Van Vleck modes describe all possible displacements of octahedrally coordinated ligands about a core atom. They are a useful analytical tool for analysing the distortion of octahedra, particularly for first-order Jahn–Teller distortions, but determination of the Van Vleck modes of an octahedron is complicated by the presence of angular distortion of the octahedron. This problem is most commonly resolved by calculating the bond distortion modes (Q2, Q3) along the bond axes of the octahedron, disregarding the angular distortion and losing information on the octahedral shear modes (Q4, Q5 and Q6) in the process. In this paper, the validity of assuming bond lengths to be orthogonal in order to calculate the Van Vleck modes is discussed, and a method is described for calculating Van Vleck modes without disregarding the angular distortion. A Python package for doing this, VanVleckCalculator, is introduced and some examples of its use are given. Finally, it is shown that octahedral shear and angular distortion are often, but not always, correlated, and a parameter η is proposed as the shear fraction. It is demonstrated that η can be used to predict whether the values will be correlated when varying a tuning parameter such as temperature or pressure.

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.

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.

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.

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.

NdGa hydride and deuteride phases were prepared from high-quality NdGa samples and their structures characterized by powder and single-crystal X-ray diffraction and neutron powder diffraction. NdGa with the orthorhombic CrB-type structure absorbs hydrogen at hydrogen pressures ≤ 1 bar until reaching the composition NdGaH(D)1.1, which maintains a CrB-type structure. At elevated hydrogen pressure additional hydrogen is absorbed and the maximum composition recovered under standard temperature and pressure conditions is NdGaH(D)1.6 with the Cmcm LaGaH1.66-type structure. This structure is a threefold superstructure with respect to the CrB-type structure. The hydrogen atoms are ordered and distributed on three fully occupied Wyckoff positions corresponding to tetrahedral (4c, 8g) and trigonal–bipyramidal (8g) voids in the parent structure. The threefold superstructure is maintained in the H-deficient phases NaGaH(D)x until 1.6 ≥ x ≥ 1.2. At lower H concentrations, coinciding with the composition of the hydride obtained from hydrogenation at atmospheric pressure, the unit cell of the CrB-type structure is resumed. This phase can also display H deficiency, NdGaH(D)y (1.1 ≥ y ≥ 0.9), with H(D) exclusively situated in partially empty tetrahedral voids. The phase boundary between the threefold superstructure (LaGaH1.66 type) and the onefold structure (NdGaH1.1 type) is estimated on the basis of phase–composition isotherms and neutron powder diffraction to be x = 1.15.

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.

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.

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.

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.

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.

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.

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

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

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

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.

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.

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

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.

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

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

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

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

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.

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.

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.

SUBGROUPS is a free online program at the Bilbao Crystallographic Server (https://www.cryst.ehu.es/). It permits the exploration of all possible symmetries resulting from the distortion of a higher-symmetry parent structure, provided that the relation between the lattices of the distorted and parent structures is known. The program calculates all the subgroups of the parent space group which comply with this relation. The required minimal input is the space-group information of the parent structure and the relation of the unit cell of the distorted or pseudo-symmetric structure with that of the parent structure. Alternatively, the wavevector(s) observed in the diffraction data characterizing the distortion can be introduced. Additional conditions can be added, including filters related to space-group representations. The program provides very detailed information on all the subgroups, including group–subgroup hierarchy graphs. If a Crystallographic Information Framework (CIF) file of the parent high-symmetry structure is uploaded, the program generates CIF files of the parent structure described under each of the chosen lower symmetries. These CIF files may then be used as starting points for the refinement of the distorted structure under these possible symmetries. They can also be used for density functional theory calculations or for any other type of analysis. The power and efficiency of the program are illustrated with a few examples.

