Model of grain refinement in solidification of undercooled melts

Microstructural transitions from coarse-grained (CG) dendritic to grain-refined (GR) equiaxed microstructures are commonly observed in undercooled metallic melts. A simple model to predict the occurrence of these transitions is presented. This model is based on the assumption that fine equiaxed grains are the product of the fragmentation of dendrites by remelting during the period following recalescence where the inter-dendritic melt solidifies. Two mechanisms for the spheroidization of the primary dendrite trunks are considered: (i) capillary forces that tend to minimize interfacial area, and (ii) the radial gradient of trapped supersaturated solute inside the trunk that provides the driving force for a morphological instability via diffusion in the solid. Both of these mechanisms can be important depending on the ratio of the solute diffusivities in the solid and liquid phases and the alloy composition. The model predicts that above some minimal alloy composition C-0(min), there should generically be four microstructural transitions occurring at cooling-rate-dependent critical undercoolings, Delta T-0* < Delta T-2* < Delta T-2* < Delta T-3*, yielding the sequence of microstructures CG --> GR --> CG --> GR --> CG, with increasing Delta T. Only two of these transitions, Delta T-2* and Delta T-3*, should be present for sufficiently dilute alloys ( C-0< C-0(min)) and pure melts, with the corresponding sequence CG --> GR --> CG. In addition, the model predicts that the upper three transitions should be relatively sharp, but the lower undercooling one (Delta T-0*) should be too broad to be observable as a sharp transition. These predictions are in good overall quantitative agreement with existing experimental observations in a wide range of metallic systems that are surveyed here.