The mold integration method for the calculation of the crystal-fluid interfacial free energy from simulations

TL;DR

This paper introduces a new simulation method using a mold of potential wells to accurately calculate the crystal-fluid interfacial free energy, accounting for anisotropy and applicable in common simulation packages.

Contribution

A novel reversible pathway-based simulation technique using potential energy wells to compute interfacial free energy between crystal and fluid phases.

Findings

Validated method on hard spheres and Lennard-Jones systems

Accurately captures anisotropy of interfacial free energy

Compatible with Monte Carlo and Molecular Dynamics simulations

Abstract

The interfacial free energy between a crystal and a fluid, {\gamma} cf, is a highly relevant parameter in phenomena such as wetting or crystal nucleation and growth. Due to the difficulty of measuring {\gamma} cf experimentally, computer simulations are often used to study the crystal-fluid interface. Here, we present a novel simulation methodology for the calculation of {\gamma} cf . The methodology consists in using a mold composed of potential energy wells to induce the formation of a crystal slab in the fluid at coexistence conditions. This induction is done along a reversible pathway along which the free energy difference between the initial and the final states is obtained by means of thermodynamic integration. The structure of the mold is given by that of the crystal lattice planes, which allows to easily obtain the free energy for different crystal orientations. The method is validated by calculating {\gamma} cf for previously studied systems, namely, the hard spheres and the Lennard-Jones systems. Our results for the latter show that the method is accurate enough to deal with the anisotropy of {\gamma} cf with respect to the crystal orientation. We also calculate {\gamma} cf for a recently proposed continuous version of the hard sphere potential and obtain the same {\gamma} cf as for the pure hard sphere system. The method can be implemented both in Monte Carlo and Molecular Dynamics. In fact, we show that it can be easily used in combination with the popular Molecular Dynamics package GROMACS.