Owing to their exceptional properties, hard materials such as advanced ceramics, metals and composites have enormous economic and societal value, with applications across numerous industries. Understanding their microstructural characteristics is crucial for enhancing their performance, materials development and unleashing their potential for future innovative applications. However, their microstructures are unambiguously hierarchical and typically span several length scales, from sub-ångstrom to micrometres, posing demanding challenges for their characterization, especially for in situ characterization which is critical to understanding the kinetic processes controlling microstructure formation. This review provides a comprehensive description of the rapidly developing technique of ultra-small angle X-ray scattering (USAXS), a nondestructive method for probing the nano-to-micrometre scale features of hard materials. USAXS and its complementary techniques, when developed for and applied to hard materials, offer valuable insights into their porosity, grain size, phase composition and inhomogeneities. We discuss the fundamental principles, instrumentation, advantages, challenges and global status of USAXS for hard materials. Using selected examples, we demonstrate the potential of this technique for unveiling the microstructural characteristics of hard materials and its relevance to advanced materials development and manufacturing process optimization. We also provide our perspective on the opportunities and challenges for the continued development of USAXS, including multimodal characterization, coherent scattering, time-resolved studies, machine learning and autonomous experiments. Our goal is to stimulate further implementation and exploration of USAXS techniques and inspire their broader adoption across various domains of hard materials science, thereby driving the field toward discoveries and further developments.

Identifying and characterizing metal-binding sites (MBS) within macromolecular structures is imperative for elucidating their biological functions. CheckMyMetal (CMM) is a web based tool that facilitates the interactive valid­ation of MBS in structures determined through X-ray crystallography and cryo-electron microscopy (cryo-EM). Recent updates to CMM have significantly enhanced its capability to efficiently handle large datasets generated from cryo-EM structural analyses. In this study, we address various challenges inherent in validating MBS within both X-ray and cryo-EM structures. Specifically, we examine the difficulties associated with accurately identifying metals and modeling their coordination environments by considering the ongoing reproducibility challenges in structural biology and the critical importance of well annotated, high-quality experimental data. CMM employs a sophisticated framework of rules rooted in the valence bond theory for MBS validation. We explore how CMM validation parameters correlate with the resolution of experimentally derived structures of macromolecules and their complexes. Additionally, we showcase the practical utility of CMM by analyzing a representative cryo-EM structure. Through a comprehensive examination of experimental data, we demonstrate the capability of CMM to advance MBS characterization and identify potential instances of metal misassignment.

Biological materials have outstanding properties. With ease, challenging mechanical, optical or electrical properties are realised from comparatively `humble' building blocks. The key strategy to realise these properties is through extensive hierarchical structuring of the material from the millimetre to the nanometre scale in 3D. Though hierarchical structuring in biological materials has long been recognized, the 3D characterization of such structures remains a challenge. To understand the behaviour of materials, multimodal and multi-scale characterization approaches are needed. In this review, we outline current X-ray analysis approaches using the structures of bone and shells as examples. We show how recent advances have aided our understanding of hierarchical structures and their functions, and how these could be exploited for future research directions. We also discuss current roadblocks including radiation damage, data quantity and sample preparation, as well as strategies to address them.

Ultrafast, high-intensity X-ray free-electron lasers can perform diffraction imaging of single protein molecules. Various algorithms have been developed to determine the orientation of each single-particle diffraction pattern and reconstruct the 3D diffraction intensity. Most of these algorithms rely on the premise that all diffraction patterns originate from identical protein molecules. However, in actual experiments, diffraction patterns from multiple different molecules may be collected simultaneously. Here, we propose a predicted model-aided one-step classification–multireconstruction algorithm that can handle mixed diffraction patterns from various molecules. The algorithm uses predicted structures of different protein molecules as templates to classify diffraction patterns based on correlation coefficients and determines orientations using a correlation maximization method. Tests on simulated data demonstrated high accuracy and efficiency in classification and reconstruction.

A significant part of the present and future of optoelectronic devices lies on thin multilayer heterostructures. Their optical properties depend strongly on strain, being essential to the knowledge of the stress level to optimize the growth process. Here the structural and microstructural characteristics of sub-micron a-ZnO epilayers (12 to 770 nm) grown on r-sapphire by metal–organic chemical vapour deposition are studied. Morphological and structural studies have been made using scanning electron microscopy and high-resolution X-ray diffraction. Plastic unit-cell distortion and corresponding strain have been determined as a function of film thickness. A critical thickness has been observed as separating the non-elastic/elastic states with an experimental value of 150–200 nm. This behaviour has been confirmed from ultraviolet photoelectron spectroscopy, X-ray photoelectron spectroscopy and high-resolution transmission electron microscopy measurements. An equation that gives the balance of strains is proposed as an interesting method to experimentally determine this critical thickness. It is concluded that in the thinnest films an elongation of the Zn—O bond takes place and that the plastic strained ZnO films relax through nucleation of misfit dislocations, which is a consequence of three-dimensional surface morphology.

The title compound dipotassium gadolinium(III) phosphate(V) molybdate(VI), K2Gd(PO4)(MoO4), was synthesized from a high-temperature melt starting from GdF3 as a source of gadolinium. Its structure is isotypic with other MI2MIII(MVIO4)(PO4) compounds, where MI = Na, K or Cs, and MIII = rare-earth cation, MVI = Mo or W. The three-dimensional framework is built up from [Gd(PO4)(MoO4)] anionic sheets, which are organized by adhesion of [GdPO4] layers and [MoO4] tetra­hedra stacked above and below these layers. The inter­stitial space is occupied by K cations having eightfold oxygen coordination. The polyhedron of GdO8 was estimated to be a triangular dodeca­hedron by the continuous shape measurement method.

