A Nonlinear Stability Analysis of a Model Equation for Alloy Solidification

Abstract

Controlled plane front solidification of alloys and other binary substances under an imposed temperature gradient is used in practice to grow single crystals, refine materials (e.g., zone refining), and obtain uniform or non-uniform composition within the material grown [1]. The most important industrial applications of this type of solidification are for growth of crystals for metal oxide semiconductors (MOS's) [1]. Growth of oxide crystals for jewels is another, much older commercial application of single crystal growth [1]. Another important application is in growth of oxides for laser systems and other optical devices [1]. Further industrial applications arise in ingot casting and in the steel and glass industries [2]. For all of these solidification situations involving binary materials, quantitative predictions of interfacial cellular morphology, including information on cell size and intracellular solute distribution, prove to be extremely valuable and are of a particular aid to industrial researchers.