Thermodynamic Properties of Solid Argon and Krypton

Abstract

Selected thermodynamic properties of solid argon and krypton have been calculated using an improved self-consistent phonon theory (ISC) that includes explicitly some of the odd derivative terms that arise in the Helmholtz energy. The potential energy of the solid is assumed to be the sum of pair-wise additive potentials recently derived by Barker and his co-workers plus the triple-dipole three-body force. The ISC theory is known to be adequate up to about $\frac{3}{4}$ of the melting temperature so that up to this temperature we can test our assumed potential energy. We find that the Bobetic-Barker (BB) potentials for Ar and Kr which were parametrized in part by fitting to the zero-temperature lattice-constant, Debye temperature, and sublimation energy, both give expansion coefficients that are too large when compared with experiment. The BB Ar potential is compared and contrasted with the recent refined Ar potential of Barker, Fisher, and Watts (BFW). We find that for these potentials the specific heat $C_V$ and bulk modulus $B_T$ differ by only about 1% over the whole temperature range. The BFW expansivity is, however, ∼5% lower than the BB potential and is in excellent agreement with experiment over a large temperature range.