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Slow‐cooled CF8M duplex stainless steel is used for critical parts of the primary coolant pipes of nuclear reactors. This steel can endure severe service conditions, but it tends to become more brittle upon very long‐term aging (tens of years). Therefore, it is essential to understand its specific microstructure and temporal evolution. As revealed by electron backscatter diffraction (EBSD) analyses, the microstructure consists of millimetre‐scale ferritic grains within which austenite lath packets have grown with preferred crystallographic orientations concerning the parent ferritic phase far from the ferrite grain boundaries. In these lath packets where the austenite phase is nucleated, the lath morphology and crystal orientation accommodate the two ferrite orientations. Globally, the Pitsch orientation relationship appears to display the best agreement with the experimental data compared with other classical relationships. The austenite lath packets are parallel plate‐shaped laths, characterized by their normal n. A novel methodology is introduced to elucidate the expected relationship between n and the crystallographic orientation given the coarse interfaces, even though n is only partly known from the observation surface, in contrast to the 3D crystal orientations measured by EBSD. The distribution of retrieved normals n is shown to be concentrated over a set of discrete orientations. Assuming that the ferrite and austenite obey the Pitsch orientation relationship, the determined lath normals are close to an invariant direction of the parent phase given by the same orientation relationship. [ABSTRACT FROM AUTHOR]

Bragg edge imaging using pulsed neutrons is a non-destructive technique for studying microstructure and texture of materials. It provides two-dimensional visualization of crystallographic information using a pixelated gas electron multiplier detector and a time-of-flight method. In this work, the properties of type 304 austenitic stainless steel samples were studied via Bragg edge imaging. The samples included hot-rolled, cold-rolled and heat-treated specimens, which were characterized to investigate texture, phase fraction and grain growth. The results showed that the crystallite size increased with increasing annealing temperature. The cold-rolled and annealed samples exhibited strong textures, while the hot-rolled sample showed no preferred orientation. The phase volume fraction of induced martensite in the cold-rolled sample was also obtained. Twodimensional maps of microstructures and textures were obtained without destructive processes. The results were validated by electron backscatter diffraction and found to be consistent. This work provides valuable information for non-destructive characterization of bulk materials by performing Bragg edge imaging using the Hokkaido University compact accelerator neutron source. [ABSTRACT FROM AUTHOR]

Microtexture heterogeneities are commonly found in titanium forgings because of the thermomechanical processing. Also known as macrozones, these regions can reach millimetres in length, with grains sharing a similar crystallographic orientation leading to less resistance to crack propagation. Since the link between macrozones and the reduction of cold‐dwell‐fatigue performance on rotative components in gas turbine engines was established, efforts have been put into macrozone definition and characterization. The electron backscatter diffraction (EBSD) technique, widely used for texture analysis, allows for a qualitative macrozone characterization; however, further processing is required to define the boundaries and disorientation spread of each macrozone. Current approaches often use c‐axis misorientation criteria, but this can sometimes lead to a large disorientation spread within a macrozone. This article describes the development and application of a computational tool implemented in MATLAB for automatic macrozone identification from EBSD data sets on the basis of a more conservative approach where both the c‐axis tilting and rotation are considered. The tool allows for detection of macrozones according to the disorientation angle and density‐fraction criteria. The clustering efficiency is validated by pole‐figure plots, and the effects of the key parameters defining the macrozone clustering (disorientation and fraction) are discussed. In addition, this tool was successfully applied to both fully equiaxed and bimodal microstructures of titanium forgings. [ABSTRACT FROM AUTHOR]

A pseudosymmetric description of the crystal lattice derived from a single wide‐angle Kikuchi pattern can have several causes. The small size (<15%) of the sector covered by an electron backscatter diffraction pattern, the limited precision of the projection centre position and the Kikuchi band definition are crucial. Inherent pseudosymmetries of the crystal lattice and/or structure also pose a challenge in the analysis of Kikuchi patterns. To eliminate experimental errors as much as possible, simulated Kikuchi patterns of 350 phases have been analysed using the software CALM [Nolze et al. (2021). J. Appl. Cryst.54, 1012–1022] in order to estimate the frequency of and reasons for pseudosymmetric crystal lattice descriptions. Misinterpretations occur in particular when the atomic scattering factors of non‐equivalent positions are too similar and reciprocal‐lattice points are systematically missing. As an example, a pseudosymmetry prediction depending on the elements involved is discussed for binary AB compounds with B1 and B2 structure types. However, since this is impossible for more complicated phases, this approach cannot be directly applied to compounds of arbitrary composition and structure. [ABSTRACT FROM AUTHOR]

