HARD-SPHERE RADIAL-DISTRIBUTION FUNCTIONS FOR FACE-CENTERED CUBIC AND HEXAGONAL CLOSE-PACKED PHASES - REPRESENTATION AND USE IN A SOLID-STATE PERTURBATION-THEORY

The hard-sphere radial distribution functions, g(HS) (r/d,eta), for the face-centered cubic and hexagonal close-packed phases have been computed by the Monte Carlo method at nine values of the packing fraction, eta[= (pi/6)rho-d3], ranging from 4% below the melting density to 99% of the close-packed density. The Monte Carlo data are used to improve available analytic expressions for g(HS) (r/d,eta). By utilizing the new g(HS) (r/d,eta) in the Henderson and Grundke method [J. Chem. Phys. 63, 601 (1975)], we next derive an expression for y(HS) (r/d,eta) [ = g(HS) (r/d)exp{beta-V(Hs)(r)}] inside the hard-sphere diameter, d. These expressions are employed in a solid-state perturbation theory [J. Chem. Phys. 84, 4547 (1986)] to compute solid-state and melting properties of the Lennard-Jones and inverse-power potentials. Results are in close agreement with Monte Carlo and lattice-dynamics calculations performed in this and previous work. The new g(HS) (r/d,eta) shows a reasonable thermodynamic consistency as required by the Ornstein-Zernike relation. As an application, we have constructed a high-pressure phase diagram for a truncated Lennard-Jones potential. From this study, we conclude that the new g(HS) (r/d,eta) is an improvement over available expressions and that it is useful for solid-state calculations.