The nature of oscillations of the crystallization front in a diluted binary melt during the initial transient process

The cause of oscillations of the crystallization rate of a binary melt that arise in the initial transient process and have been revealed earlier in numerical experiments is investigated theoretically. Within a simple time-dependent model of directed crystallization, the problem of impurity diffusion in the melt from which a crystal is drawn at constant rate is solved in a linear approximation. It is shown that, under certain conditions, the solution represents a superposition of two concentration waves, a traveling and a standing wave. The concept of a characteristic distance of directed crystallization of a binary melt is introduced. It is established that the nonmonotonic behavior of the crystallization rate during the initial transient process, in particular, its damped oscillations, is attributed to the accumulation of impurities in the melt that is excessive with respect to its distribution in the stationary regime. Impurities in the melt are accumulated excessively when the characteristic distance of directed crystallization starts to exceed the characteristic diffusion length of the impurity in the melt.