Modeling of the neighborhood topological effect on grain growth in presence of particles pinning

A model for grain growth with the particles effect is suggested. This model, which presents an extension of the von Neumann–Mullins law in presence of pinning particles, predicts two-grain critical numbers. Greater than the minimal critical number or less than the maximal critical number the grain boundary can be moving. Between the two limiting numbers no grain growth takes place. These limiting numbers permit us to introduce the preferential influence of particles on grain boundaries in the simulation procedure. Currently, it is very difficult to include this preferential interaction directly in the classical simulation models. A computer simulation by a modified Monte-Carlo potts technique is used to test our proposed model.