Theoretical calculations of thermodynamic properties for inert gas elements

Abstract

We present statistical mechanical calculations for krypton and xenon, employing accurate pair potentials with and without condensed-phase modifications. A unique feature of the present work is that solid- and fluid-phase thermodynamic properties are both computed within a single theoretical framework, using our recently-developed hard-sphere perturbation theory (KLRR: Kang-Lee-Ree-Ree perturbation theory). Results are applied to analyze experimental fluid, solid, and fluid-solid transition data, ranging up to $2×10^6$ atmospheres at several temperatures. Effective pair potentials for both krypton and xenon, inferred from the analysis, contain short- and long-range modifications to the pair potential of Aziz and Slaman. The long-range correction is repulsive and originates from the well-known Axilrod-Teller three-body potential, while the short-range correction is attractive and is needed for describing high-compression data. Experimental isotherms above 50 GPa for xenon require a further softening of the short-range repulsion from Barker``s correction(obtained from experimental data below 50 GPa). Implications of the short-range correction and its possible relation to many-body forces are discussed. Additional tests of the present rare-gas calculations against available computer simulations and Monte Carlo and lattice-dynamics calculations carried out in this work show satisfactory agreement. Computation of solid-fluid transition properties shows that the Axilrod-Teller three-body potential must be included to obtain reliable agreement with experimental melting and freezing data. For helium, thermodynamic properties are calculated with the KLRR perturbation theory and the MCR(Mansoori-Canfield-Ross) theory using exponential-6 potential and the Azia potential, and compared with the results of the Monte Carlo simulation and lattice-dynamics, and experiments. Pressure and Helmholtz free energy of solid helium at 327.04 K calculated with the KLRR theory excellently...