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

The interfacial free energy between a crystal and a fluid, γcf, is a highly relevant parameter in phenomena such as wetting or crystal nucleation and growth. Due to the difficulty of measuring γcf experimentally, computer simulations are often used to study the crystal-fluid interface. Here, we present a novel simulation methodology for the calculation of γcf. 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 γcf 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 γcf with respect to the crystal orientation. We also calculate γcf for a recently proposed continuous version of the hard sphere potential and obtain the same γcf 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.