A band width determination using the first derivative of the band profile systematically underestimates the true Bragg angle. Corrections are proposed to compensate for the resulting offset Δa/a of the mean lattice parameters derived from as many Kikuchi band widths as possible. For dynamically simulated Kikuchi patterns, Δa/a can reach up to 8% for phases with a high mean atomic number Z, whereas for much more common low‐Z materials the offset decreases linearly. A predicted offset Δa/a = f(Z) is therefore proposed, which also includes the unit‐cell volume and thus takes into account the packing density of the scatterers in the material. Since Z is not always available for unknown phases, its substitution by Zmax, i.e. the atomic number of the heaviest element in the compound, is still acceptable for an approximate correction. For simulated Kikuchi patterns the offset‐corrected lattice parameter deviation is Δa/a < 1.5%. The lattice parameter ratios, and the angles α, β and γ between the basis vectors, are not affected at all. [ABSTRACT FROM AUTHOR]

The derivation of a crystal structure and its phase‐specific parameters from a single wide‐angle backscattered Kikuchi diffraction pattern requires reliable extraction of the Bragg angles. By means of the first derivative of the lattice profile, an attempt is made to determine fully automatically and reproducibly the band widths in simulated Kikuchi patterns. Even under such ideal conditions (projection centre, wavelength and lattice plane traces are perfectly known), this leads to a lattice parameter distribution whose mean shows a linear offset that correlates with the mean atomic number Z of the pattern‐forming phase. The consideration of as many Kikuchi bands as possible reduces the errors that typically occur if only a single band is analysed. On the other hand, the width of the resulting distribution is such that higher image resolution of diffraction patterns, employing longer wavelengths to produce wider bands or the use of higher interference orders is less advantageous than commonly assumed. [ABSTRACT FROM AUTHOR]

Bragg coherent X‐ray diffraction imaging (BCDI) allows the 3D measurement of lattice strain along the scattering vector for specific microcrystals. If at least three linearly independent reflections are measured, the 3D variation of the full lattice strain tensor within the microcrystal can be recovered. However, this requires knowledge of the crystal orientation, which is typically attained via estimates based on crystal geometry or synchrotron microbeam Laue diffraction measurements. Presented here is an alternative method to determine the crystal orientation for BCDI measurements using electron backscatter diffraction (EBSD) to align Fe–Ni and Co–Fe alloy microcrystals on three different substrates. The orientation matrix is calculated from EBSD Euler angles and compared with the orientation determined using microbeam Laue diffraction. The average angular mismatch between the orientation matrices is less than ∼6°, which is reasonable for the search for Bragg reflections. The use of an orientation matrix derived from EBSD is demonstrated to align and measure five reflections for a single Fe–Ni microcrystal via multi‐reflection BCDI. Using this data set, a refined strain field computation based on the gradient of the complex exponential of the phase is developed. This approach is shown to increase accuracy, especially in the presence of dislocations. The results demonstrate the feasibility of using EBSD to pre‐align BCDI samples and the application of more efficient approaches to determine the full lattice strain tensor with greater accuracy. [ABSTRACT FROM AUTHOR]

Materials with an allotropic phase transformation can form microstructures where grains have orientation relationships determined by the transformation history. These microstructures influence the final material properties. In zirconium alloys, there is a solid‐state body‐centred cubic (b.c.c.) to hexagonal close‐packed (h.c.p.) phase transformation, where the crystal orientations of the h.c.p. phase can be related to the parent b.c.c. structure via the Burgers orientation relationship (BOR). In the present work, a reconstruction code, developed for steels and which uses a Markov chain clustering algorithm to analyse electron backscatter diffraction maps, is adapted and applied to the h.c.p./b.c.c. BOR. This algorithm is released as open‐source code (via github, as ParentBOR). The algorithm enables new post‐processing of the original and reconstructed data sets to analyse the variants of the h.c.p. α phase that are present and understand shared crystal planes and shared lattice directions within each parent β grain; it is anticipated that this will assist in understanding the transformation‐related deformation properties of the final microstructure. Finally, the ParentBOR code is compared with recently released reconstruction codes implemented in MTEX to reveal differences and similarities in how the microstructure is described. [ABSTRACT FROM AUTHOR]

