Perturbation theory of a model hcp solid

Abstract

Spherically averaged radial distribution functions of hard-sphere hexagonal close-packed (hcp) structures have been estimated by Monte Carlo simulations for a wide range of solid densities. By fitting the Monte Carlo data, an accurate analytical expression for that function was obtained for use in thermodynamic perturbation theory of the solid state. We present results of perturbation theory for hcp structures over a range of temperatures and densities in the solid region. The method of Kang et al. employed in these calculations is a generalization of the Weeks, Chandler and Andersen theory, which accurately describes high density fluids and solids. Following a calculation of the relative stability of model hcp and fcc solids, the phase boundary between these two structures was determined. For the familiar cut and shifted Lennard-Jones potential, the fcc lattice is more stable along the gas-solid line for temperatures above T* = 0·3. There is a transition to the hcp structure at lower temperatures. The differences in the free energy between the fcc and hcp structures along the melting line are extremely small and hence it is difficult to predict which structure is favoured.