Towards a Quantitative Cartography of the Grain Boundary Energy Landscape: Paths and Correlations

We apply a newly developed Voronoi fundamental zone (VFZ) framework to gain insights about grain boundary (GB) structure-property relationships in the five degree-of-freedom (5DOF) space of cubic GBs. We analyze the shape and size of a 5DOF fundamental zone (FZ), molecular statics energy uncertainty, property similarity of GBs that are crystallographically \close" (i.e. correlations), and energy pathways through 5DOF space. Considered together, these insights are important for managing tradeoffs between accuracy, complexity, and design considerations for electron backscatter diffraction/serial sectioning, high-energy diffraction microscopy, molecular statics, and density-functional theory. In terms of the shape and size of a 5DOF FZ, we discover that a FZ is smaller than expected at only ∼65° in the largest principal component. Thus, a 10° difference between two GBs, which may have previously been considered small, is actually quite large. We represent a GB by five transformed Cartesian coordinates equipped with a Euclidean distance metric. Using this representation, we find that the FZ has a low aspect-ratio shape (i.e. width, length, height, etc. are similar) which is important for 5DOF numerical differentiation. Semivariogram and numerical optimization methods reveal that grain boundary energy (GBE) in Ni and Fe are globally correlated within ∼6° to 8° in the grain boundary octonion (GBO) sense (multiply by 2 to convert to misorientation angle). For local correlation lengths of high-symmetry GBs of interest, we notice significant variation relative to global correlation lengths and an inverse relationship with the Brandon criterion. We suggest that property data with no more than ± ∼3 % error and point sets with GBs that are no more than ∼3−4° apart should be used and then paired with high-fidelity interpolation strategies. Finally, in terms of dynamic material behavior, geodesic paths through 5DOF space for Ni suggest that, under appropriate conditions, a certain low-energy Σ7 GB may transform into the frequently observed Σ3 coherent-twin GB which may be interesting to verify by experiment or simulation.