Calculation of excess interfacial entropy, stress and energy for solid-liquid interfaces

The solid-liquid interfacial free energy, $\gamma_{\rm sl}$, governs a number of important phenomena, e.g., crystal nucleation and growth, and wetting. For an equilibrium crystal-melt interface, $\gamma_{\rm sl}$ can be calculated via simulation using thermodynamic integration or capillary fluctuations [Phys. Chem. B {\bf 109}, 17802 (2005)]. The calculation of $\gamma_{\rm sl}$ away from coexistence requires the temperature and strain dependence of $\gamma_{\rm sl}$, which can be determined from the excess interfacial entropy, $\eta_{\rm sl}$, and stress tensor, $\mbox{\boldmath$\tau$}_{\rm sl}$. We determine $\eta_{\rm sl}$ and $\mbox{\boldmath$\tau$}_{\rm sl}$ for a system of Lennard-Jones particles and for particles with an inverse-power interaction [$\phi(r) = \epsilon (\sigma/r)^{n}$] for $n = $ 6, 8 (fcc and bcc) and 12, 20 (fcc). We determine $\eta_{\rm sl}$ and $\mbox{\boldmath$\tau$}_{\rm sl}$ for the (100), (110) and (111) orientations. We calculate $\eta_{\rm sl}$ using two methods, both using the Gibbs dividing surface defined so that the excess interfacial particle number is zero. In the first, we calculate $\eta_{\rm sl}$ from the temperature dependence of $\gamma_{\rm sl}$, $\mbox{\boldmath$\tau$}_{\rm sl}$ and the number density, $\rho$, along the coexistence curve. In the second, we calculate the excess interfacial energy, $e_{\rm sl}$, and use the equation $\gamma_{\rm sl} = e_{\rm sl} - T \eta_{\rm sl}$. The results agree within estimated errors. One surprising observation is that $\eta_{\rm sl}$, $e_{\rm sl}$ and $\mbox{\boldmath$\tau$}_{\rm sl}$ are significantly more anisotropic than $\gamma_{\rm sl}$.