Use of electron backscatter diffraction patterns to determine the crystal lattice. Part 1. Where is the Bragg angle?

Abstract

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.

Use of electron backscatter diffraction patterns to determine the crystal lattice. Part 3. Pseudosymmetry

“…Reciprocal lattice of centred unit cells. The derivation of the lattice metric from a single BKD pattern is based on a correlative analysis of the reciprocal lattice (Li & Han, 2015;Nolze et al, 2023a). For primitive lattices this is comparatively straightforward.…”

“…The crystallographic description of the lattice plane traces has been derived from the definition of the coordinate systems (lattice parameters used for the simulation, projection centre, crystal orientation). The trace positioning and band profile extraction are described for example by Day (2008) and Nolze et al (2021Nolze et al ( , 2023a.…”

“…For the first derivatives of a considerable number of bands asym = | min | À | max | 6 ¼ 0 holds. Kikuchi bands are not considered in the lattice parameter analysis if | asym | > 0.2 or the extracted band width deviates by more than 0.2 from the geometrically predicted value (Nolze et al, 2023a). Second, the chemical composition in terms of the atomic scattering factor f affects the band edge profile.…”

“…a lower electron energy E 0 would increase the band widths even for higher d hkl , but the band edge detection becomes less reliable and, more importantly, the number of detectable bands drastically reduces the statistical relevance of the derived lattice parameters (Nolze et al, 2023a). In any case, there remains at least the concern that the monotonicity of f el is lost for the band width range considered with falling electron energy, which tends to favour a pseudosymmetric interpretation of the derived reciprocal-lattice point arrangement.…”

“…This considerably reduces at least the purely visual detectability of symmetry for non-cubic phases. The incomplete signal also affects the reliability of the extracted information such as the lattice parameters, because even mirrorsymmetric band profiles of centrosymmetric phases become highly asymmetric due to the large missing part of the bands [Part I of this series, Nolze et al (2023a)]. This also happens for physics-based BKD pattern simulation, although they are at least not affected by excess-deficiency effects and the alreadymentioned gradually changing signal-to-noise ratio.…”