SPring-8-II is a major upgrade project of SPring-8 that was inaugurated in October 1997 as a third-generation synchrotron radiation light source. This upgrade project aims to achieve three goals simultaneously: achievement of excellent light source performance, refurbishment of aged systems, and significant reduction in power consumption for the entire facility. A small emittance of 50 pm rad will be achieved by (1) replacing the existing double-bend lattice structure with a five-bend achromat one, (2) lowering the stored beam energy from 8 to 6 GeV, (3) increasing the horizontal damping partition number from 1 to 1.3, and (4) enhancing horizontal radiation damping by installing damping wigglers in long straight sections. The use of short-period in-vacuum undulators allows ultrabrilliant X-rays to be provided while keeping a high-energy spectral range even at the reduced electron-beam energy of 6 GeV. To reduce power consumption, the dedicated, aged injector system has been shut down and the high-performance linear accelerator of SACLA, a compact X-ray free-electron laser (XFEL) facility, is used as the injector of the ring in a time-shared manner. This allows the simultaneous operation of XFEL experiments at SACLA and full/top-up injection of the electron beam into the ring. This paper overviews the concept of the SPring-8-II project, the system design of the light source and the details of the accelerator component design.

The Australian Synchrotron Imaging and Medical Beamline (IMBL) uses a superconducting multipole wiggler (SCMPW) source, dual crystal Laue monochromator and 135 m propagation distance to enable imaging and computed tomography (CT) studies of large samples with mono-energetic radiation. This study aimed to quantify two methods for CT dose reduction: wiggler source operation at reduced magnetic field strength, and beam modulation with spatial filters placed upstream from the sample. Transmission measurements with copper were used to indirectly quantify the influence of third harmonic radiation. Operation at lower wiggler magnetic field strength reduces dose rates by an order of magnitude, and suppresses the influence of harmonic radiation, which is of significance near 30 keV. Beam shaping filters modulate the incident beam profile for near constant transmitted signal, and offer protection to radio-sensitive surface organs: the eye lens, thyroid and female breast. Their effect is to reduce the peripheral dose and the dose to the scanned volume by about 10% for biological samples of 35–50 mm diameter and by 20–30% for samples of up to 160 mm diameter. CT dosimetry results are presented as in-air measurements that are specific to the IMBL, and as ratios to in-air measurements that may be applied to other beamlines. As CT dose calculators for small animals are yet to be developed, results presented here and in a previous study may be used to estimate absorbed dose to organs near the surface and the isocentre.

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional expensive-to-sample optimization problem involving the simultaneous treatment of many optical elements with correlated and nonlinear dynamics. Bayesian optimization is a strategy of efficient global optimization that has proved successful in similar regimes in a wide variety of beamline alignment applications, though it has typically been implemented for particular beamlines and optimization tasks. In this paper, we present a basic formulation of Bayesian inference and Gaussian process models as they relate to multi-objective Bayesian optimization, as well as the practical challenges presented by beamline alignment. We show that the same general implementation of Bayesian optimization with special consideration for beamline alignment can quickly learn the dynamics of particular beamlines in an online fashion through hyperparameter fitting with no prior information. We present the implementation of a concise software framework for beamline alignment and test it on four different optimization problems for experiments on X-ray beamlines at the National Synchrotron Light Source II and the Advanced Light Source, and an electron beam at the Accelerator Test Facility, along with benchmarking on a simulated digital twin. We discuss new applications of the framework, and the potential for a unified approach to beamline alignment at synchrotron facilities.

Hard X-ray microscopes with 20–30 nm spatial resolution ranges are an advanced tool for the inspection of materials at the nanoscale. However, the limited efficiency of the focusing optics, for example, a Fresnel zone plate (ZP) lens, can significantly reduce the power of a nanoprobe. Despite several reports on ZP lenses that focus hard X-rays with 20 nm resolution – mainly constructed by zone-doubling techniques – a systematic investigation into the limiting factors has not been reported. We report the structural effects on the focusing and imaging efficiency of 20–30 nm-resolution ZPs, employing a modified beam-propagation method. The zone width and the duty cycle (zone width/ring pitch) were optimized to achieve maximum efficiency, and a comparative analysis of the zone materials was conducted. The optimized zone structures were used in the fabrication of Pt-hydrogen silsesquioxane (HSQ) ZPs. The highest focusing efficiency of the Pt-HSQ-ZP with a resolution of 30 nm was 10% at 7 keV and >5% in the range 6–10 keV, whereas the highest efficiency of the Pt-HSQ-ZP with a resolution of 20 nm was realized at 7 keV with an efficiency of 7.6%. Optical characterization conducted at X-ray beamlines demonstrated significant enhancement of the focusing and imaging efficiency in a broader range of hard X-rays from 5 keV to 10 keV, demonstrating the potential application in hard X-ray focusing and imaging.

