Rep:CW4013MGO

Questions

phonon calculation: executed GULP (phonon dispersion) Npoints = 50 'calculate phonon eigenvectors' selected

1. For 1x1x1 DOS, DOS for L point calculated 2. Larger grid size => more sampling points in the Brillouin zone, hence more peaks visible (number of peaks depends on number of phonon 'bands' at each sampling point with a unique frequency etc. 3. ~12x12x12: signal:noise high enough to distinguish significant peaks; ~20x20x20: accurate peaks; ~30x30: quite smooth peaks, but significant non-negligible computation time. 4. Dispersion curve: energy of vibration as a function of wavevector; DOS(E): number of states per unit energy as a function of vibrational energy. Comparison of the two gives number of density of vibrational states as a function of wavevector. High DOS(E') means E(k) intersects the line E = E' many times, hence there are many lattice vibrational frequencies with corresponding energy E'.

Helmholtz Free Energy - harmonic approximation T = 300, P = 0 GPa 1x1x1: -40.930301 eV accurate to 1 ceV 2x2x2: -40.926609 eV accurate to 1 ceV and 0.5 meV 3x3x3: -40.926432 eV accurate to 1 meV 4x4x4: -40.926450 eV accurate to 1 meV 5x5x5: -40.926463 eV accurate to 0.1 meV

Thermal expansion: optimisation; optimise gibbs free energy; Phonon DOS; 5x5x5; P = 0 GPa 0 K: a = 2.986576 Ang; G = -40.90190633 eV 100 K: a = 2.986576 Ang; G = -40.90241401 eV 200 K: a = 2.987649 Ang; G = -40.90936535 eV 300 K: a = 2.989456 Ang; G = -40.92810665 eV 400 K: a = 2.991717 Ang; G = -40.95857035 eV 500 K: a = 2.994245 Ang; G = -40.99940660 eV 600 K: a = 2.996953 Ang; G = -41.04928075 eV 700 K: a = 2.999799 Ang; G = -41.10707943 eV 800 K: a = 3.002766 Ang; G = -41.17184710 eV 900 K: a = 3.005836 Ang; G = -41.24296855 eV 1000 K: a = 3.009008 Ang; G = -41.31979408 eV