The present study introduces a processing strategy for synchrotron scanning 3D X-ray diffraction (s3DXRD) data, aimed at addressing the challenges posed by large, highly deformed, polyphase materials such as crystalline rocks. Leveraging symmetric Bragg reflections known as Friedel pairs, our method enables diffraction events to be precisely located within the sample volume. This method allows for fitting the phase, crystal structure and unit-cell parameters at the intra-grain scale on a voxel grid. The processing workflow incorporates several new modules, designed to (i) efficiently match Friedel pairs in large s3DXRD datasets containing up to 108 diffraction peaks; (ii) assign phases to each pixel or voxel, resolving potential ambiguities arising from overlap in scattering angles between different crystallographic phases; and (iii) fit the crystal orientation and unit cell locally on a point-by-point basis. We demonstrate the effectiveness of our technique on fractured granite samples, highlighting the ability of the method to characterize complex geological materials and show their internal structure and mineral composition. Additionally, we include the characterization of a metal gasket made of a commercial aluminium alloy, which surrounded the granite sample during experiments. The results show the effectiveness of the technique in recovering information about the internal texture and residual strain of materials that have undergone high levels of plastic deformation.

Nanometric precipitates in metallic alloys often have highly anisotropic shapes. Given the large grain size and non-random texture typical of these alloys, performing small- and wide-angle X-ray scattering (SAXS/WAXS) measurements on such samples for determining their characteristics (typically size and volume fraction) results in highly anisotropic and irreproducible data. Rotations of flat samples during SAXS/WAXS acquisitions are presented here as a solution to these anisotropy issues. Two aluminium alloys containing anisotropic precipitates are used as examples to validate the approach with a −45°/45° angular range. Clear improvements can be seen on the SAXS I(q) fitting and the consistency between the different SAXS/WAXS measurements. This methodology results in more reliable measurements of the precipitate's characteristics, and thus allows for time- and space-resolved measurements with higher accuracy.

Besides traditional pinhole geometry, the multi-slit very small angle neutron scattering instrument (MS-VSANS) at the China Spallation Neutron Source also utilizes a multi-slit collimation system to focus neutrons. Using the special focusing structures, the minimum scattering vector magnitude (q) can reach 0.00028 Å−1. The special structures also lead to a significantly different smearing function. By comparing the results of theoretical calculations with experimental data, we have validated the feasibility of a smearing method based on a mature theory for slit smearing. We use the weight-averaged intensity of neutron wavelength as a representative to evaluate the effect from a broad wavelength distribution, concentrating on the effect from the geometry of the multi-slit structures and the detector. The consistency of the theoretical calculation of the smearing function with experimental VSANS scattering profiles for a series of polystyrene standards of different diameters proves the feasibility of the smearing method. This marks the inaugural use of real experimental data from an instrument employing a multi-slit collimation system.

Lead-based relaxor ferroelectrics exhibit giant piezoelectric properties owing to their heterogeneous structures. The average and local structures measured by single-crystal X-ray diffraction under DC and AC electric fields are reviewed in this article. The position-dependent local lattice strain and the distribution of polar nanodomains and nanoregions show strong electric field dependence, which contributes to the giant piezoelectric properties.

In electron microscopy the principle of reciprocity is often used to imply time reversal symmetry. While this is true for elastic scattering, its applicability to inelastic scattering is less well established. From the second law of thermodynamics, the entropy for a thermally isolated system must be constant for any reversible process. Using entropy and statistical fluctuation arguments, it is shown that, while reversibility is possible at the microscopic level, it becomes statistically less likely for higher energy transfers. The implications for reciprocal imaging modes, including energy loss and energy gain measurements, as well as Kainuma's reciprocal wave model are also discussed.

