Model of directed crystallization of binary alloy

We consider a model of directed crystallization. We write the boundary-value problem to a curvilinear coordinate frame attached to the interface. The theory of perturbations is formulated for small perturbations of temperature and component concentration. We study stability of the interface of a binary alloy. In this paper, we show the manner in which the known phenomenon of the lamination of the components in a melt, result in formation of regular eutectic structure. We also give a conclusion of analytical expression for period of this structure.