Topological theory of abnormal grain growth

Theories of abnormal grain growth (AGG) treat this interesting phenomenon in terms of the relative grain size, or grain radius, of the abnormal grains. This study, by contrast, treats AGG in terms of concepts that include both the boundary curvature and the number of faces of the abnormal grain. First, we formulate a topological AGG criterion: if a “candidate” grain is undergoing abnormal growth, then its number of faces is increasing with time. AGG initiation in a pinned matrix is analyzed. An “AGG map” summarizes the results of this analysis. Finally, we derive analytical expressions for the number of faces as a function of time for AGG in a pinned matrix, and for AGG in a matrix that is free to undergo normal grain growth. Consideration of the topological features of polyhedral grains introduces new aspects important to our understanding of the kinetics of AGG.