A new software is presented for the determination of crystal lattice parameters from the positions and widths of Kikuchi bands in a diffraction pattern. Starting with a single wide‐angle Kikuchi pattern of arbitrary resolution and unknown phase, the traces of all visibly diffracting lattice planes are manually derived from four initial Kikuchi band traces via an intuitive graphical user interface. A single Kikuchi bandwidth is then used as reference to scale all reciprocal lattice point distances. Kikuchi band detection, via a filtered Funk transformation, and simultaneous display of the band intensity profile helps users to select band positions and widths. Bandwidths are calculated using the first derivative of the band profiles as excess‐deficiency effects have minimal influence. From the reciprocal lattice, the metrics of possible Bravais lattice types are derived for all crystal systems. The measured lattice parameters achieve a precision of <1%, even for good quality Kikuchi diffraction patterns of 400 × 300 pixels. This band‐edge detection approach has been validated on several hundred experimental diffraction patterns from phases of different symmetries and random orientations. It produces a systematic lattice parameter offset of up to ±4%, which appears to scale with the mean atomic number or the backscatter coefficient. [ABSTRACT FROM AUTHOR]

Accurately indexing pseudosymmetric materials has long proven challenging for electron backscatter diffraction. The recent emergence of intensity‐based indexing approaches promises an enhanced ability to resolve pseudosymmetry compared with traditional Hough‐based indexing approaches. However, little work has been done to understand the effects of sample position and orientation on the ability to resolve pseudosymmetry, especially for intensity‐based indexing approaches. Thus, in this work the effects of crystal orientation and detector distance in a model tetragonal ZrO2 (c/a = 1.0185) material are quantitatively investigated. The orientations that are easiest and most difficult to correctly index are identified, the effect of detector distance on indexing confidence is characterized, and these trends are analyzed on the basis of the appearance of specific zone axes in the diffraction patterns. The findings also point to the clear benefit of shorter detector distances for resolving pseudosymmetry using intensity‐based indexing approaches. [ABSTRACT FROM AUTHOR]

A new method for electron backscatter diffraction ab initio indexing is reported that adopts several methods originally invented for powder indexing. Distribution rules of systematic absences and error‐stable Bravais lattice determination are used to eliminate the negative influence of non‐visible bands and erroneous information from visible bands. In addition, generalized versions of the de Wolff figures of merit are proposed as a new sorting criterion for the obtained unit‐cell parameters, which can be used in both orientation determination and ab initio indexing from Kikuchi patterns. Computational results show that the new figures of merit work well, similar to the original de Wolff Mn. The ambiguity of the indexing solutions is also pointed out, which happens in particular for low‐symmetry cells and may generate multiple distinct solutions even if very accurate positions of band centre lines and the projection centre are given. It is supposed that this is the reason why indexing was successful in an orthorhombic case but not in a triclinic cell. [ABSTRACT FROM AUTHOR]

Iron‐based Fe–Mn–Al–Ni shape‐memory alloys are of rather low materials cost and show remarkable pseudoelastic properties. To further understand the martensitic transformation giving rise to the pseudoelastic properties, different Fe–Mn–Al–Ni alloys have been heat treated at 1473 K and quenched in ice water. The martensite, which is formed from a body‐centred cubic austenite, is commonly described as face‐centered cubic (f.c.c.), even though there are also more complex, polytypical descriptions of martensite. The presently studied backscatter Kikuchi diffraction (BKD) patterns have been evaluated, showing a structure more complex than simple f.c.c. This structure can be described by nanoscale twins, diffracting simultaneously in the exciting volume. The twinned structure shows a tetragonal distortion, not uncommon for martensite in spite of the lack of interstitial elements. These features are evaluated by comparing the measured BKD patterns with dynamically simulated ones. [ABSTRACT FROM AUTHOR]

Two of the microstructural parameters most influential in the properties of polycrystalline materials are grain size and crystallographic texture. Although both properties have been extensively studied and there are a wide range of analysis tools available, they are generally considered independently, without taking into account the possible correlations between them. However, there are reasons to assume that grain size and orientation are correlated microstructural state variables, as they are the result of single microstructural formation mechanisms occurring during material processing. In this work, the grain size distribution and orientation distribution functions are combined in a single multivariate grain size orientation distribution function (GSODF). In addition to the derivation of the function, several examples of practical applications to low carbon steels are presented, in which it is shown how the GSODF can be used in the analysis of 2D and 3D electron backscatter diffraction data, as well as in the generation of representative volume elements for full‐field models and as input in simulations using mean‐field methods. [ABSTRACT FROM AUTHOR]

There is a growing interest in ab initio indexing of electron backscatter diffraction (EBSD) patterns. The methods of solving the problem are presented as innovative. The purpose of this note is to point out that ab initio EBSD indexing belongs to the field of indexing single‐crystal diffraction data, and it is solved on the same principles as indexing of patterns of other types. It is shown that reasonably accurate EBSD‐based data can be indexed by programs designed for X‐ray data. [ABSTRACT FROM AUTHOR]

