A model for evolution of shape changing precipitates in multicomponent systems

Recently the authors introduced a concept of shape factors to extend an already established model for the growth and coarsening kinetics of spherical precipitates in multicomponent multiphase environments to needle- and disc-shaped geometries. The geometry of the precipitates is kept in the original version of the concept to be self-similar with a given fixed aspect ratio. In the present treatment, the aspect ratios of individual precipitates are treated as independent evolving parameters. The evolution equations of each precipitate, described by its effective radius, mean chemical composition and the aspect ratio, are derived by application of the thermodynamic extremal principle. The driving force for the evolution of the aspect ratio of the precipitate stems from the anisotropic misfit strain of the precipitate and from the orientation dependence of the interface energy. The model is used for the simulation of the precipitation of Ti3AlN and Ti2AlN in Ti–Al–0.5 at.% N matrix.