Conic sections are commonly used in reflective X-ray optics. Hyperbolic mirrors can focus a converging light source and are frequently paired with elliptical or parabolic mirrors in Wolter type configurations. This paper derives the closed-form expression for a mirror-centered hyperbolic shape, with zero-slope at the origin. Combined with the slope and curvature, such an expression facilitates metrology, manufacturing and mirror-bending calculations. Previous works consider ellipses, parabolas, magnifying hyperbolas or employ lengthy approximations. Here, the exact shape function is given in terms of the mirror incidence angle and the source and image distances.

The Takagi–Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations are implemented in an open-source Python library crystalpy adapted for numerical applications such as crystal reflectivity calculations and ray tracing.

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

The neutralization of acidic solutions containing U (IV) and Ce (III) at room temperature in glove box atmosphere and in the presence of dithionite results in coprecipitation of these elements as amorphous solid solutions CexU1–xO2±y. The solubilities of the precipitates with different mole fractions (x) of Ce(OH)3 (x = 0.01 or 0.1) were determined in 1 M NaClO4 solutions between pH 2.2 and 12.8 under reducing conditions. The solids were investigated by a variety of methods (chemical analysis, SEM-EDX, XRD, XPS, XAS) to determine the nature of the solid solutions formed, their composition and the valence state of Ce and U. X-ray photoelectron spectroscopy confirmed the oxidation states of the solids both before and after the equilibration as Ce (III) and U (IV). The amorphous coprecipitates reached equilibrium relatively fast (∼1 week). The release of Ce from the coprecipitates was totally dominated by the release of uranium over the whole pH range. The Ce concentrations decrease slightly with the decrease of Ce content in the solid, suggesting that CexU1–xO2±y solids behave thermodynamically as solid solutions. The concentrations of U in equilibrium with the coprecipitate were in excellent agreement with the solubility of UO2(s) under reducing conditions reported in the literature. The conditional solubility product of Ce(OH)3 from the coprecipitate was several orders of magnitude (∼4 in the near neutral pH range and ∼18 in the acidic range) lower than that of pure Ce(OH)3(s). The activities and activity coefficients of Ce(OH)3(s) in the coprecipitate were also estimated. Activity coefficients are much less than 1, indicating that the mixing of Ce(OH)3 with UO2 is highly favorable.

We present first hard X-ray photoelectron spectroscopy (HAXPES) results of aqueous salt solutions and dispersions of gold nanoparticles in liquid cells equipped with specially designed microfabricated thin silicon nitride membranes, with thickness in the 15–25 nm range, mounted in a high-vacuum-compatible environment. The experiments have been performed at the HAXPES endstation of the GALAXIES beamline at the SOLEIL synchrotron radiation facility. The low-stress membranes are fabricated from 100 mm silicon wafers using standard lithography techniques. Platinum alignment marks are added to the chips hosting the membranes to facilitate the positioning of the X-ray beam on the membrane by detecting the corresponding photoemission lines. Two types of liquid cells have been used, a static one built on an Omicron-type sample holder with the liquid confined in the cell container, and a circulating liquid cell, in which the liquid can flow in order to mitigate the effects due to beam damage. We demonstrate that the membranes are mechanically robust and able to withstand 1 bar pressure difference between the liquid inside the cell and vacuum, and the intense synchrotron radiation beam during data acquisition. This opens up new opportunities for spectroscopic studies of liquids.

