Nucleation and growth of a new phase at the intermediate stage of phase transitions in metastable solutions and melts

A complete analytical solution of an integro-differential model, which describes the intermediate stage of phase transitions in one-component melts and solutions without allowance for fluctuations in the crystal growth rates, is found. An exact analytical solution of the kinetic equation is determined within the framework of this model. The density of distribution function of crystals in sizes is found. An integro-differential equation for the system metastability level (for its supercooling/supersaturation) is derived for different kinetic mechanisms of particle nucleation. A complete analytical solution of this equation is constructed on the basis of saddle-point method for the Laplace-type integral (steepest descent method). Four approximations of the analytical solution are analyzed and its convergence is shown. The kinetic mechanisms of Weber–Volmer–Frenkel–Zel’dovich and Meirs are studied. A transient behavior of the number of particles and the mean crystal size is determined for supercooled melts.