Solid-liquid interface free energy in binary systems: Theory and atomistic calculations for the (110) Cu–Ag interface

Abstract

We analyze thermodynamics of solid-liquid interfaces in binary systems when the solid is in a nonhydrostatic state of stress. The difficulty lies in the fact that chemical potential of at least one of the chemical components in a nonhydrostatic solid is an undefined quantity. We show, nevertheless, that the interface free energy gamma can be defined as excess of an appropriate thermodynamic potential that depends on the chemical potentials in the liquid phase. We derive different forms of the adsorption equation for solid-liquid interfaces, with differential coefficients representing excesses of extensive properties. This leads, in particular, to the formulation of interface stress tau(ij) as an appropriate excess over nonhydrostatic bulk stresses. The interface stress is not unique unless the solid is in a hydrostatic state of stress. We also derive Gibbs-Helmholtz type equations that can be applied for thermodynamic integration of gamma. All thermodynamic relations derived here are presented in forms suitable for atomistic simulations. In particular, the excess quantities can be computed without constructing interface profiles. As an application, we perform semigrand canonical Monte Carlo simulations of the (110) solid-liquid interface in the Cu-Ag system. We show that gamma computed by thermodynamic integration along a coexistence path decreases with increasing composition difference between the phases. At the same time, tau(ij) remains negative (i.e., the interface is in a state of compression), drastically increases in magnitude, and becomes highly anisotropic. Some of the interface excess properties are computed by different methods and demonstrate accurate agreement with each other, confirming the correctness of our analysis.