Topological changes in coarsening networks

Abstract Curvature driven grain growth proceeds by the motion of curved grain boundaries in polycrystals leading to a decrease in the total interfacial free energy. However, grain growth cannot occur without the so-called topological transitions. Indeed, it is a mathematical impossibility that a decrease in the number of grains per unit volume may take place without the topological transition that corresponds to the grain disappearance. Nonetheless, despite their importance, no previous work has studied the topological transitions in detail that take place during the transient as well as the self-similar state of coarsening. In the present work, the three classical topological changes are tracked during 2-d grain growth simulated by a Monte Carlo method. It is shown and discussed how topological transitions reach a self-similar state together with the grain size and the number of edges (faces) per grain distribution.