The Mullins-Sekerka theory: 60 years of morphological stability

Over 60 years of studying morphological stability under fundamental ideas of William Wilson Mullins and Robert Floyd Sekerka [J. Appl. Phys. 34, 323 (1963) and J. Appl. Phys. 35, 444 (1964)] it has become possible to explain the origin and selection of surface structures from planar to cellular, dendritic, and fractal patterns. The Mullins-Sekerka (MS) morphological instability theory provides a condition for stability or reconstruction of interfaces, which separates the phases during phase transformation. The MS-theory has come a long way in the conceptual understanding of the incipience of morphological instability and the formation of structures, although today, certain aspects of this theory continue to be discussed at the fundamental and quantitative level of its interpretation. In the sixtieth anniversary of this theory, we re-examine the MS-analysis under boundary conditions satisfying the smooth existence of temperature and its gradients in directional crystallization of a binary melt. These boundary conditions are dependent on the finite distance from the solidification front for providing directional solidification that quantitatively affects the amplification rate of perturbations in the solid-liquid front morphology.