TY - JOUR A1 - Nolze, Gert A1 - Tokarski, T. A1 - Rychlowski, L. T1 - Use of electron backscatter diffraction patterns to determine the crystal lattice. Part 1. Where is the Bragg angle? JF - Journal of Applied Crystallography N2 - The derivation of a crystal structure and its phase-specific parameters from a single wide-angle backscattered Kikuchi diffraction pattern requires reliable extraction of the Bragg angles. By means of the first derivative of the lattice profile, an attempt is made to determine fully automatically and reproducibly the band widths in simulated Kikuchi patterns. Even under such ideal conditions (projection centre, wavelength and lattice plane traces are perfectly known), this leads to a lattice parameter distribution whose mean shows a linear offset that correlates with the mean atomic number Z of the pattern-forming phase. The consideration of as many Kikuchi bands as possible reduces the errors that typically occur if only a single band is analysed. On the other hand, the width of the resulting distribution is such that higher image resolution of diffraction patterns, employing longer wavelengths to produce wider bands or the use of higher interference orders is less advantageous than commonly assumed. KW - Bragg angles KW - Kikuchi bands KW - Kikuchi patterns KW - First derivative KW - Lattice parameters PY - 2023 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-573141 DO - https://doi.org/10.1107/S1600576723000134 SN - 0021-8898 VL - 56 IS - Pt. 2 SP - 349 EP - 360 AN - OPUS4-57314 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Nolze, Gert A1 - Tokarski, T. A1 - Rychlowski, L. T1 - Use of electron backscatter diffraction patterns to determine the crystal lattice. Part 2. Offset corrections JF - Journal of Applied Crystallography N2 - A band width determination using the first derivative of the band profile systematically underestimates the true Bragg angle. Corrections are proposed to compensate for the resulting offset Δa/a of the mean lattice parameters derived from as many Kikuchi band widths as possible. For dynamically simulated Kikuchi patterns, Δa/a can reach up to 8% for phases with a high mean atomic number Z, whereas for much more common low-Z materials the offset decreases linearly. A predicted offset Δa/a = f(Z) is therefore proposed, which also includes the unit-cell volume and thus takes into account the packing density of the scatterers in the material. Since Z is not always available for unknown phases, its substitution by Zmax, i.e. the atomic number of the heaviest element in the compound, is still acceptable for an approximate correction. For simulated Kikuchi patterns the offset-corrected lattice parameter deviation is Δa/a < 1.5%. The lattice parameter ratios, and the angles α, β and γ between the basis vectors, are not affected at all.1.5%. The lattice parameter ratios, and the angles � , � and � between the basis vectors, are not affected at all. KW - Mean atomic number KW - Kikuchi patterns KW - Lattice parameters KW - Automated Bragg angle determination KW - Lattice parameter determination PY - 2023 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-573153 DO - https://doi.org/10.1107/s1600576723000146 SN - 0021-8898 VL - 56 IS - Pt. 2 SP - 361 EP - 366 AN - OPUS4-57315 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -