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, gHS(r/d,η), 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, η[=(π/6)ρd3], 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 gHS(r/d,η). By utilizing the new gHS(r/d,η) in the Henderson and Grundke method [J. Chem. Phys. 63, 601 (1975)], we next derive an expression for yHS(r/d,η) [=gHS(r/d)exp{βVHS(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 gHS(r/d,η) 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 gHS(r/d,η) is an improvement over available expressions and that it is useful for solid-state calculations