Solute redistribution in dendritic solidification

Analyses that include diffusion of solute in the solid phase are formulated to describe solute redistribution in dendritic solidification of metallic alloys. The analyses arc based on conditions that include negligible undercooling before nucleation of solid phases, negligible increase of solute in advance of the lips of growing dendrites, complete diffusion within the liquid over distances the order of dendrite spacings, and a platelike dendrite morphology. The classical nonequilibrium freezing equation, C-S(*) = kC(0)(1 - f(S))(k-1) accurately describes solute redistribution between dendrite arms for the solidification Processes considered, provided diffusion in the solid is negligible. To account for the effect of diffusion in the solid, an analytic expression is given which is similar in form to the classical expression. In addition, a numerical-analysis procedure is employed lo examine in more detail the effect of diffusion both during and after solidification. The analyses are intended for application to solidification of castings and ingots to describe a) final solute distribution after solidification and cooling to room temperature (microsegregation) and b) local fraction solid as a function of temperature within the solidifying casting or ingol.