Phase Transitions and Glass Formation in Binary Alloys

Abstract

The weak formulation of the classical Stefan problem is here extended to phase transitions in noneutectic binary alloys, in several dimensions of space. Glass formation is also accounted for, by assuming that the rate of phase transition is a nonmonotone function of the undercooling. In the framework of the theory of nonequilibrium thermodynamics, this phenomenon is here modeled as a multinonlinear system of PDEs. Existence of a weak solution in Sobolev spaces is proved for an initial- and boundary-value problem. A priori estimates are derived, and passage to the limit is proved via compactness, convexity, and lower semicontinuity techniques, including compactness by strict convexity.