Investigating the von Neumann-Mullins relation under triple junction dragging

The influence of triple junction mobility on the rate of size change is investigated by square-lattice Monte Carlo Potts model simulations. For normal, grain-boundary-controlled grain growth the classical von Neumann-Mullins relation (Ȧ∝n-nc) is fulfilled for individual polyhedral grains as well as for polycrystalline grain microstructures. For triple-junction-controlled grain growth the number of neighboring grains is related self-similarly to the radius change rate (Ṙ∝(n-nc)/n), which is also shown to be fulfilled for individual grains and polycrystalline microstructures.