monopole - monopole (total)= -381.73509304 eV -------------------------------------------------------------------------------- Total lattice energy = -327.92860509 eV -------------------------------------------------------------------------------- Total lattice energy = -31640.0975 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.928605 Gnorm: 0.007424 CPU: 0.782 ** Hessian has required structure Cycle: 1 Energy: -327.930751 Gnorm: 0.000010 CPU: 0.790 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.93075056 eV Final Gnorm = 0.00000003 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24876965 eV Monopole - monopole (real) = -163.11821890 eV Monopole - monopole (recip)= -218.06130130 eV Monopole - monopole (total)= -381.17952020 eV -------------------------------------------------------------------------------- Total lattice energy = -327.93075056 eV -------------------------------------------------------------------------------- Total lattice energy = -31640.3045 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.223160 0.000000 0.000000 0.000000 4.223160 0.000000 -2.091763 -2.091763 8.457998 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.223160 Angstrom dE/a 0.000001 eV/Ang b 4.223160 Angstrom dE/b 0.000001 eV/Ang c 8.960395 Angstrom dE/c 0.000001 eV/Ang alpha 103.500000 Degrees dE/alpha 0.000000 eV/Deg beta 103.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.849064 Angs**3 Density of cell = 3.549900 g/cm**3 Non-primitive cell volume = 150.849064 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 -0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 -0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 0.000000 0.000000 16 O c -0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 372.0745 163.5500 162.8176 1.0339 0.1919 0.0045 2 163.5500 372.0745 162.8176 0.1919 1.0339 0.0045 3 162.8176 162.8176 368.0457 -0.0965 -0.0965 -0.0073 4 1.0339 0.1919 -0.0965 162.8649 -0.0056 1.2248 5 0.1919 1.0339 -0.0965 -0.0056 162.8649 1.2248 6 0.0045 0.0045 -0.0073 1.2248 1.2248 163.4556 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003675 -0.001121 -0.001130 -0.000023 0.000002 0.000000 2 -0.001121 0.003675 -0.001130 0.000002 -0.000023 0.000000 3 -0.001130 -0.001130 0.003717 0.000011 0.000011 0.000000 4 -0.000023 0.000002 0.000011 0.006141 0.000001 -0.000046 5 0.000002 -0.000023 0.000011 0.000001 0.006141 -0.000046 6 0.000000 0.000000 0.000000 -0.000046 -0.000046 0.006119 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 232.27520 232.28503 232.28011 Shear Modulus (GPa) = 132.75957 139.37102 136.06529 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.11540 6.26582 6.19107 Velocity P-wave (km/s) = 10.73758 10.85272 10.79531 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00430524 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 272.12363 272.12363 269.05736 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30502 0.30398 Poissons Ratio (y) = 0.30502 0.30398 Poissons Ratio (z) = 0.30745 0.30745 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.73679 0.00008 -0.00967 y 0.00008 7.73679 -0.00967 z -0.00967 -0.00967 7.89845 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.78132 2 = 2.78149 3 = 2.81062 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 243.22 243.22 243.23 243.23 344.28 344.31 354.00 354.00 366.62 366.62 366.62 366.62 395.97 400.20 400.20 400.20 400.20 400.72 400.75 427.40 427.40 427.41 427.41 458.20 458.22 464.79 464.79 464.79 464.79 480.74 480.74 480.74 480.74 486.72 488.08 488.08 488.08 488.08 743.80 743.80 743.80 743.80 799.65 967.82 967.82 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.313739 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.8052 seconds ################################################################################ # Output for cell point 28 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.82581205 eV Monopole - monopole (real) = -163.35612875 eV Monopole - monopole (recip)= -218.39166982 eV Monopole - monopole (total)= -381.74779858 eV -------------------------------------------------------------------------------- Total lattice energy = -327.92198653 eV -------------------------------------------------------------------------------- Total lattice energy = -31639.4590 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.921987 Gnorm: 0.007541 CPU: 0.810 ** Hessian has required structure Cycle: 1 Energy: -327.924268 Gnorm: 0.000011 CPU: 0.818 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.92426789 eV Final Gnorm = 0.00000007 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24803553 eV Monopole - monopole (real) = -163.11070434 eV Monopole - monopole (recip)= -218.06159907 eV Monopole - monopole (total)= -381.17230342 eV -------------------------------------------------------------------------------- Total lattice energy = -327.92426789 eV -------------------------------------------------------------------------------- Total lattice energy = -31639.6791 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.230475 0.000000 0.000000 0.000000 4.230475 0.000000 -2.170050 -2.170050 8.428728 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.230475 Angstrom dE/a 0.000002 eV/Ang b 4.230475 Angstrom dE/b 0.000002 eV/Ang c 8.970044 Angstrom dE/c 0.000001 eV/Ang alpha 104.000000 Degrees dE/alpha 0.000000 eV/Deg beta 104.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.848261 Angs**3 Density of cell = 3.549919 g/cm**3 Non-primitive cell volume = 150.848261 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 0.000000 0.000000 16 O c -0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 367.0473 161.7806 163.7109 -2.8750 -0.5098 0.0341 2 161.7806 367.0473 163.7109 -0.5098 -2.8750 0.0341 3 163.7109 163.7109 378.0318 0.1777 0.1777 -0.0549 4 -2.8750 -0.5098 0.1777 163.5744 -0.0421 -3.4055 5 -0.5098 -2.8750 0.1777 -0.0421 163.5744 -3.4055 6 0.0341 0.0341 -0.0549 -3.4055 -3.4055 162.0538 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003728 -0.001144 -0.001119 0.000063 -0.000007 0.000000 2 -0.001144 0.003728 -0.001119 -0.000007 0.000063 0.000000 3 -0.001119 -0.001119 0.003615 -0.000027 -0.000027 0.000001 4 0.000063 -0.000007 -0.000027 0.006117 0.000004 0.000129 5 -0.000007 0.000063 -0.000027 0.000004 0.006117 0.000129 6 0.000000 0.000000 0.000001 0.000129 0.000129 0.006176 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 232.20777 232.28127 232.24452 Shear Modulus (GPa) = 132.68755 139.36877 136.02816 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.11372 6.26576 6.19021 Velocity P-wave (km/s) = 10.73541 10.85261 10.79417 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00430649 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 268.21214 268.21214 276.65237 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30687 0.30962 Poissons Ratio (y) = 0.30687 0.30962 Poissons Ratio (z) = 0.30018 0.30018 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 7.94005 0.00069 0.02857 y 0.00069 7.94005 0.02857 z 0.02857 0.02857 7.50971 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.73970 2 = 2.81769 3 = 2.81860 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 244.17 244.17 244.28 244.28 345.32 345.51 360.30 360.30 369.97 369.97 369.97 369.97 394.68 394.83 397.07 397.07 397.07 397.07 407.77 422.61 422.61 422.67 422.67 454.85 454.99 473.09 473.09 473.09 473.09 476.48 476.48 476.48 476.48 483.45 483.45 483.45 483.45 494.99 744.38 744.38 744.38 744.38 797.24 969.12 969.12 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.313884 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.8339 seconds ################################################################################ # Output for cell point 29 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.84208043 eV Monopole - monopole (real) = -163.32348339 eV Monopole - monopole (recip)= -218.40579797 eV Monopole - monopole (total)= -381.72928136 eV -------------------------------------------------------------------------------- Total lattice energy = -327.88720093 eV -------------------------------------------------------------------------------- Total lattice energy = -31636.1027 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.887201 Gnorm: 0.007662 CPU: 0.839 ** Hessian has required structure Cycle: 1 Energy: -327.889630 Gnorm: 0.000012 CPU: 0.846 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.88962997 eV Final Gnorm = 0.00000011 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.24398047 eV Monopole - monopole (real) = -163.07012055 eV Monopole - monopole (recip)= -218.06348988 eV Monopole - monopole (total)= -381.13361044 eV -------------------------------------------------------------------------------- Total lattice energy = -327.88962997 eV -------------------------------------------------------------------------------- Total lattice energy = -31636.3370 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.237791 0.000000 0.000000 0.000000 4.237791 0.000000 -2.248729 -2.248729 8.399377 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.237791 Angstrom dE/a 0.000003 eV/Ang b 4.237791 Angstrom dE/b 0.000003 eV/Ang c 8.981264 Angstrom dE/c 0.000003 eV/Ang alpha 104.500000 Degrees dE/alpha 0.000000 eV/Deg beta 104.