Characterization of a material structure with pair distribution function (PDF) analysis typically involves refining a structure model against an experimental data set, but finding or constructing a suitable atomic model for PDF modelling can be an extremely labour-intensive task, requiring carefully browsing through large numbers of possible models. Presented here is POMFinder, a machine learning (ML) classifier that rapidly screens a database of structures, here polyoxometallate (POM) clusters, to identify candidate structures for PDF data modelling. The approach is shown to identify suitable POMs from experimental data, including in situ data collected with fast acquisition times. This automated approach has significant potential for identifying suitable models for structure refinement to extract quantitative structural parameters in materials chemistry research. POMFinder is open source and user friendly, making it accessible to those without prior ML knowledge. It is also demonstrated that POMFinder offers a promising modelling framework for combined modelling of multiple scattering techniques.

The observation of neutron interference using a triple Laue interferometer formed by two separate crystals opens the way to the construction and operation of skew-symmetric interferometers with extended arm separation and length. The specifications necessary for their successful operation are investigated here: most importantly, how the manufacturing tolerance and crystal alignments impact the interference visibility. In contrast with previous studies, both incoherent sources and the three-dimensional operation of the interferometer are considered. It is found that, with a Gaussian Schell model of an incoherent source, the integrated density of the particles leaving the interferometer is the same as that yielded by a coherent Gaussian source having a radius equal to the coherence length.

Low-energy electron diffraction patterns contain precise information about the structure of the surface studied. However, retrieving the real space lattice periodicity from complex diffraction patterns is challenging, especially when the modeled patterns originate from superlattices with large unit cells composed of several symmetry-equivalent domains without a simple relation to the substrate. This work presents ProLEED Studio software, built to provide simple, intuitive and precise modeling of low-energy electron diffraction patterns. The interactive graphical user interface allows real-time modeling of experimental diffraction patterns, change of depicted diffraction spot intensities, visualization of different diffraction domains, and manipulation of any lattice points or diffraction spots. The visualization of unit cells, lattice vectors, grids and scale bars as well as the possibility of exporting ready-to-publish models in bitmap and vector formats significantly simplifies the modeling process and publishing of results.

Developing semiconductor devices requires a fast and reliable source of strain information with high spatial resolution and strain sensitivity. This work investigates the strain in an axially heterostructured 180 nm-diameter GaInP nanowire with InP segments of varying lengths down to 9 nm, simultaneously probing both materials. Scanning X-ray diffraction (XRD) is compared with Bragg projection ptychography (BPP), a fast single-projection method. BPP offers a sufficient spatial resolution to reveal fine details within the largest segments, unlike scanning XRD. The spatial resolution affects the quantitative accuracy of the strain maps, where BPP shows much-improved agreement with an elastic 3D finite element model compared with scanning XRD. The sensitivity of BPP to small deviations from the Bragg condition is systematically investigated. The experimental confirmation of the model suggests that the large lattice mismatch of 1.52% is accommodated without defects.

X-ray absorption spectroscopy (XAS) is a promising technique for determining structural information from sensitive biological samples, but high-accuracy X-ray absorption fine structure (XAFS) requires corrections of systematic errors in experimental data. Low-temperature XAS and room-temperature X-ray absorption spectro-electrochemical (XAS-EC) measurements of N-truncated amyloid-β samples were collected and corrected for systematic effects such as dead time, detector efficiencies, monochromator glitches, self-absorption, radiation damage and noise at higher wavenumber (k). A new protocol was developed using extended X-ray absorption fine structure (EXAFS) data analysis for monitoring radiation damage in real time and post-analysis. The reliability of the structural determinations and consistency were validated using the XAS measurement experimental uncertainty. The correction of detector pixel efficiencies improved the fitting χ2 by 12%. An improvement of about 2.5% of the structural fitting was obtained after dead-time corrections. Normalization allowed the elimination of 90% of the monochromator glitches. The remaining glitches were manually removed. The dispersion of spectra due to self-absorption was corrected. Standard errors of experimental measurements were propagated from pointwise variance of the spectra after systematic corrections. Calculated uncertainties were used in structural refinements for obtaining precise and reliable values of structural parameters including atomic bond lengths and thermal parameters. This has permitted hypothesis testing.

BioXTAS RAW is a free open-source program for reduction, analysis and modelling of biological small-angle scattering data. Here, the new developments in RAW version 2 are described. These include improved data reduction using pyFAI; updated automated Guinier fitting and Dmax finding algorithms; automated series (e.g. size-exclusion chromatography coupled small-angle X-ray scattering or SEC-SAXS) buffer- and sample-region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using regularized alternating least squares (REGALS); creation of electron-density reconstructions using electron density via solution scattering (DENSS); a comparison window showing residuals, ratios and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. Furthermore, there is now a RAW API, which can be used without the graphical user interface (GUI), providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.