The transformation behavior between iron oxides and oxyhydroxides like magnetite, hematite and goethite is still not entirely understood. Crystallographic similarities allow one to predict topotactic relationships between them. The related crystallographic aspects have been explored by means of electron backscatter diffraction (EBSD). Samples from natural aggregates of magnetite, hematite and goethite were collected from iron‐formation rocks that outcrop in the southeast of Brazil, in a region known for large deposits of iron and other ores. EBSD misorientation data indicate a pronounced relationship between these iron phases. The transformation seems to be related to the oxygen framework. The original close‐packed cubic arrangement of O atoms in magnetite changes to a hexagonal close‐packed framework in hematite, i.e. {111} of magnetite is parallel to {0001} of hematite. The matrix in which the magnetite grains are embedded is made of aggregates of hematite and goethite. In the matrix, the coincidence observed in the magnetite grains is not observed. On the other hand, the well known twin boundary relationships already described for these mineral phases can be observed here as an orientation relationship in three‐dimensional misorientation space. The spatial data of axis–angle pairs suggest that the twin boundaries serve as facilitating surfaces for phase transformation in the Fe–O–OH system. The main conclusion of this study is that the transformation occurred in the solid state with the newly transformed goethite inheriting the crystallographic orientations of the former crystals and that this phenomenon is better recognized by combining observations of misorientation relationships. In the matrix, such a relation is not observed and, for that reason, the minerals in the matrix are thought to have been formed by a different process, which might have involved dissolution and precipitation of the phase newly out of solution. [ABSTRACT FROM AUTHOR]

Resolving pseudosymmetry has long presented a challenge for electron backscatter diffraction and has been notoriously challenging in the case of tetragonal ZrO2 in particular. In this work, a method is proposed to resolve pseudosymmetry by building upon the dictionary indexing method and augmenting it with the application of global optimization to fit accurate pattern centers, clustering of the Hough‐indexed orientations to focus the dictionary in orientation space and interpolation to improve the accuracy of the indexed solution. The proposed method is demonstrated to resolve pseudosymmetry with 100% accuracy in simulated patterns of tetragonal ZrO2, even with high degrees of binning and noise. The method is then used to index an experimental data set, which confirms its ability to efficiently and accurately resolve pseudosymmetry in these materials. The present method can be applied to resolve pseudosymmetry in a wide range of materials, possibly even some more challenging than tetragonal ZrO2. Source code for this implementation is available online. [ABSTRACT FROM AUTHOR]

A historical tool for crystallographic analysis is provided by the Hilton net, which can be used for manually surveying the crystal lattice as it is manifested by the Kikuchi bands in a gnomonic projection. For a quantitative analysis using the Hilton net, the projection centre as the relative position of the signal source with respect to the detector plane needs to be known. Interplanar angles are accessible with a precision and accuracy which is estimated to be ≤0.3°. Angles between any directions, e.g. zone axes, are directly readable. Finally, for the rare case of an unknown projection‐centre position, its determination is demonstrated by adapting an old approach developed for photogrammetric applications. It requires the indexing of four zone axes [uvw]i in a backscattered Kikuchi diffraction pattern of a known phase collected under comparable geometric conditions. [ABSTRACT FROM AUTHOR]

The accuracy of the near‐field high‐energy diffraction microscopy (nf‐HEDM) technique is evaluated by directly comparing an nf‐HEDM reconstructed microstructure with an electron backscatter diffraction (EBSD) characterization of the same microstructure. A high‐purity gold oligocrystal was chosen for characterization in order to facilitate direct one‐to‐one comparison between the reconstructions given by each technique. By using the comparatively high spatial resolution of the EBSD reconstruction as the ground truth for the grain‐boundary network's morphology, it is determined that nf‐HEDM locates internal grain boundaries with an accuracy on average better than the resolution of the imaging detector used or within the reconstruction voxel size, whichever is larger. By taking the intragranular misorientation in well ordered grains as a proxy for orientation resolution, it is determined that standard data collection procedures determine crystallographic orientations to better than 0.1°. The effects of various modified data collection procedures are also examined. [ABSTRACT FROM AUTHOR]

Alignment of a crystal with the coordinate system of a scanning electron microscope (SEM) is essential for obtaining controlled diffraction conditions or investigating anisotropic material properties. The computer program crystalAligner was developed to enable the weighted constrained alignment of one or two crystal directions in crystals of arbitrary orientation and structure with the coordinate system of a SEM. For a given set of crystal directions, alignment objectives and rotational constraints, the algorithm simulates the rotation of the crystal on any constrained SEM stage and minimizes the misalignment of the crystal directions with prescribed coordinate axes of the SEM. The possibility of applying crystal symmetry and the use of a genetic algorithm for optimization ensure the determination of the global optimal alignment even in severely constrained conditions. In cases where ideal alignment is not obtainable, weighting factors can be applied to conflicting alignment objectives. Two application examples, the alignment of two crystal directions for a lamella lift out for nano‐mechanical testing and the rotation of an orientation‐related dual‐phase microstructure into a standard projection, demonstrate the functionality and workflow of the freely available open‐source program crystalAligner. [ABSTRACT FROM AUTHOR]

