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

Abstract

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.

The Formation of Two-Phase Periodic Structures

“…This experiment shows also the relation between instability of the interface and the period of the eutectic structure. Thus, the previously theoretically obtained result [9,10] is confirmed: the eutectic structure period is equal to the period of interface instability. It is difficult to show on this clip that decomposition of the solution occurs by spinodal scenario.…”

“…However, quantitative results that provide a good fit to experimental data are very scarce. One of them is the dependence of the eutectic structure period on the interface velocity [6][7][8][9][10]. This dependence coincides exactly with the experimental dependences for a number of materials.…”

“…The first condition is the requirement that the segregation coefficient is close to one. This condition is necessary in order to get the expressions (4)-(6) from the dispersion equation [9,10]. The second condition is the requirement that the segregation coefficient is greater than one.…”

“…Now let us explain instability of the interface during spinodal decomposition of the solution. The cited above papers [9,10] explain instability of the interface by the dependence of the interface velocity on kinetic overcooling (7). Instability occurs when the segregation coefficient in the expression (8) becomes greater than one.…”

Segregation of Components by the Interface under Phase Transitions

“…The proposed work was motivated by the experiments described in [1,2]. These experiments investigated the solidification of a layer of an aqueous dye solution.…”