Transient nucleation kinetics of crystal growth at the intermediate stage of bulk phase transitions

A complete analytical solution of an integro-differential model describing the transient nucleation of solid particles and their subsequent growth at the intermediate stage of phase transitions in metastable systems is constructed. A Fokker-Plank type equation for the density distribution function is solved exactly for arbitrary nucleation kinetics. A non-linear integral equation with memory kernel connecting the density distribution function and the system supercooling/supersaturation is analytically solved on the basis of the saddle-point method for the Laplace integral. The analytical solution obtained shows that the process at the intermediate stage is divided into three phases: initially the high rate nucleation stage occurs, then this process is accompanied by the particle growth reducing the level of metastability, and finally the mechanism of particle coarsening becomes predominant.