Three-Dimensional Grain Boundary Networks: Modeling and Connections to Experimental Data

The grain boundary network that makes up a microstructure plays an important role in determining the properties of the material. These networks are well-studied in two dimensional systems; however, most microstructures are inherently three dimensional, so an understanding of the role microstructure plays in determining properties must account for the full 3D microstructure. Here, percolation-based models are applied to 3D grain boundary networks with both regular and irregular grain shapes. The microstructures are characterized in terms of the cluster size distribution, mean cluster size, and radius of gyration; grain boundary area must be accounted for when calculating these properties in 3D. The analytical tools developed to characterize simulated microstructures can be applied to experimentally-determined data sets to extract the same metrics from those microstructures. Developing an understanding of 3D connectivity in real microstructures may elucidate the role of grain boundary character distribution on property improvement observed during grain boundary engineering.