Small-angle X-ray scattering (SAXS) is a widely used method for nanoparticle characterization. A common approach to analysing nanoparticles in solution by SAXS involves fitting the curve using a parametric model that relates real-space parameters, such as nanoparticle size and electron density, to intensity values in reciprocal space. Selecting the optimal model is a crucial step in terms of analysis quality and can be time-consuming and complex. Several studies have proposed effective methods, based on machine learning, to automate the model selection step. Deploying these methods in software intended for both researchers and industry raises several issues. The diversity of SAXS instrumentation requires assessment of the robustness of these methods on data from various machine configurations, involving significant variations in the q-space ranges and highly variable signal-to-noise ratios (SNR) from one data set to another. In the case of laboratory instrumentation, data acquisition can be time-consuming and there is no universal criterion for defining an optimal acquisition time. This paper presents an approach that revisits the nanoparticle model selection method proposed by Monge et al. [Acta Cryst. (2024), A80, 202–212], evaluating and enhancing its robustness on data from device configurations not seen during training, by expanding the data set used for training. The influence of SNR on predictor robustness is then assessed, improved, and used to propose a stopping criterion for optimizing the trade-off between exposure time and data quality.

In the realm of X-ray ptychography experiments, a considerable amount of ptychography scans are typically performed within a field of view encompassing the target sample. While it is crucial to obtain overlapping scans in small increments over the region of interest for achieving high-resolution sample reconstruction, a significant number of these scans often redundantly measure the empty background within the wide field of view. To address this inefficiency, an innovative algorithm is proposed that introduces automatic guidance for data acquisition. The algorithm first directs the scan point to actively search for the object of interest within the field of view. Subsequently, it intelligently scans along the perimeter of the sample, strategically acquiring measurements exclusively within the boundary of the region of interest. By employing this approach, a reduction in the number of measurements required to obtain high-resolution reconstruction images is demonstrated, as compared with conventional raster scanning methods. Furthermore, the automatic guidance provided by the algorithm offers the added advantage of saving valuable time during the reconstruction process. Through practical implementation on real experiments, these findings showcase the efficacy of the proposed algorithm in enhancing the efficiency and accuracy of X-ray ptychography experiments. This novel approach holds immense potential for advancing sample analysis and imaging techniques in various scientific disciplines.

xrdPlanner is a software package designed to aid in the planning and preparation of powder X-ray diffraction and total scattering beam times at synchrotron facilities. Many modern beamlines provide a flexible experimental setup and may have several different detectors available. In combination with a range of available X-ray energies, it often makes it difficult for the user to explore the available parameter space relevant for a given experiment prior to the scheduled beam time. xrdPlanner was developed to provide a fast and straightforward tool that allows users to visualize the accessible part of reciprocal space of their experiment at a given combination of photon energy and detector geometry. To plan and communicate the necessary geometry not only saves time but also helps the beamline staff to prepare and accommodate for an experiment. The program is tailored toward powder X-ray diffraction and total scattering experiments but may also be useful for other experiments that rely on an area detector and for which detector placement and achievable momentum-transfer range are important experimental parameters.

X-ray and electron scattering from free gas-phase molecules is examined using the independent atom model (IAM) and ab initio electronic structure calculations. The IAM describes the effect of the molecular geometry on the scattering, but does not account for the redistribution of valence electrons due to, for instance, chemical bonding. By examining the total, i.e. energy-integrated, scattering from three molecules, fluoroform (CHF3), 1,3-cyclohexadiene (C6H8) and naphthalene (C10H8), the effect of electron redistribution is found to predominantly reside at small-to-medium values of the momentum transfer (q ≤ 8 Å−1) in the scattering signal, with a maximum percent difference contribution at 2 ≤ q ≤ 3 Å−1. A procedure to determine the molecular geometry from the large-q scattering is demonstrated, making it possible to more clearly identify the deviation of the scattering from the IAM approximation at small and intermediate q and to provide a measure of the effect of valence electronic structure on the scattering signal.

The ForMAX beamline at the MAX IV Laboratory provides multiscale and multimodal structural characterization of hierarchical materials in the nanometre to millimetre range by combining small- and wide-angle X-ray scattering with full-field microtomography. The modular design of the beamline is optimized for easy switching between different experimental modalities. The beamline has a special focus on the development of novel fibrous materials from forest resources, but it is also well suited for studies within, for example, food science and biomedical research.

