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 ε. In the limit as ε 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)]${]}_{\mathrm{-}}^{+}$=-2M, coupled with -σ(αv+κ) =[s${]}_{\mathit{E}}${T-${\mathit{T}}_{\mathit{B}}$-[(${\mathit{T}}_{\mathit{A}}$-${\mathit{T}}_{\mathit{B}}$)/2M]ln[(1-${\mathit{c}}^{+}$)/(1-${\mathit{c}}^{\mathrm{-}}$)]}, where σ is surface tension, v is (normal) velocity of the interface, κ is the curvature, [s${]}_{\mathit{E}}$ is the jump in entropy density between phases, ${\mathit{T}}_{\mathit{A}}$ and ${\mathit{T}}_{\mathit{B}}$ are the melting temperatures of the two materials, M is related to the phase diagram, and α is a dynamical constant.

• Received 1 March 1993

DOI:https://doi.org/10.1103/PhysRevE.48.1897