It was recalled that microstructures in polycrystalline materials, coarse-grained or nano-crystalline, were characterized by a topological structure of grain-boundary networks which were composed of an array of complex geometric entities, having differing dimensions, such as: grain volume, grain-boundary plane, triple-junction line and vertex point. This ensemble of entities gave rise to statistical properties which were represented by distribution functions, means, variances and correlation functions. In contrast to Gibbs’ description, these entities were - at the atomic scale - no longer mathematically abstract geometrical objects such as simple planes, lines or points. They instead possessed finite thicknesses and volumes, as well as certain specific atomic structures and chemistries. Whereas some of these entities could be measured by experiment, a large number of them still remained inaccessible: including identification of the full range of topological properties and structure-characterization at atomic scales. Algorithms and numerical methods were presented here for systematically characterizing these entities in grain-boundary networks in polycrystalline samples which were either obtained from serial-sections of real polycrystals or from digital microstructures generated using inverse Monte Carlo methods. The resultant microstructures were represented by topological and geometrical properties such as grain volume, grain-boundary area, triple-junction length and their statistical properties. The atomic coordinates were given and the type of topological entity to which each atom belonged in the polycrystalline and nano-crystalline materials were labelled. Such previously unavailable quantitative characterization permitted a detailed and rigorous treatment of microstructures over a wide range of modelling applications; including both atomistic simulations and continuum modelling.

Topological and Atomic Scale Characterization of Grain Boundary Networks in Polycrystalline and Nanocrystalline Materials. M.Li, T.Xu: Progress in Materials Science, 2011, 56[6], 864-99