Theoretical and Numerical Study of Growth in Multi-Component Alloys

In multi-component systems, during diffusion-controlled growth of a precipitate from a supersaturated matrix, differential diffusivities lead to a selection of tie-line compositions different from the thermodynamic tie-line containing the alloy composition. In this paper, we address the multi-component version of the growth problem by extending Zener’s theory, and derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar, cylindrical, and spherical precipitates for independent as well as coupled diffusion of solutes in the scaling regime. We confirm our calculations by sharp interface and phase-field simulations in a ternary setting, in which we also extend the tie-line and growth constant predictions for two well-known limiting cases, namely partition and negligible partition under local equilibrium (PLE and NPLE).