Theory of plane front and dendritic growth in multicomponent alloys

Analytical solutions for the solute diffusion fields during plane front and dendritic growth in multicomponent alloys have been developed, taking into account the diffusive interaction between the species. It is found that th e composition field for each of the n solutes is given by a sum of n expres sions, each corresponding to the binary solution, but where the diffusion c oefficients are replaced by the eigenvalues of the diffusion matrix. An ext ended constitutional undercooling criterion is deducted from the solution f or plane front growth. A linear stability analysis of plane front growth is also presented. For dendritic growth, the diffusion field ahead of a growi ng paraboloid is calculated. Using the two latter solutions, growth of a de ndrite at marginal stability is modelled. As an example, these models are a pplied to an hypothetical ternary system. From these results, some effects of diffusional interaction are shown and discussed. (C) 2001 Acta Materiali a Inc, Published by Elsevier Science Ltd. All rights reserved.