Three-dimensional X-ray structural microscopy with submicrometre resolution

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.

Laue microdiffraction on polycrystalline samples above 1500 K achieved with the QMAX-µLaue furnace

X-ray Laue microdiffraction aims to characterize microstructural and mechanical fields in polycrystalline specimens at the sub-micrometre scale with a strain resolution of ∼10-4. Here, a new and unique Laue microdiffraction setup and alignment procedure is presented, allowing measurements at temperatures as high as 1500 K, with the objective to extend the technique for the study of crystalline phase transitions and associated strain-field evolution that occur at high temperatures. A method is provided to measure the real temperature encountered by the specimen, which can be critical for precise phase-transition studies, as well as a strategy to calibrate the setup geometry to account for the sample and furnace dilation using a standard α-alumina single crystal. A first application to phase transitions in a polycrystalline specimen of pure zirconia is provided as an illustrative example.

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.

Laboratory-based x-ray dark-field microscopy

We demonstrate the capability of laboratory-based x-ray microscopes, using intensity-modulation masks, to access the sub-micron length scale in the dark field contrast channel while maintaining micron resolution in the resolved (refraction and attenuation) channels. The dark field contrast channel reveals the presence of ensembles of samples' features below the system resolution. Resolved refraction and attenuation channels provide multi-modal high-resolution imaging down to the micron scale. We investigate the regimes of modulated and un-modulated dark field as well as refraction, quantifying their dependence on the relationship between feature size in the imaged object and aperture size in the intensity-modulation mask. We propose an analytical model to link the measured signal with the sample's microscopic properties. Finally, we demonstrate the relevance of the microscopic dark field contrast channel in applications from both the life and physical sciences, providing proof of concept results for imaging collagen bundles in cartilage and dendritic growth in lithium batteries.

Characterization of Pt-coated twin paraboloidal laboratory capillary high energy X-ray optics

Novel focusing optics composed of twin paraboloidal capillaries coated with Pt, for laboratory X-ray sources are presented and characterized. The optics are designed to focus the X-rays, resulting in an achromatic focused beam with photon energies up to 40 keV. The performance of the optics under different operational conditions is studied by comparing the energy-photon count spectra of the direct and focused beams. Based on these analyses, the optics gain and efficiency as a function of photon energy are determined. A focal spot of 8.5 µm with a divergence angle of 0.59° is observed. The obtained characteristics are discussed and related to theoretical considerations. Moreover, the suitability and advantages of the present optics for X-ray microdiffraction is demonstrated using polycrystalline aluminium. Finally, possibilities for further developments are suggested.

Real-time imaging of acoustic waves in bulk materials with X-ray microscopy

The dynamics of lattice vibrations govern many material processes, such as acoustic wave propagation, displacive phase transitions, and ballistic thermal transport. The maximum velocity of these processes and their effects is determined by the speed of sound, which therefore defines the temporal resolution (picoseconds) needed to resolve these phenomena on their characteristic length scales (nanometers). Here, we present an X-ray microscope capable of imaging acoustic waves with subpicosecond resolution within mm-sized crystals. We directly visualize the generation, propagation, branching, and energy dissipation of longitudinal and transverse acoustic waves in diamond, demonstrating how mechanical energy thermalizes from picosecond to microsecond timescales. Bulk characterization techniques capable of resolving this level of structural detail have previously been available on millisecond time scales-orders of magnitude too slow to capture these fundamental phenomena in solid-state physics and geoscience. As such, the reported results provide broad insights into the interaction of acoustic waves with the structure of materials, and the availability of ultrafast time-resolved dark-field X-ray microscopy opens a vista of new opportunities for 3D imaging of materials dynamics on their intrinsic submicrosecond time scales.

Implementation of grain mapping by diffraction contrast tomography on a conventional laboratory tomography setup with various detectors

Laboratory-based diffraction contrast tomography (LabDCT) is a novel technique used to resolve grain orientations and shapes in three dimensions at the micrometre scale using laboratory X-ray sources, allowing the user to overcome the constraint of limited access to synchrotron facilities. To foster the development of this technique, the implementation of LabDCT is illustrated in detail using a conventional laboratory-based X-ray tomography setup, and it is shown that such implementation is possible with the two most common types of detectors: CCD and flat panel. As a benchmark, LabDCT projections were acquired on an AlCu alloy sample using the two types of detectors at different exposure times. Grain maps were subsequently reconstructed using the open-source grain reconstruction method reported in the authors' previous work. To characterize the detection limit and the spatial resolution for the current implementation, the reconstructed LabDCT grain maps were compared with the map obtained from a synchrotron measurement, which is considered as ground truth. The results show that the final grain maps from measurements by the CCD and flat panel detector are similar and show comparable quality, while the CCD gives a much better contrast-to-noise ratio than the flat panel. The analysis of the grain maps reconstructed from measurements with different exposure times suggests that a grain map of comparable quality could be obtained in less than 1 h total acquisition time without a significant loss of grain reconstruction quality and indicates a clear potential for time-lapse LabDCT experiments. The current implementation is suggested to promote the generic use of the LabDCT technique for grain mapping on conventional tomography setups.

