Estimation of elastic strain by integrated image correlation on electron diffraction patterns

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.

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.

Insights into a dual-phase steel microstructure using EBSD and image-processing-based workflow

In this article, an image-analysis-based method is applied to electron backscatter diffraction (EBSD) data in order to recover specific properties in a complex microstructure, and some new dedicated tools are developed and compared with existing methods.

Quantitative metallography to understand the morphology of different crystallographic phases in a material often rests on the segmentation and classification of electron backscatter diffraction (EBSD) maps. Image analysis offers rich toolboxes to perform such tasks based on ‘scalar’ images. Embracing the entire wealth of information provided by crystallography, operations such as erosion, dilation, interpolation, smoothing and segmentation require generalizations to do justice to the very nature of crystal orientations (e.g. preserving properties like frame indifference). The present study gives such extensions based on quaternion representation of crystal orientations. A dual-phase stainless steel specimen is used to illustrate the different steps of such a procedure.

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.

Correlating results from high resolution EBSD with TEM- and ECCI-based dislocation microscopy: Approaching single dislocation sensitivity via noise reduction

High resolution electron backscatter diffraction (HREBSD), an SEM-based diffraction technique, may be used to measure the lattice distortion of a crystalline material and to infer the geometrically necessary dislocation content. Uncertainty in the image correlation process used to compare diffraction patterns leads to an uneven distribution of measurement noise in terms of the lattice distortion, which results in erroneous identification of dislocation type and density. This work presents a method of reducing noise in HREBSD dislocation measurements by removing the effect of the most problematic components of the measured distortion. The method is then validated by comparing with TEM analysis of dislocation pile-ups near a twin boundary in austenitic stainless steel and with ECCI analysis near a nano-indentation on a tantalum oligocrystal. The HREBSD dislocation microscopy technique is able to resolve individual dislocations visible in TEM and ECCI and correctly identify their Burgers vectors.