Through numerical optimization of cooling lengths and cooling groove positions for the first reflection mirror of a free-electron laser [OK?], the root mean square of the height error of the mirror's thermal deformation was minimized. The optimized mirror design effectively mitigated stray light and enhanced the peak intensity of the focus spot at the sample, thereby enhancing the optical performance of the high-heat-load mirror under high repetition rates at beamline FEL-II of the SHINE facility.

A hard X-ray single-shot spectrometer comprising thin, bent Si crystals has been developed for the Pohang Accelerator Laboratory X-ray Free-Electron Laser (XFEL), for detailed analysis of ultrafast 4.5–17 keV XFEL pulses with a high spectral resolution. This instrument facilitates shot-to-shot spectral structure monitoring and optimization of the operating conditions of the XFEL owing to its ability to provide comprehensive data on the spectral properties and fluctuations of self-amplified spontaneous emission, monochromatic and seeded XFEL modes.

The development of instrumentation as well as applications for megahertz X-ray phase contrast imaging at the Single Particles, Clusters, and Biomolecules and Serial Femtosecond Crystallography instrument of the European XFEL are introduced here.

This review focuses on low-dose near-field X-ray speckle phase imaging in the differential mode introducing the existing algorithms with their specifications and comparing their performances under various experimental conditions.

In this work, we showed that the use of ethanol to increase image contrast when imaging cardiac tissue with synchrotron X-ray phase-contrast imaging (X-PCI) leads to heterogeneous tissue shrinkage, which has an impact on the 3D organization of the myocardium.

we introduce a novel approach for a real-time dual-frequency feedback system, which has been firstly used at the hard X-ray nanoprobe beamline of SSRF. The BiBEST can then efficiently stabilize X-ray beam position and stability in parallel, making use of different optical systems in the beamline.

A slit-less wavelength-dispersive spectrometer design using a single-bounce monocapillary that aligns the sample on the Rowland circle, enhancing photon throughput and maintaining resolution. The compact design supports flexibility and reconfiguration in facilities without complex beamline infrastructure, significantly improving detection efficiency.

A general formalism is presented for the isotropically averaged single-chain scattering function (form factor) of single, double, triple and higher-order helices, as well as twisted fibres consisting of concentric layers of strands. Form factors for double and triple helices with differently sized grooves have also been derived. The formulas include the longitudinal and transverse interference over the pitch and radius of the helices, respectively. The results may be useful for the analysis of small-angle scattering data of (bio)macromolecules or molecular assemblies exhibiting a helical arrangement.

This study characterizes the microstructure and mineralogy of 132 (ODP sample), 1000 and 1880 million-year-old chert samples. By using ultra-small-angle X-ray scattering (USAXS), wide-angle X-ray scattering and other techniques, the preservation of organic matter (OM) in these samples is studied. The scarce microstructural data reported on chert contrast with many studies addressing porosity evolution in other sedimentary rocks. The aim of this work is to solve the distribution of OM and silica in chert by characterizing samples before and after combustion to pinpoint the OM distribution inside the porous silica matrix. The samples are predominantly composed of alpha quartz and show increasing crystallite sizes up to 33 ± 5 nm (1σ standard deviation or SD). In older samples, low water abundances (∼0.03%) suggest progressive dehydration. (U)SAXS data reveal a porous matrix that evolves over geological time, including, from younger to older samples, (1) a decreasing pore volume down to 1%, (2) greater pore sizes hosting OM, (3) decreasing specific surface area values from younger (9.3 ± 0.1 m2 g−1) to older samples (0.63 ± 0.07 m2 g−1, 1σ SD) and (4) a lower background intensity correlated to decreasing hydrogen abundances. The pore-volume distributions (PVDs) show that pores ranging from 4 to 100 nm accumulate the greater volume fraction of OM. Raman data show aromatic organic clusters up to 20 nm in older samples. Raman and PVD data suggest that OM is located mostly in mesopores. Observed structural changes, silica–OM interactions and the hydro­phobicity of the OM could explain the OM preservation in chert.

