  The size distribution of grains is a fundamental characteristic of
polycrystalline solids. In the absence of deformation, the grain-size
distribution is controlled by normal grain growth. The canonical model of
normal grain growth, developed by Hillert, predicts a grain-size distribution
that bears a systematic discrepancy with observed distributions. To address
this, we propose a change to the Hillert model that accounts for the influence
of heterogeneity in the local environment of grains. In our model, each grain
evolves in response to its own local environment of neighbouring grains, rather
than to the global population of grains. The local environment of each grain
evolves according to an Ornstein-Uhlenbeck stochastic process. Our results are
consistent with accepted grain-growth kinetics. Crucially, our model indicates
that the size of relatively large grains evolves as a random walk due to the
inherent variability in their local environments. This leads to a broader
grain-size distribution than the Hillert model and indicates that heterogeneity
has a critical influence on the evolution of microstructure.
