  Understanding the role of solute diffusivities in equilibrium tie-line
selection during growth of a second phase in ternary and higher multicomponent
two phase alloys is an important problem due to the strong dependence of
mechanical properties on compositions. In this paper, we derive analytical
expressions for predicting tie-lines and composition profiles in the matrix
during growth of planar and cylindrical precipitates with the assumption of
diagonal diffusivity matrices. We confirm our calculations by sharp interface
and phase field simulations. The numerical techniques are in turn utilized for
investigating the role of off-diagonal entries in the diffusivity matrix. In
addition, the sharp interface methods allow for the tracking of the tie-line
compositions during growth of 2D precipitates which contribute to an
understanding of the change in equilibrium tie-lines chosen by the system
during growth.
