Novel remapping approach for HR-EBSD based on demons registration

Measurement of the pattern shifts for HR-EBSD with larger lattice rotations

High-resolution electron backscattering diffraction (HR-EBSD) was used to measure rotations and elastic strains by matching diffraction patterns based on cross-correlation. However, the subset-based phase correlation algorithm was unable to determine pattern shifts accurately when large rotations occurred. In this paper, a new matching algorithm was proposed to measure pattern shifts and recover the elastic strain and lattice rotation with finite deformation theory. The algorithm was implemented in two steps: (a) Integral pixel matching: The pixel-related information of the Kikuchi patterns was mapped to the original three-dimensional sphere to obtain the image projected in parallel by using the feature points as the pattern center through the transformation of its spatial coordinates. The correlation between the images projected in parallel before and after deformation was then obtained. The locations of the integral pixels were determined by the peaks of the surface of correlation obtained by traversing all pixels in the search area. (b) subpixel refinement: the locations of subpixels were obtained by FAGN with an appropriate shape function involving rotation and translation. The algorithm was applied to dynamic simulated test sets, and its results were compared with those of the first-pass cross-correlation and the second-pass cross-correlation method with remapping. The proposed method was more robust in the case of rotation and solved the problem that displacement vectors could not be accurately measured when a larger lattice rotation occurred. The mean errors of the measured displacement, rotation, and strain components were 0.02 pixel, 0.5×10^-4rad, and 1×10^-4, respectively. Compared with the second-pass cross-correlation method, the angle of rotation was more precisely extracted.

An iterative method for reference pattern selection in high-resolution electron backscatter diffraction (HR-EBSD)

For high (angular) resolution electron backscatter diffraction (HR-EBSD), the selection of a reference diffraction pattern (EBSP₀) significantly affects the precision of the calculated strain and rotation maps. This effect was demonstrated in plastically deformed body-centred cubic and face-centred cubic ductile metals (ferrite and austenite grains in duplex stainless steel) and brittle single-crystal silicon, which showed that the effect is not only limited to measurement magnitude but also spatial distribution. An empirical relationship was then identified between the cross-correlation parameter and angular error, which was used in an iterative algorithm to identify the optimal reference pattern that maximises the precision of HR-EBSD.

Line-rotated remapping for high-resolution electron backscatter diffraction

A novel approach, termed line-rotated remapping (LRR), for high resolution electron backscatter diffraction is proposed to remap patterns with large rotation. In LRR, the displacements during the first-pass cross-correlation is modified to a function of the corresponding Kikuchi lines and the points on the reference pattern. Then, the finite rotation matrix to remap the test pattern to a similar orientation of the reference pattern is determined using the parameters of the Kikuchi lines. We apply LRR to simulated Si patterns with random orientations, and obtain measurement errors below ∼1.0 × 10^-3 for lattice rotations up to ∼26°. The maximum angle that may be remapped by LRR decreases with the distance between the specimen and the screen, which in turn reduces the number of matched Kikuchi lines. We also employ LRR in experiments to quantitatively characterize rotations and elastic strains of a Ni single crystal subject to nanoindentation and tension measurements. Although more experimental data on pattern center and image contrast are required to properly assess the performance of LRR, our method is a promising technique to improve strain measurements in the presence of large rotations.

An Acquisition Parameter Study for Machine-Learning-Enabled Electron Backscatter Diffraction

Methods within the domain of artificial intelligence are gaining traction for solving a range of materials science objectives, notably the use of deep neural networks for computer vision for the analysis of electron diffraction patterns. An important component of deploying these models is an understanding of the performance as experimental diffraction conditions are varied. This knowledge can inspire confidence in the classifications over a range of operating conditions and identify where performance is degraded. Elucidating the relative impact of each parameter will suggest the most important parameters to vary during the collection of future training data. Knowing which data collection efforts to prioritize is of concern given the time required to collect or simulate vast libraries of diffraction patterns for a wide variety of materials without considering varying any parameters. In this work, five parameters, frame averaging, detector tilt, sample-to-detector distance, accelerating voltage, and pattern resolution, essential to electron diffraction are individually varied during the collection of electron backscatter diffraction patterns to explore the effect on the classifications produced by a deep neural network trained from diffraction patterns captured using a fixed set of parameters. The model is shown to be resilient to nearly all the individual changes examined here.

