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 thermodynamiclike theory to explain these distributions in two- and three-dimensional systems. In particular, a bendinglike energy Ei is associated to each grain topology ti, and the probability of observing that particular topology is proportional to [1/s(ti)]e-βEi, where s(ti) is the order of an associated symmetry group and β is a thermodynamiclike constant. We explain the physical origins of this approach and provide numerical evidence in support.
Bibliographical noteFunding Information:
E. A. L. and D. J. S. acknowledge the generous support of the U.S. National Science Foundation, through Award No. DMR-1507013. The research contribution of D. J. S. was sponsored, in part, by the Army Research Office and was accomplished under Grant No. W911NF-19-1-0263. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
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