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.843347 Angs**3 Density of cell = 3.550035 g/cm**3 Non-primitive cell volume = 150.843347 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 0.000000 0.000000 16 O c -0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 362.0392 160.1994 164.5542 -6.8429 -1.1581 0.1909 2 160.1994 362.0392 164.5542 -1.1581 -6.8429 0.1909 3 164.5542 164.5542 387.6704 0.2125 0.2125 -0.3042 4 -6.8429 -1.1581 0.2125 164.2166 -0.2317 -8.1040 5 -1.1581 -6.8429 0.2125 -0.2317 164.2166 -8.1040 6 0.1909 0.1909 -0.3042 -8.1040 -8.1040 160.8747 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003788 -0.001171 -0.001111 0.000151 -0.000020 0.000001 2 -0.001171 0.003788 -0.001111 -0.000020 0.000151 0.000001 3 -0.001111 -0.001111 0.003523 -0.000059 -0.000059 0.000003 4 0.000151 -0.000020 -0.000059 0.006111 0.000024 0.000309 5 -0.000020 0.000151 -0.000059 0.000024 0.006111 0.000309 6 0.000001 0.000001 0.000003 0.000309 0.000309 0.006247 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 231.85907 232.26273 232.06090 Shear Modulus (GPa) = 132.30528 139.35765 135.83147 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.10481 6.26540 6.18563 Velocity P-wave (km/s) = 10.72396 10.85200 10.78817 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00431296 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 263.98679 263.98679 283.87905 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.30918 0.31535 Poissons Ratio (y) = 0.30918 0.31535 Poissons Ratio (z) = 0.29325 0.29325 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 8.15552 0.00410 0.07206 y 0.00410 8.15552 0.07206 z 0.07206 0.07206 7.17006 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.67576 2 = 2.85507 3 = 2.85832 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 244.77 244.77 245.38 245.38 345.74 346.74 366.50 366.50 372.48 372.48 372.48 372.48 388.43 388.94 394.24 394.24 394.24 394.24 417.64 417.64 418.02 418.02 419.08 451.17 451.96 472.02 472.02 472.02 472.02 477.06 477.06 477.06 477.06 483.37 483.37 483.37 483.37 503.20 744.96 744.96 744.96 744.96 794.99 970.41 970.41 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.313758 eV -------------------------------------------------------------------------------- Time to end of optimisation = 0.8623 seconds ################################################################################ # Output for cell point 30 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.85607403 eV Monopole - monopole (real) = -163.25629170 eV Monopole - monopole (recip)= -218.42177741 eV Monopole - monopole (total)= -381.67806911 eV -------------------------------------------------------------------------------- Total lattice energy = -327.82199508 eV -------------------------------------------------------------------------------- Total lattice energy = -31629.8113 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.821995 Gnorm: 0.007802 CPU: 0.868 ** Hessian has required structure Cycle: 1 Energy: -327.824340 Gnorm: 0.002436 CPU: 0.877 ** Hessian has required structure Cycle: 2 Energy: -327.824404 Gnorm: 0.002105 CPU: 0.889 ** Hessian has required structure Cycle: 3 Energy: -327.824478 Gnorm: 0.001649 CPU: 0.899 ** Hessian has required structure Cycle: 4 Energy: -327.824493 Gnorm: 0.001535 CPU: 0.908 ** Hessian has required structure Cycle: 5 Energy: -327.824497 Gnorm: 0.001507 CPU: 0.916 ** Hessian has required structure Cycle: 6 Energy: -327.824498 Gnorm: 0.001500 CPU: 0.923 ** Hessian has required structure Cycle: 7 Energy: -327.824499 Gnorm: 0.001496 CPU: 0.933 ** Hessian has required structure Cycle: 8 Energy: -327.824499 Gnorm: 0.001496 CPU: 0.949 ** Hessian has required structure Cycle: 9 Energy: -327.824499 Gnorm: 0.001496 CPU: 0.976 ** Hessian calculated ** **** Conditions for a minimum have not been satisfied. However **** **** no lower point can be found - treat results with caution **** **** unless gradient norm is small (less than 0.1) **** Final energy = -327.82449854 eV Final Gnorm = 0.00149565 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.35487611 eV Monopole - monopole (real) = -163.04420074 eV Monopole - monopole (recip)= -218.13517392 eV Monopole - monopole (total)= -381.17937465 eV -------------------------------------------------------------------------------- Total lattice energy = -327.82449854 eV -------------------------------------------------------------------------------- Total lattice energy = -31630.0529 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.243706 0.000000 0.000000 0.000000 4.243706 0.000000 -2.327196 -2.327196 8.367621 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.243706 Angstrom dE/a -0.048102 eV/Ang b 4.243706 Angstrom dE/b -0.048102 eV/Ang c 8.991594 Angstrom dE/c -0.022944 eV/Ang alpha 105.000000 Degrees dE/alpha 0.000000 eV/Deg beta 105.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.692838 Angs**3 Density of cell = 3.553581 g/cm**3 Non-primitive cell volume = 150.692838 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 358.5559 159.0488 165.5781 -10.8877 -1.7589 0.4803 2 159.0488 358.5559 165.5781 -1.7589 -10.8877 0.4803 3 165.5781 165.5781 398.3250 -0.0155 -0.0155 -0.7475 4 -10.8877 -1.7589 -0.0155 164.8039 -0.5656 -12.8871 5 -1.7589 -10.8877 -0.0155 -0.5656 164.8039 -12.8871 6 0.4803 0.4803 -0.7475 -12.8871 -12.8871 159.9439 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003832 -0.001193 -0.001097 0.000240 -0.000037 0.000003 2 -0.001193 0.003832 -0.001097 -0.000037 0.000240 0.000003 3 -0.001097 -0.001097 0.003422 -0.000083 -0.000083 0.000009 4 0.000240 -0.000037 -0.000083 0.006122 0.000060 0.000497 5 -0.000037 0.000240 -0.000083 0.000060 0.006122 0.000497 6 0.000003 0.000003 0.000009 0.000497 0.000497 0.006332 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 231.89002 232.87189 232.38095 Shear Modulus (GPa) = 132.01503 139.59245 135.80374 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.09507 6.26755 6.18191 Velocity P-wave (km/s) = 10.71394 10.85854 10.78648 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00431239 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 260.96921 260.96921 292.19111 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31138 0.32049 Poissons Ratio (y) = 0.31138 0.32049 Poissons Ratio (z) = 0.28625 0.28625 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 0.00000 -0.00000 y -0.00000 0.00000 -0.00000 0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 8.35276 0.01088 0.12127 y 0.01088 8.35276 0.12127 z 0.12127 0.12127 6.85574 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.61467 2 = 2.88823 3 = 2.89532 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 245.05 245.05 246.53 246.53 345.67 348.12 373.27 373.27 373.99 373.99 373.99 373.99 382.98 384.05 392.54 392.54 392.54 392.54 413.51 413.51 414.48 414.48 430.74 448.08 450.09 468.99 468.99 468.99 468.99 473.74 473.74 