Time-resolved high-energy X-ray diffraction was used during growth of ultrathin NixFe3−xO4 films with varying Ni content (0 ≤ x ≤ 1.5) deposited on MgO(001) substrates by reactive molecular beam epitaxy, providing an insight into the growth dynamics of these films. In order to obtain structural information, reciprocal-space maps were recorded and the temporal evolution of the Bragg peaks specific to the octahedral and tetrahedral lattice sites of the inverse spinel structure of NixFe3−xO4 was observed during growth of the films. A time delay, corresponding to a coverage of 1.2–1.8 nm, between the appearance of the Bragg reflections originating from octahedral sites and reflections originating exclusively from tetrahedral sites indicates that the ferrite films grow in two stages. In the initial growth phase, a rock salt interface layer is formed. Afterwards, a structural transition occurs and the films grow in an inverse spinel structure. The thickness of the initial rock salt phase was found to increase with Ni content and to be responsible for atypical strain in the thin films. Films with Ni contents x > 1 do not show a structural transition. These films remain in a (deficient) rock salt structure consisting of a mixed Ni–Fe oxide and do not form a spinel structure at all. They show an increased number of NiO clusters as detected by X-ray photoelectron spectroscopy of the valence band, accompanied by a significant roughening of the films.

In crystallographic texture analysis, ensuring that sample directions are preserved from experiment to the resulting orientation distribution is crucial to obtain physical meaning from diffraction data. This work details a procedure to ensure instrument and sample coordinates are consistent when analyzing diffraction data with a Rietveld refinement using the texture analysis software MAUD. A quartz crystal is measured on the HIPPO diffractometer at Los Alamos National Laboratory for this purpose. The methods described here can be applied to any diffraction instrument measuring orientation distributions in polycrystalline materials.

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.

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

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

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

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

An implementation of Slater-type spherical scattering factors for X-ray and electron diffraction for elements in the range Z = 1–103 is presented within the software Olex2. Both high- and low-angle Fourier behaviour of atomic electron density and electrostatic potential can thus be addressed, in contrast to the limited flexibility of the four Gaussian plus constant descriptions which are currently the most widely used method for calculating atomic scattering factors during refinement. The implementation presented here accommodates the increasing complexity of the electronic structure of heavier elements by using complete atomic wavefunctions without any interpolation between precalculated tables or intermediate fitting functions. Atomic wavefunctions for singly charged ions are implemented and made accessible, and these show drastic changes in electron diffraction scattering factors compared with the neutral atom. A comparison between the two different spherical models of neutral atoms is presented as an example for four different kinds of X-ray and two electron diffraction structures, and comparisons of refinement results using the existing diffraction data are discussed. A systematic but slight improvement in R values and residual densities can be observed when using the new scattering factors, and this is discussed relative to effects on the atomic displacement parameters and atomic positions, which are prominent near the heavier elements in a structure.

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 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.

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

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

Fluctuation X-ray scattering (FXS) offers a complementary approach for nano- and bioparticle imaging with an X-ray free-electron laser (XFEL), by extracting structural information from correlations in scattered XFEL pulses. Here a workflow is presented for single-particle structure determination using FXS. The workflow includes procedures for extracting the rotational invariants from FXS patterns, performing structure reconstructions via iterative phasing of the invariants, and aligning and averaging multiple reconstructions. The reconstruction pipeline is implemented in the open-source software xFrame and its functionality is demonstrated on several simulated structures.

This work introduces X-Ray Calc (XRC), an open-source software package designed to simulate X-ray reflectivity (XRR) and address the inverse problem of reconstructing film structures on the basis of measured XRR curves. XRC features a user-friendly graphical interface that facilitates interactive simulation and reconstruction. The software employs a recursive approach based on the Fresnel equations to calculate XRR and incorporates specialized tools for modeling periodic multilayer structures. This article presents the latest version of the X-Ray Calc software (XRC3), with notable improvements. These enhancements encompass an automatic fitting capability for XRR curves utilizing a modified flight particle swarm optimization algorithm. A novel cost function was also developed specifically for fitting XRR curves of periodic structures. Furthermore, the overall user experience has been enhanced by developing a new single-window interface.

