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.

X-ray crystallography is an established tool to probe the structure of macromolecules with atomic resolution. Compared with alternative techniques such as single-particle cryo-electron microscopy and micro-electron diffraction, X-ray crystallography is uniquely suited to room-temperature studies and for obtaining a detailed picture of macromolecules subjected to an external electric field (EEF). The impact of an EEF on proteins has been extensively explored through single-crystal X-ray crystallography, which works well with larger high-quality protein crystals. This article introduces a novel design for a 3D-printed in situ crystallization plate that serves a dual purpose: fostering crystal growth and allowing the concurrent examination of the effects of an EEF on crystals of varying sizes. The plate's compatibility with established X-ray crystallography techniques is evaluated.

In antiquity, Pb was a common element added in the production of large bronze artifacts, especially large statues, to impart fluidity to the casting process. As Pb does not form a solid solution with pure Cu or with the Sn–Cu alloy phases, it is normally observed in the metal matrix as globular droplets embedded within or in interstitial positions among the crystals of Sn-bronze (normally the α phase) as the last crystallizing phase during the cooling process of the Cu–Sn–Pb ternary melt. The disequilibrium Sn content of the Pb droplets has recently been suggested as a viable parameter to detect modern materials [Shilstein, Berner, Feldman, Shalev & Rosenberg (2019). STAR Sci. Tech. Archaeol. Res. 5, 29–35]. The application assumes a time-dependent process, with a timescale of hundreds of years, estimated on the basis of the diffusion coefficient of Sn in Pb over a length of a few micrometres [Oberschmidt, Kim & Gupta (1982). J. Appl. Phys. 53, 5672–5677]. Therefore, Pb inclusions in recent Sn-bronze artifacts are actually a metastable solid solution of Pb–Sn containing ∼3% atomic Sn. In contrast, in ancient artifacts, unmixing processes and diffusion of Sn from the micro- and nano-inclusions of Pb to the matrix occur, resulting in the Pb inclusions containing a substantially lower or negligible amount of Sn. The Sn content in the Pb inclusions relies on accurate measurement of the lattice parameter of the phase in the Pb–Sn solid solution, since for low Sn values it closely follows Vegard's law. Here, several new measurements on modern and ancient samples are presented and discussed in order to verify the applicability of the method to the detection of modern artwork pretending to be ancient.

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.

This paper introduces a new 2D representation of the orientation distribution function for an arbitrary material texture. The approach is based on the isometric square torus mapping of the Clifford torus, which allows for points on the unit quaternion hypersphere (each corresponding to a 3D orientation) to be represented in a periodic 2D square map. The combination of three such orthogonal mappings into a single RGB (red–green–blue) image provides a compact periodic representation of any set of orientations. Square torus representations of five different orientation sampling methods are compared and analyzed in terms of the Riesz s energies that quantify the uniformity of the samplings. The effect of crystallographic symmetry on the square torus map is analyzed in terms of the Rodrigues fundamental zones for the rotational symmetry groups. The paper concludes with example representations of important texture components in cubic and hexagonal materials. The new RGB representation provides a convenient and compact way of generating training data for the automated analysis of material textures by means of neural networks.

BL19U1, an energy-tunable protein complex crystallography beamline at the Shanghai Synchrotron Radiation Facility, has emerged as one of the most productive MX beamlines since opening to the public in July 2015. As of October 2023, it has contributed to over 2000 protein structures deposited in the Protein Data Bank (PDB), resulting in the publication of more than 1000 scientific papers. In response to increasing interest in structure-based drug design utilizing X-ray crystallography for fragment library screening, enhancements have been implemented in both hardware and data collection systems on the beamline to optimize efficiency. Hardware upgrades include the transition from MD2 to MD2S for the diffractometer, alongside the installation of a humidity controller featuring a rapid nozzle exchanger. This allows users to opt for either low-temperature or room-temperature data collection modes. The control system has been upgraded from Blu-Ice to MXCuBE3, which supports website-mode data collection, providing enhanced compatibility and easy expansion with new features. An automated data processing pipeline has also been developed to offer users real-time feedback on data quality.