Digital autofocusing of a coded-aperture Laue diffraction microscope

To provide optimal depth resolution with a coded-aperture Laue diffraction microscope, an accurate position of the coded-aperture and its scanning geometry need to be known. However, finding the geometry by trial and error is a time-consuming and often challenging process because of the large number of parameters involved. In this paper, we propose an optimization approach to automate the focusing process after data is collected. We demonstrate the robustness and efficiency of the proposed approach with experimental data taken at a synchrotron facility.

Reconstruction algorithms for grain mapping by laboratory X-ray diffraction contrast tomography

X-ray-based non-destructive 3D grain mapping techniques are well established at synchrotron facilities. To facilitate everyday access to grain mapping instruments, laboratory diffraction contrast tomography (LabDCT), using a laboratory-based conical polychromatic X-ray beam, has been developed and commercialized. Yet the currently available LabDCT grain reconstruction methods are either ill-suited for handling a large number of grains or require a commercial licence bound to a specific instrument. To promote the availability of LabDCT, grain reconstruction methods have been developed with multiple reconstruction algorithms based on both forward and back calculations. The different algorithms are presented in detail and their efficient implementation using parallel computing is described. The performance of different reconstruction methods is assessed on synthetic data. The code to implement all the described algorithms has been made publicly accessible with the intention of fostering the development of grain mapping techniques on widely available laboratory instruments.

Indexing of superimposed Laue diffraction patterns using a dictionary-branch-bound approach

X-ray Laue diffraction is an important method for characterizing the local crystallographic orientation and elastic strain in polycrystalline materials. Existing analysis methods are designed mainly to index a single or a few Laue diffraction pattern(s) recorded in a detector image. In this work, a novel method called dictionary-branch-bound (DBB) is presented to determine the crystallographic orientations of multiple crystals simultaneously illuminated by a parallel X-ray incident beam, using only the spot positions in a detector image. DBB is validated for simulated X-ray Laue diffraction data. In the simulation, up to 100 crystals with random crystallographic orientations are simultaneously illuminated. Fake spots are randomly added to the detector image to test the robustness of DBB. Additionally, spots are randomly removed to test the resilience of DBB against true spots that are undetected due to background noise and/or spot overlap. Poisson noise is also added to test the sensitivity of DBB to less accurate positions of detected spots. In all cases except the most challenging one, a perfect indexing with a mean angular error below 0.08° is obtained. To demonstrate the potential of DBB further, it is applied to synchrotron microdiffraction data. Finally, guidelines for using DBB in experimental data are provided.

X-ray Diffraction Imaging of Deformations in Thin Films and Nano-Objects

The quantification and localization of elastic strains and defects in crystals are necessary to control and predict the functioning of materials. The X-ray imaging of strains has made very impressive progress in recent years. On the one hand, progress in optical elements for focusing X-rays now makes it possible to carry out X-ray diffraction mapping with a resolution in the 50-100 nm range, while lensless imaging techniques reach a typical resolution of 5-10 nm. This continuous evolution is also a consequence of the development of new two-dimensional detectors with hybrid pixels whose dynamics, reading speed and low noise level have revolutionized measurement strategies. In addition, a new accelerator ring concept (HMBA network: hybrid multi-bend achromat lattice) is allowing a very significant increase (a factor of 100) in the brilliance and coherent flux of synchrotron radiation facilities, thanks to the reduction in the horizontal size of the source. This review is intended as a progress report in a rapidly evolving field. The next ten years should allow the emergence of three-dimensional imaging methods of strains that are fast enough to follow, in situ, the evolution of a material under stress or during a transition. Handling massive amounts of data will not be the least of the challenges.

Processing Laue Microdiffraction Raster Scanning Patterns with Machine Learning Algorithms: A Case Study with a Fatigued Polycrystalline Sample

The massive amount of diffraction images collected in a raster scan of Laue microdiffraction calls for a fast treatment with little if any human intervention. The conventional method that has to index diffraction patterns one-by-one is laborious and can hardly give real-time feedback. In this work, a data mining protocol based on unsupervised machine learning algorithm was proposed to have a fast segmentation of the scanning grid from the diffraction patterns without indexation. The sole parameter that had to be set was the so-called “distance threshold” that determined the number of segments. A statistics-oriented criterion was proposed to set the “distance threshold”. The protocol was applied to the scanning images of a fatigued polycrystalline sample and identified several regions that deserved further study with, for instance, differential aperture X-ray microscopy. The proposed data mining protocol is promising to help economize the limited beamtime.