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.

Rietveld refinements are widely used for many purposes in the physical sciences. Conducting a Rietveld refinement typically requires expert input because correct results may require that parameters be added to the fit in the proper order. This order will depend on the nature of the data and the initial parameter values. A mechanism for computing the next parameter to add to the refinement is shown. The fitting function is evaluated with the current parameter value set and each parameter incremented and decremented by a small offset. This provides the partial derivatives with respect to each parameter, along with information to discriminate meaningful values from numerical computational errors. The implementation of this mechanism in the open-source GSAS-II program is discussed. This new method is discussed as an important step towards the development of automated Rietveld refinement technology.

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.

Data collection at X-ray free electron lasers has particular experimental challenges, such as continuous sample delivery or the use of novel ultrafast high-dynamic-range gain-switching X-ray detectors. This can result in a multitude of data artefacts, which can be detrimental to accurately determining structure-factor amplitudes for serial crystallography or single-particle imaging experiments. Here, a new data-classification tool is reported that offers a variety of machine-learning algorithms to sort data trained either on manual data sorting by the user or by profile fitting the intensity distribution on the detector based on the experiment. This is integrated into an easy-to-use graphical user interface, specifically designed to support the detectors, file formats and software available at most X-ray free electron laser facilities. The highly modular design makes the tool easily expandable to comply with other X-ray sources and detectors, and the supervised learning approach enables even the novice user to sort data containing unwanted artefacts or perform routine data-analysis tasks such as hit finding during an experiment, without needing to write code.

The growing pressure on school curricula has meant crystals and the science of crystallography have been cut from or made optional for many educational programs. This omission is a serious disservice to the history and understanding of modern sciences, given that crystallography underpins many of the greatest advancements in science over the past century, is a critical component of many modern research papers and patents, and has 29 Nobel Prizes awarded in the field. This contribution describes a simple activity to target classroom and public engagement with crystallography, using marshmallows or equivalent sweets/candy to represent atoms and cocktail sticks to represent bonds, together with examples of how crystals are studied and how they are useful. Though it has a simple basis, this activity can be extended in numerous ways to reflect the aims of the demonstrator, and a few of these are described.

Hendrickson & Lattman [Acta Cryst. (1970), B26, 136–143] introduced a method for representing crystallographic phase probabilities defined on the unit circle. Their approach could model the bimodal phase probability distributions that can result from experimental phase determination procedures. It also provided simple and highly effective means to combine independent sources of phase information. The present work discusses the equivalence of the Hendrickson–Lattman distribution and the generalized von Mises distribution of order two, which has been studied in the statistical literature. Recognizing this connection allows the Hendrickson–Lattman distribution to be expressed in an alternative form which is easier to interpret, as it involves the location and concentration parameters of the component von Mises distributions. It also allows clarification of the conditions for bimodality and access to a simplified analytical method for evaluating the trigonometric moments of the distribution, the first of which is required for computing the best Fourier synthesis in the presence of phase, but not amplitude, uncertainty.

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.

In cellulo crystallization is a rare event in nature. Recent advances that have made use of heterologous overexpression can promote the intracellular formation of protein crystals, but new tools are required to detect and characterize these targets in the complex cell environment. The present work makes use of Mask R-CNN, a convolutional neural network (CNN)-based instance segmentation method, for the identification of either single or multi-shaped crystals growing in living insect cells, using conventional bright field images. The algorithm can be rapidly adapted to recognize different targets, with the aim of extracting relevant information to support a semi-automated screening pipeline, in order to aid the development of the intracellular protein crystallization approach.

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.

A multi-slit very small angle neutron scattering (MS-VSANS) instrument has been finally accepted at the China Spallation Neutron Source (CSNS). It is the first spallation neutron source based VSANS instrument. MS-VSANS has a good signal-to-noise ratio and can cover a wide scattering vector magnitude range from 0.00028 to 1.4 Å−1. In its primary flight path, a combined curved multichannel beam bender and sections of rotary exchange drums are installed to minimize the background downstream of the instrument. An exchangeable multi-slit beam focusing system is integrated into the primary flight path, enabling access to a minimum scattering vector magnitude of 0.00028 Å−1. MS-VSANS has three modes, namely conventional SANS, polarizing SANS and VSANS modes. In the SANS mode, three motorized high-efficiency 3He tube detectors inside the detector tank cover scattering angles from 0.12 to 35° simultaneously. In the polarizing SANS mode, a double-V cavity provides highly polarized neutrons and a high-efficiency 3He polarization analyser allows full polarization analysis. In the VSANS mode, an innovative high-resolution gas electron multiplier detector covers scattering angles from 0.016 to 0.447°. The absolute scattering intensities of a selection of standard samples are obtained using the direct-beam technique; the effectiveness of this method is verified by testing the standard samples and comparing the results with those from a benchmark instrument. The MS-VSANS instrument is designed to be flexible and versatile and all the design goals have been achieved.

