Sharp-interface model for eutectic alloys. Part I: Concentration dependent surface tension

Abstract

We consider the problem of phase separation in eutectic alloy such as e.g. $SnPb$. For this we derive a phase field model from an atomistic point of view. We find the surface energy to be anisotropic, having in general a nonlinear dependence on concentration. We use matched asymptotic analysis to obtain a corresponding sharp interface model. The resulting expression for the surface tension agrees with that found on the basis of classical thermodynamics for jump conditions at singular interfaces. A boundary integral formulation of the sharp-interface model enables us to numerically describe the motion and deformation of the binary alloy.