Direct calculation of the crystal-melt interfacial free energy via molecular dynamics computer simulation

We review our recent work on the direct calculation of the interfacial free energy, gamma, of the crystal-melt interface via molecular dynamics computer simulation for a number of model systems. The value of gamma as a function of crystal orientation is determined using a thermodynamic integration technique employing moving cleaving walls [Phys. Rev. Lett. 2000, 85, 4751]. The calculation is sufficiently precise to resolve the small anisotropy in gamma, which is crucial in determining the kinetics and morphology of dendritic growth. We report values of gamma for the hard-sphere and Lennard-Jones systems, as well as recent results on the series of inverse-power potentials. For the inverse sixth-, seventh-, and eighth-power systems, we determine gamma for both fcc and bcc crystal structures. For these systems, the bcc-melt gamma is lower than that for fcc crystals by about 25%, consistent with recent experiments and computer simulations on fcc-forming systems that show preferential formation of bcc nuclei in the initial stages of crystallization. In addition, we show that our results give a molecular interpretation of Turnbull's rule, which is the empirical relationship between gamma and the enthalpy of fusion.