Theory of plane front and dendritic growth in multicomponent alloys Original Research Article

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 the composition field for each of the n solutes is given by a sum of n expressions, each corresponding to the binary solution, but where the diffusion coefficients are replaced by the eigenvalues of the diffusion matrix. An extended constitutional undercooling criterion is deducted from the solution for plane front growth. A linear stability analysis of plane front growth is also presented. For dendritic growth, the diffusion field ahead of a growing paraboloid is calculated. Using the two latter solutions, growth of a dendrite at marginal stability is modelled. As an example, these models are applied to an hypothetical ternary system. From these results, some effects of diffusional interaction are shown and discussed.