Three-dimensional grain resolved strain mapping using laboratory X-ray diffraction contrast tomography: theoretical analysis

Laboratory diffraction contrast tomography (LabDCT) is a recently developed technique to map crystallographic orientations of polycrystalline samples in three dimensions non-destructively using a laboratory X-ray source. In this work, a new theoretical procedure, named LabXRS, expanding LabDCT to include mapping of the deviatoric strain tensors on the grain scale, is proposed and validated using simulated data. For the validation, the geometries investigated include a typical near-field LabDCT setup utilizing Laue focusing with equal source-to-sample and sample-to-detector distances of 14 mm, a magnified setup where the sample-to-detector distance is increased to 200 mm, a far-field Laue focusing setup where the source-to-sample distance is also increased to 200 mm, and a near-field setup with a source-to-sample distance of 200 mm. The strain resolution is found to be in the range of 1–5 × 10−4, depending on the geometry of the experiment. The effects of other experimental parameters, including pixel binning, number of projections and imaging noise, as well as microstructural parameters, including grain position, grain size and grain orientation, on the strain resolution are examined. The dependencies of these parameters, as well as the implications for practical experiments, are discussed.

Supersaturation-Controlled Growth of Monolithically Integrated Lead-Free Halide Perovskite Single-Crystalline Thin Film for High-Sensitivity Photodetectors

Monolithical integration of the promising optoelectronic material with mature and inexpensive silicon circuitry contributes to simplifying device geometry, enhancing performance, and expanding new functionalities. Herein, a lead-free halide perovskite Cs₃ Bi₂ I₉ single-crystalline thin film (SCTF), with thickness ranging from 900 nm to 4.1 µm and aspect ratio up to 1666, is directly integrated on various substrates including Si wafer, through a facile and low-temperature solution-processing method. The growth kinetics of the lead-free halide perovskite SCTF are elucidated by in situ observation, and the solution supersaturation is controlled to reduce the inverse-temperature crystallization nucleation density and elongate the evaporation growth. The excellent lattice match and band alignment between Si(111) and Cs₃ Bi₂ I₉ (001) facets promote photogenerated charge dissociation and extraction, resulting in boosting the photoelectric sensitivity by 10-200 times compared with photodetectors based on other substrates. More importantly, this silicon-compatible perovskite SCTF photodetector exhibits a high switching ratio of 3000 and a fast response of 1.5 µs, which are higher than most reported state-of-the-art lead-free halide perovskite photodetectors. This work not only gives an in-depth understanding of the perovskite precursor solution chemistry, but also demonstrates the great potential of monolithical integration of lead-free halide perovskite SCTF with a silicon wafer for high-performance photodetectors.

Deep learning for improving non-destructive grain mapping in 3D

Laboratory X-ray diffraction contrast tomography (LabDCT) is a novel imaging technique for non-destructive 3D characterization of grain structures. An accurate grain reconstruction critically relies on precise segmentation of diffraction spots in the LabDCT images. The conventional method utilizing various filters generally satisfies segmentation of sharp spots in the images, thereby serving as a standard routine, but it also very often leads to over or under segmentation of spots, especially those with low signal-to-noise ratios and/or small sizes. The standard routine also requires a fine tuning of the filtering parameters. To overcome these challenges, a deep learning neural network is presented to efficiently and accurately clean the background noise, thereby easing the spot segmentation. The deep learning network is first trained with input images, synthesized using a forward simulation model for LabDCT in combination with a generic approach to extract features of experimental backgrounds. Then, the network is applied to remove the background noise from experimental images measured under different geometrical conditions for different samples. Comparisons of both processed images and grain reconstructions show that the deep learning method outperforms the standard routine, demonstrating significantly better grain mapping.

Improved grain mapping by laboratory X-ray diffraction contrast tomography

Laboratory diffraction contrast tomography (LabDCT) is a novel technique for non-destructive imaging of the grain structure within polycrystalline samples. To further broaden the use of this technique to a wider range of materials, both the spatial resolution and detection limit achieved in the commonly used Laue focusing geometry have to be improved. In this work, the possibility of improving both grain indexing and shape reconstruction was investigated by increasing the sample-to-detector distance to facilitate geometrical magnification of diffraction spots in the LabDCT projections. LabDCT grain reconstructions of a fully recrystallized iron sample, obtained in the conventional Laue focusing geometry and in a magnified geometry, are compared to one characterized by synchrotron X-ray diffraction contrast tomography, with the latter serving as the ground truth. It is shown that grain indexing can be significantly improved in the magnified geometry. It is also found that the magnified geometry improves the spatial resolution and the accuracy of the reconstructed grain shapes. The improvement is shown to be more evident for grains smaller than 40 µm than for larger grains. The underlying reasons are clarified by comparing spot features for different LabDCT datasets using a forward simulation tool.

Crystallographic tomography and molecular modelling of structured organic polycrystalline powders

Novel combination of crystallographic tomography and molecular modelling is used to examine the powder packing behaviour and crystal interactions for an organic polycrystalline powder bed.

Molecular to Macroscale Energy Absorption Mechanisms in Biological Body Armour Illuminated by Scanning X-ray Diffraction with In Situ Compression

Determining multiscale, concurrent strain, and deformation mechanisms in hierarchical biological materials is a crucial engineering goal, to understand structural optimization strategies in Nature. However, experimentally characterizing complex strain and displacement fields within a 3D hierarchical composite, in a multiscale full-field manner, is challenging. Here, we determined the in situ strains at the macro-, meso-, and molecular-levels in stomatopod cuticle simultaneously, by exploiting the anisotropy of the 3D fiber diffraction coupled with sample rotation. The results demonstrate the method, using the mineralized 3D α-chitin fiber networks as strain sensors, can capture submicrometer deformation of a single lamella (mesoscale), can extract strain information on multiple constituents concurrently, and shows that α-chitin fiber networks deform elastically while the surrounding matrix deforms plastically before systematic failure under compression. Further, the results demonstrate a molecular-level prestrain gradient in chitin fibers, resulting from different mineralization degrees in the exo- and endo cuticle.

