Cellular Instability in Binary Solidification

Abstract

<p>The steady-state growth of cells in binary alloy single phase solidification is examined theoretically and experimentally. The failure of the marginal-stability calculations to predict and describe the growth of stable cells indicates a theoretical gap in this field. The Zener-Hillert type model for cellular solidification proposed by Kirkaldy is discussed. In this theory the physics of cell growth demands that the interface be a non-equilibrium interface stabilized by Kinetic and crystallographic effects. A quantitative model following this line is advanced for the steady-state growth of two-dimensional cells. The solution to the free boundary diffusion problem requires, in addition to the boundary conditions, two extra constraints. A principle of minimum cell root radius, surrogate to the principle of minimum rate of entropy production, is used to provide the additional conditions. Cell growth in the succinonitrile-salol system was studied experimentally. For a given set of growth conditions the cells have a unique steadystate spacing and length. Perturbation experiments about the steady-state support the validity of the optimization procedure used in the calculations. Quantitative predictions on steady-state growth are verified by the experiments.</p>