Three-dimensional cryo electron microscopy reconstructions are obtained by extracting information from a large number of projections of the object. These projections correspond to different `views' or `orientations', i.e. directions in which these projections show the reconstructed object. Uneven distribution of these views and the presence of dominating preferred orientations may distort the reconstructed spatial images. This work describes the program VUE (views on uniform grids for cryo electron microscopy), designed to study such distributions. Its algorithms, based on uniform virtual grids on a sphere, allow an easy calculation and accurate quantitative analysis of the frequency distribution of the views. The key computational element is the Lambert azimuthal equal-area projection of a spherical uniform grid onto a disc. This projection keeps the surface area constant and represents the frequency distribution with no visual bias. Since it has multiple tunable parameters, the program is easily adaptable to individual needs, and to the features of a particular project or of the figure to be produced. It can help identify problems related to an uneven distribution of views. Optionally, it can modify the list of projections, distributing the views more uniformly. The program can also be used as a teaching tool.

Scintillator-based ZnS:Ag/6LiF neutron detectors have been under development at ISIS for more than three decades. Continuous research and development aim to improve detector capabilities, achieve better performance and meet the increasingly demanding requirements set by neutron instruments. As part of this program, a high-efficiency 2D position-sensitive scintillator detector with wavelength-shifting fibres has been developed for neutron-diffraction applications. The detector consists of a double scintillator-fibre layer to improve detection efficiency. Each layer is made up of two orthogonal fibre planes placed between two ZnS:Ag/6LiF scintillator screens. Thin reflective foils are attached to the front and back scintillators of each layer to minimize light cross-talk between layers. The detector has an active area of 192 × 192 mm with a square pixel size of 3 × 3 mm. As part of the development process of the double-layer detector, a single-layer detector was built, together with a prototype detector in which the two layers of the detector could be read out separately. Efficiency calculations and measurements of all three detectors are discussed. The novel double-layer detector has been installed and tested on the SXD diffractometer at ISIS. The detector performance is compared with the current scintillator detectors employed on SXD by studying reference crystal samples. More than a factor of 3 improvement in efficiency is achieved with the double-layer wavelength-shifting-fibre detector. Software routines for further optimizations in spatial resolution and uniformity of response have been implemented and tested for 2D detectors. The methods and results are discussed in this manuscript.

Macromolecular crystallography contributes significantly to understanding diseases and, more importantly, how to treat them by providing atomic resolution 3D structures of proteins. This is achieved by collecting X-ray diffraction images of protein crystals from important biological pathways. Spotfinders are used to detect the presence of crystals with usable data, and the spots from such crystals are the primary data used to solve the relevant structures. Having fast and accurate spot finding is essential, but recent advances in synchrotron beamlines used to generate X-ray diffraction images have brought us to the limits of what the best existing spotfinders can do. This bottleneck must be removed so spotfinder software can keep pace with the X-ray beamline hardware improvements and be able to see the weak or diffuse spots required to solve the most challenging problems encountered when working with diffraction images. In this paper, we first present Bragg Spot Detection (BSD), a large benchmark Bragg spot image dataset that contains 304 images with more than 66 000 spots. We then discuss the open source extensible U-Net-based spotfinder Bragg Spot Finder (BSF), with image pre-processing, a U-Net segmentation backbone, and post-processing that includes artifact removal and watershed segmentation. Finally, we perform experiments on the BSD benchmark and obtain results that are (in terms of accuracy) comparable to or better than those obtained with two popular spotfinder software packages (Dozor and DIALS), demonstrating that this is an appropriate framework to support future extensions and improvements.

This study reports the synthesis and crystal structure determination of a novel CrTe3 phase using various experimental and theoretical methods. The average stoichiometry and local phase separation of this quenched high-pressure phase were characterized by ex situ synchrotron powder X-ray diffraction and total scattering. Several structural models were obtained using simulated annealing, but all suffered from an imperfect Rietveld refinement, especially at higher diffraction angles. Finally, a novel stoichiometrically correct crystal structure model was proposed on the basis of electron diffraction data and refined against powder diffraction data using the Rietveld method. Scanning electron microscopy–energy-dispersive X-ray spectrometry (EDX) measurements verified the targeted 1:3 (Cr:Te) average stoichiometry for the starting compound and for the quenched high-pressure phase within experimental errors. Scanning transmission electron microscopy (STEM)–EDX was used to examine minute variations of the Cr-to-Te ratio at the nanoscale. Precession electron diffraction (PED) experiments were applied for the nanoscale structure analysis of the quenched high-pressure phase. The proposed monoclinic model from PED experiments provided an improved fit to the X-ray patterns, especially after introducing atomic anisotropic displacement parameters and partial occupancy of Cr atoms. Atomic resolution STEM and simulations were conducted to identify variations in the Cr-atom site-occupancy factor. No significant variations were observed experimentally for several zone axes. The magnetic properties of the novel CrTe3 phase were investigated through temperature- and field-dependent magnetization measurements. In order to understand these properties, auxiliary theoretical investigations have been performed by first-principles electronic structure calculations and Monte Carlo simulations. The obtained results allow the observed magnetization behavior to be interpreted as the consequence of competition between the applied magnetic field and the Cr–Cr exchange interactions, leading to a decrease of the magnetization towards T = 0 K typical for antiferromagnetic systems, as well as a field-induced enhanced magnetization around the critical temperature due to the high magnetic susceptibility in this region.