The crystal structure of the title compound {systematic name: (4S,4aS,5aR,12aR)-4,7-bis­(di­methyl­amino)-9-[(2,2-di­methyl­propyl­amino)­meth­yl]-1,10,11,12a-tetra­hydroxy-3,12-dioxo-4a,5,5a,6-tetra­hydro-4H-tetra­cene-2-carb­oxamide dihydrate, C29H40N4O7·2H2O} has been solved and refined using synchrotron X-ray powder diffraction data: it crystallizes in space group R3 with a = 24.34430 (7), c = 14.55212 (4) Å, V = 7468.81 (2) Å3 and Z = 9. Most of the hydrogen bonds are intra­molecular, but two classical N—H⋯O inter­molecular hydrogen bonds (along with probable weak C—H⋯O and C—H⋯N hydrogen bonds) link the mol­ecules into a three-dimensional framework. The framework contains voids, which contain disordered water mol­ecules. Keto–enol tautomerism is apparently important in this mol­ecule, and the exact mol­ecular structure is ambiguous.

A hard X-ray single-shot spectrometer comprising thin, bent Si crystals has been developed for the Pohang Accelerator Laboratory X-ray Free-Electron Laser (XFEL), for detailed analysis of ultrafast 4.5–17 keV XFEL pulses with a high spectral resolution. This instrument facilitates shot-to-shot spectral structure monitoring and optimization of the operating conditions of the XFEL owing to its ability to provide comprehensive data on the spectral properties and fluctuations of self-amplified spontaneous emission, monochromatic and seeded XFEL modes.

The development of instrumentation as well as applications for megahertz X-ray phase contrast imaging at the Single Particles, Clusters, and Biomolecules and Serial Femtosecond Crystallography instrument of the European XFEL are introduced here.

This review focuses on low-dose near-field X-ray speckle phase imaging in the differential mode introducing the existing algorithms with their specifications and comparing their performances under various experimental conditions.

In this work, we showed that the use of ethanol to increase image contrast when imaging cardiac tissue with synchrotron X-ray phase-contrast imaging (X-PCI) leads to heterogeneous tissue shrinkage, which has an impact on the 3D organization of the myocardium.

we introduce a novel approach for a real-time dual-frequency feedback system, which has been firstly used at the hard X-ray nanoprobe beamline of SSRF. The BiBEST can then efficiently stabilize X-ray beam position and stability in parallel, making use of different optical systems in the beamline.

Time-resolved high-energy X-ray diffraction was used during growth of ultrathin NixFe3−xO4 films with varying Ni content (0 ≤ x ≤ 1.5) deposited on MgO(001) substrates by reactive molecular beam epitaxy, providing an insight into the growth dynamics of these films. In order to obtain structural information, reciprocal-space maps were recorded and the temporal evolution of the Bragg peaks specific to the octahedral and tetrahedral lattice sites of the inverse spinel structure of NixFe3−xO4 was observed during growth of the films. A time delay, corresponding to a coverage of 1.2–1.8 nm, between the appearance of the Bragg reflections originating from octahedral sites and reflections originating exclusively from tetrahedral sites indicates that the ferrite films grow in two stages. In the initial growth phase, a rock salt interface layer is formed. Afterwards, a structural transition occurs and the films grow in an inverse spinel structure. The thickness of the initial rock salt phase was found to increase with Ni content and to be responsible for atypical strain in the thin films. Films with Ni contents x > 1 do not show a structural transition. These films remain in a (deficient) rock salt structure consisting of a mixed Ni–Fe oxide and do not form a spinel structure at all. They show an increased number of NiO clusters as detected by X-ray photoelectron spectroscopy of the valence band, accompanied by a significant roughening of the films.

An implementation of Slater-type spherical scattering factors for X-ray and electron diffraction for elements in the range Z = 1–103 is presented within the software Olex2. Both high- and low-angle Fourier behaviour of atomic electron density and electrostatic potential can thus be addressed, in contrast to the limited flexibility of the four Gaussian plus constant descriptions which are currently the most widely used method for calculating atomic scattering factors during refinement. The implementation presented here accommodates the increasing complexity of the electronic structure of heavier elements by using complete atomic wavefunctions without any interpolation between precalculated tables or intermediate fitting functions. Atomic wavefunctions for singly charged ions are implemented and made accessible, and these show drastic changes in electron diffraction scattering factors compared with the neutral atom. A comparison between the two different spherical models of neutral atoms is presented as an example for four different kinds of X-ray and two electron diffraction structures, and comparisons of refinement results using the existing diffraction data are discussed. A systematic but slight improvement in R values and residual densities can be observed when using the new scattering factors, and this is discussed relative to effects on the atomic displacement parameters and atomic positions, which are prominent near the heavier elements in a structure.

INSIGHT is a Python-based software tool for processing and reducing 2D grazing-incidence wide- and small-angle X-ray scattering (GIWAXS/GISAXS) data. It offers the geometric transformation of the 2D GIWAXS/GISAXS detector image to reciprocal space, including vectorized and parallelized pixel-wise intensity correction calculations. An explicit focus on efficient data management and batch processing enables full control of large time-resolved synchrotron and laboratory data sets for a detailed analysis of kinetic GIWAXS/GISAXS studies of thin films. It processes data acquired with arbitrarily rotated detectors and performs vertical, horizontal, azimuthal and radial cuts in reciprocal space. It further allows crystallographic indexing and GIWAXS pattern simulation, and provides various plotting and export functionalities. Customized scripting offers a one-step solution to reduce, process, analyze and export findings of large in situ and operando data sets.

