A DERIVATION AND ANALYSIS OF PHASE FIELD MODELS OF THERMAL ALLOYS

We derive a system of equations describing a binary mixture with thermal properties and a phase transition. The system involves the concentration, c, the temperature, T, and phase or order parameter, phi, and is the generalization of the phase field model for a pure material. Transition layers of width epsilon are exhibited by phi, c, and del T.($) over cap n. In the limit as epsilon approaches zero, with all other physical parameters held fixed, one attains a limiting set of sharp interface equations which generalize the traditional small c systems of equations. The derivation is accomplished by a systematic use of thermodynamic principles and includes as a special case the phase field equations for a pure material. The phase diagram is recovered in equilibrium. (C) 1995 Academic Press. Inc.