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Euler angles and crystal symmetry

  • 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 coloringFor 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.zeige mehrzeige weniger

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Metadaten
Autoren/innen:Gert Nolze
Dokumenttyp:Zeitschriftenartikel
Veröffentlichungsform:Verlagsliteratur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):Crystal research and technology
Jahr der Erstveröffentlichung:2015
Organisationseinheit der BAM:5 Werkstofftechnik
5 Werkstofftechnik / 5.1 Materialographie, Fraktographie und Alterung technischer Werkstoffe
Verlag:Wiley-VCH Verlag GmbH & Co. KGaA
Verlagsort:Weinheim
Jahrgang/Band:50
Ausgabe/Heft:2
Erste Seite:188
Letzte Seite:201
Freie Schlagwörter:Crystal orientation; EBSD; Pattern indexing; Subgroup relationship
DOI:https://doi.org/10.1002/crat.201400427
URL:http://onlinelibrary.wiley.com/doi/10.1002/crat.201400427/full
ISSN:0023-4753
ISSN:1521-4079
ISSN:0232-1300
Verfügbarkeit des Volltexts:Volltext-PDF im Netzwerk der BAM verfügbar ("Closed Access")
Datum der Freischaltung:20.02.2016
Referierte Publikation:Nein