The two computer methods of Monte Carlo and lattice dynamics are used to determine fluid and face-centered-cubic solid thermodynamic properties for classical particles interacting with pairwise-additive inverse 4th, 6th, and 9th power potentials. These results, together with those already on hand for 12th power and hard-sphere potentials, provide a complete, and remarkably simple, description of the dependence of the pure-phase thermodynamics and the melting transition on the “softness” of the pair potential.
Synopsis
•Results from Monte-Carlo computer experiments for energy, pressure, specific heat, Griineisen y, 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.
Monte Carlo calculations of thermodynamic properties for solid argon are carried out using both the Lennard-Jones and the exponential-six pair potentials. When quantum corrections are taken into account the calculated energies and pressures derived from the Lennard-Jones potential agree better with experiment. Neither pair potential successfully reproduces the experimental elastic constants.
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