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Introduction to PowderCell
(2015)
The kinetic energy of keV electrons backscattered from a rutile (TiO2) surface depends measurably on the mass of the scattering atom. This makes it possible to determine separately the angular distribution of electrons backscattered elastically from either Ti or O. Diffraction effects of these backscattered electrons inside the rutile crystal lead to the formation of Kikuchi patterns. The element-resolved Kikuchi patterns of Ti and O differ characteristically, but each can be described fairly well in terms of the dynamical theory of diffraction. Qualitatively, much of the differences can be understood by considering the relative arrangement of the Ti and O atoms with respect to planes defined by the crystal lattice.
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.