The suitability of point focus X-ray beam and area detector techniques for the determination of the uniaxial symmetry axis (fibre texture) of the natural mineral satin spar is demonstrated. Among the various diffraction techniques used in this report, including powder diffraction, 2D pole figures, rocking curves looped on φ and 2D X-ray diffraction, a single simple symmetric 2D scan collecting the reciprocal plane perpendicular to the apparent fibre axis provided sufficient information to determine the crystallographic orientation of the fibre axis. A geometrical explanation of the `wing' feature formed by diffraction spots from the fibre-textured satin spar in 2D scans is provided. The technique of wide-range reciprocal space mapping restores the `wing' featured diffraction spots on the 2D detector back to reciprocal space layers, revealing the nature of the fibre-textured samples.

The maximum range of perpendicular momentum transfer (qz) has been tripled for X-ray scattering from liquid surfaces when using a double-crystal deflector setup to tilt the incident X-ray beam. This is achieved by employing a higher-energy X-ray beam to access Miller indices of reflecting crystal atomic planes that are three times higher than usual. The deviation from the exact Bragg angle condition induced by misalignment between the X-ray beam axis and the main rotation axis of the double-crystal deflector is calculated, and a fast and straightforward procedure to align them is deduced. An experimental method of measuring scattering intensity along the qz direction on liquid surfaces up to qz = 7 Å−1 is presented, with liquid copper serving as a reference system for benchmarking purposes.

X-ray diffraction from dislocation half-loops consisting of a misfit segment with two threading arms extending from it to the surface is calculated by the Monte Carlo method. The diffraction profiles and reciprocal space maps are controlled by the ratio of the total lengths of the misfit and the threading segments of the half-loops. A continuous transformation from the diffraction characteristic of misfit dislocations to that of threading dislocations with increasing thickness of epitaxial film is studied. Diffraction from dislocations with edge- and screw-type threading arms is considered and the contributions of the two types of dislocations are compared.

Fluctuation X-ray scattering (FXS) offers a complementary approach for nano- and bioparticle imaging with an X-ray free-electron laser (XFEL), by extracting structural information from correlations in scattered XFEL pulses. Here a workflow is presented for single-particle structure determination using FXS. The workflow includes procedures for extracting the rotational invariants from FXS patterns, performing structure reconstructions via iterative phasing of the invariants, and aligning and averaging multiple reconstructions. The reconstruction pipeline is implemented in the open-source software xFrame and its functionality is demonstrated on several simulated structures.

This work introduces X-Ray Calc (XRC), an open-source software package designed to simulate X-ray reflectivity (XRR) and address the inverse problem of reconstructing film structures on the basis of measured XRR curves. XRC features a user-friendly graphical interface that facilitates interactive simulation and reconstruction. The software employs a recursive approach based on the Fresnel equations to calculate XRR and incorporates specialized tools for modeling periodic multilayer structures. This article presents the latest version of the X-Ray Calc software (XRC3), with notable improvements. These enhancements encompass an automatic fitting capability for XRR curves utilizing a modified flight particle swarm optimization algorithm. A novel cost function was also developed specifically for fitting XRR curves of periodic structures. Furthermore, the overall user experience has been enhanced by developing a new single-window interface.

Dark-field X-ray microscopy (DFXM) is a full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM, an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. This work explores contrast methods and optimizes the DFXM setup specifically for the case of mapping dislocations. Forward projections of detector images are generated using two complementary simulation tools based on geometrical optics and wavefront propagation, respectively. Weak and strong beam contrast and the mapping of strain components are studied. The feasibility of observing dislocations in a wall is elucidated as a function of the distance between neighbouring dislocations and the spatial resolution. Dislocation studies should be feasible with energy band widths of 10−2, of relevance for fourth-generation synchrotron and X-ray free-electron laser sources.

X-ray reflectometry (XRR) is a powerful tool for probing the structural characteristics of nanoscale films and layered structures, which is an important field of nanotechnology and is often used in semiconductor and optics manufacturing. This study introduces a novel approach for conducting quantitative high-resolution millisecond monochromatic XRR measurements. This is an order of magnitude faster than in previously published work. Quick XRR (qXRR) enables real time and in situ monitoring of nanoscale processes such as thin film formation during spin coating. A record qXRR acquisition time of 1.4 ms is demonstrated for a static gold thin film on a silicon sample. As a second example of this novel approach, dynamic in situ measurements are performed during PMMA spin coating onto silicon wafers and fast fitting of XRR curves using machine learning is demonstrated. This investigation primarily focuses on the evolution of film structure and surface morphology, resolving for the first time with qXRR the initial film thinning via mass transport and also shedding light on later thinning via solvent evaporation. This innovative millisecond qXRR technique is of significance for in situ studies of thin film deposition. It addresses the challenge of following intrinsically fast processes, such as thin film growth of high deposition rate or spin coating. Beyond thin film growth processes, millisecond XRR has implications for resolving fast structural changes such as photostriction or diffusion processes.