473.74 473.74 491.65 491.65 491.65 491.65 512.23 745.72 745.72 745.72 745.72 793.17 972.22 972.22 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.314973 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.0115 seconds ################################################################################ # Output for cell point 31 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.98575437 eV Monopole - monopole (real) = -163.20210885 eV Monopole - monopole (recip)= -218.50793819 eV Monopole - monopole (total)= -381.71004704 eV -------------------------------------------------------------------------------- Total lattice energy = -327.72429267 eV -------------------------------------------------------------------------------- Total lattice energy = -31620.3845 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.724293 Gnorm: 0.009443 CPU: 1.016 ** Hessian has required structure Cycle: 1 Energy: -327.728206 Gnorm: 0.000013 CPU: 1.023 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.72820593 eV Final Gnorm = 0.00000015 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.22353117 eV Monopole - monopole (real) = -162.87931152 eV Monopole - monopole (recip)= -218.07242558 eV Monopole - monopole (total)= -380.95173710 eV -------------------------------------------------------------------------------- Total lattice energy = -327.72820593 eV -------------------------------------------------------------------------------- Total lattice energy = -31620.7621 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.252478 0.000000 0.000000 0.000000 4.252478 0.000000 -2.407362 -2.407362 8.340179 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.252478 Angstrom dE/a 0.000003 eV/Ang b 4.252478 Angstrom dE/b 0.000003 eV/Ang c 9.008294 Angstrom dE/c 0.000006 eV/Ang alpha 105.500000 Degrees dE/alpha 0.000000 eV/Deg beta 105.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.820214 Angs**3 Density of cell = 3.550579 g/cm**3 Non-primitive cell volume = 150.820214 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 352.0339 157.6257 166.1555 -14.9502 -2.3105 0.9030 2 157.6257 352.0339 166.1555 -2.3105 -14.9502 0.9030 3 166.1555 166.1555 405.7215 -0.4270 -0.4270 -1.3772 4 -14.9502 -2.3105 -0.4270 165.3645 -1.0356 -17.6906 5 -2.3105 -14.9502 -0.4270 -1.0356 165.3645 -17.6906 6 0.9030 0.9030 -1.3772 -17.6906 -17.6906 159.2078 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.003929 -0.001240 -0.001101 0.000335 -0.000057 0.000006 2 -0.001240 0.003929 -0.001101 -0.000057 0.000335 0.000006 3 -0.001101 -0.001101 0.003366 -0.000105 -0.000105 0.000018 4 0.000335 -0.000057 -0.000105 0.006151 0.000112 0.000693 5 -0.000057 0.000335 -0.000105 0.000112 0.006151 0.000693 6 0.000006 0.000006 0.000018 0.000693 0.000693 0.006435 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 230.36473 232.18475 231.27474 Shear Modulus (GPa) = 130.56688 139.31087 134.93887 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.06411 6.26387 6.16480 Velocity P-wave (km/s) = 10.67296 10.84934 10.76151 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00434094 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 254.49266 254.49266 297.04905 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31556 0.32708 Poissons Ratio (y) = 0.31556 0.32708 Poissons Ratio (z) = 0.28022 0.28022 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 8.62926 0.02206 0.17624 y 0.02206 8.62926 0.17624 z 0.17624 0.17624 6.61214 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.56556 2 = 2.93380 3 = 2.94641 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 245.08 245.08 247.81 247.81 344.86 349.34 373.40 373.40 373.40 373.40 375.31 377.14 378.48 378.48 390.77 390.77 390.77 390.77 407.14 407.14 408.98 408.98 440.26 442.77 446.59 463.83 463.83 463.83 463.83 468.85 468.85 468.85 468.85 498.83 498.83 498.83 498.83 519.18 746.08 746.08 746.08 746.08 790.99 972.93 972.93 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.312648 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.0393 seconds ################################################################################ # Output for cell point 32 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.86729862 eV Monopole - monopole (real) = -163.00771787 eV Monopole - monopole (recip)= -218.45972330 eV Monopole - monopole (total)= -381.46744117 eV -------------------------------------------------------------------------------- Total lattice energy = -327.60014255 eV -------------------------------------------------------------------------------- Total lattice energy = -31608.4059 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.600143 Gnorm: 0.008041 CPU: 1.044 ** Hessian has required structure Cycle: 1 Energy: -327.601847 Gnorm: 0.000008 CPU: 1.051 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.60184719 eV Final Gnorm = 0.00000004 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.20674433 eV Monopole - monopole (real) = -162.72629934 eV Monopole - monopole (recip)= -218.08229217 eV Monopole - monopole (total)= -380.80859151 eV -------------------------------------------------------------------------------- Total lattice energy = -327.60184719 eV -------------------------------------------------------------------------------- Total lattice energy = -31608.5704 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.259858 0.000000 0.000000 0.000000 4.259858 0.000000 -2.487297 -2.487297 8.309976 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.259858 Angstrom dE/a -0.000001 eV/Ang b 4.259858 Angstrom dE/b -0.000001 eV/Ang c 9.023801 Angstrom dE/c -0.000001 eV/Ang alpha 106.000000 Degrees dE/alpha 0.000000 eV/Deg beta 106.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.796038 Angs**3 Density of cell = 3.551149 g/cm**3 Non-primitive cell volume = 150.796038 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 347.0337 156.6230 166.9405 -19.0667 -2.8118 1.4439 2 156.6230 347.0337 166.9405 -2.8118 -19.0667 1.4439 3 166.9405 166.9405 414.1369 -1.0791 -1.0791 -2.2064 4 -19.0667 -2.8118 -1.0791 165.8963 -1.6474 -22.5551 5 -2.8118 -19.0667 -1.0791 -1.6474 165.8963 -22.5551 6 1.4439 1.4439 -2.2064 -22.5551 -22.5551 158.7113 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004013 -0.001283 -0.001099 0.000433 -0.000081 0.000010 2 -0.001283 0.004013 -0.001099 -0.000081 0.000433 0.000010 3 -0.001099 -0.001099 0.003300 -0.000120 -0.000120 0.000032 4 0.000433 -0.000081 -0.000120 0.006200 0.000181 0.000902 5 -0.000081 0.000433 -0.000120 0.000181 0.006200 0.000902 6 0.000010 0.000010 0.000032 0.000902 0.000902 0.006557 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 229.24186 232.13468 230.68827 Shear Modulus (GPa) = 129.19857 139.28081 134.23969 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 6.03177 6.26269 6.14831 Velocity P-wave (km/s) = 10.63315 10.84730 10.74076 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00436221 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 249.21808 249.21808 302.98907 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.31978 0.33307 Poissons Ratio (y) = 0.31978 0.33307 Poissons Ratio (z) = 0.27396 0.27396 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 8.89119 0.03831 0.23796 y 0.03831 8.89119 0.23796 z 0.23796 0.23796 6.38215 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.51763 2 = 2.97538 3 = 2.99553 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: 0.00 0.00 0.00 244.83 244.83 249.16 249.16 343.62 350.70 368.41 371.22 371.44 371.44 371.44 371.44 384.25 384.25 390.28 390.28 390.28 390.28 401.61 401.61 404.61 404.61 438.01 444.29 450.23 459.68 459.68 459.68 459.68 465.13 465.13 465.13 465.13 506.59 506.59 506.59 506.59 526.94 746.66 746.66 746.66 746.66 789.22 974.17 974.17 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.311700 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.0676 seconds ################################################################################ # Output for cell point 33 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.86675862 eV Monopole - monopole (real) = -162.82355992 eV Monopole - monopole (recip)= -218.48454733 eV Monopole - monopole (total)= -381.30810725 eV -------------------------------------------------------------------------------- Total lattice energy = -327.44134863 eV -------------------------------------------------------------------------------- Total lattice energy = -31593.0847 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.441349 Gnorm: 0.008174 CPU: 1.073 ** Hessian has required structure Cycle: 1 Energy: -327.444473 Gnorm: 0.000007 CPU: 1.080 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.44447335 eV Final Gnorm = 0.00000038 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.18508945 eV Monopole - monopole (real) = -162.53252927 eV Monopole - monopole (recip)= -218.09703353 eV Monopole - monopole (total)= -380.62956280 eV -------------------------------------------------------------------------------- Total lattice energy = -327.44447335 eV -------------------------------------------------------------------------------- Total lattice energy = -31593.3862 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.267251 0.000000 0.000000 0.000000 4.267251 0.000000 -2.567662 -2.567662 8.279265 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.267251 Angstrom dE/a 0.000013 eV/Ang b 4.267251 Angstrom dE/b 0.000013 eV/Ang c 9.040575 Angstrom dE/c 0.000002 eV/Ang alpha 106.500000 Degrees dE/alpha 0.000000 eV/Deg beta 106.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.760730 Angs**3 Density of cell = 3.551980 g/cm**3 Non-primitive cell volume = 150.760730 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 342.0339 155.8188 167.7286 -23.2298 -3.2578 2.1191 2 155.8188 342.0339 167.7286 -3.2578 -23.2298 2.1191 3 167.7286 167.7286 422.1131 -1.9438 -1.9438 -3.2149 4 -23.2298 -3.2578 -1.9438 166.4137 -2.3831 -27.4697 5 -3.2578 -23.2298 -1.9438 -2.3831 166.4137 -27.4697 6 2.1191 2.1191 -3.2149 -27.4697 -27.4697 158.4487 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004106 -0.001334 -0.001099 0.000535 -0.000109 0.000015 2 -0.001334 0.004106 -0.001099 -0.000109 0.000535 0.000015 3 -0.001099 -0.001099 0.003242 -0.000131 -0.000131 0.000050 4 0.000535 -0.000109 -0.000131 0.006270 0.000269 0.001125 5 -0.000109 0.000535 -0.000131 0.000269 0.006270 0.001125 6 0.000015 0.000015 0.000050 0.001125 0.001125 0.006702 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 227.87837 232.08143 229.97990 Shear Modulus (GPa) = 127.47951 139.24889 133.36420 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.99080 6.26124 6.12751 Velocity P-wave (km/s) = 10.58339 10.84479 10.71489 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00438831 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 243.57224 243.57224 308.46171 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.32483 0.33912 Poissons Ratio (y) = 0.32483 0.33912 Poissons Ratio (z) = 0.26778 0.26778 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 9.17212 0.06089 0.30705 y 0.06089 9.17212 0.30705 z 0.30705 0.30705 6.18016 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.47378 2 = 3.01848 3 = 3.04854 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 244.33 244.33 250.60 250.60 341.88 352.12 361.26 365.30 368.32 368.32 368.32 368.32 389.72 389.72 390.01 390.01 390.01 390.01 396.04 396.04 400.36 400.36 432.87 442.30 455.24 455.24 455.24 455.24 459.81 462.33 462.33 462.33 462.33 514.12 514.12 514.12 514.12 534.52 747.25 747.25 747.25 747.25 787.63 975.39 975.39 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.310497 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.0957 seconds ################################################################################ # Output for cell point 34 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.86119867 eV Monopole - monopole (real) = -162.59707798 eV Monopole - monopole (recip)= -218.51457195 eV Monopole - monopole (total)= -381.11164992 eV -------------------------------------------------------------------------------- Total lattice energy = -327.25045126 eV -------------------------------------------------------------------------------- Total lattice energy = -31574.6661 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.250451 Gnorm: 0.008309 CPU: 1.100 ** Hessian has required structure Cycle: 1 Energy: -327.252544 Gnorm: 0.000008 CPU: 1.108 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.25254395 eV Final Gnorm = 0.00000025 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.15790989 eV Monopole - monopole (real) = -162.29500714 eV Monopole - monopole (recip)= -218.11544670 eV Monopole - monopole (total)= -380.41045384 eV -------------------------------------------------------------------------------- Total lattice energy = -327.25254395 eV -------------------------------------------------------------------------------- Total lattice energy = -31574.8680 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.274721 0.000000 0.000000 0.000000 4.274721 0.000000 -2.648465 -2.648465 8.247948 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.274721 Angstrom dE/a 0.000009 eV/Ang b 4.274721 Angstrom dE/b 0.000009 eV/Ang c 9.058553 Angstrom dE/c -0.000001 eV/Ang alpha 107.000000 Degrees dE/alpha 0.000000 eV/Deg beta 107.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.716722 Angs**3 Density of cell = 3.553018 g/cm**3 Non-primitive cell volume = 150.716722 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c 0.000000 -0.000000 -0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 336.9967 155.2194 168.5374 -27.4325 -3.6615 2.9172 2 155.2194 336.9967 168.5374 -3.6615 -27.4325 2.9172 3 168.5374 168.5374 429.6142 -3.0126 -3.0126 -4.4030 4 -27.4325 -3.6615 -3.0126 166.9342 -3.2388 -32.4254 5 -3.6615 -27.4325 -3.0126 -3.2388 166.9342 -32.4254 6 2.9172 2.9172 -4.4030 -32.4254 -32.4254 158.4260 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004211 -0.001393 -0.001102 0.000643 -0.000140 0.000020 2 -0.001393 0.004211 -0.001102 -0.000140 0.000643 0.000020 3 -0.001102 -0.001102 0.003191 -0.000136 -0.000136 0.000074 4 0.000643 -0.000140 -0.000136 0.006363 0.000378 0.001367 5 -0.000140 0.000643 -0.000136 0.000378 0.006363 0.001367 6 0.000020 0.000020 0.000074 0.001367 0.001367 0.006873 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 226.26787 232.02179 229.14483 Shear Modulus (GPa) = 125.38614 139.21309 132.29961 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.94054 6.25952 6.10212 Velocity P-wave (km/s) = 10.52315 10.84181 10.68367 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00441954 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 237.49838 237.49838 313.39987 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.33085 0.34523 Poissons Ratio (y) = 0.33085 0.34523 Poissons Ratio (z) = 0.26162 0.26162 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 9.47628 0.09129 0.38449 y 0.09129 9.47628 0.38449 z 0.38449 0.38449 6.00324 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.43354 2 = 3.06349 3 = 3.10623 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 -0.00 243.60 243.60 252.14 252.14 339.63 353.58 353.82 359.34 364.46 364.46 364.46 364.46 389.35 389.35 389.35 389.35 389.39 389.39 395.86 395.86 396.21 396.21 427.29 440.61 450.44 450.44 450.44 450.44 460.60 460.60 460.60 460.60 469.01 521.41 521.41 521.41 521.41 541.90 747.87 747.87 747.87 747.87 786.18 976.57 976.57 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.309000 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.1240 seconds ################################################################################ # Output for cell point 35 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.84997178 eV Monopole - monopole (real) = -162.32528952 eV Monopole - monopole (recip)= -218.54860970 eV Monopole - monopole (total)= -380.87389921 eV -------------------------------------------------------------------------------- Total lattice energy = -327.02392744 eV -------------------------------------------------------------------------------- Total lattice energy = -31552.8100 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -327.023927 Gnorm: 0.008449 CPU: 1.129 ** Hessian has required structure Cycle: 1 Energy: -327.027459 Gnorm: 0.000016 CPU: 1.136 ** Hessian has required structure **** Optimisation achieved **** Final energy = -327.02745938 eV Final Gnorm = 0.00000071 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.12498185 eV Monopole - monopole (real) = -162.01256718 eV Monopole - monopole (recip)= -218.13987406 eV Monopole - monopole (total)= -380.15244123 eV -------------------------------------------------------------------------------- Total lattice energy = -327.02745938 eV -------------------------------------------------------------------------------- Total lattice energy = -31553.1508 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.282198 0.000000 0.000000 0.000000 4.282198 0.000000 -2.729741 -2.729741 8.216028 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.282198 Angstrom dE/a 0.000023 eV/Ang b 4.282198 Angstrom dE/b 0.000023 eV/Ang c 9.077780 Angstrom dE/c 0.000010 eV/Ang alpha 107.500000 Degrees dE/alpha 0.000000 eV/Deg beta 107.