SEGREGATION AND FLOW DURING THE SOLIDIFICATION OF ALLOYS

The crystallization of a binary alloy from a cooled boundary is analys ed and the structure of the resulting solid product examined. The anal ysis includes effects due to differences in densities between solid an d liquid phases and due to a non-zero segregation coefficient of the a lloy. We determine the general conditions under which the solidificati on takes place either at a planar interface or throughout a mushy laye r of solid dendrites bathed in interstitial fluid. We are able to make significant analytical progress by finding appropriate similarity sol utions of the governing differential equations, and then simplifying t hese solutions in the asymptotic limit of practical interest wherein t he compositional diffusivity is very much less than the thermal diffus ivity. Thereby we determine a simple criterion that distinguishes betw een the solidification at a planar front being controlled mainly by th e transport of the rejected component away from the phase boundary rat her than by the associated thermal transports. We also calculate the s olid fraction and the degree of micro-segregation in the mushy layer. In addition, the density difference between the liquid and solid phase s is shown to induce a flow of the liquid phase during solidification, which causes macro-segregation of the resulting solid product.