A new methodology to predict potential pseudo‐symmetric or systematically mis‐indexed orientations for an arbitrary crystal structure is presented. The method leverages the recently proposed spherical indexing algorithm to index electron backscatter diffraction patterns. Potential pseudo‐symmetric orientations are interpreted as secondary peaks in the autocorrelation of the Kikuchi sphere. The generality of the method is illustrated using a number of crystal systems, ranging from nickel, where no significant pseudo‐symmetric issues are expected, to SrTiO3, with mild occurrence of such issues, to the olivine series, γ‐TiAl and U‐6%Nb systems, where the traditional Hough method systematically mis‐indexes the pseudo‐symmetric variants. Furthermore, the method predicts the severity of potential pseudo‐symmetric matches and ranks all variants using a normalized autocorrelation coefficient. [ABSTRACT FROM AUTHOR]

This paper compares several well known sliding‐window methods for denoising crystal orientation data with variational methods adapted from mathematical image analysis. The variational methods turn out to be much more powerful in terms of preserving low‐angle grain boundaries and filling holes of non‐indexed orientations. The effect of denoising on the determination of the kernel average misorientation and the geometrically necessary dislocation density is also discussed. Synthetic as well as experimental data are considered for this comparison. The examples demonstrate that variational denoising techniques are capable of significantly improving the accuracy of properties derived from electron backscatter diffraction maps. [ABSTRACT FROM AUTHOR]

A shape‐memory effect is known to appear in red gold alloys with compositions close to Au–Cu. The aim of this paper is to study by electron backscatter diffraction (EBSD) the variant selection in the A1 → L10 transformation occurring under stress, in bending conditions. The L10 domains are successfully identified by this technique despite the c/a ratio being close to unity. The orientation relationship between the cubic and tetragonal phases is determined by a careful analysis of the EBSD data. The distortion of the lattice for each variant is then modelled and calculated from the experimental orientations. The mechanical work associated with the transformation is computed from the lattice distortion by neglecting the obliquity. Finally, the distribution of this mechanical work is compared with the case of a uniform distribution of all variants, in order to evaluate the extent of variant selection. The maximal work criterion, often used for martensitic transformations, enabled quantification of the variant selection phenomenon. [ABSTRACT FROM AUTHOR]

An implementation of smoothing splines is proposed to reduce orientation noise in electron backscatter diffraction (EBSD) data, and subsequently estimate more accurate geometrically necessary dislocation (GND) densities. The local linear adaptation of smoothing splines (LLASS) filter has two advantages over classical implementations of smoothing splines: (1) it allows for an intuitive calibration of the fitting versus smoothing trade‐off and (2) it can be applied directly and in the same manner to both square and hexagonal grids, and to 2D as well as to 3D EBSD data sets. Furthermore, the LLASS filter calculates the filtered orientation gradient, which is actually at the core of the method and which is subsequently used to calculate the GND density. The LLASS filter is applied on a simulated low‐misorientation‐angle boundary corrupted by artificial orientation noise (on a square grid), and on experimental EBSD data of a compressed Ni‐base superalloy (acquired on a square grid) and of a dual austenitic/martensitic steel (acquired on an hexagonal grid). The LLASS filter leads to lower GND density values as compared to raw EBSD data sets, as a result of orientation noise being reduced, while preserving true GND structures. In addition, the results are compared with those of filters available in the MTEX toolbox. [ABSTRACT FROM AUTHOR]

Two methods for measuring dislocation density were applied to a series of plastically deformed tensile samples of Zircaloy‐2. Samples subjected to plastic strains ranging from 4 to 17% along a variety of loading paths were characterized using both electron backscatter diffraction (EBSD) and synchrotron X‐ray line profile analysis (LPA). It was found that the EBSD‐based method gave results which were similar in magnitude to those obtained by LPA and followed a similar trend with increasing plastic strain. The effects of microscope parameters and post‐processing of the EBSD data on dislocation density measurements are also discussed. The typical method for estimating uncertainty in dislocation density measured via EBSD was shown to be overly conservative, and a more realistic method of determining uncertainty is presented as an alternative. Dislocation densities of Zircaloy‐2 tensile samples are measured using two diffraction‐based techniques. The relative sensitivities of the techniques to dislocations produced during cold work are compared. [ABSTRACT FROM AUTHOR]