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

X-ray ghost imaging with a crystal beam splitter has advantages in highly efficient imaging due to the simultaneous acquisition of signals from both the object beam and reference beam. However, beam splitting with a large field of view, uniform distribution and high correlation has been a great challenge up to now. Therefore, a dedicated beam splitter has been developed by optimizing the optical layout of a synchrotron radiation beamline and the fabrication process of a Laue crystal. A large field of view, consistent size, uniform intensity distribution and high correlation were obtained simultaneously for the two split beams. Modulated by a piece of copper foam upstream of the splitter, a correlation of 92% between the speckle fields of the object and reference beam and a Glauber function of 1.25 were achieved. Taking advantage of synthetic aperture X-ray ghost imaging (SAXGI), a circuit board of size 880 × 330 pixels was successfully imaged with high fidelity. In addition, even though 16 measurements corresponding to a sampling rate of 1% in SAXGI were used for image reconstruction, the skeleton structure of the circuit board can still be determined. In conclusion, the specially developed beam splitter is applicable for the efficient implementation of X-ray ghost imaging.

X-ray multi-projection imaging (XMPI) is an emerging experimental technique for the acquisition of rotation-free, time-resolved, volumetric information on stochastic processes. The technique is developed for high-brilliance light-source facilities, aiming to address known limitations of state-of-the-art imaging methods in the acquisition of 4D sample information, linked to their need for sample rotation. XMPI relies on a beam-splitting scheme, that illuminates a sample from multiple, angularly spaced viewpoints, and employs fast, indirect, X-ray imaging detectors for the collection of the data. This approach enables studies of previously inaccessible phenomena of industrial and societal relevance such as fractures in solids, propagation of shock waves, laser-based 3D printing, or even fast processes in the biological domain. In this work, we discuss in detail the beam-splitting scheme of XMPI. More specifically, we explore the relevant properties of X-ray splitter optics for their use in XMPI schemes, both at synchrotron insertion devices and XFEL facilities. Furthermore, we describe two distinct XMPI schemes, designed to faciliate large samples and complex sample environments. Finally, we present experimental proof of the feasibility of MHz-rate XMPI at the European XFEL. This detailed overview aims to state the challenges and the potential of XMPI and act as a stepping stone for future development of the technique.

In synchrotron X-ray radiography, achieving high image resolution and an optimal signal-to-noise ratio (SNR) is crucial for the subsequent accurate image analysis. Traditional methods often struggle to balance these two parameters, especially in situ applications where rapid data acquisition is essential to capture specific dynamic processes. For quantitative image data analysis, using monochromatic X-rays is essential. A double multilayer monochromator (DMM) is successfully used for this aim at the BAMline, BESSY II (Helmholtz Zentrum Berlin, Germany). However, such DMMs are prone to producing an unstable horizontal stripe pattern. Such an unstable pattern renders proper signal normalization difficult and thereby causes a reduction of the SNR. We introduce a novel approach to enhance SNR while preserving resolution: dynamic tilting of the DMM. By adjusting the orientation of the DMM during the acquisition of radiographic projections, we optimize the X-ray imaging quality, thereby enhancing the SNR. The corresponding shift of the projection during this movement is corrected in post-processing. The latter correction allows a good resolution to be preserved. This dynamic tilting technique enables the homogenization of the beam profile and thereby effectively reduces noise while maintaining high resolution. We demonstrate that data captured using this proposed technique can be seamlessly integrated into the existing radiographic data workflow, as it does not need hardware modifications to classical X-ray imaging beamline setups. This facilitates further image analysis and processing using established methods.

Geological samples are inherently multi-scale. Understanding their bulk physical and chemical properties requires characterization down to the nano-scale. A powerful technique to study the three-dimensional microstructure is X-ray tomography, but it lacks information about the chemistry of samples. To develop a methodology for measuring the multi-scale 3D microstructure of geological samples, correlative X-ray micro- and nanotomography were performed on two rocks followed by scanning electron microscopy with energy-dispersive spectroscopy (SEM-EDS) analysis. The study was performed in five steps: (i) micro X-ray tomography was performed on rock sample cores, (ii) samples for nanotomography were prepared using laser milling, (iii) nanotomography was performed on the milled sub-samples, (iv) samples were mounted and polished for SEM analysis and (v) SEM imaging and compositional mapping was performed on micro and nanotomography samples for complimentary information. Correlative study performed on samples of serpentine and basalt revealed multiscale 3D structures involving both solid mineral phases and pore networks. Significant differences in the volume fraction of pores and mineral phases were also observed dependent on the imaging spatial resolution employed. This highlights the necessity for the application of such a multiscale approach for the characterization of complex aggregates such as rocks. Information acquired from the chemical mapping of different phases was also helpful in segmentation of phases that did not exhibit significant contrast in X-ray imaging. Adoption of the protocol used in this study can be broadly applied to 3D imaging studies being performed at the Advanced Light Source and other user facilities.