Dark-field X-ray microscopy (DFXM) is a full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM, an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. This work explores contrast methods and optimizes the DFXM setup specifically for the case of mapping dislocations. Forward projections of detector images are generated using two complementary simulation tools based on geometrical optics and wavefront propagation, respectively. Weak and strong beam contrast and the mapping of strain components are studied. The feasibility of observing dislocations in a wall is elucidated as a function of the distance between neighbouring dislocations and the spatial resolution. Dislocation studies should be feasible with energy band widths of 10−2, of relevance for fourth-generation synchrotron and X-ray free-electron laser sources.

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.

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

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

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

The strong metal–support interaction (SMSI) is a phenomenon observed in supported metal catalyst systems in which reducible metal oxide supports can form overlayers over the surface of active metal nanoparticles (NPs) under a hydrogen (H2) environment at elevated temperatures. SMSI has been shown to affect catalyst performance in many reactions by changing the type and number of active sites on the catalyst surface. Laboratory methods for the analysis of SMSI at the nanoparticle-ensemble level are lacking and mostly based on indirect evidence, such as gas chemisorption. Here, we demonstrate the possibility to detect and characterize SMSIs in Co/TiOx model catalysts using the laboratory X-ray standing wave (XSW) technique for a large ensemble of NPs at the bulk scale. We designed a thermally stable MoNx/SiNx periodic multilayer to retain XSW generation after reduction with H2 gas at 600°C. The model catalyst system was synthesized here by deposition of a thin TiOx layer on top of the periodic multilayer, followed by Co NP deposition via spare ablation. A partial encapsulation of Co NPs by TiOx was identified by analyzing the change in Ti atomic distribution. This novel methodological approach can be extended to observe surface restructuring of model catalysts in situ at high temperature (up to 1000°C) and pressure (≤3 mbar), and can also be relevant for fundamental studies in the thermal stability of membranes, as well as metallurgy.

Due to the ambiguity related to the lack of phase information, determining the physical parameters of multilayer thin films from measured neutron and X-ray reflectivity curves is, on a fundamental level, an underdetermined inverse problem. This ambiguity poses limitations on standard neural networks, constraining the range and number of considered parameters in previous machine learning solutions. To overcome this challenge, a novel training procedure has been designed which incorporates dynamic prior boundaries for each physical parameter as additional inputs to the neural network. In this manner, the neural network can be trained simultaneously on all well-posed subintervals of a larger parameter space in which the inverse problem is underdetermined. During inference, users can flexibly input their own prior knowledge about the physical system to constrain the neural network prediction to distinct target subintervals in the parameter space. The effectiveness of the method is demonstrated in various scenarios, including multilayer structures with a box model parameterization and a physics-inspired special parameterization of the scattering length density profile for a multilayer structure. In contrast to previous methods, this approach scales favourably when increasing the complexity of the inverse problem, working properly even for a five-layer multilayer model and a periodic multilayer model with up to 17 open parameters.

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

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

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

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

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

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 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.

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

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

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

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

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

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

Presented and discussed here is the implementation of a software solution that provides prompt X-ray diffraction data analysis during fast dynamic compression experiments conducted within the dynamic diamond anvil cell technique. It includes efficient data collection, streaming of data and metadata to a high-performance cluster (HPC), fast azimuthal data integration on the cluster, and tools for controlling the data processing steps and visualizing the data using the DIOPTAS software package. This data processing pipeline is invaluable for a great number of studies. The potential of the pipeline is illustrated with two examples of data collected on ammonia–water mixtures and multiphase mineral assemblies under high pressure. The pipeline is designed to be generic in nature and could be readily adapted to provide rapid feedback for many other X-ray diffraction techniques, e.g. large-volume press studies, in situ stress/strain studies, phase transformation studies, chemical reactions studied with high-resolution diffraction etc.

Small-angle scattering (SAS) is a key experimental technique for analyzing nanoscale structures in various materials. In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting. This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models. The performance of the method is assessed through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that this proposed analysis approach yields highly accurate and interpretable results. The ability of the method to analyze a range of mixing ratios and particle size ratios for mixed components is also discussed, along with its precision in model evaluation by the degree of fitting. The proposed method effectively facilitates quantitative analysis of nanoscale sample structures in SAS, which has traditionally been challenging, and is expected to contribute significantly to advancements in a wide range of fields.

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

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

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

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