The strong metal–support interaction (SMSI) is a phenomenon observed in supported metal catalyst systems in which reducible metal oxide supports can form overlayers over the surface of active metal nanoparticles (NPs) under a hydrogen (H2) environment at elevated temperatures. SMSI has been shown to affect catalyst performance in many reactions by changing the type and number of active sites on the catalyst surface. Laboratory methods for the analysis of SMSI at the nanoparticle-ensemble level are lacking and mostly based on indirect evidence, such as gas chemisorption. Here, we demonstrate the possibility to detect and characterize SMSIs in Co/TiOx model catalysts using the laboratory X-ray standing wave (XSW) technique for a large ensemble of NPs at the bulk scale. We designed a thermally stable MoNx/SiNx periodic multilayer to retain XSW generation after reduction with H2 gas at 600°C. The model catalyst system was synthesized here by deposition of a thin TiOx layer on top of the periodic multilayer, followed by Co NP deposition via spare ablation. A partial encapsulation of Co NPs by TiOx was identified by analyzing the change in Ti atomic distribution. This novel methodological approach can be extended to observe surface restructuring of model catalysts in situ at high temperature (up to 1000°C) and pressure (≤3 mbar), and can also be relevant for fundamental studies in the thermal stability of membranes, as well as metallurgy.

This article describes a correction procedure for the removal of indirect background contributions to measured small-angle X-ray scattering patterns. The high scattering power of a sample in the ultra-small-angle region may serve as a secondary source for a window placed in front of the detector. The resulting secondary scattering appears as a sample-dependent background in the measured pattern that cannot be directly subtracted. This is an intricate problem in measurements at ultra-low angles, which can significantly reduce the useful dynamic range of detection. Two different procedures are presented to retrieve the real scattering profile of the sample.

Due to the ambiguity related to the lack of phase information, determining the physical parameters of multilayer thin films from measured neutron and X-ray reflectivity curves is, on a fundamental level, an underdetermined inverse problem. This ambiguity poses limitations on standard neural networks, constraining the range and number of considered parameters in previous machine learning solutions. To overcome this challenge, a novel training procedure has been designed which incorporates dynamic prior boundaries for each physical parameter as additional inputs to the neural network. In this manner, the neural network can be trained simultaneously on all well-posed subintervals of a larger parameter space in which the inverse problem is underdetermined. During inference, users can flexibly input their own prior knowledge about the physical system to constrain the neural network prediction to distinct target subintervals in the parameter space. The effectiveness of the method is demonstrated in various scenarios, including multilayer structures with a box model parameterization and a physics-inspired special parameterization of the scattering length density profile for a multilayer structure. In contrast to previous methods, this approach scales favourably when increasing the complexity of the inverse problem, working properly even for a five-layer multilayer model and a periodic multilayer model with up to 17 open parameters.

Processing of single-crystal X-ray diffraction data from area detectors can be separated into two steps. First, raw intensities are obtained by integration of the diffraction images, and then data correction and reduction are performed to determine structure-factor amplitudes and their uncertainties. The second step considers the diffraction geometry, sample illumination, decay, absorption and other effects. While absorption is only a minor effect in standard macromolecular crystallography (MX), it can become the largest source of uncertainty for experiments performed at long wavelengths. Current software packages for MX typically employ empirical models to correct for the effects of absorption, with the corrections determined through the procedure of minimizing the differences in intensities between symmetry-equivalent reflections; these models are well suited to capturing smoothly varying experimental effects. However, for very long wavelengths, empirical methods become an unreliable approach to model strong absorption effects with high fidelity. This problem is particularly acute when data multiplicity is low. This paper presents an analytical absorption correction strategy (implemented in new software AnACor) based on a volumetric model of the sample derived from X-ray tomography. Individual path lengths through the different sample materials for all reflections are determined by a ray-tracing method. Several approaches for absorption corrections (spherical harmonics correction, analytical absorption correction and a combination of the two) are compared for two samples, the membrane protein OmpK36 GD, measured at a wavelength of λ = 3.54 Å, and chlorite dismutase, measured at λ = 4.13 Å. Data set statistics, the peak heights in the anomalous difference Fourier maps and the success of experimental phasing are used to compare the results from the different absorption correction approaches. The strategies using the new analytical absorption correction are shown to be superior to the standard spherical harmonics corrections. While the improvements are modest in the 3.54 Å data, the analytical absorption correction outperforms spherical harmonics in the longer-wavelength data (λ = 4.13 Å), which is also reflected in the reduced amount of data being required for successful experimental phasing.

The capillary wave model of a liquid surface predicts both the X-ray specular reflection and the diffuse scattering around it. A quantitative method is presented to obtain the X-ray reflectivity (XRR) from a liquid surface through the diffuse scattering data around the specular reflection measured using a grazing incidence X-ray off-specular scattering (GIXOS) geometry at a fixed horizontal offset angle with respect to the plane of incidence. With this approach the entire Qz-dependent reflectivity profile can be obtained at a single, fixed incident angle. This permits a much faster acquisition of the profile than with conventional reflectometry, where the incident angle must be scanned point by point to obtain a Qz-dependent profile. The XRR derived from the GIXOS-measured diffuse scattering, referred to in this paper as pseudo-reflectivity, provides a larger Qz range compared with the reflectivity measured by conventional reflectometry. Transforming the GIXOS-measured diffuse scattering profile to pseudo-XRR opens up the GIXOS method to widely available specular XRR analysis software tools. Here the GIXOS-derived pseudo-XRR is compared with the XRR measured by specular reflectometry from two simple vapor–liquid interfaces at different surface tension, and from a hexadecyltri­methyl­ammonium bromide monolayer on a water surface. For the simple liquids, excellent agreement (beyond 11 orders of magnitude in signal) is found between the two methods, supporting the approach of using GIXOS-measured diffuse scattering to derive reflectivities. Pseudo-XRR obtained at different horizontal offset angles with respect to the plane of incidence yields indistinguishable results, and this supports the robustness of the GIXOS-XRR approach. The pseudo-XRR method can be extended to soft thin films on a liquid surface, and criteria are established for the applicability of the approach.