The pair angle distribution function (PADF) is a three- and four-atom correlation function that characterizes the local angular structure of disordered materials, particles or nanocrystalline materials. The PADF can be measured using X-ray or electron fluctuation diffraction data, which can be collected by scanning or flowing a structurally disordered sample through a focused beam. It is a natural generalization of established pair distribution methods, which do not provide angular information. The software package pypadf provides tools to calculate the PADF from fluctuation diffraction data. The package includes tools for calculating the intensity correlation function, which is a necessary step in the PADF calculation and also the basis for other fluctuation scattering analysis techniques.

Propagation-based phase contrast, for example in the form of edge enhancement contrast, is well established within X-ray imaging but is not widely used in neutron imaging. This technique can help increase the contrast of low-attenuation samples but may confuse quantitative absorption measurements. Therefore, it is important to understand the experimental parameters that cause and amplify or dampen this effect in order to optimize future experiments properly. Two simulation approaches have been investigated, a wave-based simulation and a particle-based simulation conducted in McStas [Willendrup & Lefmann (2020). J. Neutron Res. 22, 1–16], and they are compared with experimental data. The experiment was done on a sample of metal foils with weakly and strongly neutron absorbing layers, which were measured while varying the rotation angle and propagation distance from the sample. The experimental data show multiple signals: attenuation, phase contrast and reflection. The wave model reproduces the sample attenuation and the phase peaks but it does not reproduce the behavior of these peaks as a function of rotation angle. The McStas simulation agrees better with the experimental data, as it reproduces attenuation, phase peaks and reflection, as well as the change in these signals as a function of rotation angle and distance. This suggests that the McStas simulation approach, where the particle description of the neutron facilitates the incorporation of multiple effects, is the most convenient way of modeling edge enhancement in neutron imaging.

Polymer-derived ceramics (PDCs) remain at the forefront of research for a variety of applications including ultra-high-temperature ceramics, energy storage and functional coatings. Despite their wide use, questions remain about the complex structural transition from polymer to ceramic and how local structure influences the final microstructure and resulting properties. This is further complicated when nanofillers are introduced to tailor structural and functional properties, as nanoparticle surfaces can interact with the matrix and influence the resulting structure. The inclusion of crystalline nanofiller produces a mixed crystalline–amorphous composite, which poses characterization challenges. With this study, we aim to address these challenges with a local-scale structural study that probes changes in a polysiloxane matrix with incorporated copper nanofiller. Composites were processed at three unique temperatures to capture mixing, pyrolysis and initial crystallization stages for the pre-ceramic polymer. We observed the evolution of the nanofiller with electron microscopy and applied synchrotron X-ray diffraction with differential pair distribution function (d-PDF) analysis to monitor changes in the matrix's local structure and interactions with the nanofiller. The application of the d-PDF to PDC materials is novel and informs future studies to understand interfacial interactions between nanofiller and matrix throughout PDC processing.

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.

Understanding the symmetries described by subperiodic groups – frieze, rod and layer groups – has been instrumental in predicting various properties (band structures, optical absorption, Raman spectra, diffraction patterns, topological properties etc.) of `low-dimensional' crystals. This knowledge is crucial in the tailored design of materials for specific applications across electronics, photonics and materials engineering. However, there are materials that have the property of being periodic only in one direction and whose symmetry cannot be described by the subperiodic rod groups. Describing the symmetry of these materials necessitates the application of line group theory. This paper gives an overview of subperiodic groups while briefly introducing line groups in order to acquaint the crystallographic community with these symmetries and direct them to pertinent literature. Since line groups are generally not sub­periodic, they have thus far remained outside the realm of symmetries traditionally considered in crystallography, although there are numerous `one-dimensional' crystals (i.e. monoperiodic structures) possessing line group symmetry.

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.