Physical optics simulations for beamlines and experiments allow users to test experiment feasibility and optimize beamline settings ahead of beam time in order to optimize valuable beam time at synchrotron light sources like NSLS-II. Further, such simulations also help to develop and test experimental data processing methods and software in advance. The Synchrotron Radiation Workshop (SRW) software package supports such complex simulations. We demonstrate how recent developments in SRW significantly improve the efficiency of physical optics simulations, such as end-to-end simulations of time-dependent X-ray photon correlation spectroscopy experiments with partially coherent undulator radiation (UR). The molecular dynamics simulation code LAMMPS was chosen to model the sample: a solution of silica nanoparticles in water at room temperature. Real-space distributions of nanoparticles produced by LAMMPS were imported into SRW and used to simulate scattering patterns of partially coherent hard X-ray UR from such a sample at the detector. The partially coherent UR illuminating the sample can be represented by a set of orthogonal coherent modes obtained by simulation of emission and propagation of this radiation through the coherent hard X-ray (CHX) scattering beamline followed by a coherent-mode decomposition. GPU acceleration is added for several key functions of SRW used in propagation from sample to detector, further improving the speed of the calculations. The accuracy of this simulation is benchmarked by comparison with experimental data.

To characterize an electron beam, visible synchrotron light is often used and dedicated beamlines at synchrotron sources are becoming a more common feature as instruments and methods for the diagnostics are, along with the accelerators, further developed. At KARA (Karlsruhe Research Accelerator), such a beamline exists and is based on a typical infrared/visible-light configuration. From experience at such beamlines no significant radiation was expected (dose rates larger than 0.5 µSv h−1). This was found not to be the case and a higher dose was measured which fortunately could be shielded to an acceptable level with 0.3 mm of aluminium foil or 2.0 mm of Pyrex glass. The presence of this radiation led to further investigation by both experiment and calculation. A custom setup using a silicon drift detector for energy-dispersive spectroscopy (Ketek GmbH) and attenuation experiments showed the radiation to be predominantly copper K-shell fluorescence and is confirmed by calculation. The measurement of secondary radiation from scattering of synchrotron and other radiation, and its calculation, is important for radiation protection, and, although a lot of experience exists and methods for radiation protection are well established, changes in machine, beamlines and experiments mean a constant appraisal is needed.

Synchrotron-radiation-based techniques are a powerful tool for the investigation of materials. In particular, the availability of highly brilliant sources has opened the possibility to develop techniques sensitive to dynamics at the atomic scale such as X-ray photon correlation spectroscopy (XPCS). XPCS is particularly relevant in the study of glasses, which have been often investigated at the macroscopic scale by, for example, differential scanning calorimetry. Here, we show how to adapt a Flash calorimeter to combine XPCS and calorimetric scans. This setup paves the way to novel experiments requiring dynamical and thermodynamic information, ranging from the study of the crystallization kinetics to the study of the glass transition in systems that can be vitrified thanks to the high cooling rates reachable with an ultrafast calorimeter.

The infrared beamline at BESSY II storage ring was upgraded recently to extend the capabilities of infrared microscopy. The endstations available at the beamline are now facilitating improved characterization of molecules and materials at different length scales and time resolutions. Here, the current outline of the beamline is reported and an overview of the endstations available is given. In particular, the first results obtained by using a new microscope for nano-spectroscopy that was implemented are presented. The capabilities of the scattering-type near-field optical microscope (s-SNOM) are demonstrated by investigating cellulose microfibrils, representing nanoscopic objects of a hierarchical structure. It is shown that the s-SNOM coupled to the beamline allows imaging to be performed with a spatial resolution of less than 30 nm and infrared spectra to be collected from an effective volume of less than 30 nm × 30 nm × 12 nm. Potential steps for further optimization of the beamline performance are discussed.

The users of synchrotron light are now tens of thousands throughout the world. Paradoxically, many of them do not know much about the early history of their domain. This is regrettable, since education about the initial developments makes it easier to fully understand synchrotron radiation and effectively use its amazing features. Scarcely known, in particular, is the key role of scientists working in Frascati, Italy. Partly based on his personal experiences, the author reports here relevant aspects of this story, including a pioneering French–Italian experiment that started in the early 1960s, and the Frascati contributions in the 1970s and 1980s to the birth of synchrotron light research. Finally, the unwise strategic decisions that prevented Italy from achieving absolute leadership in this domain – in spite of its unique initial advantages – are analyzed.

