STABILITY OF AN ARRAY OF DEEP CELLS IN DIRECTIONAL SOLIDIFICATION

We develop an effective interface formalism to perform the linear stability analysis of long-wavelength perturbations of a periodic array of fingerlike cells in the small-Péclet-number limit of directional solidification. The growth rate for perturbations of wave number q is found to have two branches. The first branch 1(q) is stable for all wave numbers. The second branch is of the diffusive form 2(q)=-Bq2, where B is proportional to the derivative d T/d of the thermal undercooling T with respect to the cell spacing. The point of marginal array stability in this system therefore coincides with the point of minimum undercooling in an analogous way to lamellar eutectics. © 1990 The American Physical Society.