From the historical roots of metalworking to the forefront of modern nanotechnology, functional materials have played a pivotal role in transforming societies, and their influence is poised to persist into the future. Encompassing a wide array of solid-state materials, spanning semiconductors to polymers, molecular crystals to nanoparticles, functional materials find application in critical sectors such as electronics, computers, information, communication, bio­technology, aerospace, defense, environment, energy, medicine and consumer products. This feature article delves into diverse instances of functional materials, exploring their structures, their properties and the underlying mechanisms that contribute to their outstanding performance across fields like batteries, photovoltaics, magnetics and heterogeneous catalysts. The field of structural sciences serves as the cornerstone for unraveling the intricate relationship between structure, dynamics and function. Acting as a bridge, it connects the fundamental understanding of materials to their practical applications.

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.

Neutron spectroscopy uniquely and non-destructively accesses diffusive dynamics in soft and biological matter, including for instance proteins in hydrated powders or in solution, and more generally dynamic properties of condensed matter on the molecular level. Given the limited neutron flux resulting in long counting times, it is important to optimize data acquisition for the specific question, in particular for time-resolved (kinetic) studies. The required acquisition time was recently significantly reduced by measurements of discrete energy transfers rather than quasi-continuous neutron scattering spectra on neutron backscattering spectrometers. Besides this reduction in acquisition times, smaller amounts of samples can be measured with better statistics, and most importantly, kinetically changing samples, such as aggregating or crystallizing samples, can be followed. However, given the small number of discrete energy transfers probed in this mode, established analysis frameworks for full spectra can break down. Presented here are new approaches to analyze measurements of diffusive dynamics recorded within fixed windows in energy transfer, and these are compared with the analysis of full spectra. The new approaches are tested by both modeled scattering functions and a comparative analysis of fixed energy window data and full spectra on well understood reference samples. This new approach can be employed successfully for kinetic studies of the dynamics focusing on the short-time apparent center-of-mass diffusion.

The spatial orientation of α lamellae in a metastable β-Ti matrix of Timetal LCB (Ti–6.8 Mo–4.5 Fe–1.5 Al in wt%) was examined and the orientation of the hexagonal close-packed α lattice in the α lamella was determined. For this purpose, a combination of methods of small-angle X-ray scattering, scanning electron microscopy and electron backscatter diffraction was used. The habit planes of α laths are close to {111}β, which corresponds to (1320)α in the hexagonal coordinate system of the α phase. The longest α lamella direction lies approximately along one of the 〈110〉β directions which are parallel to the specific habit plane. Taking into account the average lattice parameters of the β and α phases in aged conditions in Timetal LCB, it was possible to index all main axes and faces of an α lath not only in the cubic coordinate system of the parent β phase but also in the hexagonal system of the α phase.

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.

A deep-learning algorithm is proposed for the inpainting of Bragg coherent diffraction imaging (BCDI) patterns affected by detector gaps. These regions of missing intensity can compromise the accuracy of reconstruction algorithms, inducing artefacts in the final result. It is thus desirable to restore the intensity in these regions in order to ensure more reliable reconstructions. The key aspect of the method lies in the choice of training the neural network with cropped sections of diffraction data and subsequently patching the predictions generated by the model along the gap, thus completing the full diffraction peak. This approach enables access to a greater amount of experimental data for training and offers the ability to average overlapping sections during patching. As a result, it produces robust and dependable predictions for experimental data arrays of any size. It is shown that the method is able to remove gap-induced artefacts on the reconstructed objects for both simulated and experimental data, which becomes essential in the case of high-resolution BCDI experiments.

Using the well known Rn ratio method, a protocol has been elaborated for determining the lattice direction for the 15 most common cubic zone axis spot patterns. The method makes use of the lengths of the three shortest reciprocal-lattice vectors in each pattern and the angles between them. No prior pattern calibration is required for the method to work, as the Rn ratio method is based entirely on geometric relationships. In the first step the pattern is assigned to one of three possible pattern types according to the angles that are measured between the three reciprocal-lattice vectors. The lattice direction [uvw] and possible Bravais type(s) and Laue indices of the corresponding reflections can then be determined by using lookup tables. In addition to determining the lattice direction, this simple geometric analysis allows one to distinguish between the P, I and F Bravais lattices for spot patterns aligned along [013], [112], [114] and [233]. Moreover, the F lattice can always be uniquely identified from the [011] and [123] patterns.

