Simulating Fluid–Solid Equilibrium with the Gibbs Ensemble

Abstract

The Gibbs ensemble is employed to simulate fluid–solid equilibrium for a shifted-force Lennard-Jones system. This is achieved by generating an accurate canonical Helmholtz free-energy model of the (defect-free) solid phase. This free-energy model is easily generated, with accuracy limited only by finite-size effects, by a single isothermal–isobaric simulation at a pressure not too far from coexistence for which the chemical potential is known. We choose to illustrate this method at the known triple-point because the chemical potential is easily calculated from the coexisting gas. Alternatively, our methods can be used to locate fluid–solid coexistence and the triple-point of pure systems if the chemical potential of the solid phase can be efficiently calculated at a pressure not too far from the actual coexistence pressure. Efficient calculation of the chemical potential of solids would also enable the Gibbs ensemble simulation of bulk solid–solid equilibrium and the grand-canonical ensemble simulation of bulk solids.

Keywords:

• Gibbs ensemble
• Grand-canonical ensemble
• Solid–fluid
• Solid–solid
• Triple point