Rep:MoD:MgO YZ19114

Results and Discussions

Lattice Vibrations - Computing the Phonons

Figure 2: Phonon Dispersion graph of MgO

Table 1: MgO phonon DOS with different grid sizes
Phonon DOS with 1x1x1 grid size	Phonon DOS with 2x2x2 grid size	Phonon DOS with 4x4x4 grid size	Phonon DOS with 8x8x8 grid size
Phonon DOS with 12x12x12 grid size	Phonon DOS with 16x16x16 grid size	Phonon DOS with 24x24x24 grid size	Phonon DOS with 36x36x36 grid size

Calculating the Free Energy in the Harmonic Approximation

Table 2: Helmholtz free energy with different grid sizes
Grid size	Free Energy/ eV	ΔA/ meV compared with free energy of 32x32x32 grid
1x1x1	-40.930301	-3.818
2x2x2	-40.926609	-0.126
3x3x3	-40.926432	0.051
4x4x4	-40.926450	0.033
6x6x6	-40.926471	0.012
8x8x8	-40.926478	0.005
12x12x12	-40.926481	0.002
16x16x16	-40.926482	0.001
20x20x20	-40.926483	0
32x32x32	-40.926483	0

The Thermal Expansion of MgO

Figure 3: Helmholtz free energy versus temperature (QHA)

Figure 4: Lattice constant versus temperature (QHA)

Figure 5: Cell volume per formula unit versus temperature (QHA)

Molecular Dynamics

Figure 6: Cell volume per formula unit versus temperature (MD)

Figure 7: Comparison between plots of cell volume versus temperature calculated by Quasi-harmonic approximation and Molecular Dynamics