Robert F. Sekerka, Sam R. Coriell, Geoffrey B. McFadden
The theory of morphological stability provides a dynamical analysis of the stability of the interface that separates phases during a phase transformation. We focus on crystallization from either a pure or alloy melt. One solves the governing equations for heat flow, including diffusion for alloys, and uses perturbation theory to analyze the stability of a base state, such as a planar or spherical interface. A linear stability analysis for small perturbations shows for a pure melt that thermal effects are destabilizing if more of the latent heat flows into supercooled liquid than onto the solid, but capillary effects of interfacial free energy are stabilizing. Stability depends on competition of heat flow and capillarity effects. For alloys growing into a positive liquid temperature gradient, the effect of solute is destabilizing and competes with thermal and capillary effects to determine stability. This is the dynamical replacement for the principle of constitutional supercooling. Instability first occurs for perturbations of a given wavelength but neighboring wavelengths become unstable for more severe conditions of instability. A nonlinear analysis shows that non-planar periodic steady-state interfaces can sometimes be stable for a range of wavelengths. This can lead to cellular interfaces that can be computed numerically for even larger amplitudes. A number of other extensions of the Mullins-Sekerka analysis are discussed briefly.
Handbook of Crystal Growth (2nd edition)
Elsevier Science Publishers, Amsterdam, -1
morhological stability, directional solidification, constitutional supercooling, linear stability, solidification