  So far the problem of interface behavior upon phase transition has not yet
acquired a satisfactory mathematical formulation due to a variety of the
physical phenomena involved. Analytical solutions exist only for elementary
problems describing the free interface behavior in directed crystallization
conditions, for instance, for those implying a clearly shaped isothermal
interface. Numerical calculations of the interface behavior also present
significant difficulties since the instability of moving interface does not
enable calculations by means of known algorithms. The general solution of this
problem does not seem possible now, so quantitative analysis of phase
transition is made after significant simplifications of the problem commonly
reduced to the so-called quasi-equilibrium problem setting. It was used to
study the reasons for the interface instability during phase transition.
However, the solutions of the quasi-equilibrium problem are, as a rule,
inherently qualitative. In this paper we present a detailed discussion of the
boundary conditions of the directed crystallization problem, a formulation of
the model considering temperature fields of external sources, the mechanism of
attachment of particles to the growing solid surface, the influence of
interphase component absorption on the phase distribution ratio of the
components as well as the calculation of the period of the morphological
interface instability which is made with due regard of all the aforementioned
conditions.
