A three-dimensional polyhedral unit model for grain boundary structure in fcc metals

One of the biggest challenges in developing truly bottom-up models for the performance of polycrystalline materials is the lack of robust quantitative structure-property relationships for interfaces. As a first step in analyzing such relationships, we present a polyhedral unit model to classify the geometrical nature of atomic packing along grain boundaries. While the atomic structure in disordered systems has been a topic of interest for many decades, geometrical analyses of grain boundaries has proven to be particularly challenging because of the wide range of structures that are possible depending on the underlying macroscopic crystallographic character. In this article, we propose an algorithm that can partition the atomic structure into a connected array of three-dimensional polyhedra, and thus, present a three-dimensional polyhedral unit model for grain boundaries. A point-pattern matching algorithm is also provided for quantifying the distortions of the observed grain boundary polyhedral units. The polyhedral unit model is robust enough to capture the structure of high-Sigma, mixed character interfaces and, hence, provides a geometric tool for comparing grain boundary structures across the five-parameter crystallographic phase-space. Since the obtained polyhedral units circumscribe the voids present in the structure, such a description provides valuable information concerning segregation sites within the grain boundary. We anticipate that this technique will serve as a powerful tool in the analysis of grain boundary structure. The polyhedral unit model is also applicable to a wide array of material systems as the proposed algorithm is not limited by the underlying lattice structure.