A novel in situ/operando method is introduced to measure the photon beam stability of synchrotron radiation based on orthogonal diffraction imaging of a Laue crystal/analyzer, which can decouple the energy/wavelength and Bragg angle of the photon beam using the dispersion effect in the diffraction process. The method was used to measure the energy jitter and drift of the photon beam on BL09B and BL16U at the Shanghai Synchrotron Radiation Facility. The experimental results show that this method can provide a fast way to measure the beam stability of different light sources including bending magnet and undulator with meV-level energy resolution and ms-level time response.

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

The upgrade of the Swiss Light Source, called SLS 2.0, necessitates comprehensive updates to all 18 user front ends. This upgrade is driven by the increased power of the synchrotron beam, reduced floor space, changing source points, new safety regulations and enhanced beam properties, including a brightness increase by up to a factor of 40. While some existing front-end components are being thoroughly refurbished and upgraded for safety reasons, other components, especially those designed to tailor the new synchrotron beam, are being completely rebuilt. These new designs feature innovative and enhanced cooling systems to manage the high-power load and meet new requirements such as mechanical stability and compact footprints.

VMXm joins the suite of operational macromolecular crystallography beamlines at Diamond Light Source. It has been designed to optimize rotation data collections from protein crystals less than 10 µm and down to below 1 µm in size. The beamline has a fully focused beam of 0.3 × 2.3 µm (vertical × horizontal) with a tuneable energy range (6–28 keV) and high flux (1.6 × 1012 photons s−1 at 12.5 keV). The crystals are housed within a vacuum chamber to minimize background scatter from air. Crystals are plunge-cooled on cryo-electron microscopy grids, allowing much of the liquid surrounding the crystals to be removed. These factors improve the signal-to-noise during data collection and the lifetime of the microcrystals can be prolonged by exploiting photoelectron escape. A novel in vacuo sample environment has been designed which also houses a scanning electron microscope to aid with sample visualization. This combination of features at VMXm allows measurements at the physical limits of X-ray crystallography on biomacromolecules to be explored and exploited.

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

We describe an ultra-compact setup for in situ X-ray diffraction on the inelastic X-ray scattering beamline ID20 at the European Synchrotron Radiation Facility. The main motivation for the design and construction of this setup is the increasing demand for on-the-fly sample characterization, as well as ease of navigation through a sample's phase diagram, for example subjected to high-pressure and/or high-temperature conditions. We provide technical details and demonstrate the performance of the setup.

Onchocerca volvulus causes blindness, onchocerciasis, skin infections and devastating neurological diseases such as nodding syndrome. New treatments are needed because the currently used drug, ivermectin, is contraindicated in pregnant women and those co-infected with Loa loa. The Seattle Structural Genomics Center for Infectious Disease (SSGCID) produced, crystallized and determined the apo structure of N-terminally hexahistidine-tagged O. volvulus macrophage migration inhibitory factor-1 (His-OvMIF-1). OvMIF-1 is a possible drug target. His-OvMIF-1 has a unique jellyfish-like structure with a prototypical macrophage migration inhibitory factor (MIF) trimer as the `head' and a unique C-terminal `tail'. Deleting the N-terminal tag reveals an OvMIF-1 structure with a larger cavity than that observed in human MIF that can be targeted for drug repurposing and discovery. Removal of the tag will be necessary to determine the actual biological oligomer of OvMIF-1 because size-exclusion chomatographic analysis of His-OvMIF-1 suggests a monomer, while PISA analysis suggests a hexamer stabilized by the unique C-terminal tails.

The title compound, [Ni(C40H30N2O2)] (1), with an optically active Schiff base ligand derived from 2-hydroxybenzophenone and (1S,2S)-1,2-diphenylethylenediamine, was crystallized as the solvent-free and ethanol solvate forms (1 and 1·2C2H5OH). In both structures, the two phenyl groups on the stereogenic centers of the O,N,N,O-tetradentate ligand are axially oriented, and the conformation of the central diamine chelate ring is λ. The circular dichroism (CD) spectra of 1 and the analogous nickel(II) complex [Ni(C30H26N2O2)] (2) in solution show partially similar patterns in the 350–450 nm range, but are mirror images in the longer wavelength region (450–650 nm). In the latter region, the sign of CD for these complexes is sensitive to the substituents on the C=N carbon atoms (phenyl for 1 and methyl for 2) rather than the diamine chelate ring conformation.

Reaction between equimolar amounts of 3,3,3',3'-tetraethyl-1,1'-(furan-2,5-dicarbonyl)bis(thiourea) (H2L) and CuCl2·2H2O in methanol in the presence of the supporting base Et3N gave rise to a neutral dinuclear complex bis[μ-3,3,3',3'-tetraethyl-1,1'-(furan-2,5-dicarbonyl)bis(thioureato)]dicopper(II) dichloromethane disolvate, [Cu2(C16H22N4O3S2)2]·2CH2Cl2 or [Cu2(L)2]·2CH2Cl2. The aroylbis(thioureas) are doubly deprotonated and the resulting anions {L2–} bond to metal ions through (S,O)-chelating moieties. The copper atoms adopt a virtually cis-square-planar environment. In the crystal, adjacent [Cu2(L)2]·2CH2Cl2 units are linked into polymeric chains along the a-axis direction by intermolecular coordinative Cu...S interactions. The co-crystallized solvent molecules play a vital role in the crystal packing. In particular, weak C—Hfuran...Cl and C—Hethyl...Cl contacts consolidate the three-dimensional supramolecular architecture.

The etoxazole metabolite R13, systematic name 4-(4-tert-butyl-2-ethoxyphenyl)-2-(2,6-difluorophenyl)oxazole (C21H21F2NO2), results from the oxidation of etoxazole, a chitin synthesis inhibitor belonging to the oxazoline class, widely used as an insecticide/acaricide since 1998. The structure of R13 features a central oxazole ring with attached 2,6-difluorophenyl and 4-t-butyl-2-ethoxyphenyl moieties. The overall conformation gives dihedral angles between these rings and the oxazole of 24.91 (5)° (with difluorophenyl) and 15.30 (6)° (with t-butyl-ethoxyphenyl), indicating an overall deviation from planarity. Additionally, torsion angles of the ethoxy and t-butyl groups define the orientation of these substituents relative to their benzene ring. In the crystal packing, no significant hydrogen bonds are present, but a Hirshfeld surface analysis highlights weak intermolecular contacts leading to π–π-stacked dimers linked by weak C—H...N contacts. The packing analysis confirms that most intermolecular interactions involve hydrogen atoms.

In the title compound, C8H9BrN2O2, the C—O—C—C torsion angle between isonicotine and the ethyl group is 180.0 (2)°. Intramolecular N—H...O and C—H...O interactions consolidate the molecular structure. In the crystal, N—H...N interaction form S(5) zigzag chains along [010]. The most significant contributions to the Hirshfeld surface arise from H...H (33.2%), Br...H/H...Br (20.9%), O...H/H...O (11.2%), C...H/H...C (11.1%) and N...H/H...N (10%) contacts. The topology of the three-dimensional energy frameworks was generated using the B3LYP/6–31 G(d,p) model to calculate the total interaction energy. The net interaction energies for the title compound are Eele = 59.2 kJ mol−1, Epol = 15.5 kJ mol−1, Edis = 140.3 kJ mol−1 and Erep = 107.2 kJ mol−1 with a total interaction energy Etot of 128.8 kJ mol−1. The molecular structure was optimized by density functional theory (DFT) at the B3LYP/6–311+G(d,p) level and the theoretical and experimentally obtained parameters were compared. The frontier molecular orbitals HOMO and LUMO were generated, giving an energy gap ΔE of 4.0931 eV. The MEP was generated to identify active sites in the molecule and molecular docking studies carried out with the title compound (ligand) and the covid-19 main protease PDB ID: 6LU7, revealing a moderate binding affinity of −5.4 kcal mol−1.