Neutron diffraction beamlines have traditionally relied on deploying large detector arrays of 3He tubes or neutron-sensitive scintillators coupled with photomultipliers to efficiently probe crystallographic and microstructure information of a given material. Given the large upfront cost of custom-made data acquisition systems and the recent scarcity of 3He, new diffraction beamlines or upgrades to existing ones demand innovative approaches. This paper introduces a novel Timepix3-based event-mode imaging neutron diffraction detector system as well as first results of a silicon powder diffraction measurement made at the HIPPO neutron powder diffractometer at the Los Alamos Neutron Science Center. Notably, these initial measurements were conducted simultaneously with the 3He array on HIPPO, enabling direct comparison. Data reduction for this type of data was implemented in the MAUD code, enabling Rietveld analysis. Results from the Timepix3-based setup and HIPPO were benchmarked against McStas simulations, showing good agreement for peak resolution. With further development, systems such as the one presented here may substantially reduce the cost of detector systems for new neutron instrumentation as well as for upgrades of existing beamlines.

Small-angle X-ray and neutron scattering (SAXS and SANS) patterns from certain semicrystalline polymers and liquid crystals contain discrete reflections from ordered assemblies and central diffuse scattering (CDS) from uncorrelated structures. Systems with imperfectly ordered lamellar structures aligned by stretching or by a magnetic field produce four distinct SAXS patterns: two-point `banana', four-point pattern, four-point `eyebrow' and four-point `butterfly'. The peak intensities of the reflections lie not on a layer line, or the arc of a circle, but on an elliptical trajectory. Modeling shows that randomly placed lamellar stacks modified by chain slip and stack rotation or interlamellar shear can create these forms. On deformation, the isotropic CDS becomes an equatorial streak with an oval, diamond or two-bladed propeller shape, which can be analyzed by separation into isotropic and oriented components. The streak has elliptical intensity contours, a natural consequence of the imperfect alignment of the elongated scattering objects. Both equatorial streaks and two- and four-point reflections can be fitted in elliptical coordinates with relatively few parameters. Equatorial streaks can be analyzed to obtain the size and orientation of voids, fibrils or surfaces. Analyses of the lamellar reflection yield lamellar spacing, stack orientation (interlamellar shear) angle α and chain slip angle ϕ, as well as the size distribution of the lamellar stacks. Currently available computational tools allow these microstructural parameters to be rapidly refined.

Predicting crystal symmetry simply from chemical composition has remained challenging. Several machine-learning approaches can be employed, but the predictive value of popular crystallographic databases is relatively modest due to the paucity of data and uneven distribution across the 230 space groups. In this work, virtually all crystallographic information available to science has been compiled and used to train and test multiple machine-learning models. Composition-driven random-forest classification relying on a large set of descriptors showed the best performance. The predictive models for crystal system, Bravais lattice, point group and space group of inorganic compounds are made publicly available as easy-to-use software downloadable from https://gitlab.com/vishsoft/cosy.

Portland cements (PCs) and cement blends are multiphase materials of different fineness, and quantitatively analysing their hydration pathways is very challenging. The dissolution (hydration) of the initial crystalline and amorphous phases must be determined, as well as the formation of labile (such as ettringite), reactive (such as portlandite) and amorphous (such as calcium silicate hydrate gel) components. The microstructural changes with hydration time must also be mapped out. To address this robustly and accurately, an innovative approach is being developed based on in situ measurements of pastes without any sample conditioning. Data are sequentially acquired by Mo Kα1 laboratory X-ray powder diffraction (LXRPD) and microtomography (µCT), where the same volume is scanned with time to reduce variability. Wide capillaries (2 mm in diameter) are key to avoid artefacts, e.g. self-desiccation, and to have excellent particle averaging. This methodology is tested in three cement paste samples: (i) a commercial PC 52.5 R, (ii) a blend of 80 wt% of this PC and 20 wt% quartz, to simulate an addition of supplementary cementitious materials, and (iii) a blend of 80 wt% PC and 20 wt% limestone, to simulate a limestone Portland cement. LXRPD data are acquired at 3 h and 1, 3, 7 and 28 days, and µCT data are collected at 12 h and 1, 3, 7 and 28 days. Later age data can also be easily acquired. In this methodology, the amounts of the crystalline phases are directly obtained from Rietveld analysis and the amorphous phase contents are obtained from mass-balance calculations. From the µCT study, and within the attained spatial resolution, three components (porosity, hydrated products and unhydrated cement particles) are determined. The analyses quantitatively demonstrate the filler effect of quartz and limestone in the hydration of alite and the calcium aluminate phases. Further hydration details are discussed.