Electron backscatter diffraction (EBSD) is a technique used to measure crystallographic features in the scanning electron microscope. The technique is highly automated and readily accessible in many laboratories. EBSD pattern indexing is conventionally performed with raw electron backscatter patterns. These patterns are software processed to locate the band centres (and sometimes edges) from which the crystallographic index of each band is determined. Once a consistent index for many bands is obtained, the crystal orientation with respect to a reference sample and detector orientation can be determined and presented. Unfortunately, because of challenges related to crystal symmetry, there are limited available pattern‐indexing approaches and this has probably hampered open development of the technique. In this article, a new method of pattern indexing is presented, based upon a method with which satellites locate themselves in the night sky, and its effectiveness is systematically demonstrated using dynamical simulations and real experimental patterns. The benefit of releasing this new algorithm as open‐source software is demonstrated when this indexing process is utilized, together with dynamical solutions, to provide some of the first accuracy assessments of an indexing solution. In disclosing a new indexing algorithm, and software processing toolkit, the authors hope to open up EBSD developments to more users. The software code and example data are released alongside this article for third party developments. A method to automatically index electron backscatter diffraction patterns is introduced and demonstrated with dynamical diffraction simulations and experimental patterns. [ABSTRACT FROM AUTHOR]

The relationship between the crystallographic orientation and habit plane normal of transformed α laths in titanium alloys is discussed according to the Burgers orientation relationship and the three‐dimensional structure of the α lath. A new method (orientation–trace method) is developed to determine the orientation of the parent β phase using the orientation of the α lath, which was measured by electron backscatter diffraction, and the microstructural morphology of that α variant. This approach is validated in a near‐α titanium alloy. Moreover, the habit plane normal direction of the transformed α lath can be obtained from the crystallographic orientations of the α lath itself and its parent β grain. The verification and the corresponding discussion show the reliability of this approach. [ABSTRACT FROM AUTHOR]

The X‐ray Laue microdiffraction (µLaue) technique has been establishing itself as a reliable means for microstrain analysis for the past few decades. One problem with this technique is that when the crystal size is significantly smaller than the probed volume and when the diffracting crystals are closely oriented, a large number of individual µLaue patterns are superimposed in a complex way on the recorded diffraction images. In that case, because of the difficulty of isolating unambiguously a single‐grain µLaue pattern, a reliable analysis of strains is tedious manually and hardly achievable with current automated methods. This issue is even more severe for low‐symmetry crystals or when high‐energy X‐rays are used, since each single‐crystal µLaue pattern already contains a large number of spots. This paper proposes overcoming this challenge through the development of a combined approach coupling µLaue and electron backscatter diffraction (EBSD). The capabilities of this `EBSD‐assisted µLaue' automated method are illustrated on a monoclinic zirconia‐based specimen and µLaue diffraction patterns are analysed with the crystal orientation input from EBSD. The obtained results are statistically reliable, reproducible and provide a physical insight into the micromechanical characteristics of the material. [ABSTRACT FROM AUTHOR]

Rhombohedral twinning in alumina (aluminium oxide, α-Al2O3) is an important mechanism for plastic deformation under high-temperature-pressure conditions. Rhombohedral twins in a polycrystalline alumina sample deformed in a D-DIA apparatus at 965 K and 4.48 GPa have been characterized. Three classes of grains were imaged, containing single, double and mosaic twins, using electron channeling contrast imaging (ECCI) in a field emission scanning electron microscope. These twinned grains were analyzed using electron backscatter diffraction (EBSD). The methodology for twin identification presented here is based on comparison of theoretical pole figures for a rhombohedral twin with experimental pole figures obtained with EBSD crystal orientation mapping. An 85°⟨021⟩ angle-axis pair of misorientation was identified for rhombohedral twin boundaries in alumina, which can be readily used in EBSD post-processing software to identify the twin boundaries in EBSD maps and distinguish the rhombohedral twins from basal twins. Elastic plastic self-consistent (EPSC) modeling was then used to model the synchrotron X-ray diffraction data from the D-DIA experiments utilizing the rhombohedral twinning law. From these EPSC models, a critical resolved shear stress of 0.25 GPa was obtained for rhombohedral twinning under the above experimental conditions, which is internally consistent with the value estimated from the applied load and Schmid factors determined by EBSD analysis. [ABSTRACT FROM AUTHOR]

