Mechanism of growth of a crystalline nucleus in a supercooled melt at large deviations from equilibrium

A nonequilibrium model of the growth of a spherical crystal in a supercooled melt has been presented. The model includes correctly the effect of melt heating near the phase boundary, which considerably affects the growth rate of the crystal. The analytical solution of the problem has been found under the conditions of a strongly nonstationary process and large deviations from equilibrium. It has been shown that the previous solutions found in the quasi-steady-state approximation are the special cases of the solution found in this work. It has been demonstrated that the equilibrium is achieved at the crystallization front after some time if the initial supercooling is below the thermal effect of the phase transition (the Kutateladze criterion is greater than unity). In this case, the solution of the problem becomes self-similar. The crystal grows all the time under essentially nonequilibrium conditions if the initial supercooling is above the critical one. The effect of substance shrinkage on the growth rate of the crystal has been investigated.