Free energies of crystalline solids: a lattice-switch Monte Carlo method

TL;DR

This paper introduces a Monte Carlo method for directly calculating free energy differences between two crystalline structures with different symmetries by sampling configurations along a transformation path.

Contribution

A novel lattice-switch Monte Carlo technique that enables direct free energy difference evaluation between crystalline phases of different symmetry.

Findings

Successfully applied to compare fcc and hcp phases of hard spheres.

Demonstrates accurate free energy difference measurements.

Provides a new tool for phase stability analysis in crystalline solids.

Abstract

We present a method for the direct evaluation of the difference between the free energies of two crystalline structures, of different symmetry. The method rests on a Monte Carlo procedure which allows one to sample along a path, through atomic-displacement-space, leading from one structure to the other by way of an intervening transformation that switches one set of lattice vectors for another. The configurations of both structures can thus be sampled within a single Monte Carlo process, and the difference between their free energies evaluated directly from the ratio of the measured probabilities of each. The method is used to determine the difference between the free energies of the fcc and hcp crystalline phases of a system of hard spheres.