TY - JOUR A1 - Nolze, Gert A1 - Winkelmann, Aimo T1 - Crystallometric and projective properties of Kikuchi diffraction patterns JF - Journal of Applied Crystallography N2 - Kikuchi diffraction patterns can provide fundamental information about the lattice metric of a crystalline phase. In order to improve the possible precision and accuracy of lattice parameter determination from the features observed in Kikuchi patterns, some useful fundamental relationships of geometric crystal-lography are reviewed, which hold true independently of the actual crystal symmetry. The Kikuchi band positions and intersections and the Kikuchi band widths are highly interrelated, which is illustrated by the fact that all lattice plane trace positions of the crystal are predetermined by the definition of only four traces. If, additionally, the projection centre of the gnomonic projection is known, the lattice parameter ratios and the angles between the basis vectors are fixed. A further definition of one specific Kikuchi band width is sufficient to set the absolute sizes of all lattice parameters and to predict the widths of all Kikuchi bands. The mathematical properties of the gnomonic projection turn out to be central to an improved interpretation of Kikuchi pattern data, emphasizing the importance of the exact knowledge of the projection centre. KW - EBSD KW - Crystallography KW - Kikuchi patterns KW - Projective geometry PY - 2017 DO - https://doi.org/10.1107/S1600576716017477 SN - 1600-5767 VL - 50 IS - Part 1 SP - 102 EP - 119 PB - International Union of Crystallography AN - OPUS4-39061 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -