Elastic Constants of Solid Ar, Kr, and Xe: A Monte Carlo Study

The elastic constants of classical systems of 108 particles arranged (with periodic boundary conditions) on an fcc lattice and interacting with pairwise-additive forces have been evaluated to an accuracy of about 2% by a Monte Carlo procedure closely related to that used by Hoover and his co-workers. For Ar(80 ^∘{}K) and Kr(85 and 115 ^∘{}K) we have used the Bobetic-Barker pair potentials and also included the corrections for the truncated tail of the pair potential, quantum effects, and three-body forces. For Ar(80 ^∘{}K) and Xe(156 ^∘{}K) we have carried out a similar calculation for the familiar Lennard-Jones 6:12 potential. Our 6:12 Ar(80 ^∘{}K) elastic constants agree well with the previous work of Hoover et al. but unfortunately differ only little from the more realistic Bobetic-Barker Ar(80 ^∘{}K) values. Bulk moduli for both potentials are compatible with the currently available experimental data. Comparison of our Kr results with experimental data indicates a need for refinement of the Bobetic-Barker Kr potential. The Xe(156 ^∘{}K) results agree very well with the recent Brillouin-scattering work of Gornall and Stoicheff which is to some extent disappointing because the same 6:12 potential is in poor agreement with the low-temperature heat capacity.