Efficient few-shot machine learning for classification of EBSD patterns

Deep learning is quickly becoming a standard approach to solving a range of materials science objectives, particularly in the field of computer vision. However, labeled datasets large enough to train neural networks from scratch can be challenging to collect. One approach to accelerating the training of deep learning models such as convolutional neural networks is the transfer of weights from models trained on unrelated image classification problems, commonly referred to as transfer learning. The powerful feature extractors learned previously can potentially be fine-tuned for a new classification problem without hindering performance. Transfer learning can also improve the results of training a model using a small amount of data, known as few-shot learning. Herein, we test the effectiveness of a few-shot transfer learning approach for the classification of electron backscatter diffraction (EBSD) pattern images to six space groups within the [Formula: see text] point group. Training history and performance metrics are compared with a model of the same architecture trained from scratch. In an effort to make this approach more explainable, visualization of filters, activation maps, and Shapley values are utilized to provide insight into the model's operations. The applicability to real-world phase identification and differentiation is demonstrated using dual phase materials that are challenging to analyze with traditional methods.

Identification of Star Defects in Gallium Nitride with HREBSD and ECCI

This paper characterizes novel “star” defects in GaN films grown with metal–organic vapor phase deposition (MOVPE) on GaN substrates with electron channeling contrast imaging (ECCI) and high-resolution electron backscatter diffraction (HREBSD). These defects are hundreds of microns in size and tend to aggregate threading dislocations at their centers. They are the intersection of six nearly ideal low-angle tilt boundaries composed of $\langle a\rangle$-type pyramidal edge dislocations, each on a unique slip system.

Integrated correction of optical distortions for global HR-EBSD techniques

Optical distortions caused by camera lenses affect the accuracy of the elastic strains and lattice rotations measured by high-angular resolution techniques. This article introduces an integrated correction of optical distortions for global HR-EBSD/HR-TKD approaches. The digital image correlation analysis is directly applied to optically distorted patterns, avoiding the pattern pre-processing step conducted so far while preserving the numerical efficiency of the Gauss-Newton algorithm. The correction implementation is first described and its numerical cost is assessed considering a homography-based HR-EBSD approach. The correction principle is validated numerically for various levels of first-order radial distortion over a wide range of disorientation angles (0 to 14°) and elastic strain (0 to 5×10^-2). The errors induced when neglecting such distortions as well as the influence of both the radial distortion coefficient and the pattern centre and optical centre locations are quantified. Even when both reference and target patterns are distorted, the correction appears necessary whatever the disorientation between those patterns. The required accuracy on the true distortion parameters for an effective correction is consequently determined.

Deep Neural Network Enabled Space Group Identification in EBSD

Electron backscatter diffraction (EBSD) is one of the primary tools in materials development and analysis. The technique can perform simultaneous analyses at multiple length scales, providing local sub-micron information mapped globally to centimeter scale. Recently, a series of technological revolutions simultaneously increased diffraction pattern quality and collection rate. After collection, current EBSD pattern indexing techniques (whether Hough-based or dictionary pattern matching based) are capable of reliably differentiating between a "user selected" set of phases, if those phases contain sufficiently different crystal structures. EBSD is currently less well suited for the problem of phase identification where the phases in the sample are unknown. A pattern analysis technique capable of phase identification, utilizing the information-rich diffraction patterns potentially coupled with other data, such as EDS-derived chemistry, would enable EBSD to become a high-throughput technique replacing many slower (X-ray diffraction) or more expensive (neutron diffraction) methods. We utilize a machine learning technique to develop a general methodology for the space group classification of diffraction patterns; this is demonstrated within the $\lpar 4/m\comma \;\bar{3}\comma \;\;2/m\rpar$ point group. We evaluate the machine learning algorithm's performance in real-world situations using materials outside the training set, simultaneously elucidating the role of atomic scattering factors, orientation, and pattern quality on classification accuracy.