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Understanding the role of solute diffusivities in equilibrium tie-lineselection during growth of a second phase in ternary and higher multicomponenttwo phase alloys is an important problem due to the strong dependence ofmechanical properties on compositions. In this paper, we derive analyticalexpressions for predicting tie-lines and composition profiles in the matrixduring growth of planar and cylindrical precipitates with the assumption ofdiagonal diffusivity matrices. We confirm our calculations by sharp interfaceand phase field simulations. The numerical techniques are in turn utilized forinvestigating the role of off-diagonal entries in the diffusivity matrix. Inaddition, the sharp interface methods allow for the tracking of the tie-linecompositions during growth of 2D precipitates which contribute to anunderstanding of the change in equilibrium tie-lines chosen by the systemduring growth.

Growth in multi-component alloys: Theoretical and numerical determination of phase concentrations