X-ray photon correlation spectroscopy (XPCS) is a powerful tool for the investigation of dynamics covering a broad range of timescales and length scales. The two-time correlation function (TTC) is commonly used to track non-equilibrium dynamical evolution in XPCS measurements, with subsequent extraction of one-time correlations. While the theoretical foundation for the quantitative analysis of TTCs is primarily established for equilibrium systems, where key parameters such as the diffusion coefficient remain constant, non-equilibrium systems pose a unique challenge. In such systems, different projections (`cuts') of the TTC may lead to divergent results if the underlying fundamental parameters themselves are subject to temporal variations. This article explores widely used approaches for TTC calculations and common methods for extracting relevant information from correlation functions, particularly in the light of comparing dynamics in equilibrium and non-equilibrium systems.

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.

For a reliable characterization of materials and systems featuring multiple structural levels, a broad length scale from a few ångström to hundreds of nanometres must be analyzed and an extended Q range must be covered in X-ray and neutron scattering experiments. For certain samples or effects, it is advantageous to perform such characterization with a single instrument. Neutrons offer the unique advantage of contrast variation and matching by D-labeling, which is of great value in the characterization of natural or synthetic polymers. Some time-of-flight small-angle neutron scattering (TOF-SANS) instruments at neutron spallation sources can cover an extended Q range by using a broad wavelength band and a multitude of detectors. The detectors are arranged to cover a wide range of scattering angles with a resolution that allows both large-scale morphology and crystalline structure to be resolved simultaneously. However, for such analyses, the SANS instruments at steady-state sources operating in conventional monochromatic pinhole mode rely on additional wide-angle neutron scattering (WANS) detectors. The resolution must be tuned via a system of choppers and a TOF data acquisition option to reliably measure the atomic to mesoscale structures. The KWS-2 SANS diffractometer at Jülich Centre for Neutron Science allows the exploration of a wide Q range using conventional pinhole and lens focusing modes and an adjustable resolution Δλ/λ between 2 and 20%. This is achieved through the use of a versatile mechanical velocity selector combined with a variable slit opening and rotation frequency chopper. The installation of WANS detectors planned on the instrument required a detailed analysis of the quality of the data measured over a wide angular range with variable resolution. This article presents an assessment of the WANS performance by comparison with a McStas [Willendrup, Farhi & Lefmann (2004). Physica B, 350, E735–E737] simulation of ideal experimental conditions at the instrument.

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.

This article presents a Python-based program, DFT2FEFFIT, to regress theoretical extended X-ray absorption fine structure (EXAFS) spectra calculated from density functional theory structure models against experimental EXAFS spectra. To showcase its application, Ce-doped fluorapatite [Ca10(PO4)6F2] is revisited as a representative of a material difficult to analyze by conventional multi-shell least-squares fitting of EXAFS spectra. The software is open source and publicly available.

Structural modelling of operando pair distribution function (PDF) data of complex functional materials can be highly challenging. To aid the understanding of complex operando PDF data, this article demonstrates a toolbox for PDF analysis. The tools include denoising using principal component analysis together with the structureMining, similarityMapping and nmfMapping apps available through the online service `PDF in the cloud' (PDFitc, https://pdfitc.org/). The toolbox is used for both ex situ and operando PDF data for 3 nm TiO2-bronze nanocrystals, which function as the active electrode material in a Li-ion battery. The tools enable structural modelling of the ex situ and operando PDF data, revealing two pristine TiO2 phases (bronze and anatase) and two lithiated LixTiO2 phases (lithiated versions of bronze and anatase), and the phase evolution during galvanostatic cycling is characterized.

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.

Characterization of crystallization processes in situ is of great importance to furthering knowledge of how nucleation and growth processes direct the assembly of organic and inorganic materials in solution and, critically, understanding the influence that these processes have on the final physico-chemical properties of the resulting solid form. With careful specification and design, as demonstrated here, it is now possible to bring combined X-ray diffraction and Raman spectroscopy, coupled to a range of fully integrated segmented and continuous flow platforms, to the laboratory environment for in situ data acquisition for timescales of the order of seconds. The facility used here (Flow-Xl) houses a diffractometer with a micro-focus Cu Kα rotating anode X-ray source and a 2D hybrid photon-counting detector, together with a Raman spectrometer with 532 and 785 nm lasers. An overview of the diffractometer and spectrometer setup is given, and current sample environments for flow crystallization are described. Commissioning experiments highlight the sensitivity of the two instruments for time-resolved in situ data collection of samples in flow. Finally, an example case study to monitor the batch crystallization of sodium sulfate from aqueous solution, by tracking both the solute and solution phase species as a function of time, highlights the applicability of such measurements in determining the kinetics associated with crystallization processes. This work illustrates that the Flow-Xl facility provides high-resolution time-resolved in situ structural phase information through diffraction data together with molecular-scale solution data through spectroscopy, which allows crystallization mechanisms and their associated kinetics to be analysed in a laboratory setting.

