Precipitate growth kinetics under inhomogeneous concentration fields using a phase-field model

We investigate precipitation dynamics in the presence of a local solute gradient using phase-field simulations. During the homogenization heat treatment of the solidified Inconel 718 alloy, high Nb concentration within the Laves phases or at the core of the secondary arms results in Nb diffusion into the $\ensuremath{\gamma}$ matrix. The volume fraction and spatial distribution of precipitation during subsequent annealing can be controlled by tailoring the Nb concentration gradient in the matrix during homogenization. We use a surrogate Ni-Fe-Nb alloy for Inconel 718 to explore the growth dynamics of $\ensuremath{\delta}$ precipitates related to the local Nb concentration levels. The simulations indicate that in the presence of a Nb concentration gradient the growth rate of $\ensuremath{\delta}$ precipitates is higher than in a matrix of uniform average Nb concentration. The higher growth rate is a result of the higher local thermodynamic driving force at the interface between the solute-rich matrix and the $\ensuremath{\delta}$ interface. We propose a phenomenological model to describe the diffusion-controlled growth kinetics of the $\ensuremath{\delta}$ phase under a solute concentration gradient.