Beyond modified mean field: a case for a stochastic grain growth model

ABSTRACT

We address the basic mechanism of grain growth in two and three dimensions in single phase metallic systems. It is argued, a comprehensive grain growth model is best based on a stochastic process described by a Fokker Planck equation. This concept is sufficient to determine almost all features of grain growth in general terms. The existence of the von Neumann law and its counterpart in three dimensions enables us to provide an explicit form of the Fokker Planck equation and thus determine many features of grain growth in great detail. Finally, we illustrate this model by determining the salient features of grain growth in three dimensions in the long time limit, and comparing them with experimental and computational results.

KEYWORDS:

• Stochastic
• grain growth
• Fokker Planck equation
• mean field theory

Acknowledgements

Funding for this project was provided by the Office of Naval Research (ONR) through the Naval Research Laboratory's 6.1 Research Program.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Alex E. Moser http://orcid.org/0000-0002-9532-6497

Additional information

Funding

This work was supported by Office of Naval Research Global.