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, $I_{hkl}^{{\rm kin}} $, as well as the average Hough transform peak intensity, $I_{hkl}^{{\rm HSP}} $ 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 forsterite data set showed an appreciable improvement in the median confidence index (0.15 to 0.35) when βhkl is used instead of $I_{hkl}^{{\rm kin}} $ for ranking the reflectors.

We present a deep learning approach to the indexing of electron backscatter diffraction (EBSD) patterns. We design and implement a deep convolutional neural network architecture to predict crystal orientation from the EBSD patterns. We design a differentiable approximation to the disorientation function between the predicted crystal orientation and the ground truth; the deep learning model optimizes for the mean disorientation error between the predicted crystal orientation and the ground truth using stochastic gradient descent. The deep learning model is trained using 374,852 EBSD patterns of polycrystalline nickel from simulation and evaluated using 1,000 experimental EBSD patterns of polycrystalline nickel. The deep learning model results in a mean disorientation error of 0.548° compared to 0.652° using dictionary based indexing.

The magnetization configuration of a novel nano-chessboard structure consisting of L10 and L12 phases in a Co40Pt60 alloy is investigated using Lorentz transmission electron microscopy (LTEM) and micro-magnetic simulations. We show high-resolution LTEM images of nano-size magnetic features acquired through spherical aberration correction in Lorentz Fresnel mode. Phase reconstructions and LTEM image simulations are carried out to fully understand the magnetic microstructure. The experimental Fresnel images of the nano-chessboard structure show zig-zag shaped magnetic domain walls at the inter-phase boundaries between L10 and L12 phases. A circular magnetization distribution with vortex and anti-vortex type arrangement is evident in the phase reconstructed magnetic induction maps as well as simulated maps. The magnetic contrast in experimental LTEM images is interpreted with the help of magnetic induction maps simulated for various relative electron beam-sample orientations inside the TEM.

We demonstrate that the surface topography of a sample can be reconstructed from electron backscatter diffraction (EBSD) patterns collected with a commercial EBSD system. This technique combines the location of the maximum background intensity with a correction from Monte Carlo simulations to determine the local surface normals at each point in an EBSD scan. A surface height map is then reconstructed from the local surface normals. In this study, a Ni sample was machined with a femtosecond laser, which causes the formation of a laser-induced periodic surface structure (LIPSS). The topography of the LIPSS was analyzed using atomic force microscopy (AFM) and reconstructions from EBSD patterns collected at 5 and 20 kV. The LIPSS consisted of a combination of low frequency waviness due to curtaining and high frequency ridges. The morphology of the reconstructed low frequency waviness and high frequency ridges matched the AFM data. The reconstruction technique does not require any modification to existing EBSD systems and so can be particularly useful for measuring topography and its evolution during in situ experiments.