Beamline B21 at the Diamond Light Source synchrotron in the UK is a small-angle X-ray scattering (SAXS) beamline that specializes in high-throughput measurements via automated sample delivery systems. A system has been developed whereby a sample can be illuminated by a focused beam of light coincident with the X-ray beam. The system is compatible with the highly automated sample delivery system at the beamline and allows a beamline user to select a light source from a broad range of wavelengths across the UV and visible spectrum and to control the timing and duration of the light pulse with respect to the X-ray exposure of the SAXS measurement. The intensity of the light source has been characterized across the wavelength range enabling experiments where a quantitative measure of dose is important. Finally, the utility of the system is demonstrated via measurement of several light-responsive samples.

Nanoscale structural and electronic heterogeneities are prevalent in condensed matter physics. Investigating these heterogeneities in 3D has become an important task for understanding material properties. To provide a tool to unravel the connection between nanoscale heterogeneity and macroscopic emergent properties in magnetic materials, scanning transmission X-ray microscopy (STXM) is combined with X-ray magnetic circular dichroism. A vector tomography algorithm has been developed to reconstruct the full 3D magnetic vector field without any prior noise assumptions or knowledge about the sample. Two tomographic scans around the vertical axis are acquired on single-crystalline Nd2Fe14B pillars tilted at two different angles, with 2D STXM projections recorded using a focused 120 nm X-ray beam with left and right circular polarization. Image alignment and iterative registration have been implemented based on the 2D STXM projections for the two tilts. Dichroic projections obtained from difference images are used for the tomographic reconstruction to obtain the 3D magnetization distribution at the nanoscale.

Understanding the correlation between chemical and microstructural properties is critical for unraveling the fundamental relationship between materials chemistry and physical structures that can benefit materials science and engineering. Here, we demonstrate novel in situ correlative imaging of the X-ray Compton scattering computed tomography (XCS-CT) technique for studying this fundamental relationship. XCS-CT can image light elements that do not usually exhibit strong signals using other X-ray characterization techniques. This paper describes the XCS-CT setup and data analysis method for calculating the valence electron momentum density and lithium-ion concentration, and provides two examples of spatially and temporally resolved chemical properties inside batteries in 3D. XCS-CT was applied to study two types of rechargeable lithium batteries in standard coin cell casings: (1) a lithium-ion battery containing a cathode of bespoke microstructure and liquid electrolyte, and (2) a solid-state battery containing a solid-polymer electrolyte. The XCS-CT technique is beneficial to a wide variety of materials and systems to map chemical composition changes in 3D structures.

X-ray and neutron scattering have long been used for structural characterization of cellulose in plants. Due to averaging over the illuminated sample volume, these measurements traditionally overlooked the compositional and morphological heterogeneity within the sample. Here, a scanning tomographic imaging method is described, using contrast derived from the X-ray scattering intensity, for virtually sectioning the sample to reveal its internal structure at a resolution of a few micrometres. This method provides a means for retrieving the local scattering signal that corresponds to any voxel within the virtual section, enabling characterization of the local structure using traditional data-analysis methods. This is accomplished through tomographic reconstruction of the spatial distribution of a handful of mathematical components identified by non-negative matrix factorization from the large dataset of X-ray scattering intensity. Joint analysis of multiple datasets, to find similarity between voxels by clustering of the decomposed data, could help elucidate systematic differences between samples, such as those expected from genetic modifications, chemical treatments or fungal decay. The spatial distribution of the microfibril angle can also be analyzed, based on the tomographically reconstructed scattering intensity as a function of the azimuthal angle.

Achieving diffraction-limited performance in fourth-generation synchrotron radiation sources demands monochromator crystals that can preserve the wavefront across an unprecedented extensive range. There is an urgent need for techniques of absolute crystal diffraction wavefront measurement. At the Beijing Synchrotron Radiation Facility (BSRF), a novel edge scan wavefront metrology technique has been developed. This technique employs a double-edge tracking method, making diffraction-limited level absolute crystal diffraction wavefront measurement a reality. The results demonstrate an equivalent diffraction surface slope error below 70 nrad (corresponding to a wavefront phase error of 4.57% λ) r.m.s. within a nearly 6 mm range for a flat crystal in the crystal surface coordinate. The double-edge structure contributes to exceptional measurement precision for slope error reproducibility, achieving levels below 15 nrad (phase error reproducibility < λ/100) even at a first-generation synchrotron radiation source. Currently, the measurement termed double-edge scan (DES) has already been regarded as a critical feedback mechanism in the fabrication of next-generation crystals.