Observation of Transient and Asymptotic Driven Structural States of Tungsten Exposed to Radiation

Combining spatially resolved x-ray Laue diffraction with atomic-scale simulations, we observe how ion-irradiated tungsten undergoes a series of nonlinear structural transformations with increasing radiation exposure. Nanoscale defect-induced deformations accumulating above 0.02 displacements per atom (dpa) lead to highly fluctuating strains at ∼0.1  dpa, collapsing into a driven quasisteady structural state above ∼1  dpa. The driven asymptotic state is characterized by finely dispersed vacancy defects coexisting with an extended dislocation network and exhibits positive volumetric swelling, due to the creation of new crystallographic planes through self-interstitial coalescence, but negative lattice strain.

A flexible and standalone forward simulation model for laboratory X-ray diffraction contrast tomography

Laboratory X-ray diffraction contrast tomography (LabDCT) has recently been developed as a powerful technique for non-destructive mapping of grain microstructures in bulk materials. As the grain reconstruction relies on segmentation of diffraction spots, it is essential to understand the physics of the diffraction process and resolve all the spot features in detail. To this aim, a flexible and standalone forward simulation model has been developed to compute the diffraction projections from polycrystalline samples with any crystal structure. The accuracy of the forward simulation model is demonstrated by good agreements in grain orientations, boundary positions and shapes between a virtual input structure and that reconstructed based on the forward simulated diffraction projections of the input structure. Further experimental verification is made by comparisons of diffraction spots between simulations and experiments for a partially recrystallized Al sample, where a satisfactory agreement is found for the spot positions, sizes and intensities. Finally, applications of this model to analyze specific spot features are presented.

Charging Reactions Promoted by Geometrically Necessary Dislocations in Battery Materials Revealed by In Situ Single-Particle Synchrotron Measurements

Crystallographic defects exist in many redox active energy materials, e.g., battery and catalyst materials, which significantly alter their chemical properties for energy storage and conversion. However, there is lack of quantitative understanding of the interrelationship between crystallographic defects and redox reactions. Herein, crystallographic defects, such as geometrically necessary dislocations, are reported to influence the redox reactions in battery particles through single-particle, multimodal, and in situ synchrotron measurements. Through Laue X-ray microdiffraction, many crystallographic defects are spatially identified and statistically quantified from a large quantity of diffraction patterns in many layered oxide particles, including geometrically necessary dislocations, tilt boundaries, and mixed defects. The in situ and ex situ measurements, combining microdiffraction and X-ray spectroscopy imaging, reveal that LiCoO₂ particles with a higher concentration of geometrically necessary dislocations provide deeper charging reactions, indicating that dislocations may facilitate redox reactions in layered oxides during initial charging. The present study illustrates that a precise control of crystallographic defects and their distribution can potentially promote and homogenize redox reactions in battery materials.

Combining Laue diffraction with Bragg coherent diffraction imaging at 34-ID-C

Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding a signal from a single nanoscale crystal object which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with (hkl) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus localizing in reciprocal space other Bragg reflections becomes time-consuming or requires good knowledge of the orientation of the crystal. Here, the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables, through rapid switching from monochromatic to broadband (pink) beam, the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction patterns near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. The design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal are discussed.

Grain morphology reconstruction of crystalline materials from Laue three-dimensional neutron diffraction tomography

The macroscopic properties of advanced engineering and functional materials are highly dependent on their overall grain orientation distribution, size, and morphology. Here we present Laue 3D neutron diffraction tomography providing reconstructions of the grains constituting a coarse-grained polycrystalline material. Reconstructions of the grain morphology of a highly pure Fe cylinder and a Cu cube sample are presented. A total number of 23 and 9 grains from the Fe and Cu samples, respectively, were indexed and reconstructed. Validation of the grain morphological reconstruction is performed by post-mortem EBSD of the Cu specimen.

Surface morphology smoothing of a 2 inch-diameter GaN homoepitaxial layer observed by X-ray diffraction topography

We investigated the surface morphology changes in a 2 inch-diameter, c-plane, free-standing GaN wafer using X-ray diffraction topography in a grazing-incidence geometry. We observed a decrease in the peak intensity and increase in the full width at half maximum of the GaN 112̄4 Bragg peak after the deposition of a homoepitaxial layer on the same GaN wafer. However, the lattice plane bending angles did not change after homoepitaxial layer deposition. Distorted-wave Born approximation calculations near the total external reflection condition revealed a decrease in the X-ray incidence angle of the 112̄4 Bragg peak after the homoepitaxial layer deposition. The decrease in both X-ray penetration and incidence angle induced broader and weaker diffraction peaks from the surface instead of the bulk GaN.

