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arXiv · 2007.02167

Distribution of Topological Types in Grain-Growth Microstructures

Emanuel A. Lazar·Jeremy K. Mason·Robert D. MacPherson·David J. Srolovitz
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Abstract

An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We introduce a thermodynamic-like theory to explain these distributions in two- and three-dimensional systems. In particular, a bending-like energy $E_i$ is associated to each grain topology $t_i$, and the probability of observing that particular topology is proportional to $\frac{1}{s(t_i)}e^{-\beta E_i}$, where $s(t_i)$ is the order of an associated symmetry group and $\beta$ is a thermodynamic-like constant. We explain the physical origins of this approach, and provide numerical evidence in support.

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Emanuel A. Lazar, Jeremy K. Mason, Robert D. MacPherson, David J. Srolovitz. 2020-07-04. Distribution of Topological Types in Grain-Growth Microstructures. https://doi.org/10.1103/physrevlett.125.015501

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