PHASE-FIELD AND SHARP-INTERFACE ALLOY MODELS

We consider a phase-field model of a binary mixture or alloy which has a phase boundary. The model identifies all macroscopic parameters and the interface thickness epsilon. In the limit as epsilon approaches zero, an alternative two-phase alloy solidification model (with a sharp interface) is obtained. For small concentrations, we recover the classical sharp-interface problems, the theory of which is reviewed. We obtain, in the simplest phase-field system, a new (nonlinear) interface relation for concentration c which is discontinuous across the interface and subject to [ln[c/(1 - c)]]-+ = - 2M, coupled with - sigma(alphav + kappa) = [s]E{T - T(B) - [(T(A) - T(B))/2M]ln[(1 - c+)/(1 - c-)]}, where sigma is surface tension, v is (normal) velocity of the interface, kappa is the curvature, [S]E is the jump in entropy density between phases, T(A) and T(B) are the melting temperatures of the two materials, M is related to the phase diagram, and alpha is a dynamical constant.