Intragranular three-dimensional stress tensor fields in plastically deformed polycrystals

The failure of polycrystalline materials used in infrastructure and transportation can be catastrophic. Multiscale modeling, which requires multiscale measurements of internal stress fields, is the key to predicting the deformation and failure of alloys. We determined the three-dimensional intragranular stress tensor fields in plastically deformed bulk steel using a high-energy x-ray microbeam. We observed intragranular local stresses that deviated greatly from the grain-averaged stresses and exceeded the macroscopic tensile strength. Even under deformation smaller than the uniform elongation, the intragranular stress fields were in highly triaxial stress states, which cannot be determined from the grain-averaged stresses. The ability to determine intragranular stress tensor fields can facilitate the understanding and prediction of the deformation and failure of materials through multiscale modeling.

Fast and quantitative 2D and 3D orientation mapping using Raman microscopy

Non-destructive orientation mapping is an important characterization tool in materials science and geoscience for understanding and/or improving material properties based on their grain structure. Confocal Raman microscopy is a powerful non-destructive technique for chemical mapping of organic and inorganic materials. Here we demonstrate orientation mapping by means of Polarized Raman Microscopy (PRM). While the concept that PRM is sensitive to orientation changes is known, to our knowledge, an actual quantitative orientation mapping has never been presented before. Using a concept of ambiguity-free orientation determination analysis, we present fast and quantitative single-acquisition Raman-based orientation mapping by simultaneous registration of multiple Raman scattering spectra obtained at different polarizations. We demonstrate applications of this approach for two- and three-dimensional orientation mapping of a multigrain semiconductor, a pharmaceutical tablet formulation and a polycrystalline sapphire sample. This technique can potentially move traditional X-ray and electron diffraction type experiments into conventional optical laboratories.

Although polarized Raman microscopy is sensitive to orientation changes, quantitative information has been missing. Here, the authors use simultaneous registration of multiple Raman scattering spectra obtained at different polarizations and show quantitative orientation mapping

Hardening and Strain Localisation in Helium-Ion-Implanted Tungsten

Tungsten is the main candidate material for plasma-facing armour components in future fusion reactors. In-service, fusion neutron irradiation creates lattice defects through collision cascades. Helium, injected from plasma, aggravates damage by increasing defect retention. Both can be mimicked using helium-ion-implantation. In a recent study on 3000 appm helium-implanted tungsten (W-3000He), we hypothesized helium-induced irradiation hardening, followed by softening during deformation. The hypothesis was founded on observations of large increase in hardness, substantial pile-up and slip-step formation around nano-indents and Laue diffraction measurements of localised deformation underlying indents. Here we test this hypothesis by implementing it in a crystal plasticity finite element (CPFE) formulation, simulating nano-indentation in W-3000He at 300 K. The model considers thermally-activated dislocation glide through helium-defect obstacles, whose barrier strength is derived as a function of defect concentration and morphology. Only one fitting parameter is used for the simulated helium-implanted tungsten; defect removal rate. The simulation captures the localised large pile-up remarkably well and predicts confined fields of lattice distortions and geometrically necessary dislocation underlying indents which agree quantitatively with previous Laue measurements. Strain localisation is further confirmed through high resolution electron backscatter diffraction and transmission electron microscopy measurements on cross-section lift-outs from centre of nano-indents in W-3000He.

Recent advances in characterising irradiation damage in tungsten for fusion power

Tungsten is the front-runner candidate for building the plasma-facing armour components for future fusion reactors. However, in-service irradiation by fusion-neutrons and helium will create lattice-defects in the material, compromising its properties and lifetime. Improving the component’s resilience to radiation damage and accurately predicting the lifetime of irradiated components is key for commercial feasibility of the reactor. For this purpose, understanding the creation and evolution of radiation damage is essential. This paper reviews recent advances in characterising radiation damage through experimental and modelling techniques. Tungsten-ion- and helium-ion-implantation are commonly used to mimic the damage created by neutron- and helium-irradiation respectively. Defects (> 1.5 nm) can be directly imaged using transmission electron microscopy while all defects (size-independent), may be indirectly probed by measuring lattice strains induced by them (using diffraction techniques; synchrotron X-rays or high-resolution electron-backscatter). Neutron-irradiation produces mainly ½〈111〉 prismatic loops. Loop-interaction and structural organisation evolves with changing implantation dose and temperature. Helium-irradiation, < 573 K, induces formation of small helium-vacancy clusters, which evolve into bubbles, blisters and “fuzz” structure with changing temperature and dose. Nano-indentation or micro-cantilever bending tests can be used to examine mechanical properties of ion-implanted layers. Both helium- and neutron-implantation defects induce increased hardening often followed by subsequent strain-softening and localised deformation. Such irradiation-induced alterations are detrimental to material ductility and long-term structural integrity of tungsten-based components. Development of physically-based material models that capture the physics of underlying irradiation-induced changes, inspire confidence of reliably using simulations to predict mechanical behaviour and in-service performance of irradiated engineering components in future.

