Determination of the solid-liquid interfacial free energy along a coexistence line by Gibbs-Cahn integration

We calculate the solid-liquid interfacial free energy gamma(sl) for the Lennard-Jones (LJ) system at several points along the pressure-temperature coexistence curve using molecular-dynamics simulation and Gibbs-Cahn integration. This method uses the excess interfacial energy (e) and stress (tau) along the coexistence curve to determine a differential equation for gamma(sl) as a function of temperature. Given the values of gamma(sl) for the (100), (110), and (111) LJ interfaces at the triple-point temperature (T( *)=kT/varepsilon=0.618), previously obtained using the cleaving method by Davidchack and Laird [J. Chem. Phys. 118, 7657 (2003)], this differential equation can be integrated to obtain gamma(sl) for these interfaces at higher coexistence temperatures. Our values for gamma(sl) calculated in this way at T( *)=1.0 and 1.5 are in good agreement with those determined previously by cleaving, but were obtained with significantly less computational effort than required by either the cleaving method or the capillary fluctuation method of Hoyt, Asta, and Karma [Phys. Rev. Lett. 86, 5530 (2001)]. In addition, the orientational anisotropy in the excess interface energy, stress and entropy, calculated using the conventional Gibbs dividing surface, are seen to be significantly larger than the relatively small anisotropies in gamma(sl) itself.