Master equation approach to configurational kinetics of non-equilibrium alloys and its applications to studies of phase transformations

We review a series of works where the fundamental master equation is used to develop a consistent description of the evolution of non-equilibrium atomic distributions in an alloy. we derive exact equations for the temporal evolution of local concentrations and correlators of their fluctuations, as well as for the free energy of a non-equilibrium alloy. We discuss various approximate methods for treatments of these equations, such as the kinetic meanfield method and the kinetic cluster methods. In particular, to study L1(2) and L1(0) orderings in FCG alloys we develop a kinetic cluster field method which combines a high accuracy in the description of thermodynamics with a great simplification of calculations. We also present a microscopical model for deformational interactions in concentrated alloys to treat phase transitions with a lattice symmetry change, such as the tetragonal distortion under L1(0) ordering. We describe some recent applications of the developed methods to studies of alloy orderings with more than two types of ordered domains, such as the D0(3), L1(2) and L1(0) orderings. These studies reveal a number of new and interesting microstructural effects, many of them agreeing well with experimental observations.