A geometrical method for the determination and indexing of electron diffraction patterns (original) (raw)
Indexation of electron diffraction patterns at grain boundaries
Materials Characterization, 2021
Grain boundaries play a vital role in materials science, and they are extensively studied through experimental and numerical methods. Electron backscatter diffraction (EBSD) is commonly used to characterize crystalline materials, yet its performance is often compromised at grain boundaries. The key difficulty is to index the overlapped electron backscatter patterns, where Kikuchi bands from multiple crystal orientations coexist. Houghindexation often fails in treating overlapped EBSP, while the recently proposed dictionary indexation and sphere indexation give only one triplet of Euler angles from overlapped patterns. For all these methods, the orientation indexing precision drops for overlapped EBSP. Here we propose an integrated Digital Image Correlation (DIC) procedure to determine simultaneously and precisely multiple crystal orientations by registering the overlapped EBSP and the master pattern. The contribution ratio of each crystal orientation to the overlapped pattern is also available. Through an experimental EBSD dataset around a triple point, multiple benefits of the rich results from the method are demonstrated, such as refining grain boundaries, revealing EBSD scan errors and quantifying spatial resolution of EBSD. At the grain boundaries, the crystal orientation measurement uncertainty is 0.03°for both indexed crystal orientations, the same order for grain interiors, while their contribution ratios of uncertainty around 0.02 are obtained.
Structures of nanometre-size crystals determined from selected-area electron diffraction data
Acta Crystallographica Section A Foundations of Crystallography, 2000
The structure of a new modi®cation of Ti 2 Se, the -phase, and several related inorganic crystal structures containing elements with atomic numbers between 16 and 40 have been solved by quasi-automatic direct methods from singlecrystal electron diffraction patterns of nanometre-size crystals, using the kinematical aproximation. The crystals were several thousand times smaller than the minimum size required for single-crystal X-ray diffraction. Atomic coordinates were found with an average accuracy of 0.2 A Ê or better. Experimental data were obtained by standardized techniques for recording and quantifying electron diffraction patterns. The SIR97 program for solving crystal structures from three-dimensional X-ray diffraction data by direct methods was modi®ed to work also with two-dimensional electron diffraction data.
Automatic analysis of electron backscatter diffraction patterns
Metallurgical Transactions A, 1992
The ability to measure lattice orientation in individual crystallites enables a more complete characterization of microstructure by combining lattice orientation with morphological features. Lattice orientation can be obtained by analyzing electron backscatter diffraction patterns (EBSPs). However, current computer-aided EBSP analysis techniques make it impractical to obtain the number of measurements needed for statistically reliable characterizations of microstructure. An effective fully automated technique for determining crystallographic orientation from EBSPs is described. Bands are identified by linear regions of correlation in the image intensity gradient direction. The most probable orientation is then found using the angles between the detected bands. The reliability of the technique was tested using a set of 1000 patterns obtained from annealed oxygen-free electrical grade (OFEC) copper. The orientation of each test pattern found using automatic indexing was checked against the corresponding orientation as determined by manual indexing. Ninety-nine percent of auto-indexed orientations were found to lie within 5 deg of the misorientation angle of the manual-indexed orientations. By simulating noise in the test patterns, it was found that image quality has a strong effect on the reliability of the technique. An image quality parameter is described which allows the reliability of the technique to be predicted for a pattern of given quality.
Acta Crystallographica Section A Foundations of Crystallography, 1993
The interrelation between the symmetries of convergentbeam electron diffraction (CBED) patterns and the (3+l)-dimeusional point groups of one-dimensional incommensurately modulated crystals is discussed. The symmetry subsymbol 1 for the modulated structure implies that the incommensurate reflections show no symmetry in the CBED pattern. The symmetry subsymbols other than T imply that the incommensurate reflections exhibit the same symmetries as those of the average structure. These results are demonstrated using the CBED patterns obtained from the one-dimensional incommensurately modulated crystals of Sr2Nb207 and BizSr2CaCugO8+6. It is shown that the CBED method can identify the (3+l)-dimensional point groups of onedimensional incommensurately modulated structures.
Quantitative analysis of Electron Diffraction Ring Patterns using the MAUD program
The full quantitative characterization of nanopowders using transmission electron microscopy scattering patterns is shown. This study demonstrates the feasibility of the application of so-called combined analysis, a global approach for phase identification, structure refinement, characterization of anisotropic crystallite sizes and shapes, texture analysis and texture variations with the probed scale, using electron diffraction patterns of TiO 2 and Mn 3 O 4 nanocrystal aggregates and platinum films. Electron diffraction pattern misalignments, positioning, and slight changes from pattern to pattern are directly integrated and refined within this approach. The use of a newly developed full-pattern search-match methodology for phase identification of nanopowders and the incorporation of the two-wave dynamical correction for diffraction patterns are also reported and proved to be efficient.
Reflector Selection for the Indexing of Electron Backscatter Diffraction Patterns
Microscopy and Microanalysis
We propose a new methodology for ranking the reflectors used in traditional Hough-based indexing of electron backscatter diffraction (EBSD) patterns. Instead of kinematic X-ray or electron structure factors (Fhkl) currently utilized, we propose the integrated Kikuchi band intensity parameter (βhkl) based on integrated dynamical electron backscatter intensities. The proposed parameter is compared with the traditional kinematical intensity, IhklrmkinI_{hkl}^{{\rm kin}} Ihklrmkin, as well as the average Hough transform peak intensity, IhklrmHSPI_{hkl}^{{\rm HSP}} IhklrmHSP and used to index EBSD patterns for a number of different material systems of varying unit cell complexities including nickel, silicon, rutile, and forsterite. For elemental structures, βhkl closely follows the kinematical ranking. However, significant ranking differences arise for more complex unit cells, with the βhkl parameter showing a better correlation with the integrated Hough intensities. Finally, Hough-based indexing of a simulated forster...