Small-angle-scattering tensor tomography is a technique for studying anisotropic nanostructures of millimetre-sized samples in a volume-resolved manner. It requires the acquisition of data through repeated tomographic rotations about an axis which is subjected to a series of tilts. The tilt that can be achieved with a typical setup is geometrically constrained, which leads to limits in the set of directions from which the different parts of the reciprocal space map can be probed. Here, we characterize the impact of this limitation on reconstructions in terms of the missing wedge problem of tomography, by treating the problem of tensor tomography as the reconstruction of a three-dimensional field of functions on the unit sphere, represented by a grid of Gaussian radial basis functions. We then devise an acquisition scheme to obtain complete data by remounting the sample, which we apply to a sample of human trabecular bone. Performing tensor tomographic reconstructions of limited data sets as well as the complete data set, we further investigate and validate the missing wedge problem by investigating reconstruction errors due to data incompleteness across both real and reciprocal space. Finally, we carry out an analysis of orientations and derived scalar quantities, to quantify the impact of this missing wedge problem on a typical tensor tomographic analysis. We conclude that the effects of data incompleteness are consistent with the predicted impact of the missing wedge problem, and that the impact on tensor tomographic analysis is appreciable but limited, especially if precautions are taken. In particular, there is only limited impact on the means and relative anisotropies of the reconstructed reciprocal space maps.

To date, computed tomography experiments, carried-out at synchrotron radiation facilities worldwide, pose a tremendous challenge in terms of the breadth and complexity of the experimental datasets produced. Furthermore, near real-time three-dimensional reconstruction capabilities are becoming a crucial requirement in order to perform high-quality and result-informed synchrotron imaging experiments, where a large amount of data is collected and processed within a short time window. To address these challenges, we have developed and deployed a synchrotron computed tomography framework designed to automatically process online the experimental data from the synchrotron imaging beamlines, while leveraging the high-performance computing cluster capabilities to accelerate the real-time feedback to the users on their experimental results. We have, further, integrated it within a modern unified national authentication and data management framework, which we have developed and deployed, spanning the entire data lifecycle of a large-scale scientific facility. In this study, the overall architecture, functional modules and workflow design of our synchrotron computed tomography framework are presented in detail. Moreover, the successful integration of the imaging beamlines at the Shanghai Synchrotron Radiation Facility into our scientific computing framework is also detailed, which, ultimately, resulted in accelerating and fully automating their entire data processing pipelines. In fact, when compared with the original three-dimensional tomography reconstruction approaches, the implementation of our synchrotron computed tomography framework led to an acceleration in the experimental data processing capabilities, while maintaining a high level of integration with all the beamline processing software and systems.

An innovative dual-thickness semi-transparent beamstop designed to enhance the performance of small-angle X-ray scattering (SAXS) experiments is introduced. This design integrates two absorbers of differing thicknesses side by side into a single attenuator, known as a beamstop. Instead of completely stopping the direct beam, it attenuates it, allowing the SAXS detector to measure the transmitted beam through the sample. This approach achieves true synchronization in measuring both scattered and transmitted signals and effectively eliminates higher-order harmonic contributions when determining the transmission light intensity through the sample. This facilitates and optimizes signal detection and background subtraction. This contribution details the theoretical basis and practical implementation of this solution at the SAXS station on the 1W2A beamline at the Beijing Synchrotron Radiation Facility. It also anticipates its application at other SAXS stations, including that at the forthcoming High Energy Photon Source, providing an effective solution for high-precision SAXS experiments.

Phenuiviridae nucleoprotein is the main structural and functional component of the viral cycle, protecting the viral RNA and mediating the essential replication/transcription processes. The nucleoprotein (N) binds the RNA using its globular core and polymerizes through the N-terminus, which is presented as a highly flexible arm, as demonstrated in this article. The nucleoprotein exists in an `open' or a `closed' conformation. In the case of the closed conformation the flexible N-terminal arm folds over the RNA-binding cleft, preventing RNA adsorption. In the open conformation the arm is extended in such a way that both RNA adsorption and N polymerization are possible. In this article, single-crystal X-ray diffraction and small-angle X-ray scattering were used to study the N protein of Toscana virus complexed with a single-chain camelid antibody (VHH) and it is shown that in the presence of the antibody the nucleoprotein is unable to achieve a functional assembly to form a ribonucleoprotein complex.