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.659078 Angs**3 Density of cell = 3.554377 g/cm**3 Non-primitive cell volume = 150.659078 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 -0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 331.9608 154.8225 169.3764 -31.6794 -4.0218 3.8588 2 154.8225 331.9608 169.3764 -4.0218 -31.6794 3.8588 3 169.3764 169.3764 436.5974 -4.2712 -4.2712 -5.7649 4 -31.6794 -4.0218 -4.2712 167.4672 -4.2096 -37.4261 5 -4.0218 -31.6794 -4.2712 -4.2096 167.4672 -37.4261 6 3.8588 3.8588 -5.7649 -37.4261 -37.4261 158.6412 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004329 -0.001462 -0.001106 0.000757 -0.000176 0.000027 2 -0.001462 0.004329 -0.001106 -0.000176 0.000757 0.000027 3 -0.001106 -0.001106 0.003147 -0.000136 -0.000136 0.000104 4 0.000757 -0.000176 -0.000136 0.006484 0.000509 0.001631 5 -0.000176 0.000757 -0.000136 0.000509 0.006484 0.001631 6 0.000027 0.000027 0.000104 0.001631 0.001631 0.007075 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 224.41828 231.96327 228.19078 Shear Modulus (GPa) = 122.90643 139.17803 131.04223 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.88038 6.25754 6.07189 Velocity P-wave (km/s) = 10.45197 10.83837 10.64693 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00445597 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 231.02611 231.02611 317.74607 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.33787 0.35137 Poissons Ratio (y) = 0.33787 0.35137 Poissons Ratio (z) = 0.25548 0.25548 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 9.80431 0.13130 0.47138 y 0.13130 9.80431 0.47138 z 0.47138 0.47138 5.85036 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.39673 2 = 3.11015 3 = 3.16886 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 242.63 242.63 253.79 253.79 336.88 346.11 353.39 355.07 360.15 360.15 360.15 360.15 383.35 383.35 388.01 388.01 388.01 388.01 392.21 392.21 401.02 401.02 421.29 439.29 445.40 445.40 445.40 445.40 459.97 459.97 459.97 459.97 477.81 528.42 528.42 528.42 528.42 549.04 748.52 748.52 748.52 748.52 784.90 977.73 977.73 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.307240 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.1525 seconds ################################################################################ # Output for cell point 36 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.83279999 eV Monopole - monopole (real) = -162.00689886 eV Monopole - monopole (recip)= -218.58902557 eV Monopole - monopole (total)= -380.59592444 eV -------------------------------------------------------------------------------- Total lattice energy = -326.76312445 eV -------------------------------------------------------------------------------- Total lattice energy = -31527.6465 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -326.763124 Gnorm: 0.008591 CPU: 1.157 ** Hessian has required structure Cycle: 1 Energy: -326.766873 Gnorm: 0.000025 CPU: 1.165 ** Hessian has required structure **** Optimisation achieved **** Final energy = -326.76687358 eV Final Gnorm = 0.00000084 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.08583881 eV Monopole - monopole (real) = -161.68280761 eV Monopole - monopole (recip)= -218.16990479 eV Monopole - monopole (total)= -379.85271239 eV -------------------------------------------------------------------------------- Total lattice energy = -326.76687358 eV -------------------------------------------------------------------------------- Total lattice energy = -31528.0082 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.289726 0.000000 0.000000 0.000000 4.289726 0.000000 -2.811489 -2.811489 8.183383 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.289726 Angstrom dE/a 0.000027 eV/Ang b 4.289726 Angstrom dE/b 0.000027 eV/Ang c 9.098170 Angstrom dE/c 0.000014 eV/Ang alpha 108.000000 Degrees dE/alpha 0.000000 eV/Deg beta 108.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.588571 Angs**3 Density of cell = 3.556041 g/cm**3 Non-primitive cell volume = 150.588571 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 -0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 326.8975 154.6358 170.2581 -35.9672 -4.3450 4.9362 2 154.6358 326.8975 170.2581 -4.3450 -35.9672 4.9362 3 170.2581 170.2581 443.0466 -5.7067 -5.7067 -7.2986 4 -35.9672 -4.3450 -5.7067 168.0252 -5.2898 -42.4669 5 -4.3450 -35.9672 -5.7067 -5.2898 168.0252 -42.4669 6 4.9362 4.9362 -7.2986 -42.4669 -42.4669 159.1020 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004462 -0.001544 -0.001112 0.000880 -0.000216 0.000036 2 -0.001544 0.004462 -0.001112 -0.000216 0.000880 0.000036 3 -0.001112 -0.001112 0.003111 -0.000129 -0.000129 0.000143 4 0.000880 -0.000216 -0.000129 0.006637 0.000667 0.001923 5 -0.000216 0.000880 -0.000129 0.000667 0.006637 0.001923 6 0.000036 0.000036 0.000143 0.001923 0.001923 0.007316 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 222.31765 231.90506 227.11136 Shear Modulus (GPa) = 120.01434 139.14311 129.57873 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.80943 6.25529 6.03648 Velocity P-wave (km/s) = 10.36907 10.83448 10.60433 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00449807 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 224.10681 224.10681 321.44372 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.34605 0.35752 Poissons Ratio (y) = 0.34605 0.35752 Poissons Ratio (z) = 0.24926 0.24926 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 10.16109 0.18328 0.56924 y 0.18328 10.16109 0.56924 z 0.56924 0.56924 5.71957 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.36293 2 = 3.15877 3 = 3.23736 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 241.43 241.43 255.55 255.55 333.60 338.09 347.42 355.49 355.49 355.49 355.49 356.61 376.89 376.89 385.82 385.82 385.82 385.82 388.35 388.35 406.16 406.16 414.83 438.34 440.13 440.13 440.13 440.13 460.37 460.37 460.37 460.37 486.24 535.15 535.15 535.15 535.15 555.95 749.21 749.21 749.21 749.21 783.77 978.84 978.84 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.305192 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.1816 seconds ################################################################################ # Output for cell point 37 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.80925046 eV Monopole - monopole (real) = -161.63950510 eV Monopole - monopole (recip)= -218.63542782 eV Monopole - monopole (total)= -380.27493292 eV -------------------------------------------------------------------------------- Total lattice energy = -326.46568245 eV -------------------------------------------------------------------------------- Total lattice energy = -31498.9479 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -326.465682 Gnorm: 0.008736 CPU: 1.186 ** Hessian has required structure Cycle: 1 Energy: -326.469658 Gnorm: 0.000035 CPU: 1.194 ** Hessian has required structure **** Optimisation achieved **** Final energy = -326.46965847 eV Final Gnorm = 0.00000096 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.04003344 eV Monopole - monopole (real) = -161.30370709 eV Monopole - monopole (recip)= -218.20598483 eV Monopole - monopole (total)= -379.50969191 eV -------------------------------------------------------------------------------- Total lattice energy = -326.46965847 eV -------------------------------------------------------------------------------- Total lattice energy = -31499.3315 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.297314 0.000000 0.000000 0.000000 4.297314 0.000000 -2.893720 -2.893720 8.149941 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.297314 Angstrom dE/a 0.000030 eV/Ang b 4.297314 Angstrom dE/b 0.000030 eV/Ang c 9.119691 Angstrom dE/c 0.000017 eV/Ang alpha 108.500000 Degrees dE/alpha 0.000000 eV/Deg beta 108.