Controlling the shape and size dispersivity and crystallinity of nanoparticles (NPs) has been a challenge in identifying these parameters' role in the physical and chemical properties of NPs. The need for reliable quantitative tools for analyzing the dispersivity and crystallinity of NPs is a considerable problem in optimizing scalable synthesis routes capable of controlling NP properties. The most common tools are electron microscopy (EM) and X-ray scattering techniques. However, each technique has different susceptibility to these parameters, implying that more than one technique is necessary to characterize NP systems with maximum reliability. Wide-angle X-ray scattering (WAXS) is mandatory to access information on crystallinity. In contrast, EM or small-angle X-ray scattering (SAXS) is required to access information on whole NP sizes. EM provides average values on relatively small ensembles in contrast to the bulk values accessed by X-ray techniques. Besides the fact that the SAXS and WAXS techniques have different susceptibilities to size distributions, SAXS is easily affected by NP–NP interaction distances. Because of all the variables involved, there have yet to be proposed methodologies for cross-analyzing data from two techniques that can provide reliable quantitative results of dispersivity and crystallinity. In this work, a SAXS/WAXS-based methodology is proposed for simultaneously quantifying size distribution and degree of crystallinity of NPs. The most reliable easy-to-access size result for each technique is demonstrated by computer simulation. Strategies on how to compare these results and how to identify NP–NP interaction effects underneath the SAXS intensity curve are presented. Experimental results are shown for cubic-like CeO2 NPs. WAXS size results from two analytical procedures are compared, line-profile fitting of individual diffraction peaks in opposition to whole pattern fitting. The impact of shape dispersivity is also evaluated. Extension of the proposed methodology for cross-analyzing EM and WAXS data is possible.

Conformational change mediates the biological functions of macromolecules. Crystallographic measurements can map these changes with extraordinary sensitivity as a function of mutations, ligands and time. A popular method for detecting structural differences between crystallographic data sets is the isomorphous difference map. These maps combine the phases of a chosen reference state with the observed changes in structure factor amplitudes to yield a map of changes in electron density. Such maps are much more sensitive to conformational change than structure refinement is, and are unbiased in the sense that observed differences do not depend on refinement of the perturbed state. However, even modest changes in unit-cell properties can render isomorphous difference maps useless. This is unnecessary. Described here is a generalized procedure for calculating observed difference maps that retains the high sensitivity to conformational change and avoids structure refinement of the perturbed state. This procedure is implemented in an open-source Python package, MatchMaps, that can be run in any software environment supporting PHENIX [Liebschner et al. (2019). Acta Cryst. D75, 861–877] and CCP4 [Agirre et al. (2023). Acta Cryst. D79, 449–461]. Worked examples show that MatchMaps `rescues' observed difference electron-density maps for poorly isomorphous crystals, corrects artifacts in nominally isomorphous difference maps, and extends to detecting differences across copies within the asymmetric unit or across altogether different crystal forms.

It is demonstrated that high-resolution energy-dispersive X-ray fluorescence mapping devices based on a micro-focused beam are not restricted to high-speed analyses of element distributions or to the detection of different grains, twins and subgrains in crystalline materials but can also be used for the detection of dislocations in high-quality single crystals. Si single crystals with low dislocation densities were selected as model materials to visualize the position of dis­locations by the spatially resolved measurement of Bragg-peak intensity fluctuations. These originate from the most distorted planes caused by the stress fields of dislocations. The results obtained by this approach are compared with laboratory-based Lang X-ray topographs. The presented methodology yields comparable results and it is of particular interest in the field of crystal growth, where fast chemical and microstructural characterization feedback loops are indispensable for short and efficient development times. The beam divergence was reduced via an aperture management system to facilitate the visualization of dislocations for virtually as-grown, non-polished and non-planar samples with a very pronounced surface profile.

Recent developments in synchrotron radiation facilities have increased the amount of data generated during acquisitions considerably, requiring fast and efficient data processing techniques. Here, the application of dense neural networks (DNNs) to data treatment of X-ray diffraction computed tomography (XRD-CT) experiments is presented. Processing involves mapping the phases in a tomographic slice by predicting the phase fraction in each individual pixel. DNNs were trained on sets of calculated XRD patterns generated using a Python algorithm developed in-house. An initial Rietveld refinement of the tomographic slice sum pattern provides additional information (peak widths and integrated intensities for each phase) to improve the generation of simulated patterns and make them closer to real data. A grid search was used to optimize the network architecture and demonstrated that a single fully connected dense layer was sufficient to accurately determine phase proportions. This DNN was used on the XRD-CT acquisition of a mock-up and a historical sample of highly heterogeneous multi-layered decoration of a late medieval statue, called `applied brocade'. The phase maps predicted by the DNN were in good agreement with other methods, such as non-negative matrix factorization and serial Rietveld refinements performed with TOPAS, and outperformed them in terms of speed and efficiency. The method was evaluated by regenerating experimental patterns from predictions and using the R-weighted profile as the agreement factor. This assessment allowed us to confirm the accuracy of the results.

