Phase Transition of the Lennard-Jones System. II. High-Temperature Limit

Abstract

The high-temperature part of the fluid-solid coexistence curve for Lennard-Jones systems is investigated by "exact" Monte Carlo calculations. The interaction potential is separated into its repulsive ($\frac{4}{{r}^{12}}$) and attractive ($\ensuremath{-}\frac{4}{{r}^{6}}$) parts. The repulsive part is treated "exactly" by Monte Carlo computations with a 864-atom system, and the attractive part is treated as a perturbation. The "unperturbed" potential, which is homogeneous in the coordinates of the interacting particles, has trivial scaling properties which greatly simplify the computations. The attractive perturbation is treated to first order; the second-order corrections are shown to be very small at not-too-low temperatures. A high-temperature equation of state is obtained for the Lennard-Jones fluid, which is in excellent agreement with exact Monte Carlo computations at temperatures as low as about twice the critical temperature. Using the Hoover-Ree scheme, the free energy of the solid is determined and the transition densities and pressures calculated in the first-order approximation, which is shown to be quite satisfactory. The validity of Lindemann's melting "law" and a crystallization criterion based on the maximum of the structure factor are investigated.