Computer simulation study of free energy barriers in crystal nucleation

Abstract

We show how relatively standard Monte Carlo techniques can be used to probe the free-energy barrier that separates the crystalline phase from the supercooled liquid. As an illustration, we apply our approach to a system of soft, repulsive spheres [v(r)=ε(σ/r)12]. This system is known to have a stable face-centered-cubic (fcc) crystal structure up to the melting temperature. However, in our simulations, we find that there is a surprisingly low free-energy barrier for the formation of body-centered-cubic (bcc) crystallites from the melt. In contrast, there appears to be no ‘easy’ path from the melt to the (stable) fcc phase. These observations shed new light on the results of previous simulations that studied the dynamics of crystal nucleation in the r−12 system. We argue that the techniques developed in this paper can be used to gain insight in the process of homogeneous nucleation under conditions where direct, dynamical simulations are inconclusive or prohibitively expensive.