The influence of various combinations of residual stress, composition and grain interaction gradients in polycrystalline materials with cubic symmetry on energy-dispersive X-ray stress analysis is theoretically investigated. For the evaluation of the simulated sin2ψ distributions, two different strategies are compared with regard to their suitability for separating the individual gradients. It is shown that the separation of depth gradients of the strain-free lattice parameter a0(z) from residual stress gradients σ(z) is only possible if the data analysis is carried out in section planes parallel to the surface. The impact of a surface layer z* that is characterized by a direction-dependent grain interaction model in contrast to the volume of the material is quantified by comparing a ferritic and an austenitic steel, which feature different elastic anisotropy. It is shown to be of minor influence on the resulting residual stress depth profiles if the data evaluation is restricted to reflections hkl with orientation factors Γhkl close to the model-independent orientation Γ*. Finally, a method is proposed that allows the thickness of the anisotropic surface layer z* to be estimated on the basis of an optimization procedure.

Presented and discussed here is the implementation of a software solution that provides prompt X-ray diffraction data analysis during fast dynamic compression experiments conducted within the dynamic diamond anvil cell technique. It includes efficient data collection, streaming of data and metadata to a high-performance cluster (HPC), fast azimuthal data integration on the cluster, and tools for controlling the data processing steps and visualizing the data using the DIOPTAS software package. This data processing pipeline is invaluable for a great number of studies. The potential of the pipeline is illustrated with two examples of data collected on ammonia–water mixtures and multiphase mineral assemblies under high pressure. The pipeline is designed to be generic in nature and could be readily adapted to provide rapid feedback for many other X-ray diffraction techniques, e.g. large-volume press studies, in situ stress/strain studies, phase transformation studies, chemical reactions studied with high-resolution diffraction etc.

Small-angle scattering (SAS) is a key experimental technique for analyzing nanoscale structures in various materials. In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting. This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models. The performance of the method is assessed through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that this proposed analysis approach yields highly accurate and interpretable results. The ability of the method to analyze a range of mixing ratios and particle size ratios for mixed components is also discussed, along with its precision in model evaluation by the degree of fitting. The proposed method effectively facilitates quantitative analysis of nanoscale sample structures in SAS, which has traditionally been challenging, and is expected to contribute significantly to advancements in a wide range of fields.

Small-angle X-ray tensor tomography and the related wide-angle X-ray tensor tomography are X-ray imaging techniques that tomographically reconstruct the anisotropic scattering density of extended samples. In previous studies, these methods have been used to image samples where the scattering density depends slowly on the direction of scattering, typically modeling the directionality, i.e. the texture, with a spherical harmonics expansion up until order ℓ = 8 or lower. This study investigates the performance of several established algorithms from small-angle X-ray tensor tomography on samples with a faster variation as a function of scattering direction and compares their expected and achieved performance. The various algorithms are tested using wide-angle scattering data from an as-drawn steel wire with known texture to establish the viability of the tensor tomography approach for such samples and to compare the performance of existing algorithms.

X-ray ptychography is a lensless imaging technique that visualizes the nano­structure of a thick specimen which cannot be observed with an electron microscope. It reconstructs a complex-valued refractive index of the specimen from observed diffraction patterns. This reconstruction problem is called phase retrieval (PR). For further improvement in the imaging capability, including expansion of the depth of field, various PR algorithms have been proposed. Since a high-quality PR method is built upon a base PR algorithm such as ePIE, developing a well performing base PR algorithm is important. This paper proposes an improved iterative algorithm named CRISP. It exploits subgradient projection which allows adaptive step size and can be expected to avoid yielding a poor image. The proposed algorithm was compared with ePIE, which is a simple and fast-convergence algorithm, and its modified algorithm, rPIE. The experiments confirmed that the proposed method improved the reconstruction performance for both simulation and real data.

With the emergence of ultrafast X-ray sources, interest in following fast processes in small molecules and macromolecules has increased. Most of the current research into ultrafast structural dynamics of macromolecules uses X-ray free-electron lasers. In parallel, small-scale laboratory-based laser-driven ultrafast X-ray sources are emerging. Continuous development of these sources is underway, and as a result many exciting applications are being reported. However, because of their low flux, such sources are not commonly used to study the structural dynamics of macromolecules. This article examines the feasibility of time-resolved powder diffraction of macromolecular microcrystals using a laboratory-scale laser-driven ultrafast X-ray source.

High-energy X-ray diffraction methods can non-destructively map the 3D microstructure and associated attributes of metallic polycrystalline engineering materials in their bulk form. These methods are often combined with external stimuli such as thermo-mechanical loading to take snapshots of the evolving microstructure and attributes over time. However, the extreme data volumes and the high costs of traditional data acquisition and reduction approaches pose a barrier to quickly extracting actionable insights and improving the temporal resolution of these snapshots. This article presents a fully automated technique capable of rapidly detecting the onset of plasticity in high-energy X-ray microscopy data. The technique is computationally faster by at least 50 times than the traditional approaches and works for data sets that are up to nine times sparser than a full data set. This new technique leverages self-supervised image representation learning and clustering to transform massive data sets into compact, semantic-rich representations of visually salient characteristics (e.g. peak shapes). These characteristics can rapidly indicate anomalous events, such as changes in diffraction peak shapes. It is anticipated that this technique will provide just-in-time actionable information to drive smarter experiments that effectively deploy multi-modal X-ray diffraction methods spanning many decades of length scales.