Super-Resolution Scanning Transmission X-Ray Imaging Using Single Biconcave Parabolic Refractive Lens Array

A new super resolution imaging technique which potentially enables sub-µm spatial resolution, using a detector of pixels much larger than the spatial resolution, is proposed. The method utilizes sample scanning through a large number of identical X-ray microprobes periodically spaced (the period corresponds to a multiple of the pixel size), which reduces drastically the scanning time. The information about the sample illuminated by the microprobes is stored by large detector pixels. Using these data and sample position information, a super-resolution image reconstruction is performed. With a one-dimensional (1D) high aspect ratio nickel single lens array designed for theoretically expected sub-µm microprobes at 17 keV and fabricated by deep X-ray lithography and electroforming technique, 2 µm X-ray microprobes with a period of 10 µm were achieved. We performed a first experiment at KARA synchrotron facility, and it was demonstrated that the smallest structure of a test pattern with a size of 1.5 µm could be easily resolved by using images generated from a detector having a pixel size of 10.4 µm. This new approach has a great potential for providing a new microscopic imaging modality with a large field of view and short scan time.

Alignment of sample position and rotation during in situ synchrotron X-ray micro-diffraction experiments using a Laue cross-correlation approach

Laue micro-diffraction has proven to be able to reveal material properties at the sub-grain scale for many polycrystalline materials and is now routinely available at several synchrotron facilities, providing an approach for nondestructive three-dimensional probing of the microstructures and mechanical states of materials. However, for in situ experiments, maintaining the positioning of the sample throughout the experiment, to achieve a good alignment of the characterized volumes, is a challenging issue. The aim of the present work is to address this problem by developing an approach based on digital image correlation of focused-beam Laue diffraction patterns. The method uses small changes in the diffraction signal as a focused X-ray beam is scanned over a surface region to allow corrections to be made for both sample lateral movement and rotation. The method is demonstrated using a tensile deformation experiment on an Al sample with 2.5 µm average grain size. The results demonstrate an accuracy of 0.5 µm for sample position registration and a precision in sample rotation of ∼0.01°. The proposed method is fast to implement and does not require the use of additional surface markers.

3D grain reconstruction from laboratory diffraction contrast tomography

A novel reconstruction method to retrieve grain structure from laboratory diffraction contrast tomography is presented and evaluated.

A method for reconstructing the three-dimensional grain structure from data collected with a recently introduced laboratory-based X-ray diffraction contrast tomography system is presented. Diffraction contrast patterns are recorded in Laue-focusing geometry. The diffraction geometry exposes shape information within recorded diffraction spots. In order to yield the three-dimensional crystallographic microstructure, diffraction spots are extracted and fed into a reconstruction scheme. The scheme successively traverses and refines solution space until a reasonable reconstruction is reached. This unique reconstruction approach produces results efficiently and fast for well suited samples.

Laue three dimensional neutron diffraction

This article presents a measurement technique and data analysis tool to perform 3D grain distribution mapping and indexing of oligocrystalline samples using neutrons: Laue three-dimensional neutron diffraction (Laue3DND). The approach builds on forward modelling used for correlation and multiple fitting of the measured diffraction spots relative to individual grains. This enables not only to identify individual grains, but also their position and orientation in the sample. The feasibility and performance of the Laue3DND approach are tested using multi-grain synthetic datasets from cubic (α-Fe) and tetragonal (YBaCuFeO₅) symmetries. Next, experimental results from two data sets measured at the FALCON instrument of Helmholtz-Zentrum Berlin are presented: A cylindrical alpha iron (α-Fe) reference sample with 5 mm diameter and 5 mm height, as well as a 2 mm³ layered perovskite (YBaCuFeO₅). Using Laue3DND, we were able to retrieve the position and orientation of 97 out of 100 grains from a synthetic α-Fe data set, as well as 24 and 9 grains respectively from the α-Fe and YBaCuFeO₅ sample measured at FALCON. Results from the synthetic tests also indicate that Laue3DND is capable of indexing 10 out of 10 grains for both symmetries in two extreme scenarios: using only 6 Laue projections and using 360 projections with extremely noisy data. The precision achieved in terms of spatial and orientation resolution for the current version of the method is 430 μm and 1° respectively. Based on these results obtained, we are confident to present a tool that expands the capabilities of standard Laue diffraction, providing the number, position, orientation and relative size of grains in oligocrystalline samples.

High Resolution Mapping of Orientation and Strain Gradients in Metals by Synchrotron 3D X-ray Laue Microdiffraction

Synchrotron 3D X-ray Laue microdiffraction, available at beamline 34-ID-E at Advanced Photon Source in Argonne National Laboratory, is a powerful tool for 3D non-destructive mapping of local orientations and strains at sub-micron scale in the bulk. With this technique, it is possible to study local residual stresses developed during manufacturing or while in service due to interactions between, for example, different phases and/or grains with different orientations in materials containing multiple or single phase(s). Such information is essential for understanding mechanical properties and designing advanced materials, but is largely non-existent in the current generation of materials models. In the present paper, the principle and experimental set-up of the 3D microdiffraction are introduced, followed by a description of a method for quantification of the local plastic deformation based on high-angular-resolution orientation maps. The quantification of local residual stresses in two model materials, ductile cast iron (two phases) and partially recrystallized pure nickel (single phase), using 3D microdiffraction will then be presented. The results show that 3D microdiffraction is important for understanding the origin of local residual stresses and to relate them to the microstructural evolution. Finally, the limitations of the 3D microdiffraction on the current generation synchrotron source and new possibilities after the synchrotron upgrade are discussed.

