Linear morphological stability analysis of the solid-liquid interface in rapidsolidification of a binary system

The interface stability against small perturbations of the planar solid-liquid interface is considered analytically in linear approximation. Following the analytical procedure of Trivedi and Kurz [ R. Trivedi and W. Kurz Acta Metall. 34 1663 (1986)], which is advancing the original treatment of morphological stability by Mullins and Sekerka [ W. W. Mullins and R. F. Sekerka J. Appl. Phys. 35 444 (1964)] to the case of rapid solidification, we extend the model by introducing the local nonequilibrium in the solute diffusion field around the interface. A solution to the heat- and mass-transport problem around the perturbed interface is given in the presence of the local nonequilibrium solute diffusion. Using the developing local nonequilibrium model of solidification, the self-consistent analysis of linear morphological stability is presented with the attribution to the marginal (neutral) and absolute morphological stability of a rapidly moving interface. Special consideration of the interface stability for the cases of solidification in negative and positive thermal gradients is given. A quantitative comparison of the model predictions for the absolute morphological stability is presented with regard to experimental results of Hoglund and Aziz [D. E. Hoglund and M. J. Aziz, in Kinetics of Phase Transformations, edited by M.O. Thompson, M. J. Aziz, and G. B. Stephenson, MRS Symposia Proceedings No. 205 (Materials Research Society, Pittsburgh, 1991), p. 325] on critical solute concentration for the interface breakdown during rapid solidification of Si-Sn alloys.