Evolution Equations for Phase Separation and Ordering in Binary Alloys

摘要

The authors explore two phenomenological approaches leading to systems of coupled Cahn-Hilliard and Cahn-Allen equations for describing the dynamics of systems which can undergo first-order phase separation and order-disorder transitions simulateneously, starting from the same discrete lattice free energy function. In the first approach, a quasicontinuum limit is taken for this discrete energy and the evolution of the system is then assumed to be given by gradient flow. In the second approach, a discrete set of gradient flow evolution equations is derived for the lattice dynamics and a quasicontinuum limit is then taken. The authors demonstrate in the context of BCC Fe-Al binary alloys that it is important that variables be chosen that accommodate the variations in the average concentration as well as the underlying ordered structure of the possible coexistent phases. Only then will the two approaches lead to roughly the same continuum descriptions.