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.

Geological formations provide a promising environment for the long-term and short-term storage of gases, including carbon dioxide, hydrogen and hydro­carbons, controlled by the rock-specific small-scale pore structure. This study investigates the nanoscale structure and gas uptake in a highly porous silica aerogel (a synthetic proxy for natural rocks) using transmission electron microscopy, X-ray diffraction, and small-angle and ultra-small-angle neutron scattering with a tracer of deuterated methane (CD4) at pressures up to 1000 bar. The results show that the adsorption of CD4 in the porous silica matrix is scale dependent. The pore space of the silica aerogel is fully accessible to the invading gas, which quickly equilibrates with the external pressure and shows no condensation on the sub-nanometre scale. In the 2.5–50 nm pore size region a classical two-phase adsorption behaviour is observed. The structure of the aerogel returns to its original state after the CD4 pressure has been released.

The first Federation of European Biochemical Societies Advanced Course on macromolecular crystallization was launched in the Czech Republic in October 2004. Over the past two decades, the course has developed into a distinguished event, attracting students, early career postdoctoral researchers and lecturers. The course topics include protein purification, characterization and crystallization, covering the latest advances in the field of structural biology. The many hands-on practical exercises enable a close interaction between students and teachers and offer the opportunity for students to crystallize their own proteins. The course has a broad and lasting impact on the scientific community as participants return to their home laboratories and act as nuclei by communicating and implementing their newly acquired knowledge and skills.

Energy-dispersive Laue diffraction (EDLD) is a powerful method to obtain position-resolved texture information in inhomogeneous biological samples without the need for sample rotation. This study employs EDLD texture scanning to investigate the impact of two salivary peptides, statherin (STN) and histatin-1 (HTN) 21 N-terminal peptides (STN21 and HTN21), on the crystallographic structure of dental enamel. These proteins are known to play crucial roles in dental caries progression. Three healthy incisors were randomly assigned to three groups: artificially demineralized, demineralized after HTN21 peptide pre-treatment and demineralized after STN21 peptide pre-treatment. To understand the micro-scale structure of the enamel, each specimen was scanned from the enamel surface to a depth of 250 µm using microbeam EDLD. Via the use of a white beam and a pixelated detector, where each pixel functions as a spectrometer, pole figures were obtained in a single exposure at each measurement point. The results revealed distinct orientations of hydroxyapatite crystallites and notable texture variation in the peptide-treated demineralized samples compared with the demineralized control. Specifically, the peptide-treated demineralized samples exhibited up to three orientation populations, in contrast to the demineralized control which displayed only a single orientation population. The texture index of the demineralized control (2.00 ± 0.21) was found to be lower than that of either the STN21 (2.32 ± 0.20) or the HTN21 (2.90 ± 0.46) treated samples. Hence, texture scanning with EDLD gives new insights into dental enamel crystallite orientation and links the present understanding of enamel demineralization to the underlying crystalline texture. For the first time, the feasibility of EDLD texture measurements for quantitative texture evaluation in demineralized dental enamel samples is demonstrated.

X-ray scattering has become a major tool in the structural characterization of nanoscale materials. Thanks to the widely available experimental and computational atomic models, coordinate-based X-ray scattering simulation has played a crucial role in data interpretation in the past two decades. However, simulation of real-space pair distance distribution functions (PDDFs) from small- and wide-angle X-ray scattering, SAXS/WAXS, has been relatively less exploited. This study presents a comparison of PDDF simulation methods, which are applied to molecular structures that range in size from β-cyclo­dextrin [1 kDa molecular weight (MW), 66 non-hydrogen atoms] to the satellite tobacco mosaic virus capsid (1.1 MDa MW, 81 960 non-hydrogen atoms). The results demonstrate the power of interpretation of experimental SAXS/WAXS from the real-space view, particularly by providing a more intuitive method for understanding of partial structure contributions. Furthermore, the computational efficiency of PDDF simulation algorithms makes them attractive as approaches for the analysis of large nanoscale materials and biological assemblies. The simulation methods demonstrated in this article have been implemented in stand-alone software, SolX 3.0, which is available to download from https://12idb.xray.aps.anl.gov/solx.html.

