The role of grain-environment heterogeneity in normal grain growth: A stochastic approach

Thomas Breithaupt, Lars N. Hansen, Srikanth Toppaladoddi, Richard F. Katz

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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 the microstructure.

Original languageEnglish (US)
Article number116699
JournalActa Materialia
StatePublished - May 1 2021

Bibliographical note

Funding Information:
We thank the reviewers for their comments, which have improved the manuscript. The authors acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out this work ( ). This research received funding from the European Research Council under Horizon 2020 research and innovation program grant agreement number 772255 . T.B. was supported by a Natural Environment Research Council ( NERC NE/L002612/1) studentship in the Oxford NERC Doctoral Training Partnership. S.T. acknowledges a Research Fellowship from All Souls College, Oxford. Source code and data used in the production of figures can be found in [ 54 ].

Publisher Copyright:
© 2021 Acta Materialia Inc. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (


  • Grain growth
  • Grain size distribution
  • Heterogeneity
  • Monte Carlo simulation


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