Analytical treatment of diffusion during precipitate growth in multicomponent systems

We propose an approximate growth rate equation that takes into account both cross-diffusion and high supersaturations for modeling precipitation in multicomponent systems. We then apply it to an Fe-alloy in which interstitial C atoms diffuse much faster than substitutional solutes, and predict a spontaneous transition from slow growth under ortho-equilibrium to fast growth under the non-partitioning local equilibrium condition. The transition is caused by the decrease in the Gibbs–Thomson effect as the growing particle becomes larger. The results agree with DICTRA simulations where full diffusion fields are calculated.