Analytical model for equiaxed globular solidification in multicomponent alloys

We present a solidification model for equiaxed globular microstructure based on an analytical solution of the diffusion fields in the liquid with cross-diffusion terms for multicomponent alloys. It is demonstrated that the solute profiles for any element can be defined after computation of the eigenvalues and the eigenvectors of the liquid diffusion matrix. The interface velocity and the solute profiles are compared and validated with a numerical solution developed with a front tracking approach. A comprehensive application to the Al–7 wt.%Si–1 wt.%Mg alloy shows the effect of interdiffusion phenomena on the solidification path. This application is developed with an integral approach for the computation of the liquid composition far from the interface. It appears to be the only relevant choice in order to compute the expected driving force. Analytical solutions of the diffusion profile can also be computed for planar and cylindrical geometries. Coupling of this microsegregation model with thermodynamic equilibrium calculations is finally proposed and discussed.