Extension of the Aggregation-Volume-Bias Monte Carlo Method to the Calculation of Phase Properties of Solid Systems: A Lattice-Based Cluster Approach

Abstract

The aggregation-volume-bias Monte Carlo method, which has been successful in the calculation of the formation free energies of liquid clusters, is extended to solid systems. This extension is motivated by early studies where disordered clusters are observed when the original method is applied at a temperature even far below the triple point. In order to avoid the formation of disordered aggregates, the insertion of particles is targeted directly toward those crystal lattice sites. Specifically, the insertion volume used to be defined as a spherical volume centered around a given target molecule is now restricted to be around each of the crystal lattice sites near a given target molecule. The free energies obtained for both liquid and solid clusters are then used to extrapolate bulk-phase information such as the chemical potential of the liquid and solid phases at coexistence. Using the temperature and pressure dependencies of the chemical potential information obtained for both liquid and solid phases, the location of the triple point can be determined. For Lennard-Jonesium, the results were found to be in good agreement with previous simulation studies using other approaches.