On dendritic solidification of multicomponent alloys with unequal liquid diffusion coefficients

A model has been developed previously by Rappaz and Thevoz (Acta metall., 1987, 35, 1478; 1987, 35, 2929) for the solidification of binary alloys having an equiaxed dendritic morphology. The extension of this model to multicomponent alloys is straightforward if the diffusion coefficients in the liquid of the various solute elements are equal. When they are different however, it becomes necessary to distinguish the concentrations at the dendrite tip position. governing the growth kinetics, from the average concentrations within the interdendritic liquid region. A model is presented which couples the dendrite growth kinetics with an overall solute balance performed at the scale of the grain. The diffusion profile outside the grain envelope is calculated using a Landau transformation and an implicit scheme. The calculated solidification paths during and after recalescence are compared with the Scheil approximation for various conditions. Additionally, a model predicting the secondary dendrite arm spacing in multicomponent alloys is briefly described. (C) 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.