Kinetics of formation of a phase with an arbitrary stoichiometric composition in a multicomponent solid solution.

A kinetic theory of nucleation and growth of a evolving phase with a given stoichiometric composition in a multicomponent solid solution is developed. It is assumed naturally that the phase grows as a result of individual atom incorporation into the phase domain in a stoichiometric ratio. As it is shown, for the case of phase formation in a multicomponent system the basic kinetic equations, describing the nucleation-growth process, can be reduced formally to the respective expression derived for nucleation-growth processes in one-component systems. However, the effective diffusion coefficients and the effective supersaturation are expressed as nontrivial combinations of the thermodynamic and kinetic parameters of the different components involved in the phase formation process. In the determination of these properties, the theory is not restricted in its applicability to perfect solutions but extended to phase formation in real mixtures. Thus, the theory may be applied directly towards the interpretation of experimental data. In the present paper, particular attention is devoted to the analysis of the two stages of the overall transformation process: (1) the stage of quasi-steady-state nucleation and (2) the transient stage of coarsening. As the results of this analysis, the quasi-steady-state nucleation rate, the number of clusters formed via nucleation and growth, and the time evolution of the cluster size distributions are established. Moreover, estimates are given for the duration of the different stages of the transformation process.