A perturbation theory of classical solids

Abstract

We have developed a new perturbation theory that extends our earlier perturbation theory of fluids to solids and that is reliable over a wide solid region. Characteristic features of this new theory are the use of an optimized reference potential whose repulsive range shrinks with density and its ability to deal with both harmonic and anharmonic thermodynamic properties on equal footing. Thermodynamic properties of face-centered-cubic crystals are computed from the new theory for the Lennard-Jones system, the exponential-6 system, and the inverse nth-power (n=12, 9, 6, and 4) systems. Monte Carlo simulations are also performed to supplement available data. A comparison of theory and computer simulation shows excellent agreement, except for the softest repulsive system (n=4). The agreement extends from an anharmonic region near the melting line to a harmonic region, where the hard-sphere reference system achieves close to 92% of the close-packed density. Beyond this region errors in the analytic fits to the hard-sphere radial distribution functions used in this work make an accurate test of the new theory difficult. Since the present formulation is the same for both solid and fluid phases, we used the theory to compute the melting and freezing data of the aforementioned model systems. Agreement with the corresponding Monte Carlo data is satisfactory. Comparison with other theoretical models of solids is also discussed.