Blind lattice-parameter determination of cubic and tetragonal phases with high accuracy using a single EBSD pattern

Abstract

The Bravais lattices and their lattice parameters are blindly determined using electron backscatter diffraction (EBSD) patterns of materials with cubic or tetragonal crystal structures. Since the geometric relationships in a single EBSD pattern are overdetermined, the relative errors of determining the lattice parameters as well as the axial ratios are confined to about 0.7 ± 0.4% and 0.07 ± 0.03%, respectively, for ideal simulated EBSD patterns. The accuracy of the crystal orientation determination reaches about 0.06 ± 0.03°. With careful manual band detection, the accuracy of determining lattice parameters from experimental patterns can be as good as from simulated patterns, although the results from simulated patterns are often better than expermental patterns, which are lower quality and contain uncertain systematic errors. The reasonably high accuracy is obtained primarily because the detection of the diffracting‐plane traces and zone axes is relatively accurate. The results here demonstrate that the developed procedure based on the EBSD technique presents a reliable tool for crystallographic characterization of the Bravais lattices of unknown phases.

Crystallographic analysis of the lattice metric (CALM) from single electron backscatter diffraction or transmission Kikuchi diffraction patterns

“…The most promising approach for lattice parameter determination and Bravais lattice type derivation so far was provided by a Chinese group around Ming Han. They showed with the software EBSDL (Li et al, 2014) that with only information on the electron wavelength and a single KD pattern a derivation of the crystal lattice is possible (Li & Han, 2015;Han et al, 2018;Han & Zhao, 2018a,b). This includes not only the lattice parameters and Bravais lattice types derived from the band positions and widths but also the simultaneous determination of the projection centre.…”

Automated Reconstruction of Spherical Kikuchi Maps

“…The state-of-the-art EBSD technology does couple with EDS data to incorporate a phase identification function, to assist in identifying unknown phases. Similar to ab-initio analysis on diffraction patterns developed for convergent beam electron diffraction (CBED) (Ayer, 1989; Page, 1992), phase identification using just EBSD patterns (Michael & Goehner, 1999; Michael & Eades, 2000; Dingley & Wright, 2009; Li et al, 2014; Li & Han, 2015; Han et al, 2018 a ; Kaufmann et al, 2019), chemical-sensitive holography (Lühr et al, 2016), or combinations with EDS data (Small & Michael, 2001; Nowell & Wright, 2004) have also been extensively studied to compete with the more traditional XRD method. Due to the inherent nature of diffuse scattering, the accuracy of any electron diffraction-based method to measure lattice parameters is unlikely to reach that of XRD without a sophisticated band localization algorithm (Ram et al, 2014), although correct classification of the Bravais lattice with a reasonably accurate lattice parameter is already possible (Michael & Goehner, 1999, 2000; Han et al, 2018 a , 2018 b ).…”

“…Similar to ab-initio analysis on diffraction patterns developed for CBED (Ayer, 1989;Page, 1992), phase identification using just EBSD patterns (Dingley & Wright, 2009;Han, Chen, et al, 2018;Li et al, 2014;Li & Han, 2015;Michael & Eades, 2000;Michael & Goehner, 1999;Kaufmann et al, 2019), chemical-sensitive holography (Lühr et al, 2016) or in combination with EDS data (Nowell & Wright, 2004;Small & Michael, 2001) have also been extensively studied to compete with the more traditional XRD method. Due to the inherent nature of diffuse scattering, the accuracy of any electron diffractionbased method to measure lattice parameters is unlikely to reach that of XRD without a sophisticated band localization algorithm (Ram et al, 2014), although correct classification of the Bravais lattice with a reasonably accurate lattice parameter is already possible Han, Chen, et al, 2018;Michael, J. R., & Goehner, 2000;Michael & Goehner, 1999). In order to determine the symmetry elements from EBSPs, (e.g.…”

Identifying rotational symmetry axes in Kikuchi patterns by reciprocal vectors

“…Because the crystal structure is evident once the symmetry axis is accurately identified, and the complicated voting process can be omitted. Han 16 regarded the reciprocal vector length as approximately proportional to the Kikuchi bandwidth due to the large error of calculated interplanar spacing. Strictly speaking, the reciprocal vector length should be inversely proportional to the interplanr spacing rather than the bandwidth.…”

“…But when the calculation error of the interplanar spacing is large, although this approach (the reciprocal vector length is proportional to the bandwidth) will introduce additional errors, it seems that there is no better way. Most previous methods used the naked eye to determine the position and width of Kikuchi bands 16–18 . Relying on visual recognition is not only time consuming due to the generally manual definition of band positions and widths, but also has low accuracy.…”