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.

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.