Solid-liquid interface free energy through metadynamics simulations

Abstract

The solid-liquid interface free energy ${\ensuremath{\gamma}}_{sl}$ is a key parameter controlling nucleation and growth during solidification and other phenomena. There are intrinsic difficulties in obtaining accurate experimental values, and the previous approaches to compute ${\ensuremath{\gamma}}_{sl}$ with atomistic simulations are computationally demanding. We present an approach which is to obtain ${\ensuremath{\gamma}}_{sl}$ from a free-energy map of the phase transition reconstructed by metadynamics. We apply this to the benchmark case of a Lennard-Jones potential, and the results confirm the most reliable data obtained previously. We demonstrate several advantages of our approach: it is simple to implement, robust and free of hysteresis problems, it allows a rigorous and unbiased estimate of the statistical uncertainty, and it returns a good estimate of the thermodynamic limit with system sizes of a just a few hundred atoms. It is therefore attractive for applications which require more realistic and specific models of interatomic forces.