Solid–Melt Interface Stability during Directional Solidification: A Phenomenological Theory

Abstract

A mathematical model is developed that makes it possible, within the framework of a single phenomenological approach, to investigate the stability of a planar phase boundary during directional solidification of binary alloy, taking into account the effect of a density change and heat transfer in the solid phase. The study reveals a complex picture of alternating areas of stability and instability, which is sensitive to changes in parameters of growth and temperature gradient at the interface. Areas of instability are formed by the development of a set of disturbances of different frequencies and rates of propagations. As shown, the irreducible liquid-phase flow caused by density change plays a major role in the loss of stability of the solidification front and is realized for perturbations with any wave number k > 0.

Keywords

• binary alloy
• solid–liquid interface
• directional solidification
• morphological stability
• density jump
• latent melting heat
• dispersion equation