Schlegel description of grain form evolution in grain growth

Abstract The paths of evolution of topological grain forms during grain growth are described in terms of number of faces, edges per face and face arrangements, as depicted by Schlegel diagrams and the topological events that change them. This “Schlegel tree” describes transitions to higher face classes by grain encounters at corners and to lower face classes by grain-pair separation at three-edged faces. Transitions within face classes are described through rearrangements that occur to neighboring grains during these events. The process is further described by probabilities of the different paths in terms of numbers of edges, corners and three-edged faces at which face gain and loss events occur. Schlegel data from separated grains and three-dimensional Monte Carlo and front-tracking simulations show good comparison. Grain form frequencies increase with increasing number of transition paths into them from other forms. The highest frequency forms have few or no three-edged faces, while those with the most three-edged faces are present the least. These observations suggest that three-edged faces are catalysts for topological change, and forms with higher frequencies of these have shorter residence times before transitioning to lower classes.