Employing Constrained Nonnegative Matrix Factorization for Microstructure Segmentation.

Materials characterization using electron backscatter diffraction (EBSD) requires indexing the orientation of the measured region from Kikuchi patterns. The quality of Kikuchi patterns can degrade due to pattern overlaps arising from two or more orientations, in the presence of defects or grain boundaries. In this work, we employ constrained nonnegative matrix factorization to segment a microstructure with small grain misorientations, (<1∘), and predict the amount of pattern overlap. First, we implement the method on mixed simulated patterns-that replicates a pattern overlap scenario, and demonstrate the resolution limit of pattern mixing or factorization resolution using a weight metric. Subsequently, we segment a single-crystal dendritic microstructure and compare the results with high-resolution EBSD. By utilizing weight metrics across a low-angle grain boundary, we demonstrate how very small misorientations/low-angle grain boundaries can be resolved at a pixel level. Our approach constitutes a versatile and robust tool, complementing other fast indexing methods for microstructure characterization.

Diffraction-Based Multiscale Residual Strain Measurements.

Modern analytical tools, from microfocus X-ray diffraction (XRD) to electron microscopy-based microtexture measurements, offer exciting possibilities of diffraction-based multiscale residual strain measurements. The different techniques differ in scale and resolution, but may also yield significantly different strain values. This study, for example, clearly established that high-resolution electron backscattered diffraction (HR-EBSD) and high-resolution transmission Kikuchi diffraction (HR-TKD) [sensitive to changes in interplanar angle (Δθθ)], provide quantitatively higher residual strains than micro-Laue XRD and transmission electron microscope (TEM) based precession electron diffraction (PED) [sensitive to changes in interplanar spacing (Δdd)]. Even after correcting key known factors affecting the accuracy of HR-EBSD strain measurements, a scaling factor of ∼1.57 (between HR-EBSD and micro-Laue) emerged. We have then conducted "virtual" experiments by systematically deforming an ideal lattice by either changing an interplanar angle (α) or a lattice parameter (a). The patterns were kinematically and dynamically simulated, and corresponding strains were measured by HR-EBSD. These strains showed consistently higher values for lattice(s) distorted by α, than those altered by a. The differences in strain measurements were further emphasized by mapping identical location with HR-TKD and TEM-PED. These measurements exhibited different spatial resolution, but when scaled (with ∼1.57) provided similar lattice distortions numerically.

Imaging and Segmenting Grains and Subgrains Using Backscattered Electron Techniques.

We present two new methods of processing data from backscattered electron signals in a scanning electron microscope to image grains and subgrains. The first combines data from multiple backscattered electron images acquired at different specimen geometries to (1) better reveal grain boundaries in recrystallized microstructures and (2) distinguish between recrystallized and unrecrystallized regions in partially recrystallized microstructures. The second utilizes spherical harmonic transform indexing of electron backscatter diffraction patterns to produce high angular resolution orientation data that enable the characterization of subgrains. Subgrains are produced during high-temperature plastic deformation and have boundary misorientation angles ranging from a few degrees down to a few hundredths of a degree. We also present an algorithm to automatically segment grains from combined backscattered electron image data or grains and subgrains from high angular resolution electron backscatter diffraction data. Together, these new techniques enable rapid measurements of individual grains and subgrains from large populations.

Selected Area Electron Beam Induced Deposition of Pt and W for EBSD Backgrounds.

Applying high-resolution electron backscatter diffraction (HR-EBSD) to materials without regions that are amenable to the acquisition of backgrounds for static flat fielding (background subtraction) can cause analysis problems. To address this difficulty, the efficacy of electron beam induced deposition (EBID) of material as a source for an amorphous background signal is assessed and found to be practical. Using EBID material for EBSD backgrounds allows single crystal and large-grained samples to be analyzed using HR-EBSD for strain and small angle rotation measurement.

Influence of Noise-Generating Factors on Cross-Correlation Electron Backscatter Diffraction (EBSD) Measurement of Geometrically Necessary Dislocations (GNDs).

Studies of dislocation density evolution are fundamental to improved understanding in various areas of deformation mechanics. Recent advances in cross-correlation techniques, applied to electron backscatter diffraction (EBSD) data have particularly shed light on geometrically necessary dislocation (GND) behavior. However, the framework is relatively computationally expensive-patterns are typically saved from the EBSD scan and analyzed offline. A better understanding of the impact of EBSD pattern degradation, such as binning, compression, and various forms of noise, is vital to enable optimization of rapid and low-cost GND analysis. This paper tackles the problem by setting up a set of simulated patterns that mimic real patterns corresponding to a known GND field. The patterns are subsequently degraded in terms of resolution and noise, and the GND densities calculated from the degraded patterns using cross-correlation ESBD are compared with the known values. Some confirmation of validity of the computational degradation of patterns by considering real pattern degradation is also undertaken. The results demonstrate that the EBSD technique is not particularly sensitive to lower levels of binning and image compression, but the precision is sensitive to Poisson-type noise. Some insight is also gained concerning effects of mixed patterns at a grain boundary on measured GND content.

Performance of Dynamically Simulated Reference Patterns for Cross-Correlation Electron Backscatter Diffraction.

High-resolution (or "cross-correlation") electron backscatter diffraction analysis (HR-EBSD) utilizes cross-correlation techniques to determine relative orientation and distortion of an experimental electron backscatter diffraction pattern with respect to a reference pattern. The integrity of absolute strain and tetragonality measurements of a standard Si/SiGe material have previously been analyzed using reference patterns produced by kinematical simulation. Although the results were promising, the noise levels were significantly higher for kinematically produced patterns, compared with real patterns taken from the Si region of the sample. This paper applies HR-EBSD techniques to analyze lattice distortion in an Si/SiGe sample, using recently developed dynamically simulated patterns. The results are compared with those from experimental and kinematically simulated patterns. Dynamical patterns provide significantly more precision than kinematical patterns. Dynamical patterns also provide better estimates of tetragonality at low levels of distortion relative to the reference pattern; kinematical patterns can perform better at large values of relative tetragonality due to the ability to rapidly generate patterns relating to a distorted lattice. A library of dynamically generated patterns with different lattice parameters might be used to achieve a similar advantage. The convergence of the cross-correlation approach is also assessed for the different reference pattern types.

Analysis of traction-free assumption in high-resolution EBSD measurements.

The effects of using a traction-free (plane-stress) assumption to obtain the full distortion tensor from high-resolution EBSD measurements are analyzed. Equations are derived which bound the traction-free error arising from angular misorientation of the sample surface; the error in recovered distortion is shown to be quadratic with respect to that misorientation, and the maximum 'safe' angular misorientation is shown to be 2.7 degrees. The effects of localized stress fields on the traction-free assumption are then examined by a numerical case study, which uses the Boussinesq formalism to model stress fields near a free surface. Except in cases where localized stress field sources occur very close to sample points, the traction-free assumption appears to be admirably robust.

A Study of the Internal Deformation Fields and the Related Microstructure Evolution during Thermal Fatigue Tests of a Single-Crystal Ni-Base Superalloy.

Ni-base superalloys operate in harsh service conditions where cyclic heating and cooling introduce deformation fields that need to be investigated in detail. We used the high-angular-resolution electron backscatter diffraction method to study the evolution of internal stress fields and dislocation density distributions in carbides, dendrites, and notch tips. The results indicate that the stress concentrations decay exponentially away from the notch, and this pattern of distribution was modified by the growth of cracks and the emission of dislocations from the crack tip. Crack initiation follows crystallographic traces and is weakly correlated with carbides and dendrites. Thermal cycles introduce local plasticity around carbides, the dendrite boundary, and cracks. The dislocations lead to higher local stored energy than the critical value that is often cited to induce recrystallization. No large-scale onset of recrystallization was detected, possibly due to the mild temperature (800 °C); however, numerous recrystallized grains were detected in carbides after 50 and 80 cycles. The results call for a detailed investigation of the microstructure-related, thermally assisted recrystallization phenomenon and may assist in the microstructure control and cooling channel design of turbine blades.

Mechanism of Fatigue-Life Extension Due to Dynamic Strain Aging in Low-Carbon Steel at High Temperature.

An enhancement in fatigue life for ferrite-pearlite low-carbon steel (LCS) at high temperature (HT) has been discovered, where it increased from 190,873 cycles at room temperature (RT) to 10,000,000 cycles at 400 °C under the same stress conditions. To understand the mechanism behind this phenomenon, the evolution of microstructure and dislocation density during fatigue tests was comprehensively investigated. High-power X-ray diffraction (XRD) was employed to analyze the evolution of total dislocation density, while Electron Backscatter Diffraction (EBSD) and High-Resolution EBSD (HR-EBSD) were conducted to reveal the evolutions of kernel average misorientation (KAM), geometrically necessary dislocations (GND) and elastic strains. Results indicate that the enhancement was attributed to the dynamic strain aging (DSA) effect above the upper temperature limit, where serration and jerky flow disappeared but hindrance of dislocations persisted. Due to the DSA effect, periods of increase and decrease in the total dislocations were observed during HT fatigue tests, and the fraction of screw dislocations increased continuously, caused by viscous movement of the screw dislocations. Furthermore, the increased fraction of screw dislocations resulted in a lower energy configuration, reducing slip traces on sample surfaces and preventing fatigue-crack initiation.

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.

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.

A Denoising Autoencoder for Improved Kikuchi Pattern Quality and Indexing in Electron Backscatter Diffraction.

The rapid collection and indexing of electron diffraction patterns as produced via electron backscatter diffraction (EBSD) has enabled crystallographic orientation and structural determination, as well as additional property-determining strain and dislocation density information with increasing speed, resolution, and efficiency. Pattern indexing quality is reliant on the noise of the collected electron diffraction patterns, which is often convoluted by sample preparation and data collection parameters. EBSD acquisition is sensitive to many factors and thus can result in low confidence index (CI), poor image quality (IQ), and improper minimization of fit, which can result in noisy datasets and misrepresent the microstructure. In an attempt to enable both higher speed EBSD data collection and enable greater orientation fit accuracy with noisy datasets, an image denoising autoencoder was implemented to improve pattern quality. We show that EBSD data processed through the autoencoder results in a higher CI, IQ, and a more accurate degree of fit. In addition, using denoised datasets in HR-EBSD cross correlative strain analysis can result in reduced phantom strain from erroneous calculations due to the increased indexing accuracy and improved correspondence between collected and simulated patterns.

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.

Effect of sample thinning on strains and lattice rotations measured from Transmission Kikuchi diffraction in the SEM.

Cross correlation based high angular resolution EBSD (or HR-EBSD) has been developed for measurement of elastic strains, lattice rotations (and estimating GND density). Recent advances in Transmission Kikuchi diffraction (TKD), especially the on-axis geometry allows the possibility of acquiring patterns at higher spatial resolution. However, some controversy remains as to whether stresses/strains measured after the sample thinning process are still representative of the bulk sample. In this paper, we explore a way of applying the HR-EBSD method to study strains and lattice rotations in an initially bulk sample, that is then progressively thinned down until a similar analysis can be performed on thin (and electron transparent) samples. Thus, HR-TKD will be compared as a possible alternative to HR-EBSD, in scenarios when it is not always possible to perform EBSD on the surface of the sample. An estimate of strain relaxation in the sample as a result of sample thinning is presented.

EBSD pattern simulations for an interaction volume containing lattice defects.

A quantitative understanding of the effect of the spatial distribution and density of lattice defects on the electron backscatter diffraction patterns requires careful consideration of the electron-matter interaction volume and the traction free boundary condition on the deformation field for near-surface defects. In this work, we couple a depth-specific dynamical electron scattering simulation with an approximate crystal deformation model to generate a single diffraction pattern from an interaction volume containing lattice defects. Two case studies are considered, namely a single edge dislocation and a low angle grain boundary. Their displacement fields, derived from the three-dimensional Yoffe-Shaibani-Hazzeldine's dislocation field model, are fed into the simulation and the resulting diffraction patterns are cross-validated using the HR-EBSD technique. In addition, diffraction contrast associated with defect deformation field is investigated with the virtual beam technique. Pattern diffuseness is quantitatively analyzed in the frequency domain as a function of dislocation density.

Novel remapping approach for HR-EBSD based on demons registration.

In this study, the possibility of utilizing a computer vision algorithm, i.e., demons registration, to accurately remap electron backscatter diffraction patterns for high resolution electron backscatter diffraction (HR-EBSD) applications is presented. First, the angular resolution of demons registration is demonstrated to be lower than the conventional cross-correlation based method, particularly at misorientation angles >0.157 rad. In addition, GPU acceleration has been applied to significantly boost the speed of iterative registration between a pair of patterns with 0.175 rad misorientation to under 1 s. Second, demons registration is implemented as a first-pass remapping, followed by a second pass cross-correlation method, which results in angular resolution of ~0.5 × 10-4 rad, a phantom stress value of ~35 MPa and phantom strain of ~2 × 10-4, on dynamically simulated patterns, without the need of implementing robust fitting or iterative remapping. Lastly, the new remapping method is applied to a large experimental dataset collected from an as-built additively-manufactured Inconel 625 cube, which shows significant residual stresses built-up near the large columnar grain region and regularly arranged GND structures.

Pattern matching analysis of electron backscatter diffraction patterns for pattern centre, crystal orientation and absolute elastic strain determination - accuracy and precision assessment.

Pattern matching between target electron backscatter patterns (EBSPs) and dynamically simulated EBSPs was used to determine the pattern centre (PC) and crystal orientation, using a global optimisation algorithm. Systematic analysis of error and precision with this approach was carried out using dynamically simulated target EBSPs with known PC positions and orientations. Results showed that the error in determining the PC and orientation was <10-5 of pattern width and <0.01° respectively for the undistorted full resolution images (956 × 956 pixels). The introduction of noise, optical distortion and image binning was shown to have some influence on the error although better angular resolution was achieved with the pattern matching than using conventional Hough transform-based analysis. The accuracy of PC determination for the experimental case was explored using the High Resolution (HR-) EBSD method but using dynamically simulated EBSP as the reference pattern. This was demonstrated through a sample rotation experiment and strain analysis around an indent in interstitial free steel.

Assessing the influence of crystallographic orientation, stress and local deformation on magnetic domains using electron backscatter diffraction and forescatter electron imaging.

The magnetic properties of non-oriented electrical steel (NOES) used in an electrical engine play an important role in the transformation process from electric to mechanic energy. In this process the NOES is subjected to cyclic loading and strong tensile forces. Until now the dependence of the magnetic properties with respect to a through stress changing microstructure is not fully understood. In this paper a setup for a quasi-static in situ deformation experiment with a SEM is presented in which the surface magnetic domains of a NOES were captured by revealing type 2 magnetic contrast with forescatter diodes, the crystallographic texture was mapped through EBSD and the local relative strains and rotations were calculated with CrossCourt. The magnetic domains were related to the angles between the easy axes and the surface as well as the angle differences between the easy axes of neighboring grains. For small differences wide boundary-crossing domain patterns occurred. In contrast, for high ones predominantly compensating domains emerged. Thus a distinct influence of neighboring grains was present. Reaching a certain stress level, a strong tendency of domain alignment along the easy axes closest to the stress direction could be observed. Locally exceeding the elastic limit, slip lines appeared but had no visible influence on the domains. After unloading, in those areas a clear hindrance of domain alignment was apparent, which was attributed to the dislocation accumulations. CrossCourt enables the estimation of GND accumulations, which can be used to detect domain wall pinning. In conclusion, the presented method provides a way to link the magnetic properties of NOES to the texture and a through stress changing microstructure.

Comparison of dislocation characterization by electron channeling contrast imaging and cross-correlation electron backscattered diffraction.

In this work, the relative capabilities and limitations of electron channeling contrast imaging (ECCI) and cross-correlation electron backscattered diffraction (CC-EBSD) have been assessed by studying the dislocation distributions resulting from nanoindentation in body centered cubic Ta. Qualitative comparison reveals very similar dislocation distributions between the CC-EBSD mapped GNDs and the ECC imaged dislocations. Approximate dislocation densities determined from ECC images compare well to those determined by CC-EBSD. Nevertheless, close examination reveals subtle differences in the details of the distributions mapped by these two approaches. The details of the dislocation Burgers vectors and line directions determined by ECCI have been compared to those determined using CC-EBSD and reveal good agreement.

A consistent full-field integrated DIC framework for HR-EBSD.

A general, transparent, finite-strain Integrated Digital Image Correlation (IDIC) framework for high angular resolution EBSD (HR-EBSD) is proposed, and implemented through a rigorous derivation of the optimization scheme starting from the fundamental brightness conservation equation in combination with a clear geometric model of the Electron BackScatter Pattern (EBSP) formation. This results in a direct one-step correlation of the full field-of-view of EBSPs, which is validated here on dynamically simulated patterns. Strain and rotation component errors are, on average, (well) below 10-5 for small (Eeq=0.05%) and medium (Eeq=0.2%) strain, and below 3×10-5 for large strain (Eeq=1%), all for large rotations up to 10° and 2% image noise. High robustness against poor initial guesses (1° misorientation and zero strain) and typical convergence in 5 iterations is consistently observed for, respectively, image noise up to 20% and 5%. This high accuracy and robustness rivals, when comparing validation on dynamically simulated patterns, the most accurate HR-EBSD algorithms currently available which combine sophisticated filtering and remapping strategies with an indirect two-step correlation approach of local subset ROIs. The proposed general IDIC/HR-EBSD framework lays the foundation for future extensions towards more accurate EBSP formation models or even absolute HR-EBSD.