Quantifying microstructures in isotropic grain growth from phase field modeling: Topological properties

In a previous work [Acta Materialia 2012;60:4787], we developed a new method that utilizes discrete, voxel-based data for microstructure quantification. We successfully calculated some relatively simple microstructural quantities and relations. In this paper, we apply and extend this method to compute more complex microstructural quantities and, in particular, map out the connection between grain growth rate and various topological properties. We present detailed results for several local and average topological and geometric properties of the microstructures during grain coarsening, including the curvature of grain boundaries and triple junction lines, grain cell shape, and their relations with growth dynamics. We also examine several well-known topological relations, i.e. Euler relations, the Lewis rule and the Aboav-Weaire law. These quantities and relations are the centerpiece of the grain growth models and theories developed so far. We also compare our results with some existing results in three dimensions. The quantitative description of the dynamic behaviors of the microstructural attributes adds a valuable data set to grain growth that can be used for benchmarking for phase field modeling and comparison with other approaches.