Two approaches are proposed for the refinement of electron diffraction pattern indexing. The approaches require two basic ingredients: an accurate physics-based forward model and an algorithm to search the local orientation neighborhood. Forward models for electron backscatter diffraction (EBSD) and electron channeling pattern (ECP) modalities are coupled with either a multi-resolution brute-force search algorithm or a bound optimization by quadratic approximation algorithm. The efficacy of the methods is evaluated for varying levels of error in the pattern projection center. The EBSD modality shows an orientation improvement when the projection center error is within ±1% of the full detector width, whereas the ECP modality shows improvement up to a ±5% error. The algorithms are applied to an experimental EBSD scan for partially recrystallized 90/10 brass; the results show that the refinement is necessary to remove the artifacts introduced by the discrete sampling nature of the dictionary indexing method. Finally, a pattern center correction factor is derived for orientations obtained from dictionary indexing for large-area EBSD scans. [ABSTRACT FROM AUTHOR]

In a polycrystal, the heterogeneity of plastic deformation in a particular grain is greatly enhanced by adjacent grains that constrain the grain's local behavior, often imposing orientation gradients. This work aims to characterize and quantify the local orientation gradients near grain boundaries (GBs). Electron backscatter diffraction (EBSD) measurements were made on a 0.67 mm thick aluminium-killed drawing quality (AKDQ) steel sheet subjected to different loading paths that are typical of forming operations. A statistical analysis shows that a considerable fraction of the analyzed GB profiles can be described by an orientation profile with a constant slope near the GB. In order to quantify this behavior, as well as the degree of localization, two new parameters, based on the local orientation gradient assessed by EBSD, are proposed: BET (boundary effective thickness) and GAS (gradient average severity). These parameters should be considered together, the BET as an effective thickness of the GB zone where the orientation gradient takes place and the GAS as a measure of the magnitude or severity of the orientation gradient. Additionally, the GAS parameter shows a strong correlation with the accumulated macroscopic strain for the investigated deformation levels and loading paths, while the BET profile clearly reveals the influence of the GB on the misorientation profiles. Tension and biaxial stretching results lead to a BET value between 1.5 and 2 µm. Finally, it is shown that the local misorientation in the GB zone, on both sides of the GB line, is disperse and it does not correlate simply with misorientation or even the slip-transfer geometry across the GB. Moreover, the observed average local misorientation dispersions in GB zones are different for each loading condition. [ABSTRACT FROM AUTHOR]

The twin distribution in topological insulators Bi2Te3 and Bi2Se3 was imaged by electron backscatter diffraction (EBSD) and scanning X-ray diffraction microscopy (SXRM). The crystal orientation at the surface, determined by EBSD, is correlated with the surface topography, which shows triangular pyramidal features with edges oriented in two different orientations rotated in the surface plane by 60°. The bulk crystal orientation is mapped out using SXRM by measuring the diffracted X-ray intensity of an asymmetric Bragg peak using a nano-focused X-ray beam scanned over the sample. By comparing bulk- and surface-sensitive measurements of the same area, buried twin domains not visible on the surface are identified. The lateral twin domain size is found to increase with the film thickness. [ABSTRACT FROM AUTHOR]

Kikuchi diffraction patterns can provide fundamental information about the lattice metric of a crystalline phase. In order to improve the possible precision and accuracy of lattice parameter determination from the features observed in Kikuchi patterns, some useful fundamental relationships of geometric crystallography are reviewed, which hold true independently of the actual crystal symmetry. The Kikuchi band positions and intersections and the Kikuchi band widths are highly interrelated, which is illustrated by the fact that all lattice plane trace positions of the crystal are predetermined by the definition of only four traces. If, additionally, the projection centre of the gnomonic projection is known, the lattice parameter ratios and the angles between the basis vectors are fixed. A further definition of one specific Kikuchi band width is sufficient to set the absolute sizes of all lattice parameters and to predict the widths of all Kikuchi bands. The mathematical properties of the gnomonic projection turn out to be central to an improved interpretation of Kikuchi pattern data, emphasizing the importance of the exact knowledge of the projection centre. [ABSTRACT FROM AUTHOR]

Twins in plagioclase, which are abundant in rocks, have important implications for the growth history and subsequent transformation. There are many twin laws in plagioclase and some of them are difficult to identify. This paper presents an electron backscatter diffraction (EBSD) analysis combined with electron microprobe analysis of plagioclase twinning in the Niutoushan alkali basalt. Theoretical pole figures of 12 different twin laws for plagioclase were generated. By comparing the pole figures obtained from EBSD with the theoretical ones, 11 twin laws have been identified in the alkali basalt, and their frequency has also been determined: Albite (28%), Carlsbad (25%), Albite-Carlsbad (34%), Pericline (3%), Ala (2%), Manebach (1%), Albite-Ala (1%), Prism {110} (2%), Prism {10} (1%), Prism {130} (1%) and Prism {10} (1%). All the plagioclase twins in the alkali basalt are growth twins. The anorthite content of the plagioclase has a negative correlation with the frequency of the Pericline and Albite twin laws but a positive correlation with the frequency of all the other twin laws, which is consistent with previous results. The theoretical pole figures of twin laws for plagioclase introduced in this paper can be applied to investigating plagioclase twin laws in all plagioclase-bearing rocks, and the relationship between twin pattern and crystallization conditions of the rocks can be established. [ABSTRACT FROM AUTHOR]

