On the theory of grain growth in systems with anisotropic boundary mobility

Abstract

We analyze grain growth kinetics in systems with anisotropic grain boundary mobility. In contrast to most previous studies of grain growth dynamics, we relax self-similarity assumptions that strongly constrain the dynamics and statistics during microstructural evolution in polycrystalline materials. We derive analytical expressions for the average growth rate within each topological class of n-sided grains as well as for the growth rate of the average grain area; we explain the results using underlying symmetries. Although anisotropic grain growth may in general be non-linear in time, we show, even in the absence of the self-similarity constraint, that the evolution kinetics obeys the von Neumann–Mullins relationship in the two limiting cases of textured and fully random microstructure with a time dependence solely determined by changes in the misorientation distribution. Our analytical results agree well with recent computer simulations using a generalized phase field approach.