Here, a morphologically based approach is used for the in situ characterization of 3D growth rates of facetted crystals from the solution phase. Crystal images of single crystals of the β-form of l-glutamic acid are captured in situ during their growth at a relative supersaturation of 1.05 using transmission optical microscopy. The crystal growth rates estimated for both the {101} capping and {021} prismatic faces through image processing are consistent with those determined using reflection light mode [Jiang, Ma, Hazlehurst, Ilett, Jackson, Hogg & Roberts (2024). Cryst. Growth Des. 24, 3277–3288]. The growth rate in the {010} face is, for the first time, estimated from the shadow widths of the {021} prismatic faces and found to be typically about half that of the {021} prismatic faces. Analysis of the 3D shape during growth reveals that the initial needle-like crystal morphology develops during the growth process to become more tabular, associated with the Zingg factor evolving from 2.9 to 1.7 (>1). The change in relative solution supersaturation during the growth process is estimated from calculations of the crystal volume, offering an alternative approach to determine this dynamically from visual observations.

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

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

High-repetition-rate free-electron lasers impose stringent requirements on the thermal deformation of beamline optics. The Shanghai HIgh-repetition-rate XFEL aNd Extreme light facility (SHINE) experiences high average thermal power and demands wavefront preservation. To deeply study the thermal field of the first reflection mirror M1 at the FEL-II beamline of SHINE, thermal analysis under a photon energy of 400 eV was executed by fluid and solid heat transfer method. According to the thermal analysis results and the reference cooling water temperature of 30 °C, the temperature of the cooling water at the flow outlet is raised by 0.15 °C, and the wall temperature of the cooling tube increases by a maximum of 0.5 °C. The maximum temperature position of the footprint centerline in the meridian direction deviates away from the central position, and this asymmetrical temperature distribution will directly affect the thermal deformation of the mirror and indirectly affect the focus spot of the beam at the sample.

Soft X-ray spectroscopy is an important technique for measuring the fundamental properties of materials. However, for measurements of samples in the sub-millimetre range, many experimental setups show limitations. Position drifts on the order of hundreds of micrometres during thermal stabilization of the system can last for hours of expensive beam time. To compensate for drifts, sample tracking and feedback systems must be used. However, in complex sample environments where sample access is very limited, many existing solutions cannot be applied. In this work, we apply a robust computer vision algorithm to automatically track and readjust the sample position in the dozens of micrometres range. Our approach is applied in a complex sample environment, where the sample is in an ultra-high vacuum chamber, surrounded by cooled thermal shields to reach sample temperatures down to 2.5 K and in the center of a superconducting split coil. Our implementation allows sample-position tracking and adjustment in the vertical direction since this is the dimension where drifts occur during sample temperature change in our setup. The approach can be easily extended to 2D. The algorithm enables a factor of ten improvement in the overlap of a series of X-ray absorption spectra in a sample with a vertical size down to 70 µm. This solution can be used in a variety of experimental stations, where optical access is available and sample access by other means is reduced.

The design and first results of a high-transmission soft X-ray spectrometer operated at the X-SPEC double-undulator beamline of the KIT Light Source are presented. As a unique feature, particular emphasis was placed on optimizing the spectrometer transmission by maximizing the solid angle and the efficiencies of spectrometer gratings and detector. A CMOS detector, optimized for soft X-rays, allows for quantum efficiencies of 90% or above over the full energy range of the spectrometer, while simultaneously offering short readout times. Combining an optimized control system at the X-SPEC beamline with continuous energy scans (as opposed to step scans), the high transmission of the spectrometer, and the fast readout of the CMOS camera, enable the collection of entire rapid resonant inelastic soft X-ray scattering maps in less than 1 min. Series of spectra at a fixed energy can be taken with a frequency of up to 5 Hz. Furthermore, the use of higher-order reflections allows a very wide energy range (45 to 2000 eV) to be covered with only two blazed gratings, while keeping the efficiency high and the resolving power E/ΔE above 1500 and 3000 with low- and high-energy gratings, respectively.

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