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.504190 Angs**3 Density of cell = 3.558035 g/cm**3 Non-primitive cell volume = 150.504190 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 -0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 321.8007 154.6645 171.1928 -40.2957 -4.6357 6.1513 2 154.6645 321.8007 171.1928 -4.6357 -40.2957 6.1513 3 171.1928 171.1928 448.9368 -7.3037 -7.3037 -9.0014 4 -40.2957 -4.6357 -7.3037 168.6184 -6.4745 -47.5466 5 -4.6357 -40.2957 -7.3037 -6.4745 168.6184 -47.5466 6 6.1513 6.1513 -9.0014 -47.5466 -47.5466 159.8137 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004614 -0.001641 -0.001121 0.001012 -0.000262 0.000045 2 -0.001641 0.004614 -0.001121 -0.000262 0.001012 0.000045 3 -0.001121 -0.001121 0.003082 -0.000116 -0.000116 0.000191 4 0.001012 -0.000262 -0.000116 0.006828 0.000857 0.002251 5 -0.000262 0.001012 -0.000116 0.000857 0.006828 0.002251 6 0.000045 0.000045 0.000191 0.002251 0.002251 0.007604 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 219.95267 231.84870 225.90068 Shear Modulus (GPa) = 116.68417 139.10931 127.89674 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.72665 6.25278 5.99549 Velocity P-wave (km/s) = 10.27349 10.83013 10.55548 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00454643 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 216.71483 216.71483 324.42277 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.35554 0.36364 Poissons Ratio (y) = 0.35554 0.36364 Poissons Ratio (z) = 0.24291 0.24291 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 10.55111 0.25019 0.67990 y 0.25019 10.55111 0.67990 z 0.67990 0.67990 5.61003 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.33188 2 = 3.20951 3 = 3.31265 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 240.00 240.00 257.42 257.42 329.71 329.78 341.43 350.56 350.56 350.56 350.56 358.18 370.14 370.14 382.78 382.78 382.78 382.78 384.65 384.65 407.90 411.16 411.16 434.68 434.68 434.68 434.68 437.79 461.72 461.72 461.72 461.72 494.30 541.60 541.60 541.60 541.60 562.62 749.96 749.96 749.96 749.96 782.77 979.90 979.90 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.302847 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.2111 seconds ################################################################################ # Output for cell point 38 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.77887915 eV Monopole - monopole (real) = -161.22103586 eV Monopole - monopole (recip)= -218.68828398 eV Monopole - monopole (total)= -379.90931984 eV -------------------------------------------------------------------------------- Total lattice energy = -326.13044069 eV -------------------------------------------------------------------------------- Total lattice energy = -31466.6022 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -326.130441 Gnorm: 0.008885 CPU: 1.216 ** Hessian has required structure Cycle: 1 Energy: -326.134653 Gnorm: 0.000046 CPU: 1.223 ** Hessian has required structure **** Optimisation achieved **** Final energy = -326.13465318 eV Final Gnorm = 0.00000110 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.98714121 eV Monopole - monopole (real) = -160.87322983 eV Monopole - monopole (recip)= -218.24856455 eV Monopole - monopole (total)= -379.12179439 eV -------------------------------------------------------------------------------- Total lattice energy = -326.13465318 eV -------------------------------------------------------------------------------- Total lattice energy = -31467.0086 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.304967 0.000000 0.000000 0.000000 4.304967 0.000000 -2.976447 -2.976447 8.115632 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.304967 Angstrom dE/a 0.000034 eV/Ang b 4.304967 Angstrom dE/b 0.000034 eV/Ang c 9.142317 Angstrom dE/c 0.000021 eV/Ang alpha 109.000000 Degrees dE/alpha 0.000000 eV/Deg beta 109.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.404903 Angs**3 Density of cell = 3.560384 g/cm**3 Non-primitive cell volume = 150.404903 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c -0.000000 -0.000000 -0.000000 0.000000 4 Mg c -0.000000 -0.000000 -0.000000 0.000000 5 Mg c -0.000000 -0.000000 -0.000000 0.000000 6 Mg c -0.000000 -0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c -0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c -0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 316.6650 154.9147 172.1898 -44.6654 -4.8990 7.5068 2 154.9147 316.6650 172.1898 -4.8990 -44.6654 7.5068 3 172.1898 172.1898 454.2439 -9.0450 -9.0450 -10.8717 4 -44.6654 -4.8990 -9.0450 169.2563 -7.7597 -52.6645 5 -4.8990 -44.6654 -9.0450 -7.7597 169.2563 -52.6645 6 7.5068 7.5068 -10.8717 -52.6645 -52.6645 160.7823 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004789 -0.001755 -0.001132 0.001156 -0.000314 0.000058 2 -0.001755 0.004789 -0.001132 -0.000314 0.001156 0.000058 3 -0.001132 -0.001132 0.003062 -0.000094 -0.000094 0.000251 4 0.001156 -0.000314 -0.000094 0.007066 0.001086 0.002624 5 -0.000314 0.001156 -0.000094 0.001086 0.007066 0.002624 6 0.000058 0.000058 0.000251 0.002624 0.002624 0.007950 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 217.30231 231.79585 224.54908 Shear Modulus (GPa) = 112.88658 139.07761 125.98210 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.63083 6.25000 5.94848 Velocity P-wave (km/s) = 10.16408 10.82532 10.49991 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00460188 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 208.82228 208.82228 326.60197 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.36649 0.36967 Poissons Ratio (y) = 0.36649 0.36967 Poissons Ratio (z) = 0.23636 0.23636 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 10.97985 0.33588 0.80573 y 0.33588 10.97985 0.80573 z 0.80573 0.80573 5.52145 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.30335 2 = 3.26251 3 = 3.39584 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 -0.00 0.00 238.34 238.34 259.42 259.42 320.97 325.39 335.41 345.38 345.38 345.38 345.38 359.78 363.09 363.09 378.97 378.97 378.97 378.97 381.10 381.10 400.48 416.00 416.00 429.02 429.02 429.02 429.02 437.69 463.87 463.87 463.87 463.87 502.00 547.76 547.76 547.76 547.76 569.05 750.76 750.76 750.76 750.76 781.91 980.91 980.91 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.300194 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.2397 seconds ################################################################################ # Output for cell point 39 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.74126469 eV Monopole - monopole (real) = -160.74939776 eV Monopole - monopole (recip)= -218.74806728 eV Monopole - monopole (total)= -379.49746505 eV -------------------------------------------------------------------------------- Total lattice energy = -325.75620036 eV -------------------------------------------------------------------------------- Total lattice energy = -31430.4937 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -325.756200 Gnorm: 0.009037 CPU: 1.245 ** Hessian has required structure Cycle: 1 Energy: -325.760658 Gnorm: 0.000059 CPU: 1.252 ** Hessian has required structure **** Optimisation achieved **** Final energy = -325.76065898 eV Final Gnorm = 0.00000125 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.92672420 eV Monopole - monopole (real) = -160.38929629 eV Monopole - monopole (recip)= -218.29808689 eV Monopole - monopole (total)= -378.68738318 eV -------------------------------------------------------------------------------- Total lattice energy = -325.76065898 eV -------------------------------------------------------------------------------- Total lattice energy = -31430.9239 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.312691 0.000000 0.000000 0.000000 4.312691 0.000000 -3.059683 -3.059683 8.080392 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.312691 Angstrom dE/a 0.000039 eV/Ang b 4.312691 Angstrom dE/b 0.000039 eV/Ang c 9.166027 Angstrom dE/c 0.000025 eV/Ang alpha 109.500000 Degrees dE/alpha 0.000000 eV/Deg beta 109.500000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.289686 Angs**3 Density of cell = 3.563113 g/cm**3 Non-primitive cell volume = 150.289686 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c 0.000000 0.000000 -0.000000 0.000000 4 Mg c 0.000000 -0.000000 -0.000000 0.000000 5 Mg c 0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 -0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c 0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 -0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 311.4855 155.3937 173.2576 -49.0773 -5.1405 9.0056 2 155.3937 311.4855 173.2576 -5.1405 -49.0773 9.0056 3 173.2576 173.2576 458.9449 -10.9115 -10.9115 -12.9087 4 -49.0773 -5.1405 -10.9115 169.9471 -9.1421 -57.8205 5 -5.1405 -49.0773 -10.9115 -9.1421 169.9471 -57.8205 6 9.0056 9.0056 -12.9087 -57.8205 -57.8205 162.0152 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.004990 -0.001892 -0.001145 0.001315 -0.000373 0.000072 2 -0.001892 0.004990 -0.001145 -0.000373 0.001315 0.000072 3 -0.001145 -0.001145 0.003050 -0.000062 -0.000062 0.000326 4 0.001315 -0.000373 -0.000062 0.007362 0.001364 0.003057 5 -0.000373 0.001315 -0.000062 0.001364 0.007362 0.003057 6 0.000072 0.000072 0.000326 0.003057 0.003057 0.008372 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 214.33479 231.74819 223.04149 Shear Modulus (GPa) = 108.58764 139.04903 123.81834 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.52046 6.24697 5.89492 Velocity P-wave (km/s) = 10.03931 10.82006 10.43699 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00466560 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 200.39804 200.39804 327.88511 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.37908 0.37552 Poissons Ratio (y) = 0.37908 0.37552 Poissons Ratio (z) = 0.22951 0.22951 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z -0.00000 -0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 11.45410 0.44540 0.94972 y 0.44540 11.45410 0.94972 z 0.94972 0.94972 5.45413 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.27716 2 = 3.31794 3 = 3.48829 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 236.45 236.45 261.55 261.55 311.81 320.37 329.37 339.97 339.97 339.97 339.97 355.74 355.74 361.40 374.49 374.49 374.49 374.49 377.74 377.74 392.56 420.66 420.66 423.16 423.16 423.16 423.16 438.05 466.69 466.69 466.69 466.69 509.34 553.61 553.61 553.61 553.61 575.21 751.63 751.63 751.63 751.63 781.18 981.86 981.86 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.297221 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.2683 seconds ################################################################################ # Output for cell point 40 # ################################################################################ Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 53.69597205 eV Monopole - monopole (real) = -160.22244599 eV Monopole - monopole (recip)= -218.81524484 eV Monopole - monopole (total)= -379.03769082 eV -------------------------------------------------------------------------------- Total lattice energy = -325.34171878 eV -------------------------------------------------------------------------------- Total lattice energy = -31390.5026 kJ/(mole unit cells) -------------------------------------------------------------------------------- Number of variables = 48 Maximum number of calculations = 1000 Maximum Hessian update interval = 10 Maximum step size = 1.000000000 Maximum parameter tolerance = 0.000010000 Maximum function tolerance = 0.000010000 Maximum gradient tolerance = 0.001000000 Maximum gradient component = 0.010000000 Symmetry not applied to optimisation Cell parameters to be optimised directly RFO method to be used DFP hessian update to be used Lower half triangular hessian to be used Start of bulk optimisation : Cycle: 0 Energy: -325.341719 Gnorm: 0.009193 CPU: 1.273 ** Hessian has required structure Cycle: 1 Energy: -325.346432 Gnorm: 0.000064 CPU: 1.284 ** Hessian has required structure **** Optimisation achieved **** Final energy = -325.34643242 eV Final Gnorm = 0.00006485 Components of energy : -------------------------------------------------------------------------------- Interatomic potentials = 52.86292412 eV Monopole - monopole (real) = -159.85470203 eV Monopole - monopole (recip)= -218.35465452 eV Monopole - monopole (total)= -378.20935654 eV -------------------------------------------------------------------------------- Total lattice energy = -325.34643242 eV -------------------------------------------------------------------------------- Total lattice energy = -31390.9574 kJ/(mole unit cells) -------------------------------------------------------------------------------- Final fractional coordinates of atoms : -------------------------------------------------------------------------------- No. Atomic x y z Radius Label (Frac) (Frac) (Frac) (Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c 0.250000 0.250000 0.500000 0.000000 3 Mg c 0.125000 0.625000 0.250000 0.000000 4 Mg c 0.375000 0.875000 0.750000 0.000000 5 Mg c 0.625000 0.125000 0.250000 0.000000 6 Mg c 0.875000 0.375000 0.750000 0.000000 7 Mg c 0.500000 0.500000 -0.000000 0.000000 8 Mg c 0.750000 0.750000 0.500000 0.000000 9 O c 0.625000 0.625000 0.250000 0.000000 10 O c 0.875000 0.875000 0.750000 0.000000 11 O c 0.500000 -0.000000 -0.000000 0.000000 12 O c 0.750000 0.250000 0.500000 0.000000 13 O c -0.000000 0.500000 -0.000000 0.000000 14 O c 0.250000 0.750000 0.500000 0.000000 15 O c 0.125000 0.125000 0.250000 0.000000 16 O c 0.375000 0.375000 0.750000 0.000000 -------------------------------------------------------------------------------- Final Cartesian lattice vectors (Angstroms) : 4.320687 0.000000 0.000000 0.000000 4.320687 0.000000 -3.143173 -3.143173 8.043473 Final cell parameters and derivatives : -------------------------------------------------------------------------------- a 4.320687 Angstrom dE/a 0.000977 eV/Ang b 4.320687 Angstrom dE/b 0.000977 eV/Ang c 9.190023 Angstrom dE/c -0.002790 eV/Ang alpha 110.000000 Degrees dE/alpha 0.000000 eV/Deg beta 110.000000 Degrees dE/beta 0.000000 eV/Deg gamma 90.000000 Degrees dE/gamma 0.000000 eV/Deg -------------------------------------------------------------------------------- Primitive cell volume = 150.158263 Angs**3 Density of cell = 3.566232 g/cm**3 Non-primitive cell volume = 150.158263 Angs**3 Final internal derivatives : -------------------------------------------------------------------------------- No. Atomic a b c Radius Label (eV) (eV) (eV) (eV/Angs) -------------------------------------------------------------------------------- 1 Mg c 0.000000 0.000000 0.000000 0.000000 2 Mg c -0.000000 -0.000000 -0.000000 0.000000 3 Mg c 0.000000 0.000000 -0.000000 0.000000 4 Mg c 0.000000 -0.000000 -0.000000 0.000000 5 Mg c 0.000000 0.000000 -0.000000 0.000000 6 Mg c -0.000000 0.000000 -0.000000 0.000000 7 Mg c 0.000000 0.000000 -0.000000 0.000000 8 Mg c 0.000000 0.000000 -0.000000 0.000000 9 O c -0.000000 -0.000000 0.000000 0.000000 10 O c -0.000000 -0.000000 -0.000000 0.000000 11 O c 0.000000 -0.000000 0.000000 0.000000 12 O c 0.000000 0.000000 0.000000 0.000000 13 O c -0.000000 0.000000 