Diffuse scattering is a promising method to gain additional insight into protein dynamics from macromolecular crystallography experiments. Bragg intensities yield the average electron density, while the diffuse scattering can be processed to obtain a three-dimensional reciprocal-space map that is further analyzed to determine correlated motion. To make diffuse scattering techniques more accessible, software for data processing called mdx2 has been created that is both convenient to use and simple to extend and modify. mdx2 is written in Python, and it interfaces with DIALS to implement self-contained data-reduction workflows. Data are stored in NeXus format for software interchange and convenient visualization. mdx2 can be run on the command line or imported as a package, for instance to encapsulate a complete workflow in a Jupyter notebook for reproducible computing and education. Here, mdx2 version 1.0 is described, a new release incorporating state-of-the-art techniques for data reduction. The implementation of a complete multi-crystal scaling and merging workflow is described, and the methods are tested using a high-redundancy data set from cubic insulin. It is shown that redundancy can be leveraged during scaling to correct systematic errors and obtain accurate and reproducible measurements of weak diffuse signals.

The determination of the atomic resolution structure of biomacromolecules is essential for understanding details of their function. Traditionally, such a structure determination has been performed with crystallographic or nuclear resonance methods, but during the last decade, cryogenic transmission electron microscopy (cryo-TEM) has become an equally important tool. As the blotting and flash-freezing of the samples can induce conformational changes, external validation tools are required to ensure that the vitrified samples are representative of the solution. Although many validation tools have already been developed, most of them rely on fully resolved atomic models, which prevents early screening of the cryo-TEM maps. Here, a novel and automated method for performing such a validation utilizing small-angle X-ray scattering measurements, publicly available through the new software package AUSAXS, is introduced and implemented. The method has been tested on both simulated and experimental data, where it was shown to work remarkably well as a validation tool. The method provides a dummy atomic model derived from the EM map which best represents the solution structure.

Single-particle imaging using X-ray free-electron lasers (XFELs) is a promising technique for observing nanoscale biological samples under near-physiological conditions. However, as the sample's orientation in each diffraction pattern is unknown, advanced algorithms are required to reconstruct the 3D diffraction intensity volume and subsequently the sample's density model. While most approaches perform 3D reconstruction via determining the orientation of each diffraction pattern, a correlation-based approach utilizes the averaged spatial correlations of diffraction intensities over all patterns, making it well suited for processing experimental data with a poor signal-to-noise ratio of individual patterns. Here, a method is proposed to determine the 3D structure of a sample by analyzing the double, triple and quadruple spatial correlations in diffraction patterns. This ab initio method can reconstruct the basic shape of an irregular unsymmetric 3D sample without requiring any prior knowledge of the sample. The impact of background and noise on correlations is investigated and corrected to ensure the success of reconstruction under simulated experimental conditions. Additionally, the feasibility of using the correlation-based approach to process incomplete partial diffraction patterns is demonstrated. The proposed method is a variable addition to existing algorithms for 3D reconstruction and will further promote the development and adoption of XFEL single-particle imaging techniques.

Our study compares short-range order parameters refined from the diffuse scattering in single-crystal X-ray and single-crystal electron diffraction data. Nb0.84CoSb was chosen as a reference material. The correlations between neighbouring vacancies and the displacements of Sb and Co atoms were refined from the diffuse scattering using a Monte Carlo refinement in DISCUS. The difference between the Sb and Co displacements refined from the diffuse scattering and the Sb and Co displacements refined from the Bragg reflections in single-crystal X-ray diffraction data is 0.012 (7) Å for the refinement on diffuse scattering in single-crystal X-ray diffraction data and 0.03 (2) Å for the refinement on the diffuse scattering in single-crystal electron diffraction data. As electron diffraction requires much smaller crystals than X-ray diffraction, this opens up the possibility of refining short-range order parameters in many technologically relevant materials for which no crystals large enough for single-crystal X-ray diffraction are available.

Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235–244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740–751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92–109; Jha et al. (2021). J. Appl. Cryst. 54, 1234–1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyl­uracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.

Appreciating that the role of the solute–solvent and other outer-sphere interactions is essential for understanding chemistry and chemical dynamics in solution, experimental approaches are needed to address the structural consequences of these interactions, complementing condensed-matter simulations and coarse-grained theories. High-energy X-ray scattering (HEXS) combined with pair distribution function analysis presents the opportunity to probe these structures directly and to develop quantitative, atomistic models of molecular systems in situ in the solution phase. However, at concentrations relevant to solution-phase chemistry, the total scattering signal is dominated by the bulk solvent, prompting researchers to adopt a differential approach to eliminate this unwanted background. Though similar approaches are well established in quantitative structural studies of macromolecules in solution by small- and wide-angle X-ray scattering (SAXS/WAXS), analogous studies in the HEXS regime—where sub-ångström spatial resolution is achieved—remain underdeveloped, in part due to the lack of a rigorous theoretical description of the experiment. To address this, herein we develop a framework for differential solution scattering experiments conducted at high energies, which includes concepts of the solvent-excluded volume introduced to describe SAXS/WAXS data, as well as concepts from the time-resolved X-ray scattering community. Our theory is supported by numerical simulations and experiment and paves the way for establishing quantitative methods to determine the atomic structures of small molecules in solution with resolution approaching that of crystallography.

In this work, regenerated cellulose textile fibers, Ioncell-F, dry-wet spun with different draw ratios, have been investigated by scanning wide-angle X-ray scattering (WAXS) using a mesoscopic X-ray beam. The fibers were found to be homogeneous on the 500 nm length scale. Analysis of the azimuthal angular dependence of a crystalline Bragg spot intensity revealed a radial dependence of the degree of orientation of crystallites that was found to increase with the distance from the center of the fiber. We attribute this to radial velocity gradients during the extrusion of the spin dope and the early stage of drawing. On the other hand, the fiber crystallinity was found to be essentially homogeneous over the fiber cross section.

Crystallography is a quintessential method for determining the atomic structure of crystals. The most common implementation of crystallography uses single crystals that must be of sufficient size, typically tens of micrometres or larger, depending on the complexity of the crystal structure. The emergence of serial data-collection methods in crystallography, particularly for time-resolved experiments, opens up opportunities to develop new routes to structure determination for nanocrystals and ensembles of crystals. Fluctuation X-ray scattering is a correlation-based approach for single-particle imaging from ensembles of identical particles, but has yet to be applied to crystal structure determination. Here, an iterative algorithm is presented that recovers crystal structure-factor intensities from fluctuation X-ray scattering correlations. The capabilities of this algorithm are demonstrated by recovering the structure of three small-molecule crystals and a protein crystal from simulated fluctuation X-ray scattering correlations. This method could facilitate the recovery of structure-factor intensities from crystals in serial crystallography experiments and relax sample requirements for crystallography experiments.

Stimulated by informal conversations at the XVII International Small Angle Scattering (SAS) conference (Traverse City, 2017), an international team of experts undertook a round-robin exercise to produce a large dataset from proteins under standard solution conditions. These data were used to generate consensus SAS profiles for xylose isomerase, urate oxidase, xylanase, lysozyme and ribonuclease A. Here, we apply a new protocol using maximum likelihood with a larger number of the contributed datasets to generate improved consensus profiles. We investigate the fits of these profiles to predicted profiles from atomic coordinates that incorporate different models to account for the contribution to the scattering of water molecules of hydration surrounding proteins in solution. Programs using an implicit, shell-type hydration layer generally optimize fits to experimental data with the aid of two parameters that adjust the volume of the bulk solvent excluded by the protein and the contrast of the hydration layer. For these models, we found the error-weighted residual differences between the model and the experiment generally reflected the subsidiary maxima and minima in the consensus profiles that are determined by the size of the protein plus the hydration layer. By comparison, all-atom solute and solvent molecular dynamics (MD) simulations are without the benefit of adjustable parameters and, nonetheless, they yielded at least equally good fits with residual differences that are less reflective of the structure in the consensus profile. Further, where MD simulations accounted for the precise solvent composition of the experiment, specifically the inclusion of ions, the modelled radius of gyration values were significantly closer to the experiment. The power of adjustable parameters to mask real differences between a model and the structure present in solution is demonstrated by the results for the conformationally dynamic ribonuclease A and calculations with pseudo-experimental data. This study shows that, while methods invoking an implicit hydration layer have the unequivocal advantage of speed, care is needed to understand the influence of the adjustable parameters. All-atom solute and solvent MD simulations are slower but are less susceptible to false positives, and can account for thermal fluctuations in atomic positions, and more accurately represent the water molecules of hydration that contribute to the scattering profile.

