TY - JOUR A1 - Nolze, Gert T1 - Euler angles and crystal symmetry T2 - Crystal research and technology N2 - For the description of (single) crystal orientations, e.g. as measured by electron backscatter diffraction (EBSD) & X-ray diffraction (XRD), Euler angles are still generally used to import and export data. However, because of the lack of standard definitions for the unit cell reference settings and specimen axes, several transformation descriptions exist which produce different sets of Euler angles for the same orientation. There is also no recommended region within the minimal Euler orientation space into which orientations should be placed. This is the reason why different sets of Euler angles for the same orientation are generated by the available software packages for indexing EBSD patterns. These issues are reviewed and addressed. The influence of crystal symmetry in form of chiral (enantiomorphic) groups is discussed, as well as how multiple, but symmetry-equivalent sets of Euler angles can be reduced in order to deliver a unique orientation description. The Euler coloring algorithms applied to EBSD map data is critically discussed. The specific case of cubic symmetry, especially the effect of the three-fold rotation on the Euler space is investigated in more detail for the highest-symmetric chiral group 432. Recommendations for standard settings of the unit cell to orthogonal coordinate system transformation are given which exploit inherent symmetry. PB - Wiley-VCH Verlag GmbH & Co. KGaA CY - Weinheim KW - EBSD KW - Crystal orientation KW - Pattern indexing KW - Subgroup relationship PY - 2015 UR - https://opus4.kobv.de/opus4-bam/frontdoor/index/index/docId/32545 AN - OPUS4-32545 UR - http://onlinelibrary.wiley.com/doi/10.1002/crat.201400427/full SN - 0023-4753 SN - 1521-4079 SN - 0232-1300 VL - 50 IS - 2 SP - 188 EP - 201 AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany