High-throughput determination of grain size distributions by EBSD with low-discrepancy sampling.

Because microstructure plays an important role in the mechanical properties of structural materials, developing the capability to quantify microstructures rapidly is important to enabling high-throughput screening of structural materials. Electron backscatter diffraction (EBSD) is a common method for studying microstructures and extracting information such as grain size distributions (GSDs), but is not particularly fast and thus could be a bottleneck in high-throughput systems. One approach to accelerating EBSD is to reduce the number of points that must be scanned. In this work, we describe an iterative method for reducing the number of scan points needed to measure GSDs using incremental low-discrepancy sampling, including on-the-fly grain size calculations and a convergence test for the resulting GSD based on the Kolmogorov-Smirnov test. We demonstrate this method on five real EBSD maps collected from magnesium AZ31B specimens and compare the effectiveness of sampling according to two different low discrepancy sequences, the Sobol and R2 sequences, and random sampling. We find that R2 sampling is able to produce GSDs that are statistically very similar to the GSDs of the full density grids using, on average, only 52% of the total scan points. For EBSD maps that contained monodisperse GSDs and over 1000 grains, R2 sampling only required an average of 39% of the total EBSD points.

An alignment algorithm using coherent twin boundaries as internal reference in 3D-EBSD.

A three-dimensional (3D) microstructural volume is reconstructed from a stack of two-dimensional sections which was obtained by serial sectioning coupled with electron back scattering diffraction (EBSD) mapping of a 316L austenitic stainless steel. A new alignment algorithm named linear translation by minimising the indicator (LTMI) is proposed to reduce the translational misalignments between adjacent sections by referencing to coherent twin boundaries which are flat and lying on {111} planes. The angular difference between the measured orientation of a flat twin boundary and that of the {111} plane is used as an indicator of the accuracy of the alignment operations. This indicator is minimised through linear translations of the centroids of triangular facets, which constitute grain boundaries at a distance not restricted by the in-plane step size of the EBSD maps. And hence the systematic trend in the translational misalignments can be effectively reduced. The LTMI alignment procedure proposed herein effectively corrects the misalignments remained by other methods on a 3D-EBSD data prepared using serial sectioning methods. The accuracy in distinguishing between coherent and incoherent twin boundaries is significantly improved.

Simultaneous mapping of cathodoluminescence spectra and backscatter diffraction patterns in a scanning electron microscope.

Electron backscatter diffraction and cathodoluminescence are complementary scanning electron microscopy modes widely used in the characterisation of semiconductor films, respectively revealing the strain state of a crystalline material and the effect of this strain on the light emission from the sample. Conflicting beam, sample and detector geometries have meant it is not generally possible to acquire the two signals together during the same scan. Here, we present a method of achieving this simultaneous acquisition, by collecting the light emission through a transparent sample substrate. We apply this combination of techniques to investigate the strain field and resultant emission wavelength variation in a deep-ultraviolet micro-LED. For such compatible samples, this approach has the benefits of avoiding image alignment issues and minimising beam damage effects.

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.

Patterns of crystal organization and calcite twin formation in planktonic, rotaliid, foraminifera shells and spines.

The foraminiferal order Rotaliida represents one third of the extant genera of foraminifers. The shells of these organisms are extensively used to decipher characteristics of marine ecosystems and global climate events. It was shown that shell calcite of benthic Rotaliida is twinned. We extend our previous work on microstructure and texture characterization of benthic Rotaliida and investigate shell calcite organization for planktonic rotaliid species. Based on results gained from electron backscattered diffraction (EBSD) and field emission electron microscopy (FESEM) imaging of chemically etched/fixed shell surfaces we show for the planktonic species Globigerinoides sacculifer, Pulleniatina obliquiloculata, Orbulina universa (belonging to the two main planktonic, the globigerinid and globorotaliid, clades): very extensive 60°-{001}-twinning of the calcite and describe a new and specific microstructure for the twinned crystals. We address twin and crystal morphology development from nucleation within a biopolymer template (POS) to outermost shell surfaces. We demonstrate that the calcite of the investigated planktonic Rotaliida forms through competitive growth. We complement the structural knowledge gained on the clade 1 and clade 2 species with EBSD results of Globigerinita glutinata and Candeina nitida shells (clade 3 planktonic species). The latter are significantly less twinned and have a different shell calcite microstructure. We demonstrate that the calcite of all rotaliid species is twinned, however, to different degrees. We discuss for the species of the three planktonic clades characteristics of the twinned calcite and of other systematic misorientations. We address the strong functionalization of foraminiferal calcite and indicate how the twinning affects biocalcite material properties.

EBSD patterns simulating multilayer twins based on dynamical theory of electron diffraction.

Electron backscatter diffraction (EBSD) can be employed to determine crystal structures but has not been used alone to identify defects at the atom scale due to the lack of understanding of the EBSD patterns generated by various structure defects. In the present work, the EBSD patterns of FCC-Fe with 9-layer, 6-layer and 3-layer twin structures are simulated, respectively, using the revised real space (RRS) method and compared with the counterpart of perfect crystals. Our results show that when the electron beam is incident along a direction parallel to the twin plane, the pattern appears symmetrical with respect to the corresponding Kikuchi band of the twin plane, and the diffraction details within the Kikuchi band also exhibit symmetry with respect to the middle line of the Kikuchi band. Moreover, the overall clarity of the patterns decreases, and the pattern becomes more blurred with increasing the distance from the Kikuchi band corresponding to the twin plane. By contrast, the incident electron beam along the direction perpendicular to the twin plane results in diffraction superposition of the matrix region and the shear region, which shows twofold rotational symmetry with respect to the Kikuchi pole corresponding to the normal to the twin plane. In addition, some extra Kikuchi bands appear in the EBSD patterns due to the long-period structures of the multilayer twins. As the number of multilayer twins decreases, the number of extra Kikuchi bands decreases and the area of the blurring pattern increases. The correlation between twin structures and EBSD patterns provides theoretical insights for identifying twin structures by the EBSD technique.

Imaging Threading Dislocations and Surface Steps in Nitride Thin Films Using Electron Backscatter Diffraction.

Extended defects, like threading dislocations, are detrimental to the performance of optoelectronic devices. In the scanning electron microscope, dislocations are traditionally imaged using diodes to monitor changes in backscattered electron intensity as the electron beam is scanned over the sample, with the sample positioned so the electron beam is at, or close to the Bragg angle for a crystal plane/planes. Here, we use a pixelated detector instead of single diodes, specifically an electron backscatter diffraction (EBSD) detector. We present postprocessing techniques to extract images of dislocations and surface steps, for a nitride thin film, from measurements of backscattered electron intensities and intensity distributions in unprocessed EBSD patterns. In virtual diode (VD) imaging, the backscattered electron intensity is monitored for a selected segment of the unprocessed EBSD patterns. In center of mass (COM) imaging, the position of the center of the backscattered electron intensity distribution is monitored. Additionally, both methods can be combined (VDCOM). Using both VD and VDCOM, images of only threading dislocations, or dislocations and surface steps can be produced, with VDCOM images exhibiting better signal-to-noise. The applicability of VDCOM imaging is demonstrated across a range of nitride semiconductor thin films, with varying surface step and dislocation densities.

Character and Distribution of Geometrically Necessary Dislocations in Polycrystalline Tantalum.

Geometrically necessary dislocations (GNDs) play a key role in accommodating strain incompatibility between neighboring grains in polycrystalline materials. One critical step toward accurately capturing GNDs in deformation models involves studying the microstructural features that promote GND accumulation and the resulting character of GND fields. This study utilizes high-resolution electron backscatter diffraction to map GND populations in a large polycrystalline sample of pure tantalum, under simple tension. A total of 1,989 grains, 3,518 grain boundaries (GBs), and 3,207 triple junctions (TJs) were examined in a subsurface region of the sample. Correlations between GND density and GB character, and to some extent, TJ character, are investigated. Statistical geometrical relationships between these entities are quantified, and also visualized, using a novel application of two-point statistics. The nature of GNDs across the sample is also visualized and assessed using a recently developed method of mapping the local net Burgers vectors. The different approaches to characterizing GND distribution are compared in terms of how they quantify the size of near boundary gradient zones.

Statistical Comparison of Substructures in Pure Aluminum Before and After Creep Deformation, Based on EBSD Image Data.

Electron backscatter diffraction (EBSD) images of extruded pure aluminum were statistically analyzed to investigate creep-induced subgrain structures after applying two different levels of creep stress, corresponding to the power law (PL) and power-law breakdown (PLB) regimes. Kernel average misorientation analysis of EBSD measurements revealed 2D morphologies, which were subdivided by a multi-step segmentation procedure into subgranular arrangements. Various descriptors were employed to characterize the "subgrains" quantitatively, including their size, shape, spatial arrangement, and crystallographic orientation. In particular, the analysis of the orientations of subgrains was conducted by neglecting rotations around the loading axis. This approach facilitated the individual investigation of the {001} and {111} subgrain families with respect to the loading axis for two investigated stress levels plus a reference specimen. For the PL regime, the statistical analysis of subgrain descriptors computed from segmented image data revealed a similar degree of strain accumulation for {111} and {001} subgrains. In contrast, for the PLB regime, the analyzed descriptors indicate that {111} subgrains tend to accumulate significantly more strain than {001} ones. These observations suggest that the mechanisms leading to PLB may be associated with strain localization dependent on intergranular stress, hindering the recovery process within {111} grains.

Comparison of Laboratory Diffraction Contrast Tomography and Electron Backscatter Diffraction Results: Application to Naturally Occurring Chromites.

Understanding how minerals are spatially distributed within natural materials and their textures is indispensable to understanding the fundamental processes of how these materials form and how they will behave from a mining engineering perspective. In the past few years, laboratory diffraction contrast tomography (LabDCT) has emerged as a nondestructive technique for 3D mapping of crystallographic orientations in polycrystalline samples. In this study, we demonstrate the application of LabDCT on both chromite sand and a complex chromitite sample from the Merensky Reef (Bushveld Complex, South Africa). Both samples were scanned using LabDCT and Electron Backscatter Diffraction (EBSD), and the obtained results were rigorously evaluated using a comprehensive set of qualitative and quantitative characterization techniques. The quality of LabDCT results was accessed by using the "completeness" value, while the inaccuracies were thoroughly discussed, along with proposed potential solutions. The results indicate that the grain orientations obtained from LabDCT are comparable to that of 2D EBSD but have the advantage of collecting true 3D size, shape, and textural information. This study highlights the significant contribution of LabDCT in the understanding of complex rock materials from an earth science perspective, particularly in characterizing mineral texture and crystallography in 3D.

Hydrogen Embrittlement of CrCoNi Medium-Entropy Alloy with Millimeter-Scale Grain Size: An In Situ Hydrogen Charging Study.

In this study, we examined the effect of charging current density on the hydrogen embrittlement (HE) of MEA and the associated HE mechanisms using electron backscattered diffraction (EBSD). Results show that MEA is susceptible to HE, but is stronger than as-rolled and 3D-printed Cantor alloy and stainless steel. The HE susceptibility of MEA decreases with increasing current density. Ductile fracture with transgranular dimples switches to intergranular brittle fracture with clear slip bands in the interior of grains. EBSD results uncovered that hydrogen facilitates localized slips and deformation twins. Hydrogen-enhanced localized plasticity and hydrogen decohesion are the possible HE mechanisms.

Implementing and evaluating far-field 3D X-ray diffraction at the I12 JEEP beamline, Diamond Light Source.

Three-dimensional X-ray diffraction (3DXRD) is shown to be feasible at the I12 Joint Engineering, Environmental and Processing (JEEP) beamline of Diamond Light Source. As a demonstration, a microstructually simple low-carbon ferritic steel was studied in a highly textured and annealed state. A processing pipeline suited to this beamline was created, using software already established in the 3DXRD user community, enabling grain centre-of-mass positions, orientations and strain tensor elements to be determined. Orientations, with texture measurements independently validated from electron backscatter diffraction (EBSD) data, possessed a ∼0.1° uncertainty, comparable with other 3DXRD instruments. The spatial resolution was limited by the far-field detector pixel size; the average of the grain centre of mass position errors was determined as ±âˆ¼80 µm. An average per-grain error of ∼1 × 10-3 for the elastic strains was also measured; this could be reduced in future experiments by improving sample preparation, geometry calibration, data collection and analysis techniques. Application of 3DXRD onto I12 shows great potential, where its implementation is highly desirable due to the flexible, open architecture of the beamline. User-owned or designed sample environments can be used, thus 3DXRD could be applied to previously unexplored scientific areas.

Conditions near a crack tip: Advanced experiments for dislocation analysis and local strain measurement.

The local stress state and microstructure near the crack-tip singularity control the fracture process. In ductile materials multiple toughening mechanisms are at play that dynamically influence stress and microstructure at the crack tip. In metals, crack-tip shielding is typically associated with the emission of dislocations. Therefore, to understand crack propagation on the most fundamental level, in situ techniques are required that are capable to combine imaging and stress mapping at high resolution. Recent experimental advances in x-ray diffraction, scanning electron microscopy, and transmission electron microscopy enable quantifying deformation stress fields from the bulk level down to the individual dislocation. Furthermore, through modern detector technology the temporal resolution has sufficiently improved to enable stress mapping during in situ experiments.

Implications of gnomonic distortion on electron backscatter diffraction and transmission Kikuchi diffraction.

The effect of gnomonic distortion on orientation indexing of electron backscatter diffraction patterns is explored through simulation of electron diffraction patterns for sample-to-detector geometries associated with transmission Kikuchi diffraction (TKD) and electron backscatter diffraction (EBSD). Simulated data were analysed by computing a similarity index for both Hough transformed data and simulated patterns to determine the sensitivity of each method for detecting subtle differences in the effect of gnomonic distortions on electron diffraction patterns. These results indicate that the increased gnomonic distortions in electron diffraction patterns for a TKD geometry enhance the sensitivity for detecting subtle differences in interband angles. Additionally, the utilisation of a Hough transform-based indexing approach further enhances the sensitivity.

