Topological event rates and the evolution of the grain face distribution in grain growth

Abstract A theory is formulated that relates the rates of the three topological events to the evolution of the face distribution function. Implementation of the theory requires introduction of the concept of participation probabilities which reflect the face distribution of those grains that are incident upon the events. The prediction of the evolving face distribution is tested with a 3-D Monte Carlo simulation of the grain growth process that permits evaluation of the topological event rates by face class and the participation probabilities. The theory also develops a relation between the average number of faces per grain and the topological rates as well as the asymptotic distribution function; these results are also tested using the simulation. The transient period prior to normal grain growth is explained in terms of the evolution of the event rates that control the creation of small grains and evolve the face distribution to its final shape.