Scanning 3DXRD Measurement of Grain Growth, Stress, and Formation of Cu6Sn5 around a Tin Whisker during Heat Treatment

The 3D microstructure around a tin whisker, and its evolution during heat treatment were studied using scanning 3DXRD. The shape of each grain in the sample was reconstructed using a filtered-back-projection algorithm. The local lattice parameters and grain orientations could then be refined, using forward modelling of the diffraction data, with a spatial resolution of 250 nm. It was found that the tin coating had a texture where grains were oriented such that their c-axes were predominantly parallel to the sample surface. Grains with other orientations were consumed by grain growth during the heat treatment. Most of the grain boundaries were found to have misorientations larger than 15∘, and many coincidence site lattice (CSL) or other types of low-energy grain boundaries were identified. None of the grains with CSL grain boundaries were consumed by grain growth. During the heat treatment, growth of preexisting Cu₆Sn₅ occurred; these grains were indexed as a hexagonal η phase, which is usually documented to be stable only at temperatures exceeding 186 ∘C. This indicates that the η phase can exist in a metastable state for long periods. The tin coating was found to be under compressive hydrostatic stress, with a negative gradient in hydrostatic stress extending outwards from the root of the whisker. Negative stress gradients are generally believed to play an essential role in providing the driving force for diffusion of material to the whisker root.

In situ analysis of deformation twins within a magnesium polycrystal: (II) twin growth

The process of twin growth is difficult to be captured instantaneously. Synchrotron polychromatic X-ray microdiffraction (micro-XRD) is applied to in situ study twin growth in extruded Mg-3Al-1Zn polycrystal subjected to uniaxial tension. The micro-XRD data is used to map an area of 396 × 200 μm² under the loading levels from 12 MPa to 73 MPa. The orientations of seven parents and ten resultant twins are determined by indexing Laue patterns, while their morphologies are mapped by the integrated intensities of particular reflections. {101¯2} twins are detected at 64 MPa. The maximum SF criterion for twin variant selection is invalid here. Twin growth rates are deduced from the variation of integrated intensities between 64 MPa and 68 MPa. It is found that twin growth rates in the HCP material are not proportional to active twin's SF values, though the SF value is related to the magnitude of driving resource. Twin growth rate exhibits obvious anisotropy, either for lengthwise growth rate or thickness growth rate. When two twins within a parent belong to the same twin variant, they exhibit similar growth rates. Meanwhile, when two twins within a parent come across, one can block the other and the latter occur shrinking.

Methods for operando coherent X-ray diffraction of battery materials at the Advanced Photon Source

Bragg coherent X-ray diffraction imaging has become valuable for visualization of the structural, morphological and strain evolution of crystals in operando electrode materials. As the electrode material particles (either in a single-crystal form or an aggregation form of single crystals) are evenly dispersed and randomly oriented in the electrode laminate, the submicrometer-sized coherentX-ray beam can be used to probe the local properties of electrode material crystals using two approaches. Coherent multi-crystal diffraction provides collective structural information of phase transitions in tens of crystals simultaneously as well as the individual behavior from single crystals, which are oriented at the Bragg condition in the X-ray illumination volume. Bragg coherent diffractive imaging enables one to monitor the evolution of the morphology and strain in individual crystals. This work explores and highlights the Bragg coherent X-ray diffraction measurements of battery electrode materials in operando conditions at the 34-ID-C beamline at the Advanced Photon Source. The experiment is demonstrated with NaNi_1/3Fe_1/3Mn_1/3O₂, a sodium-ion cathode material loaded in a half cell. The paper will discuss, in detail, the beamline setup, sample mounting and handling, alignment strategies and the data acquisition protocols.

Deformation twinning and grain partitioning in a hexagonal close-packed magnesium alloy

Pervasive deformation twinning in magnesium greatly affects its strength and formability. The local stress fields associated with twinning play a key role on deformation behavior and fracture but are extremely difficult to characterize experimentally. In this study, we perform synchrotron experiments with differential-aperture X-ray microscopy to measure the 3D stress fields in the vicinity of a twin with a spatial resolution of 0.5 micrometer. The measured local stress field aids to identify the sequence of events involved with twinning. We find that the selected grain deforms elastically before twinning, and the twin formation splits the grain into two non-interacting domains. Under further straining one domain of the grain continued to deform elastically, whereas the other domain deforms plastically by prismatic slip. This heterogeneous deformation behavior may be mediated by the surrounding medium and it is likely to lead to asymmetric twin growth.

