von Neumann–Mullins-type evolution equations for triple and quadruple junction controlled grain growth

The classical von Neumann–Mullins-law relates the area change rate of a grain in a two-dimensional polycrystalline microstructure to the number of neighboring grains yielding the well-known “N-6”-rule. In the present paper, we show that similar relations exist for the rate of size change as a function of number of neighboring grains for two- and three-dimensional polycrystalline grain microstructures under triple junction- and quadruple junction-control, which we find to be in very good agreement with simulation results.

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