A model for calculation of isothermal kinetics of the nucleation-and-growth type phase separation in the course of one-step heat treatment

Abstract

A model is described for calculating the kinetics of a diffusion-limited nucleation-and-growth type phase separation. A homogeneous melt of glass is cooled to a temperature, at which the nucleation, growth and Ostwald ripening of particles of a new phase are possible. In the model, a spatial inhomogeneity of nucleation rate, caused by the formation of diffusion zones around particles, and an effect of interaction of these zones on growth of particles are taken into account. Criteria for application of the model are formulated and parameters of the model are calculated for a model binary glass. A conclusion is drawn that the proposed model is applicable to systems where supersaturation is not too high. In particular, nucleation must not be so plentiful as to suppress a growth from supersaturated solution and to initiate Ostwald ripening at the nucleation stage. It is noted that such situations are observed in experiments on phase separation in glasses. The model seems to be applicable to some other types of phase transformations as well.