Fluid-structure interaction simulation of the brain-skull interface for acute subdural haematoma prediction

Traumatic brain injury is a leading cause of disability and mortality. Finite element-based head models are promising tools for enhanced head injury prediction, mitigation and prevention. The reliability of such models depends heavily on adequate representation of the brain-skull interaction. Nevertheless, the brain-skull interface has been largely simplified in previous three-dimensional head models without accounting for the fluid behaviour of the cerebrospinal fluid (CSF) and its mechanical interaction with the brain and skull. In this study, the brain-skull interface in a previously developed head model is modified as a fluid-structure interaction (FSI) approach, in which the CSF is treated on a moving mesh using an arbitrary Lagrangian-Eulerian multi-material formulation and the brain on a deformable mesh using a Lagrangian formulation. The modified model is validated against brain-skull relative displacement and intracranial pressure responses and subsequently imposed to an experimentally determined loading known to cause acute subdural haematoma (ASDH). Compared to the original model, the modified model achieves an improved validation performance in terms of brain-skull relative motion and is able to predict the occurrence of ASDH more accurately, indicating the superiority of the FSI approach for brain-skull interface modelling. The introduction of the FSI approach to represent the fluid behaviour of the CSF and its interaction with the brain and skull is crucial for more accurate head injury predictions.

Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform

Many spectral responses in materials science, physics, and chemistry experiments can be characterized as resulting from the superposition of a number of more basic individual spectra. In this context, unmixing is defined as the problem of determining the individual spectra, given measurements of multiple spectra that are spatially resolved across samples, as well as the determination of the corresponding abundance maps indicating the local weighting of each individual spectrum. Matrix factorization is a popular linear unmixing technique that considers that the mixture model between the individual spectra and the spatial maps is linear. Here, we present a tutorial paper targeted at domain scientists to introduce linear unmixing techniques, to facilitate greater understanding of spectroscopic imaging data. We detail a matrix factorization framework that can incorporate different domain information through various parameters of the matrix factorization method. We demonstrate many domain-specific examples to explain the expressivity of the matrix factorization framework and show how the appropriate use of domain-specific constraints such as non-negativity and sum-to-one abundance result in physically meaningful spectral decompositions that are more readily interpretable. Our aim is not only to explain the off-the-shelf available tools, but to add additional constraints when ready-made algorithms are unavailable for the task. All examples use the scalable open source implementation from https://github.com/ramkikannan/nmflibrary that can run from small laptops to supercomputers, creating a user-wide platform for rapid dissemination and adoption across scientific disciplines.

Three-dimensional geometrical and topological characteristics of grains in conventional and grain boundary engineered 316L stainless steel

The three-dimensional microstructures of a conventional 316L stainless steel and the same material after grain boundary (GB) engineering have been measured by serial sectioning coupled with electron backscatter diffraction mapping. While it is well known that GB engineered materials are differentiated from conventional materials because of the proportion of coincidence site lattice boundaries, the size of their twin-related domains, and their reduced random boundary connectivity, this work provides a quantitative comparison of the geometrical and topological characteristics of grains in 316L stainless steel before and after GB engineering. Specifically, the numbers of grain faces, triple lines, and quadruple unions per grain have been measured and compared. In addition, the distributions of grain sizes, surface areas, and grain boundary areas have been measured and compared. The results show that, in many ways, the three-dimensional geometrical and topological characteristics of the grains in the GB engineered and conventional materials are similar. In both materials, the distributions of the geometrical parameters are well represented by a log-normal distribution. Comparatively, the GB engineered microstructure has grains that, on average, have both fewer faces and higher (specific) surface areas that deviate more from an ideal equiaxed shape, but there are several eccentric or non-compact shaped grains that have a huge number of faces and extremely large surface area in the GB engineered material. All of these characteristics are likely to be a result of the increased number of twins in the GB engineered microstructure. These eccentric grains would have a positive influence on increasing the resistance to intergranular degradation.

Towards 3D crystal orientation reconstruction using automated crystal orientation mapping transmission electron microscopy (ACOM-TEM)

To relate the internal structure of a volume (crystallite and phase boundaries) to properties (electrical, magnetic, mechanical, thermal), a full 3D reconstruction in combination with in situ testing is desirable. In situ testing allows the crystallographic changes in a material to be followed by tracking and comparing the individual crystals and phases. Standard transmission electron microscopy (TEM) delivers a projection image through the 3D volume of an electron-transparent TEM sample lamella. Only with the help of a dedicated TEM tomography sample holder is an accurate 3D reconstruction of the TEM lamella currently possible. 2D crystal orientation mapping has become a standard method for crystal orientation and phase determination while 3D crystal orientation mapping have been reported only a few times. The combination of in situ testing with 3D crystal orientation mapping remains a challenge in terms of stability and accuracy. Here, we outline a method to 3D reconstruct the crystal orientation from a superimposed diffraction pattern of overlapping crystals without sample tilt. Avoiding the typically required tilt series for 3D reconstruction enables not only faster in situ tests but also opens the possibility for more stable and more accurate in situ mechanical testing. The approach laid out here should serve as an inspiration for further research and does not make a claim to be complete.

EBSD-assisted Laue microdiffraction for microstrain analysis

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.