Microstructure classification and the polycrystalline microstructure state space

A cornerstone of materials science is that material properties are determined by their microstructure. While the community has already developed a wide variety of approaches to describe microstructure, most of these are tailored to specific material systems or classes. This work proposes a way to quantitatively measure the similarity of microstructures based on the geometry of the grain boundary network, a feature which is fundamental to and characteristic of all polycrystalline materials. Specifically, a distance on all single-phase polycrystalline microstructures is proposed such that two microstructures that are close with regard to the distance have grain boundary networks that are statistically similar in all geometric respects below a user-specified length scale. Given a pair of micrographs, the distance is approximated by sampling windows from the micrographs, defining a distance between pairs of windows, and finding a window matching that minimizes the sum of the pairwise window distances. The approach is used to compare a variety of synthetic microstructures and to develop a procedure to query a proof-of-concept database suitable for general single-phase polycrystalline microstructures.