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.

A systematic procedure is introduced for modeling charge-neutral non-polar surfaces of ionic minerals containing polyatomic anions. By integrating distance- and charge-based clustering to identify chemical species within the mineral bulk, our pipeline, PolyCleaver, renders a variety of theoretically viable surface terminations. As a demonstrative example, this approach was applied to forsterite (Mg2SiO4), unveiling a rich interface landscape based on interactions with formaldehyde, a relevant multifaceted molecule, and more particularly in prebiotic chemistry. This high-throughput method, going beyond techniques traditionally applied in the modeling of minerals, offers new insights into the potential catalytic properties of diverse surfaces, enabling a broader exploration of synthetic pathways in complex mineral systems.

DLSIA (Deep Learning for Scientific Image Analysis) is a Python-based machine learning library that empowers scientists and researchers across diverse scientific domains with a range of customizable convolutional neural network (CNN) architectures for a wide variety of tasks in image analysis to be used in downstream data processing. DLSIA features easy-to-use architectures, such as autoencoders, tunable U-Nets and parameter-lean mixed-scale dense networks (MSDNets). Additionally, this article introduces sparse mixed-scale networks (SMSNets), generated using random graphs, sparse connections and dilated convolutions connecting different length scales. For verification, several DLSIA-instantiated networks and training scripts are employed in multiple applications, including inpainting for X-ray scattering data using U-Nets and MSDNets, segmenting 3D fibers in X-ray tomographic reconstructions of concrete using an ensemble of SMSNets, and leveraging autoencoder latent spaces for data compression and clustering. As experimental data continue to grow in scale and complexity, DLSIA provides accessible CNN construction and abstracts CNN complexities, allowing scientists to tailor their machine learning approaches, accelerate discoveries, foster interdisciplinary collaboration and advance research in scientific image analysis.

Serial crystallography experiments at synchrotron and X-ray free-electron laser (XFEL) sources are producing crystallographic data sets of ever-increasing volume. While these experiments have large data sets and high-frame-rate detectors (around 3520 frames per second), only a small percentage of the data are useful for downstream analysis. Thus, an efficient and real-time data classification pipeline is essential to differentiate reliably between useful and non-useful images, typically known as `hit' and `miss', respectively, and keep only hit images on disk for further analysis such as peak finding and indexing. While feature-point extraction is a key component of modern approaches to image classification, existing approaches require computationally expensive patch preprocessing to handle perspective distortion. This paper proposes a pipeline to categorize the data, consisting of a real-time feature extraction algorithm called modified and parallelized FAST (MP-FAST), an image descriptor and a machine learning classifier. For parallelizing the primary operations of the proposed pipeline, central processing units, graphics processing units and field-programmable gate arrays are implemented and their performances compared. Finally, MP-FAST-based image classification is evaluated using a multi-layer perceptron on various data sets, including both synthetic and experimental data. This approach demonstrates superior performance compared with other feature extractors and classifiers.

Proteins are well known `shapeshifters' which change conformation to function. In crystallography, multiple conformational states are often present within the crystal and the resulting electron-density map. Yet, explicitly incorporating alternative states into models to disentangle multi-conformer ensembles is challenging. We previously reported the tool FLEXR, which, within a few minutes, automatically separates conformational signal from noise and builds the corresponding, often missing, structural features into a multi-conformer model. To make the method widely accessible for routine multi-conformer building as part of the computational toolkit for macromolecular crystallography, we present a graphical user interface (GUI) for FLEXR, designed as a plugin for Coot 1. The GUI implementation seamlessly connects FLEXR models with the existing suite of validation and modeling tools available in Coot. We envision that FLEXR will aid crystallographers by increasing access to a multi-conformer modeling method that will ultimately lead to a better representation of protein conformational heterogeneity in the Protein Data Bank. In turn, deeper insights into the protein conformational landscape may inform biology or provide new opportunities for ligand design. The code is open source and freely available on GitHub at https://github.com/TheFischerLab/FLEXR-GUI.