0.000000 0.000000 14 O c 0.000000 0.000000 0.000000 0.000000 15 O c -0.000000 -0.000000 -0.000000 0.000000 16 O c 0.000000 0.000000 -0.000000 0.000000 -------------------------------------------------------------------------------- Maximum abs 0.000000 0.000000 0.000000 0.000000 -------------------------------------------------------------------------------- Born effective charge tensors : ------------------------------------------------------------------------------- Atom x y z ------------------------------------------------------------------------------- 1 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 2 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 3 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 4 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 5 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 6 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 7 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 8 Mg x 2.0000 0.0000 0.0000 y 0.0000 2.0000 0.0000 z 0.0000 0.0000 2.0000 ------------------------------------------------------------------------------- 9 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 10 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 11 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 12 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 13 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 14 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 15 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- 16 O x -2.0000 0.0000 0.0000 y 0.0000 -2.0000 0.0000 z 0.0000 0.0000 -2.0000 ------------------------------------------------------------------------------- Elastic Constant Matrix: (Units=GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 306.1451 156.0530 174.4283 -53.5203 -5.3518 10.6414 2 156.0530 306.1451 174.4283 -5.3518 -53.5203 10.6414 3 174.4283 174.4283 463.3223 -12.9322 -12.9322 -15.0919 4 -53.5203 -5.3518 -12.9322 170.7126 -10.6010 -62.9996 5 -5.3518 -53.5203 -12.9322 -10.6010 170.7126 -62.9996 6 10.6414 10.6414 -15.0919 -62.9996 -62.9996 163.4660 ------------------------------------------------------------------------------- Elastic Compliance Matrix: (Units=1/GPa) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- 1 0.005226 -0.002057 -0.001161 0.001492 -0.000443 0.000091 2 -0.002057 0.005226 -0.001161 -0.000443 0.001492 0.000091 3 -0.001161 -0.001161 0.003045 -0.000015 -0.000015 0.000420 4 0.001492 -0.000443 -0.000015 0.007733 0.001703 0.003567 5 -0.000443 0.001492 -0.000015 0.001703 0.007733 0.003567 6 0.000091 0.000091 0.000420 0.003567 0.003567 0.008894 ------------------------------------------------------------------------------- Mechanical properties : ------------------------------------------------------------------------------- Convention : Reuss Voigt Hill ------------------------------------------------------------------------------- Bulk Modulus (GPa) = 210.96159 231.71465 221.33812 Shear Modulus (GPa) = 103.74523 139.02512 121.38518 ------------------------------------------------------------------------------- Velocity S-wave (km/s) = 5.39361 6.24370 5.83416 Velocity P-wave (km/s) = 9.89663 10.81448 10.36572 ------------------------------------------------------------------------------- Compressibility (1/GPa) = 0.00474020 ------------------------------------------------------------------------------- Stress axis : x y z ------------------------------------------------------------------------------- Youngs Moduli (GPa) = 191.33598 191.33598 328.38138 ------------------------------------------------------------------------------- Poissons Ratio (x) = 0.39361 0.38121 Poissons Ratio (y) = 0.39361 0.38121 Poissons Ratio (z) = 0.22212 0.22212 ------------------------------------------------------------------------------- Piezoelectric Strain Matrix: (Units=C/m**2) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 y 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 z 0.00000 0.00000 0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Piezoelectric Stress Matrix: (Units=10**-11 C/N) ------------------------------------------------------------------------------- Indices 1 2 3 4 5 6 ------------------------------------------------------------------------------- x 0.00000 -0.00000 -0.00000 0.00000 -0.00000 -0.00000 y -0.00000 0.00000 -0.00000 -0.00000 0.00000 -0.00000 z 0.00000 0.00000 -0.00000 -0.00000 -0.00000 -0.00000 ------------------------------------------------------------------------------- Static dielectric constant tensor : ------------------------------------------------------------------------------- x y z ------------------------------------------------------------------------------- x 11.99456 0.58633 1.11710 y 0.58633 11.99456 1.11710 z 1.11710 1.11710 5.40395 -------------------------------------------------------------------------------- Static refractive indices : ------------------------------------------------------------------------------- 1 = 2.25202 2 = 3.37761 3 = 3.59350 ------------------------------------------------------------------------------- Phonon Calculation : Number of k points for this configuration = 1 -------------------------------------------------------------------------------- K point 1 = 0.000000 0.000000 0.000000 Weight = 1.000 -------------------------------------------------------------------------------- Frequencies (cm-1) [NB: Negative implies an imaginary mode]: -0.00 0.00 0.00 234.36 234.36 263.81 263.81 302.03 314.68 323.13 334.24 334.24 334.24 334.24 347.95 347.95 363.04 369.41 369.41 369.41 369.41 374.47 374.47 384.11 416.99 416.99 416.99 416.99 425.31 425.31 438.86 470.05 470.05 470.05 470.05 516.63 559.40 559.40 559.40 559.40 581.31 752.59 752.59 752.59 752.59 780.51 982.79 982.79 -------------------------------------------------------------------------------- Phonon properties (per mole of unit cells): Temperature = 0.000 K -------------------------------------------------------------------------------- Zero point energy = 1.293929 eV -------------------------------------------------------------------------------- Time to end of optimisation = 1.3176 seconds Final energies for configurations from scan_cell option: -------------------------------------------------------------------------------- Cell scan step number Energy (eV) Opt OK? -------------------------------------------------------------------------------- 0 -327.93171735 T 1 -327.92002565 T 2 -327.88494858 T 3 -327.82410344 T 4 -327.74118372 T 5 -327.63500423 T 6 -327.50562077 T 7 -327.35435181 T 8 -327.18004345 T 9 -326.98282510 T 10 -326.76285854 T 11 -326.52034525 T 12 -326.25553592 T 13 -325.96874232 T 14 -325.66035317 T 15 -325.33085526 T 16 -324.98086010 T 17 -324.61053912 T 18 -324.22210310 T 19 -323.81619766 T 20 -323.39447413 T 21 -322.95911422 T 22 -322.51305548 T 23 -322.06035302 T 24 -327.78908550 T 25 -327.86211261 T 26 -327.91009550 T 27 -327.93075056 T 28 -327.92426789 T 29 -327.88962997 T 30 -327.82449854 F 31 -327.72820593 T 32 -327.60184719 T 33 -327.44447335 T 34 -327.25254395 T 35 -327.02745938 T 36 -326.76687358 T 37 -326.46965847 T 38 -326.13465318 T 39 -325.76065898 T 40 -325.34643242 T -------------------------------------------------------------------------------- Peak dynamic memory used = 1.86 MB Timing analysis for GULP : -------------------------------------------------------------------------------- Task / Subroutine Time (Seconds) -------------------------------------------------------------------------------- Calculation of reciprocal space energy and derivatives 0.1077 Calculation of real space energy and derivatives 1.1336 Calculation of phonons 0.1088 Calculation and manipulation of Hessian matrix 0.0480 Calculation of matrix inversion 0.0007 Global summation overhead 0.0005 -------------------------------------------------------------------------------- Total CPU time 1.3177 -------------------------------------------------------------------------------- Dump file written as example65.res Job Finished at 15:46.07 28th July 2019