Statistical mechanical theory of face-centered cubic and hexagonal close-packed crystals and its applications to crystal stability of rare-gas solids

Abstract

The hard-sphere radial distribution functions, gHS(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 packing fraction, $\eta[=(\pi/6)\rho{d}^3]$, ranging from 4\% below the melting density to 99\% of the close-packed density. The Monte Carlo data are used to improve available analytic expression for gHS(r/d,$\eta$). By utilizing the new gHS(r/d,$\eta$) in the Henderson and Grundke method [J. Chem. Phys. 63,601 (1975)], we next derive an expressions for yHS(r/d,$\eta$) [gHS(r/d,$\eta$)exp{$\beta$V HS($\gamma$)}] 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 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,$\eta$) shows a resonable thermodynamic consistendy as required by the Ornstein-Zernike relation. As an applicaiotn, 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,$\eta$) is an improvement over available expressions and that it is useful for solid-state calculations. We have applied our solid-state perturbation theory along with our accurate analytic expressions for the hard-sphere radial distribution functions in face-centered cubic and hexagonal close-packed phases. Contray to a static energy prediction favoring an hexagonal close-packed phases, heavy rare gases are experimentally known to solidify into a face-centered cubic phase over a large range of pressure at room temperature. This has remained as an outstanding unsolved question during the last decade. A theouy which can disting guish small differences (within 0.1\%) in the Helmholtz free energy of the two phases is required to resolve this issue. Our theoret...