Nonlinear Dynamics of the Formation of a Periodic Superstructure of Impurity Bands during Rapid Directional Solidification of Binary Alloys

An analytical description is proposed for the nonlinear dynamics of formation of regular impurity superstructures during a rapid solidification of binary alloys supplemented by a numerical model calculation. It is shown that there is a stable limit cycle, and spatial profiles of the impurity concentration in a solid product are calculated. The inclusion of a finiteness of the impurity atom jump velocity is found to lead to very substantial decrease in the cycle sizes and a change in the profiles of impurity superstructures.