Determining Grain Boundary Position and Geometry from EBSD Data: Limits of Accuracy.

As the feature size of crystalline materials gets smaller, the ability to correctly interpret geometrical sample information from electron backscatter diffraction (EBSD) data becomes more important. This paper uses the notion of transition curves, associated with line scans across grain boundaries (GBs), to correctly account for the finite size of the excitation volume (EV) in the determination of the geometry of the boundary. Various metrics arising from the EBSD data are compared to determine the best experimental proxy for actual numbers of backscattered electrons that are tracked in a Monte Carlo simulation. Consideration of the resultant curves provides an accurate method of determining GB position (at the sample surface) and indicates a significant potential for error in determining GB position using standard EBSD software. Subsequently, simple criteria for comparing experimental and simulated transition curves are derived. Finally, it is shown that the EV is too shallow for the curves to reveal subsurface geometry of the GB (i.e., GB inclination angle) for most values of GB inclination.

Computationally efficient barycentric interpolation of large grain boundary octonion point sets.

We present a method for performing efficient barycentric interpolation for large grain boundary octonion point sets which reside on the surface of a hypersphere. This method includes removal of degenerate dimensions via singular value decomposition (SVD) transformations and linear projections, determination of intersecting facets via nearest neighbor (NN) searches, and interpolation. This method is useful for hyperspherical point sets for applications such as grain boundaries structure-property models, robotics, and specialized neural networks. We provide a case study of the method applied to the 7-sphere. We provide 1-sphere and 2-sphere visualizations to illustrate important aspects of these dimension reduction and interpolation methods. A MATLAB implementation is available at github.com/sgbaird-5dof/interp.•Barycentric interpolation is combined with hypersphere facet intersections, dimensionality reduction, and linear projections to reduce computational complexity without loss of information•A max nearest neighbor threshold is used in conjunction with facet intersection determination to reduce computational runtime.