An analysis of phase-field alloys and transition layers

A phase-field approach to binary alloys is studied. Formal asymptotics of the system of parabolic differential equations leads to new interface relations as part of a macroscopic model which arises in the limit of vanishing interface thickness. Under suitable conditions we prove that the phase-field system has a unique solution which converges to the limiting macroscopic solution. The concentration and phase are monotonic across the interface for a simplified system. Transition layers in concentration are induced due to the change in phase and the change in material diffusion across the interface. Excess impurities may be trapped as a consequence of these layers.