Stability of Moving Interfaces with Phase Transformation

STABILITY OF MOVING INTERFACES WITH PHASE TRANSFORMATION 

FIGURE 6.16 Transport effect on interfacial stability during phase transformation, (a) Phase transformation with transport into shrinking phase B initial situation, (b) Effect of wavy perturbation of the interface. Transport into phase B is enhanced at point P and diminishes at Q. (c) Interfacial perturbation with transport into the growing phase. Transport into phase A is enhanced at point Q and diminished at point P. 

We see from this example that heat transport is a key factor influencing stabiUty. In solidification of binary mixtures or alloys both heat and mass transport must be eonsidraed. If the solute is preferentially soluble in the hquid phase, for example, solute must diffuse from the interfaee to the bulk hquid as sohdification proeeeds. Sinee diffusion coefficimts are often mueh smalf than thermal diffu-sivities in liquids, the sohdification rate is often limited primarily by solute diffusion. By an argument similar to that given above for heat transport, we eonclude that solute (hffusion in the hquid is destabilizing and ean lead to dendritic growth. 

This equation, which assumes steady state in the moving coordinate system, has the solution 

For the remaiiung boundary condition we use an empirical expression that allows for the possibility that the kinetics of crystal structure formation at the interface may significantly influence the solidification rate  

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