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.

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.

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.

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.

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.

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.

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.

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

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

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

The 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.

This work introduces a completely rewritten version of the program RMCProfile (version 7), big-box, reverse Monte Carlo modelling software for analysis of total scattering data. The major new feature of RMCProfile7 is the ability to refine multiple phases simultaneously, which is relevant for many current research areas such as energy materials, catalysis and engineering. Other new features include improved support for molecular potentials and rigid-body refinements, as well as multiple different data sets. An empirical resolution correction and calculation of the pair distribution function as a back-Fourier transform are now also available. RMCProfile7 is freely available for download at https://rmcprofile.ornl.gov/.

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.

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.

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

X-ray 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.

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.

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.

Ptychography is a powerful computational imaging technique with microscopic imaging capability and adaptability to various specimens. To obtain an imaging result, it requires a phase-retrieval algorithm whose performance directly determines the imaging quality. Recently, deep neural network (DNN)-based phase retrieval has been proposed to improve the imaging quality from the ordinary model-based iterative algorithms. However, the DNN-based methods have some limitations because of the sensitivity to changes in experimental conditions and the difficulty of collecting enough measured specimen images for training the DNN. To overcome these limitations, a ptychographic phase-retrieval algorithm that combines model-based and DNN-based approaches is proposed. This method exploits a DNN-based denoiser to assist an iterative algorithm like ePIE in finding better reconstruction images. This combination of DNN and iterative algorithms allows the measurement model to be explicitly incorporated into the DNN-based approach, improving its robustness to changes in experimental conditions. Furthermore, to circumvent the difficulty of collecting the training data, it is proposed that the DNN-based denoiser be trained without using actual measured specimen images but using a formula-driven supervised approach that systemically generates synthetic images. In experiments using simulation based on a hard X-ray ptychographic measurement system, the imaging capability of the proposed method was evaluated by comparing it with ePIE and rPIE. These results demonstrated that the proposed method was able to reconstruct higher-spatial-resolution images with half the number of iterations required by ePIE and rPIE, even for data with low illumination intensity. Also, the proposed method was shown to be robust to its hyperparameters. In addition, the proposed method was applied to ptychographic datasets of a Simens star chart and ink toner particles measured at SPring-8 BL24XU, which confirmed that it can successfully reconstruct images from measurement scans with a lower overlap ratio of the illumination regions than is required by ePIE and rPIE.

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.

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

Metal–organic frameworks (MOFs) have garnered significant attention in recent years owing to their exceptional properties. Understanding the intricate relationship between the structure of a material and its properties is crucial for guiding the synthesis and application of these materials. (Scanning) Transmission electron microscopy (S)TEM imaging stands out as a powerful tool for structural characterization at the nanoscale, capable of detailing both periodic and aperiodic local structures. However, the high electron-beam sensitivity of MOFs presents substantial challenges in their structural characterization using (S)TEM. This paper summarizes the latest advancements in low-dose high-resolution (S)TEM imaging technology and its application in MOF material characterization. It covers aspects such as framework structure, defects, and surface and interface analysis, along with the distribution of guest molecules within MOFs. This review also discusses emerging technologies like electron ptychography and outlines several prospective research directions in this field.

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.

Small-angle neutron scattering is a widely used technique to study large-scale structures in bulk samples. The largest accessible length scale in conventional Bragg scattering is determined by the combination of the longest available neutron wavelength and smallest resolvable scattering angle. A method is presented that circumvents this limitation and is able to extract larger length scales from the low-q power-law scattering using a modification of the well known Porod law connecting the scattered intensity of randomly distributed objects to their specific surface area. It is shown that in the special case of a highly aligned domain structure the specific surface area extracted from the modified Porod law can be used to determine specific length scales of the domain structure. The analysis method is applied to study the micrometre-sized domain structure found in the intermediate mixed state of the superconductor niobium. The analysis approach allows the range of accessible length scales to be extended from 1 µm to up to 40 µm using a conventional small-angle neutron scattering setup.

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

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

This article presents a web-based framework to build a database without in-depth programming knowledge given a set of CIF dictionaries and a collection of CIFs. The framework consists of two main elements: the public site that displays the information contained in the CIFs in an ordered manner, and the restricted administrative site which defines how that information is stored, processed and, eventually, displayed. Thus, the web application allows users to easily explore, filter and access the data, download the original CIFs, and visualize the structures via JSmol. The modulated structures open database B-IncStrDB, the official International Union of Crystallography repository for this type of material and available through the Bilbao Crystallographic Server, has been re-implemented following the proposed framework.

Here, it is investigated how optical properties of single scatterers in interacting multi-particle systems influence measurable structure factors. Both particles with linear gradients of their scattering length density and core–shell structures evoke characteristic deviations between the weighted sum 〈S(Q)〉 of partial structure factors in a multi-component system and experimentally accessible measurable structure factors SM(Q). While 〈S(Q)〉 contains only the structural information of self-organizing systems, SM(Q) is additionally influenced by the optical properties of their constituents, resulting in features such as changing amplitudes, additional peaks in the low-wavevector region or splitting of higher-order maxima, which are not related to structural reasons. It is shown that these effects can be systematically categorized according to the qualitative behaviour of the form factor in the Guinier region, which enables assessing the suitability of experimentally obtained structure factors to genuinely represent the microstructure of complex systems free from any particular model assumption. Hence, a careful data analysis regarding size distribution and optical properties of single scatterers is mandatory to avoid a misinterpretation of measurable structure factors.