Dependence of period of macrostructures on kinetic parameters under directed crystallization

In our previous works [Computat. Mater. Sci. 17 (2000) 555–559; Lett. Appl. Phys. 27 (11) (2001) 86–91], we have obtained an expression for a periodic distribution component under directed crystallization of eutectic alloys. This expression coincides with the experimental dependences obtained by Minford et al. [J. Am. Ceram. Soc. (1979) 154–162]. It was obtained from a model of directed crystallization which includes equations of heat conduction and diffusion. The model of directed crystallization contains in the common form a kinetic boundary condition. Dispersion equation of this problem contains a kinetic factor that is a derivative of the interface velocity with respect to temperature. This factor is contained in the expression of period dependence of eutectic pattern on interface velocity. But the dependence of interface velocity on temperature is related to kinetics of molecules addition of material to interface. Using the works by Cahn et al. [Acta Metall. 12 (1964) 1421, 8 (1960) 554], we found the dependence of the kinetic factor on parameters of kinetic theory of crystallization. In consequence, we have obtained dependences between parameters of a kinetic problem, i.e. problem that describes process of crystallization on microscopic level, and the problem of macrostructure formation.