Mathematical Tools that Connect Different Indexing Analyses - Ryoko Oishi-Tomiyasu (Proceedings, 2020)
As mathematical tools that can be commonly used for indexing analyses from different types of experimental patterns, we have recently developed (i) rules on forbidden hkl’s that can be used even when the space group and setting are unknown, (ii) an algorithm for error-stable Bravais lattice determination, (iii) generalization of the de Wolff figure of merit for powder diffraction (1D data) to data in higher-dimensions such as Kikuchi patterns (2D data) by electron backscatter diffraction (EBSD). In particular, (ii) could be used in a variety of situations, not just for indexing. It is explained how (i)–(iii) are used in the mathematical framework of our indexing algorithms.