Geometric methods for microstructure rendition and atomic characterization of poly- and nano-crystalline materials

Polycrystalline materials of both coarse-grain and nanometer scales have complex topological structures with multi-dimensions, including vertices (zero dimension), triple junction lines (one dimension), interfaces or grain boundaries (two dimensions), and grain volumes (three dimensions). Collectively, they contribute to the properties that make these materials valuable for many applications. However, for both numerical modeling and theoretical analysis, connecting the microstructures quantitatively with the properties remains a challenge, due simply to their complexity and also limitations in direct probing of the microstructures at atomic scales in experiments. Without an accurate description of the microstructures, it is difficult, if not impossible, to determine quantitatively the factors and parameters of microstructures and their contributions to the properties. In this study, we present systematic methods, using a series of geometric constructions, to render microstructures in the polycrystalline materials and their characterization at atomic scales. We tested the methods in nanocrystalline (nc) copper using molecular dynamics simulation, as it is the only polycrystalline sample that could be handled at atomic scale. We present the first set of results of atomic scale characterization of the microstructure attributes, grain boundary profile, effects of misorientation, grain size and temperature on grain boundaries, and discuss further applications of the methods.