Thermodynamic and structural properties of model systems at solid-fluid coexistence

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Abstract
Properties of coexisting fluid and solid phases of the Lennard-Jones model potential are reported. The melting line, representing equilibrium between the solid and liquid phases, is computed by performing a thermodynamic integration along a path that follows the coexistence line itself, according to the Gibbs-Duhem integration method recently introduced by us. Monte Carlo simulations are conducted to compute the quantities needed by the method; two system sizes, with particles numbering approximately 100 and 500, respectively, are examined. The starting point for the integration is the soft sphere system obtained in the limit of high temperature. The procedure terminates at the solid-liquid-vapour triple point, and thus the entire melting line is determined. Our results for the melting pressure are about 10% higher than those reported previously in the literature, while the triple point temperature we compute is in accord with the established value. An analysis of the approach to the high-temperature limit is used to construct a functional form for the melting line; this is fitted to the data, reproducing all of them to within their estimated errors. Another integration is initiated from the triple point to compute part of the sublimation line. Several semi-empirical ‘melting rules’ are examined in the light of the new results.