Coherent diffractive imaging with X-ray free-electron lasers could enable structural studies of macromolecules at room temperature. This type of experiment could provide a means to study structural dynamics on the femtosecond timescale. However, the diffraction from a single protein is weak compared with the incoherent scattering from background sources, which negatively affects the reconstruction analysis. This work evaluates the effects of the presence of background on the analysis pipeline. Background measurements from the European X-ray Free-Electron Laser were combined with simulated diffraction patterns and treated by a standard reconstruction procedure, including orientation recovery with the expand, maximize and compress algorithm and 3D phase retrieval. Background scattering did have an adverse effect on the estimated resolution of the reconstructed density maps. Still, the reconstructions generally worked when the signal-to-background ratio was 0.6 or better, in the momentum transfer shell of the highest reconstructed resolution. The results also suggest that the signal-to-background requirement increases at higher resolution. This study gives an indication of what is possible at current setups at X-ray free-electron lasers with regards to expected background strength and establishes a target for experimental optimization of the background.

This article demonstrates the feasibility of obtaining accurate pair distribution functions of thin amorphous films down to 80 nm, using modern laboratory-based X-ray sources. The pair distribution functions are obtained using a single diffraction scan without the requirement of additional scans of the substrate or of the air. By using a crystalline substrate combined with an oblique scattering geometry, most of the Bragg scattering of the substrate is avoided, rendering the substrate Compton scattering the primary contribution. By utilizing a discriminating energy filter, available in the latest generation of modern detectors, it is demonstrated that the Compton intensity can further be reduced to negligible levels at higher wavevector values. Scattering from the sample holder and the air is minimized by the systematic selection of pixels in the detector image based on the projected detection footprint of the sample and the use of a 3D-printed sample holder. Finally, X-ray optical effects in the absorption factors and the ratios between the Compton intensity of the substrate and film are taken into account by using a theoretical tool that simulates the electric field inside the film and the substrate, which aids in planning both the sample design and the measurement protocol.

The increasing structural complexity and downscaling of modern nanodevices require continuous development of structural characterization techniques that support R&D and manufacturing processes. This work explores the capability of laboratory characterization of periodic planar nanostructures using 3D X-ray standing waves as a promising method for reconstructing atomic profiles of planar nanostructures. The non-destructive nature of this metrology technique makes it highly versatile and particularly suitable for studying various types of samples. Moreover, it eliminates the need for additional sample preparation before use and can achieve sub-nanometre reconstruction resolution using widely available laboratory setups, as demonstrated on a diffractometer equipped with a microfocus X-ray tube with a copper anode.

High-pressure crystallographic data can be measured using a diamond anvil cell (DAC), which allows the sample to be viewed only along a cell vector which runs perpendicular to the diamond anvils. Although centring a sample perpendicular to this direction is straightforward, methods for centring along this direction often rely on sample focusing, measurements of the direct beam or short data collections followed by refinement of the crystal offsets. These methods may be inaccurate, difficult to apply or slow. Described here is a method based on precise measurement of the offset in this direction using a confocal optical device, whereby the cell centre is located at the mid-point of two measurements of the distance between a light source and the external faces of the diamond anvils viewed along the forward and reverse directions of the cell vector. It is shown that the method enables a DAC to be centred to within a few micrometres reproducibly and quickly.

Understanding the structure–property relationship in electrocatalysts under working conditions is crucial for the rational design of novel and improved catalytic materials. This paper presents the Aarhus University reactor for electrochemical studies using X-rays (AUREX) operando electrocatalytic flow cell, designed as an easy-to-use versatile setup with a minimal background contribution and a uniform flow field to limit concentration polarization and handle gas formation. The cell has been employed to measure operando total scattering, diffraction and absorption spectroscopy as well as simultaneous combinations thereof on a commercial silver electrocatalyst for proof of concept. This combination of operando techniques allows for monitoring of the short-, medium- and long-range structure under working conditions, including an applied potential, liquid electrolyte and local reaction environment. The structural transformations of the Ag electrocatalyst are monitored with non-negative matrix factorization, linear combination analysis, the Pearson correlation coefficient matrix, and refinements in both real and reciprocal space. Upon application of an oxidative potential in an Ar-saturated aqueous 0.1 M KHCO3/K2CO3 electrolyte, the face-centered cubic (f.c.c.) Ag gradually transforms first to a trigonal Ag2CO3 phase, followed by the formation of a monoclinic Ag2CO3 phase. A reducing potential immediately reverts the structure to the Ag (f.c.c.) phase. Following the electrochemical-reaction-induced phase transitions is of fundamental interest and necessary for understanding and improving the stability of electrocatalysts, and the operando cell proves a versatile setup for probing this. In addition, it is demonstrated that, when studying electrochemical reactions, a high energy or short exposure time is needed to circumvent beam-induced effects.

The workshop titled `X-ray-based technologies in emerging fuel cell research', organized by Vivian Stojanoff from Brookhaven National Laboratory (BNL) and Narayanasami Sukumar from Cornell University/Advanced Photon Source-Northeastern Collaborative Access Team, was a notable segment of the National Synchrotron Light Source II and Center for Functional Nanomaterials Users' Meeting held 13–17 May 2024. This one-day event, on 13 May 2024, at BNL in New York, aimed to bring together researchers, beamline scientists, management and developers to propel fuel cell technology forward using model systems inspired by natural photosynthesis and redox enzymes. This summary encapsulates the key discussions, advancements and future implications of the workshop.

