Hard-sphere radial distribution functions for face-centered cubic and hexagonal close-packed phases: Representation and use in a solid-state perturbation theory

Abstract

The hard‐sphere radial distribution functions,g HS(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)ρd 3], 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,η). By utilizing the new g HS(r/d,η) in the Henderson and Grundke method [J. Chem. Phys. 6 3, 601 (1975)], we next derive an expression for y HS(r/d,η) [=g HS(r/d)exp{βV HS(r)}] inside the hard‐sphere diameter, d. These expressions are employed in a solid‐state perturbation theory [J. Chem. Phys. 8 4, 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,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 g HS(r/d,η) is an improvement over available expressions and that it is useful for solid‐state calculations.