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.

Crystal growth kinetics accompanied by particle growth with fluctuating rates at the intermediate stage of phase transitions is analyzed theoretically. The integro-differential model of governing equations is solved analytically for size-independent growth rates and arbitrary dependences of the nucleation frequency on supercooling/supersaturation. Two important cases of Weber-Volmer-Frenkel-Zel'dovich and Mier nucleation kinetics are detailed. A Fokker-Plank type equation for the crystal-size density distribution function is solved explicitly.

No abstract

A model is presented that describes nonstationary solidification of binary melts or solutions from a cooled boundary maintained at a time-dependent temperature. Heat and mass transfer processes are described on the basis of the principles of a mushy layer, which divides pure solid material and a liquid phase. Nonlinear equations characterizing the dynamics of the phase transition boundaries are deduced. Approximate analytical solutions of the model under consideration are constructed. A method for controlling the external temperature at a cooled wall in order to obtain a required solidification velocity is discussed.

No abstract