A VARIATIONAL THEORY OF CLASSICAL SOLIDS

We present a variational theory of classical solids based on an invers e 12th-power repulsive reference system. The reference system is in tu rn represented by a hard-sphere system and an analytic term which is s imilar to the term accounting for the softness of the inverse 12th-pow er repulsion in Ross's variational theory of fluids. Thermodynamic pro perties of the Lennard-Jones, exponential-six, and inverse nth-power r epulsive (n=4, 6, and 9) systems are calculated for a face-centered cu bic phase. At densities slightly above the melting lines to densities where atomic vibrations are nearly harmonic, calculated results are in close agreement with Monte Carlo data performed in this and previous work. For a hexagonal close-packed phase, lattice dynamics calculation s are carried out to show that the present variational theory gives re liable results, just as it does for the fcc phase. Comparisons with re sults from our recent solid-state perturbation theory are also discuss ed.