Microstructural evolution during short heat treatment of constrained groove pressed Cu-5%Zn alloy.

Severe plastic deformation (SPD) is a widely used technique to obtain superior material properties specially mechanical properties. Constrained groove pressing (CGP) is found to be the most attractive SPD technique for the deformation of sheets and plates. However, this technique results in microstructural inhomogeneity during processing. The microstructural inhomogeneity can be alleviated by employing a thermal cycle, which assists in controlled recovery and recrystallisation. The current work focuses on, the microstructure evolution of one pass as-deform CGP sample followed by a short heat-treated (SHT). A correlative imaging technique of transmission Kikuchi diffraction (TKD) and transmission electron microscopy (TEM) showed the presence of dislocation cell structure in an as-deformed condition. The short heat treatment resulted in the transformation of the dislocation cell wall to high-angle boundaries, with a further increase in heat-treatment time resulting in grain growth.

Ultrafine-Grained Microstructures of Al-Cu Alloys with Hypoeutectic and Hypereutectic Composition Produced by Extrusion Combined with Reversible Torsion.

In this study, binary as-cast Al­Cu alloys: Al25Cu (Al­25%Cu) and Al45Cu (Al­45%Cu) (in wt%) were severely plastically deformed by extrusion combined with a reversible torsion (KoBo) method to produce an ultrafine-grained structure (UFG). The binary Al­Cu alloys consist of α-Al and intermetallic Al2Cu phases. The morphology and volume fraction of α-Al and Al2Cu phases depend on the Cu content. The KoBo process was carried out using extrusion ratios of λ = 30 and λ = 98. The effect of phase refinement has been studied by means of scanning electron microscopy with electron backscattering diffraction and scanning transmission electron microscopy. The mechanical properties were assessed using compression tests. Detailed microstructural analysis shows that after the KoBo process, a large number fraction of high-angle boundaries (HABs) and a very fine grain structure (~2­4 µm) in both phases are created. An increase of λ ratio during the KoBo processing leads to a decrease in average grain size of α-Al and Al2Cu phases and an increase in fraction of HABs. UFG microstructure and high fraction of HABs provide the grain boundary sliding mechanism during KoBo deformation. UFG microstructure contributes to the enhanced mechanical properties. Compressive strength (Rc) of Al25Cu alloy increases from 172 to 340 MPa with an increase of λ. Compressive strain (Sc) for Al25Cu alloy increased from 35 to 67% with an increase of λ. High fraction of intermetallic phase in Al45Cu alloy was responsible for room temperature strengthening of alloy and low compressive strain. The deformed Al45Cu alloy with λ = 30 showed that Rc is 194 MPa and Sc is equal to 10%.

Cluster Analysis of Combined EDS and EBSD Data to Solve Ambiguous Phase Identifications.

A common problem in analytical scanning electron microscopy (SEM) using electron backscatter diffraction (EBSD) is the differentiation of phases with distinct chemistry but the same or very similar crystal structure. X-ray energy dispersive spectroscopy (EDS) is useful to help differentiate these phases of similar crystal structures but different elemental makeups. However, open, automated, and unbiased methods of differentiating phases of similar EBSD responses based on their EDS response are lacking. This paper describes a simple data analytics-based method, using a combination of singular value decomposition and cluster analysis, to merge simultaneously acquired EDS + EBSD information and automatically determine phases from both their crystal and elemental data. I use hexagonal TiB2 ceramic contaminated with multiple crystallographically ambiguous but chemically distinct cubic phases to illustrate the method. Code, in the form of a Python 3 Jupyter Notebook, and the necessary data to replicate the analysis are provided as Supplementary material.

A Pattern Processing Method to Map Nanoscale Phases by EBSD.

The crystallographic analysis of nanoscale phases with dimensions well below the spatial probing volume of electron backscatter diffraction (EBSD) traditionally rely on electron microscopy in transmission (either in SEM or TEM), because EBSD patterns are invariably dominated by the matrix phase contribution and present seemingly no trace from such nanoscale phases. Yet, this study shows that such nanoscale features generate a very faint but valuable secondary diffraction signal which can be retrieved. A diffraction pattern postprocessing method is presented which focuses on the detection of such secondary signal emitted by nanoscale minority phases in overlapped patterns dominated by a dominant matrix signal. The predominant, majority phase contribution in EBSD patterns is removed by a close-neighbor pattern subtraction routine, after which both the conventional Hough indexing method as well as pattern matching methods can be used to reveal the crystallography, spatial distribution, morphology, and orientation of nanoscale minority phases initially absent from EBSD maps. Nanolamellar pearlitic steel, which has long been out of reach for EBSD, has been chosen as an application example.