The kinetic cluster-field method and its application to studies of L12-type orderings in alloys

The earlier-described master equation approach to configurational kinetics of nonequilibrium alloys is applied to study Ll(2)-type orderings in FCC alloys. We describe the kinetic tetrahedron cluster-field method which generalizes a similar method used for equilibrium systems to the case of non-equilibrium alloys. The method developed is used to simulate Al --> Ll(2) and Al --> Al + Ll(2) transformations after a quench of an alloy from the disordered Al phase to the single-phase Ll(2) state or the two-phase Al + Ll(2) state for a number of alloy models with both short-range and long-range interactions. Simulations of the Al --> Ll(2) transition show a sharp dependence of the microstructural evolution on the type of interaction, and particularly on the interaction range. The simulations also reveal a number of peculiar features in both the transient microstructures and the transformation kinetics, many of them agreeing well with experimental observations. Microstructural evolution under Al --> Al + Ll(2) transition was found to be less sensitive to the type of the finite-range ('chemical') interaction, while in the presence of elastic interaction this evolution shows a number of specific features which were earlier discussed phenomenologically by Khachaturyan and co-workers and are illustrated by our simulations. We also consider the problem of the occurrence of a transient congruent ordering under Al --> Al + Ll(2) transformation and discuss the microstructural features of this stage.