Gazing at crystal balls: Electron backscatter diffraction pattern analysis and cross correlation on the sphere

Abstract

We present spherical analysis of electron backscatter diffraction (EBSD) patterns with two new algorithms: (1) band localisation and band profile analysis using the spherical Radon transform; (2) orientation determination using spherical cross correlation. These new approaches are formally introduced and their accuracies are determined using dynamically simulated patterns. We demonstrate their utility with an experimental dataset obtained from ferritic iron.Our results indicate that the analysis of EBSD patterns on the surface of the sphere provides an elegant method of revealing information from these rich sources of crystallographic data. Highlights 1. We present a method to approximate Kikuchi patterns by spherical functions.2. We utilize the spherical Radon transformation to localise Kikuchi bands and to analyse their profile.3. We develop a spherical cross correlation method for orientation determination from Kikuchi patterns. 4. All methods are speed optimised using fast Fourier algorithms on the sphere and the orientation space.

A phase field model for the growth and characteristic thickness of deformation-induced twins

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Indexing of diffraction patterns for determination of crystal orientations

“…The natural domain for a complete simulated diffraction pattern is a sphere. That is why it is natural to match patterns projected onto a sphere with spherical cross correlation as the pattern similarity measure (Hielscher et al, 2019;Lenthe et al, 2019). The correlation of real functions f s (simulated intensity function) and f p (experimental pattern) on the unit sphere S 2 is given by ðf s ?…”

“…The above objective function is defined via a single pattern simulated over the entire sphere, whereas the domain of the experimental pattern f p is limited to a window of the detector. This issue is addressed by modifying f p so there is a smooth decay from the values inside the window to zero outside it, and by using a correction term accounting for the shape of the window (Hielscher et al, 2019). The integrals can be estimated by direct numerical computation, but this approach is slow.…”

“…f p as a series with coefficients given by expansion coefficients of f s and f p . See Hielscher et al (2019) for details.…”

Fast Predictive Model of Crystallographic Texture Evolution in Metal Additive Manufacturing

“…Figure 1 illustrates a macroand micrograph of the printed samples. Coding for the model development was done in MATLAB and the MTEX toolbox was used to analyze texture [27][28][29]. A desktop computer equipped with a 4-Core Intel ® Xeon™ E-2024G CPU with a 3.40 GHz clock rate and 16 GB of RAM was used.…”