This work presents observations of symmetry breakages in the intensity distributions of near-zone-axis convergent-beam electron diffraction (CBED) patterns that can only be explained by the symmetry of the specimen and not the symmetry of the unit cell describing the atomic structure of the material. The specimen is an aluminium–copper–tin alloy containing voids many tens of nanometres in size within continuous single crystals of the aluminium host matrix. Several CBED patterns where the incident beam enters and exits parallel void facets without the incident beam being perpendicular to these facets are examined. The symmetries in their intensity distributions are explained by the specimen morphology alone using a geometric argument based on the multislice theory. This work shows that it is possible to deduce nanoscale morphological information about the specimen in the direction of the electron beam – the elusive third dimension in transmission electron microscopy – from the inspection of CBED patterns.

In addressing the challenges faced by laboratories and universities with limited (or no) cryo-electron microscopy (cryo-EM) infrastructure, the ESRF, in collaboration with the Grenoble Institute for Structural Biology (IBS), has implemented the cryo-EM Solution-to-Structure (SOS) pipeline. This inclusive process, spanning grid preparation to high-resolution data collection, covers single-particle analysis and cryo-electron tomography (cryo-ET). Accessible through a rolling access route, proposals undergo scientific merit and technical feasibility evaluations. Stringent feasibility criteria demand robust evidence of sample homogeneity. Two distinct entry points are offered: users can either submit purified protein samples for comprehensive processing or initiate the pipeline with already vitrified cryo-EM grids. The SOS pipeline integrates negative stain imaging (exclusive to protein samples) as a first quality step, followed by cryo-EM grid preparation, grid screening and preliminary data collection for single-particle analysis, or only the first two steps for cryo-ET. In both cases, if the screening steps are successfully completed, high-resolution data collection will be carried out using a Titan Krios microscope equipped with a latest-generation direct electron counting detector coupled to an energy filter. The SOS pipeline thus emerges as a comprehensive and efficient solution, further democratizing access to cryo-EM research.

Analysis of small-angle scattering (SAS) data requires intensive modeling to infer and characterize the structures present in a sample. This iterative improvement of models is a time-consuming process. Presented here is Scattering Equation Builder (SEB), a C++ library that derives exact analytic expressions for the form factors of complex composite structures. The user writes a small program that specifies how the sub-units should be linked to form a composite structure and calls SEB to obtain an expression for the form factor. SEB supports e.g. Gaussian polymer chains and loops, thin rods and circles, solid spheres, spherical shells and cylinders, and many different options for how these can be linked together. The formalism behind SEB is presented and simple case studies are given, such as block copolymers with different types of linkage, as well as more complex examples, such as a random walk model of 100 linked sub-units, dendrimers, polymers and rods attached to the surfaces of geometric objects, and finally the scattering from a linear chain of five stars, where each star is built up of four diblock copolymers. These examples illustrate how SEB can be used to develop complex models and hence reduce the cost of analyzing SAS data.

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.

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

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.

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.

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.

Serial crystallography (SX) involves combining observations from a very large number of diffraction patterns coming from crystals in random orientations. To compile a complete data set, these patterns must be indexed (i.e. their orientation determined), integrated and merged. Introduced here is TORO (Torch-powered robust optimization) Indexer, a robust and adaptable indexing algorithm developed using the PyTorch framework. TORO is capable of operating on graphics processing units (GPUs), central processing units (CPUs) and other hardware accelerators supported by PyTorch, ensuring compatibility with a wide variety of computational setups. In tests, TORO outpaces existing solutions, indexing thousands of frames per second when running on GPUs, which positions it as an attractive candidate to produce real-time indexing and user feedback. The algorithm streamlines some of the ideas introduced by previous indexers like DIALS real-space grid search [Gildea, Waterman, Parkhurst, Axford, Sutton, Stuart, Sauter, Evans & Winter (2014). Acta Cryst. D70, 2652–2666] and XGandalf [Gevorkov, Yefanov, Barty, White, Mariani, Brehm, Tolstikova, Grigat & Chapman (2019). Acta Cryst. A75, 694–704] and refines them using faster and principled robust optimization techniques which result in a concise code base consisting of less than 500 lines. On the basis of evaluations across four proteins, TORO consistently matches, and in certain instances outperforms, established algorithms such as XGandalf and MOSFLM [Powell (1999). Acta Cryst. D55, 1690–1695], occasionally amplifying the quality of the consolidated data while achieving superior indexing speed. The inherent modularity of TORO and the versatility of PyTorch code bases facilitate its deployment into a wide array of architectures, software platforms and bespoke applications, highlighting its prospective significance in SX.

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.

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.