The Q resolution in Bonse–Hart double-crystal diffractometers is determined for a given Bragg angle by the value of the crystallographic structure factor. To date, the reflections Si 220 or Si 111 have been used exclusively in neutron scattering, which provide resolutions for triple-bounce crystals of about 2 × 10−5 Å−1 (FWHM). The Darwin width of the GaAs 200 reflection is about a factor of 10 smaller, offering the possibility of a Q resolution of 2 × 10−6 Å−1 provided crystals of sufficient quality are available. This article reports a feasibility study with single-bounce GaAs 200, yielding a Q resolution of 4.6 × 10−6 Å−1, six times superior in comparison with a Si 220 setup.

A procedure is presented to exactly obtain the apparent average crystallite size (ACS) of powder samples using standard in-house powder diffraction experiments without any restriction originating from the Scherrer equation. Additionally, the crystallite size distribution within the sample can be evaluated. To achieve this, powder diffractograms are background corrected and long-range radial distribution functions G(r) up to 300 nm are calculated from the diffraction data. The envelope function fenv of G(r) is approximated by a procedure determining the absolute maxima of G(r) in a certain interval (r range). Fitting of an ACS distribution envelope function to this approximation gives the ACS and its distribution. The method is tested on diffractograms of LaB6 standard reference materials measured with different wavelengths to demonstrate the validity of the approach and to clarify the influence of the wavelength used. The latter results in a general description of the maximum observable average crystallite size, which depends on the instrument and wavelength used. The crystallite site distribution is compared with particle size distributions based on transmission electron microscopy investigations, providing an approximation of the average number of crystallites per particle.

Compared with batch and vapor diffusion methods, counter diffusion can generate larger and higher-quality protein crystals yielding improved diffraction data and higher-resolution structures. Typically, counter-diffusion experiments are conducted in elongated chambers, such as glass capillaries, and the crystals are either directly measured in the capillary or extracted and mounted at the X-ray beamline. Despite the advantages of counter-diffusion protein crystallization, there are few fixed-target devices that utilize counter diffusion for crystallization. In this article, different designs of user-friendly counter-diffusion chambers are presented which can be used to grow large protein crystals in a 2D polymer microfluidic fixed-target chip. Methods for rapid chip fabrication using commercially available thin-film materials such as Mylar, propyl­ene and Kapton are also detailed. Rules of thumb are provided to tune the nucleation and crystal growth to meet users' needs while minimizing sample consumption. These designs provide a reliable approach to forming large crystals and maintaining their hydration for weeks and even months. This allows ample time to grow, select and preserve the best crystal batches before X-ray beam time. Importantly, the fixed-target microfluidic chip has a low background scatter and can be directly used at beamlines without any crystal handling, enabling crystal quality to be preserved. The approach is demonstrated with serial diffraction of photoactive yellow protein, yielding 1.32 Å resolution at room temperature. Fabrication of this standard microfluidic chip with commercially available thin films greatly simplifies fabrication and provides enhanced stability under vacuum. These advances will further broaden microfluidic fixed-target utilization by crystallographers.

Online courses and innovative teaching methods have triggered a trend in education, where the integration of multimedia, online resources and interactive tools is reshaping the view of both virtual and traditional classrooms. The use of interactive tools extends beyond the boundaries of the physical classroom, offering students the flexibility to access materials at their own speed and convenience and enhancing their learning experience. In the field of crystallography, there are a wide variety of free online resources such as web pages, interactive applets, databases and programs that can be implemented in fundamental crystallography courses for different academic levels and curricula. This paper discusses a variety of resources that can be helpful for crystallographic symmetry handling and visualization, discussing four specific resources in detail: the Bilbao Crystallographic Server, the Cambridge Structural Database, VESTA and Jmol. The utility of these resources is explained and shown by several illustrative examples.

High-pressure neutron powder diffraction data from PbNCN were collected on the high-pressure diffraction beamline SNAP located at the Spallation Neutron Source (SNS) of Oak Ridge National Laboratory (Tennessee, USA). The diffraction data were analyzed using the novel method of multidimensional (two dimensions for now, potentially more in the future) Rietveld refinement and, for comparison, employing the conventional Rietveld method. To achieve two-dimensional analysis, a detailed description of the SNAP instrument characteristics was created, serving as an instrument parameter file, and then yielding both cell and spatial parameters as refined under pressure for the first time for solid-state cyanamides/carbodi­imides. The bulk modulus B0 = 25.1 (15) GPa and its derivative B'0 = 11.1 (8) were extracted for PbNCN following the Vinet equation of state. Surprisingly, an internal transition was observed beyond 2.0 (2) GPa, resulting from switching the bond multiplicities (and bending direction) of the NCN2− complex anion. The results were corroborated using electronic structure calculation from first principles, highlighting both local structural and chemical bonding details.

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.