Mean-field model for the growth and coarsening of stoichiometric precipitates at grain boundaries

In this paper, a model for growth and coarsening of precipitates at grain boundaries is developed. The concept takes into account that the evolution of grain boundary precipitates involves fast short-circuit diffusion along grain boundaries as well as slow bulk diffusion of atoms from the grain interior to the grain boundaries. The mathematical formalism is based on a mean-field approximation, utilizing the thermodynamic extremal principle. The model is applied to the precipitation of aluminum nitrides in microalloyed steel in austenite, where precipitation occurs predominately at the austenite grain boundaries. It is shown that the kinetics of precipitation predicted by the proposed model differs significantly from that calculated for randomly distributed precipitates with spherical diffusion fields. Good agreement of the numerical solution is found with experimental observations as well as theoretical treatment of precipitate coarsening.