Topological and atomic scale characterization of grain boundary networks in polycrystalline and nanocrystalline materials

Microstructure in polycrystalline materials, either coarse-grained or nano-crystalline, is characterized by the topological structure of grain boundary networks which are composed of an array of complex geometric entities with different dimensions such as grain volume, grain boundary plane, triple junction line, and vertex point. The ensemble of these entities gives rise to statistical properties represented by their distribution functions, means, variances, and correlation functions. Moreover, contrast to Gibbs’ description, on atomic scales these entities are no longer mathematically abstract geometric objects such as simple plane, line or point; rather they possess finite thickness and volumes, as well as certain specific atomic structures and chemistry. While some of these entities can be measured from experiment, a large number of them still remain inaccessible, that includes identification of the full range of topological properties and the structure characterization on atomic scales. In this article, we present algorithms and numerical methods to characterize systematically these entities in grain boundary networks in polycrystalline samples which are either from serial sectioning of real polycrystals or from digital microstructures generated using inverse Monte Carlo methods. The rendered microstructures are represented by the topological and geometric properties such as the grain volume, grain boundary area, triple junction length, and their statistical properties. Most importantly we give the atomic coordinates and label the type of the topological entities to which each atom belongs in the polycrystalline and nano-crystalline materials. Such quantitative characterization, unavailable before, enables detailed and rigorous treatment of microstructures in a wide range of modeling applications including both atomistic simulation and continuum modeling.