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

This study examines various methods for modelling the electron density and, thus, the electrostatic potential of an organometallic complex for use in crystal structure refinement against 3D electron diffraction (ED) data. It focuses on modelling the scattering factors of iron(III), considering the electron density distribution specific for coordination with organic linkers. We refined the structural model of the metal–organic complex, iron(III) acetyl­acetonate (FeAcAc), using both the independent atom model (IAM) and the transferable aspherical atom model (TAAM). TAAM refinement initially employed multipolar parameters from the MATTS databank for acetyl­acetonate, while iron was modelled with a spherical and neutral approach (TAAM ligand). Later, custom-made TAAM scattering factors for Fe—O coordination were derived from DFT calculations [TAAM-ligand-Fe(III)]. Our findings show that, in this compound, the TAAM scattering factor corresponding to Fe3+ has a lower scattering amplitude than the Fe3+ charged scattering factor described by IAM. When using scattering factors corresponding to the oxidation state of iron, IAM inaccurately represents electrostatic potential maps and overestimates the scattering potential of the iron. In addition, TAAM significantly improved the fitting of the model to the data, shown by improved R1 values, goodness-of-fit (GooF) and reduced noise in the Fourier difference map (based on the residual distribution analysis). For 3D ED, R1 values improved from 19.36% (IAM) to 17.44% (TAAM-ligand) and 17.49% (TAAM-ligand-Fe3+), and for single-crystal X-ray diffraction (SCXRD) from 3.82 to 2.03% and 1.98%, respectively. For 3D ED, the most significant R1 reductions occurred in the low-resolution region (8.65–2.00 Å), dropping from 20.19% (IAM) to 14.67% and 14.89% for TAAM-ligand and TAAM-ligand-Fe(III), respectively, with less improvement in high-resolution ranges (2.00–0.85 Å). This indicates that the major enhancements are due to better scattering modelling in low-resolution zones. Furthermore, when using TAAM instead of IAM, there was a noticeable improvement in the shape of the thermal ellipsoids, which more closely resembled those of an SCXRD-refined model. This study demonstrates the applicability of more sophisticated scattering factors to improve the refinement of metal–organic complexes against 3D ED data, suggesting the need for more accurate modelling methods and highlighting the potential of TAAM in examining the charge distribution of large molecular structures using 3D ED.

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

Single-crystal X-ray diffraction analysis of small molecule active pharmaceutical ingredients is a key technique in the confirmation of molecular connectivity, including absolute stereochemistry, as well as the solid-state form. However, accessing single crystals suitable for X-ray diffraction analysis of an active pharmaceutical ingredient can be experimentally laborious, especially considering the potential for multiple solid-state forms (solvates, hydrates and polymorphs). In recent years, methods for the exploration of experimental crystallization space of small molecules have undergone a `step-change', resulting in new high-throughput techniques becoming available. Here, the application of high-throughput encapsulated nanodroplet crystallization to a series of six di­hydro­pyridines, calcium channel blockers used in the treatment of hypertension related diseases, is described. This approach allowed 288 individual crystallization experiments to be performed in parallel on each molecule, resulting in rapid access to crystals and subsequent crystal structures for all six di­hydro­pyridines, as well as revealing a new solvate polymorph of nifedipine (1,4-dioxane solvate) and the first known solvate of nimodipine (DMSO solvate). This work further demonstrates the power of modern high-throughput crystallization methods in the exploration of the solid-state landscape of active pharmaceutical ingredients to facilitate crystal form discovery and structural analysis by single-crystal X-ray diffraction.

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

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.

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

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

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.

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.

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.

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

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

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.

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

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