Computer simulations of diffusional phase transformations: Monte Carlo algorithm and application to precipitation of ordered phases

A Monte Carlo (MC) simulation technique which is well suited for studying diffusional phase transformations is presented. This technique accounts for atom transport through vacancy migration, and allows a physically meaningful definition of time. This MC technique is used for studying the precipitation of an L1(2) ordered phase from a supersaturated, disordered f.c.c. matrix. Three alloys have been studied of compositions x(B) = 0.125, 0.15 and 0.175, with equilibrium volume fraction of the L1(2) phase of 0.23, 0.47 and 0.71, respectively. The results show that, during early stages of the transformation, both phase separation (i.e. formation of regions of different compositions) and ordering (i.e. creation of atomic order in the solute-rich regions) proceed simultaneously in all the three alloys. In particular, there is no evidence for homogeneous ordering prior to phase separation even in the most concentrated alloy with x(B) = 0.175. Thus, the results are in direct contradiction to those obtained in recent simulations by Chen and Khachaturyan, and underscore the limitations of the Bragg-Williams approximation used by them. The late stage behaviour of all the three alloys obey classical laws of coarsening: (i) the microstructures are self similar, and (ii) the cube of the characteristic microstructural length scale increases linearly with time. Thus, the range of validity of the classical laws appears to extend to large precipitate volume fractions