Comparison of the lattice-dynamics and cell-model approximations with Monte-Carlo thermodynamic properties

Results from Monte-Carlo computer experiments for energy, pressure, specific heat, Grüneisen γ, and elastic constants are compared with approximate lattice dynamics and cell-model predictions. Comparisons are made for both the Lennard-Jones 6-12 and the exponential-six pair potentials. The elastic constants predicted by lattice dynamics agree best with the Monte-Carlo results. For the other thermodynamic properties the cell model gives more accurate estimates. The effects of increasing the number of particles and of making the calculations according to quantum mechanics instead of classical mechanics are both studied.