Using a 5 µm-diameter X-ray beam, we collected scanning X-ray microdiffraction in both the small-angle (SAXS) and the wide-angle (WAXS) regimes from thin sections of fixed human brain tissue from Alzheimer's subjects. The intensity of scattering in the SAXS regime of these patterns exhibits essentially no correlation with the observed intensity in the WAXS regime, indicating that the structures responsible for these two portions of the diffraction patterns, which reflect different length scales, are distinct. SAXS scattering exhibits a power-law behavior in which the log of intensity decreases linearly with the log of the scattering angle. The slope of the log–log curve is roughly proportional to the intensity in the SAXS regime and, surprisingly, inversely proportional to the intensity in the WAXS regime. We interpret these observations as being due to the presence of sub-micrometre-sized voids formed during dehydration of the fixed tissue. The SAXS intensity is due largely to scattering from these voids, while the WAXS intensity derives from the secondary structures of macromolecular material surrounding the voids. The ability to detect and map the presence of voids within thin sections of fixed tissue has the potential to provide novel information on the degradation of human brain tissue in neurodegenerative diseases.

We describe an ultra-compact setup for in situ X-ray diffraction on the inelastic X-ray scattering beamline ID20 at the European Synchrotron Radiation Facility. The main motivation for the design and construction of this setup is the increasing demand for on-the-fly sample characterization, as well as ease of navigation through a sample's phase diagram, for example subjected to high-pressure and/or high-temperature conditions. We provide technical details and demonstrate the performance of the setup.

Here, a recently commissioned five-analyzer Johann spectrometer at the Inner Shell Spectroscopy beamline (8-ID) at the National Synchrotron Light Source II (NSLS-II) is presented. Designed for hard X-ray photon-in/photon-out spectroscopy, the spectrometer achieves a resolution in the 0.5–2 eV range, depending on the element and/or emission line, providing detailed insights into the local electronic and geometric structure of materials. It serves a diverse user community, including fields such as physical, chemical, biological, environmental and materials sciences. This article details the mechanical design, alignment procedures and data-acquisition scheme of the spectrometer, with a particular focus on the continuous asynchronous data-acquisition approach that significantly enhances experimental efficiency.

Geological samples are inherently multi-scale. Understanding their bulk physical and chemical properties requires characterization down to the nano-scale. A powerful technique to study the three-dimensional microstructure is X-ray tomography, but it lacks information about the chemistry of samples. To develop a methodology for measuring the multi-scale 3D microstructure of geological samples, correlative X-ray micro- and nanotomography were performed on two rocks followed by scanning electron microscopy with energy-dispersive spectroscopy (SEM-EDS) analysis. The study was performed in five steps: (i) micro X-ray tomography was performed on rock sample cores, (ii) samples for nanotomography were prepared using laser milling, (iii) nanotomography was performed on the milled sub-samples, (iv) samples were mounted and polished for SEM analysis and (v) SEM imaging and compositional mapping was performed on micro and nanotomography samples for complimentary information. Correlative study performed on samples of serpentine and basalt revealed multiscale 3D structures involving both solid mineral phases and pore networks. Significant differences in the volume fraction of pores and mineral phases were also observed dependent on the imaging spatial resolution employed. This highlights the necessity for the application of such a multiscale approach for the characterization of complex aggregates such as rocks. Information acquired from the chemical mapping of different phases was also helpful in segmentation of phases that did not exhibit significant contrast in X-ray imaging. Adoption of the protocol used in this study can be broadly applied to 3D imaging studies being performed at the Advanced Light Source and other user facilities.

In synchrotron X-ray radiography, achieving high image resolution and an optimal signal-to-noise ratio (SNR) is crucial for the subsequent accurate image analysis. Traditional methods often struggle to balance these two parameters, especially in situ applications where rapid data acquisition is essential to capture specific dynamic processes. For quantitative image data analysis, using monochromatic X-rays is essential. A double multilayer monochromator (DMM) is successfully used for this aim at the BAMline, BESSY II (Helmholtz Zentrum Berlin, Germany). However, such DMMs are prone to producing an unstable horizontal stripe pattern. Such an unstable pattern renders proper signal normalization difficult and thereby causes a reduction of the SNR. We introduce a novel approach to enhance SNR while preserving resolution: dynamic tilting of the DMM. By adjusting the orientation of the DMM during the acquisition of radiographic projections, we optimize the X-ray imaging quality, thereby enhancing the SNR. The corresponding shift of the projection during this movement is corrected in post-processing. The latter correction allows a good resolution to be preserved. This dynamic tilting technique enables the homogenization of the beam profile and thereby effectively reduces noise while maintaining high resolution. We demonstrate that data captured using this proposed technique can be seamlessly integrated into the existing radiographic data workflow, as it does not need hardware modifications to classical X-ray imaging beamline setups. This facilitates further image analysis and processing using established methods.

X-ray multi-projection imaging (XMPI) is an emerging experimental technique for the acquisition of rotation-free, time-resolved, volumetric information on stochastic processes. The technique is developed for high-brilliance light-source facilities, aiming to address known limitations of state-of-the-art imaging methods in the acquisition of 4D sample information, linked to their need for sample rotation. XMPI relies on a beam-splitting scheme, that illuminates a sample from multiple, angularly spaced viewpoints, and employs fast, indirect, X-ray imaging detectors for the collection of the data. This approach enables studies of previously inaccessible phenomena of industrial and societal relevance such as fractures in solids, propagation of shock waves, laser-based 3D printing, or even fast processes in the biological domain. In this work, we discuss in detail the beam-splitting scheme of XMPI. More specifically, we explore the relevant properties of X-ray splitter optics for their use in XMPI schemes, both at synchrotron insertion devices and XFEL facilities. Furthermore, we describe two distinct XMPI schemes, designed to faciliate large samples and complex sample environments. Finally, we present experimental proof of the feasibility of MHz-rate XMPI at the European XFEL. This detailed overview aims to state the challenges and the potential of XMPI and act as a stepping stone for future development of the technique.