In many inclusion-host systems with similar oxygen packing schemes, the optimum crystallographic orientation relationship (COR) between the inclusion and the host is mostly determined by matching the similar oxygen sublattices of the two structures. In contrast, the prediction of the optimum COR or even just the rationalization of the observed COR(s) between an inclusion and host with incompatible oxygen sublattices, like rutile-garnet, is not straightforward. The related documentation for such cases is therefore limited. Given the abundant crystallographic data for the rutile-garnet system acquired by transmission electron microscopy and electron backscatter diffraction methods recently, this problem can now be examined in detail for the critical structural factors dictating the selection of optimum COR in such a structurally complicated system. On the basis of the unconstrained three-dimensional lattice point match and structural polyhedron match calculated for the observed CORs, it becomes clear that the prerequisite of optimum COR for rutile (rt) in garnet (grt) is to have most of their octahedra similarly oriented/inclined in space by aligning ⟨103⟩rt and ⟨111⟩grt for needle extension growth. Further rotation along the ⟨103⟩rt//⟨111⟩grt direction then leads to the energetically most favorable COR-2 variant with a good lattice point match defined by the coincidence site lattice (CSL) and a good topotaxial match of the constituent polyhedra at the CSL points, leaving unfavorable COR-1′ in the forbidden zones. This understanding sheds light not only on hierarchical energetics for the selection of inclusion variants in a complicated inclusion-host system, but also on yet-to-be-explored [ UVW]-specific CORs and hetero-tilt boundaries for composite materials in general. [ABSTRACT FROM AUTHOR]

The inverse pole figure (IPF) coloring for a suitable evaluation of crystal orientation data is discussed. The major goal is a high correlation between encoding color and crystal orientation. Revised color distributions of the fundamental sectors are introduced which have the advantages of (1) being applicable for all point groups, (2) not causing color discontinuities within grains, (3) featuring carefully balanced regions for red, cyan, blue, magenta, green and yellow, and (4) an enlarged gray center in opposition to a tiny white center. A new set of IPF color keys is proposed which is the result of a thorough analysis of the colorization problem. The discussion considers several topics: ( a) the majority of presently applied IPF color keys generate color discontinuities for specifically oriented grains; ( b) if a unique correlation between crystal direction and color is requested, discontinuity-preventing keys are possible for all point groups, except for , and ; ( c) for a specific symmetry group several IPF color keys are available, visualizing different features of a microstructure; and ( d) for higher symmetries a simultaneous IPF mapping of two or three standard reference directions is insufficient for an unequivocal orientation assignment. All color keys are available in MTEX, a freely available MATLAB toolbox. [ABSTRACT FROM AUTHOR]

For Ni-Mn-Sb ferromagnetic multifunctional alloys, the crystal structures of martensite variants and the orientation relationships between them are decisive factors for their magnetic field-induced behaviours and are hence of importance. Such information has rarely been reported in the literature. In the present work, the crystal structure, microstructure and orientation relationships of Ni-Mn-Sb martensite were thoroughly investigated by X-ray diffraction (XRD) and electron backscatter diffraction (EBSD). Through XRD analyses, the crystal structure of the martensite, including the crystal system, the space group, the lattice parameters and the atomic coordinates, was fully resolved. The structure is orthorhombic and can be represented with a 4 O superstructure. EBSD analyses show that the Ni-Mn-Sb martensite has a lamellar form. One martensite lamella corresponds to one orientation variant. The lamellae are organized in long plate-shaped colonies. Within each colony, four distinct orientation variants ( A, B, C and D) appear repeatedly and extend in roughly the same direction. The four variants are twin related to one another, with variants A and C (or variants B and D) forming a type I twin, variants A and B (or C and D) a type II twin, and variants A and D (or B and C) a compound twin. The complete twinning elements for each twin relation were thus fully determined. The interfaces between the variants were identified to be their corresponding twinning planes. All these results provide fundamental information for Ni-Mn-Sb alloys that is useful for interpreting their magnetic and mechanical characteristics. [ABSTRACT FROM AUTHOR]