Indexing of diffraction patterns for determination of crystal orientations

Abstract

The task of determining the orientations of crystals is usually performed by indexing reflections detected on diffraction patterns. The well known underlying principle of indexing methods is universal: they are based on matching experimental scattering vectors to some vectors of the reciprocal lattice. Despite this, the standard attitude has been to devise algorithms applicable to patterns of a particular type. This paper provides a broader perspective. A general approach to indexing of diffraction patterns of various types is presented. References are made to formally similar problems in other research fields, e.g. in computational geometry, computer science, computer vision or star identification. Besides a general description of available methods, concrete algorithms are presented in detail and their applicability to patterns of various types is demonstrated; a program based on these algorithms is shown to index Kikuchi patterns, Kossel patterns and Laue patterns, among others.

Fast Radon transforms for high-precision EBSD orientation determination using PyEBSDIndex

“…Thus, for PyEBSDIndex, the final indexing of bands and orientation are calculated simultaneously. Py-EBSDIndex closely follows the tutorial of Morawiec (2020). Rather than repeat that work we will attempt to briefly summarize the problem and offer more description where implementation details differ significantly from those procedures.…”

“…Unlike Wright & Adams (1992), PyEBSDIndex does not accumulate votes directly for the orientations consistent with the triplets. Instead, PyEBSDIndex uses a modification of the procedure outlined by Morawiec (2020), where for each measured normal a vote is cast for the reflecting family that is consistent with the triplet. This algorithm deviates from the original Morawiec method by using a weighted vote scheme.…”

On automatic determination of quasicrystal orientations by indexing of detected reflections

“…The guidelines described in the previous section were used to modify KiKoCh2, a program for orientation determination via indexing of diffraction patterns, which was originally developed for dealing with periodic crystals. For a description of the original program, see Morawiec (2020).…”

Upgraded LauePt4 for rapid recognition and fitting of Laue patterns from crystals with unknown orientations

“…The program can handle any ordinary images in TIFF (8-bit), JPEG and BITMAP formats. This feature dramatically reduces the complexity of Laue pattern simulation and fitting compared with the large-scale synchrotron Laue microdiffraction programs (Barabash et al, 2001;Liu et al, 2004;Gupta & Agnew, 2009;Ulrich et al, 2011;Robach & Micha, 2015;Zhang et al, 2017;O ¨rs et al, 2018;Morawiec, 2020;Purushottam Raj Purohit et al, 2022;Gu ¨rsoy et al, 2022;Seret et al, 2022;). LauePt has another unique advantage, namely accurate intensity calculations (based on the kinematic diffraction model).…”