Model of directed crystallization of binary alloy

On Linear Analysis of the Movement of the Interface under Directed Crystallization

“…It was assumed that the mode corresponds to eutectic structure formation. Numerical calculations have been made of the interface component distribution period as a function of the interface velocity for a quadratic dependence between the interface velocity and kinetic overcooling [11]. This coincided with the experimental dependences of the eutectic structure period on the interface velocity.…”

“…Consider expansion of velocity by kinetic overcooling in the vicinity of the stationary crystallization regime for small perturbations of stationary temperature and concentration values. Then kinetic overcooling is written as a sum of perturbation and the stationary part (9) is used for function (11). For sufficiently large values of the kinetic coefficient the interface temperature is equilibrium which does not imply that kinetic overcooling is zero.…”

“…In such problem setting the cause and effect are interchanged. Indeed, it is not the spatial deviation of the interface from the stationary solution which is responsible for the deviations of the stationary solutions of temperature and concentration, rather perturbations of the temperature and concentration stationary regime can either lead to or fail to lead to spatial perturbations of the interface [8]. Spatial perturbations of the interface are determined only by rate fluctuations caused solely by kinetic overcooling.…”

“…For instance, attempts have been made to use the results of interface stability analysis during crystallization for description of periodic eutectic structure [7]. In [8] [9] a linear analysis of interface stability under the directed crystallization was made with regard to the kinetics of particle condensation to the growing crystal surface and the kinetics of the non-equilibrium solution layer in front of the interface. The problem setting allowed for kinetic overcooling which was shown to be responsible for the interface instability, the latter in its turn can lead to spatial distortions as well as temporary fluctuations of the temperature and concentration of the components on the interface during phase transition.…”

“…However, comparison of the calculated and experimental data reveals that the solutions obtained do not take into account all the conditions of phase transition that can have qualitative effects on the processes involved in the problems in question. We have recently published several papers in which the setting of the directed crystallization problem includes nonequilibrium processes affecting heat-and-mass transfer during phase transitions, [8] [9] [11]- [13] [17]. The quantitative agreement between the calculated data and the experimental dependences of the eutectic structure period on the interface velocity indicate that the problem setting in the above papers takes into consideration the conditions which can qualitatively affect the heat-and-mass transfer processes during phase transitions.…”