The crystal structure of aluminium phosphorus chloride (systematic name: phosphorus tetrachloride tetrachloridoaluminate), (PCl4)[AlCl4] or AlPCl8, was determined and refined using single-crystal X-ray diffraction data. The compound crystallizes in the orthorhombic space group Pbcm. The asymmetric unit comprises one Al atom, one P atom, and five Cl atoms. The structure is characterized by isolated AlCl4 and PCl4 tetrahedra, isostructural with FePCl8 and GaPCl8.

Crystallization of the title compound, fac-[ReBr(ppt-OMe)(CO)3] (ppt-OMe = C15H12N2OS), from CH2Cl2/n-pentane (1:5 v/v) at room temperature gave two polymorphs, which crystallize in monoclinic (P21/c; α form) and orthorhombic (Pna21; β form) space groups. The ReI complex molecules in either polymorph adopt a six-coordinate octahedral geometry with three facially-oriented carbonyl ligands, one bromido ligand, and two nitrogen atoms from one chelating ligand ppt-OMe. In the crystal, both polymorph α and β form di-periodic sheet-like architectures supported by multiple hydrogen bonds. In polymorph α, two types of hydrogen bonds (C—H...O) are found while, in polymorph β, four types of hydrogen bonds (C—H...O and C—H...Br) exist.

Algebraic expressions for averaging linear and nonlinear stiffness tensors from general anisotropy to different effective symmetries (11 Laue classes elastically representing all 32 crystal classes, and two non-crystalline symmetries: isotropic and cylindrical) have been derived by automatic symbolic computations of the arithmetic mean over the set of rotational transforms determining a given symmetry. This approach generalizes the Voigt average to nonlinear constants and desired approximate symmetries other than isotropic, which can be useful for a description of textured polycrystals and rocks preserving some symmetry aspects. Low-symmetry averages have been used to derive averages of higher symmetry to speed up computations. Relationships between the elastic constants of each symmetry have been deduced from their corresponding averages by resolving the rank-deficient system of linear equations. Isotropy has also been considered in terms of generalized Lamé constants. The results are published in the form of appendices in the supporting information for this article and have been deposited in the Mendeley database.

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.

This study introduces an alternative method to the Takagi–Taupin equations for investigating the dark-field X-ray microscopy (DFXM) of deformed crystals. In scenarios where dynamical diffraction cannot be disregarded, it is essential to assess the potential inaccuracies of data interpretation based on the kinematic diffraction theory. Unlike the Takagi–Taupin equations, this new method utilizes an exact dispersion relation, and a previously developed finite difference scheme with minor modifications is used for the numerical implementation. The numerical implementation has been validated by calculating the diffraction of a diamond crystal with three components, wherein dynamical diffraction is applicable to the first component and kinematic diffraction pertains to the remaining two. The numerical convergence is tested using diffraction intensities. In addition, the DFXM image of a diamond crystal containing a stacking fault is calculated using the new method and compared with the experimental result. The new method is also applied to calculate the DFXM image of a twisted diamond crystal, which clearly shows a result different from those obtained using the Takagi–Taupin equations.

A 6D structure model for face-centred icosahedral quasicrystals consisting of so-called pseudo-Mackay and mini-Bergman-type atomic clusters is proposed based on the structure model of the Al69.1Pd22Cr2.1Fe6.8 3/2 cubic approximant crystal (with space group Pa3, a = 40.5 Å) [Fujita et al. (2013). Acta Cryst. A69, 322–340]. The cluster centres form an icosahedral close sphere packing generated by the occupation domains similar to those in the model proposed by Katz & Gratias [J. Non-Cryst. Solids (1993), 153–154, 187–195], but their size is smaller by a factor τ2 [τ = (1 + (5)1/2)/2]. The clusters cover approximately 99.46% of the atomic structure, and the cluster arrangement exhibits 15 and 19 different local configurations, respectively, for the pseudo-Mackay and mini-Bergman-type clusters. The occupation domains that generate cluster shells are modelled and discussed in terms of structural disorder and local reorganization of the cluster arrangements (phason flip).

In powder diffraction, lattice symmetry relaxation causes a peak to split into several components which are not resolved if the degree of desymmetrization is small (pseudosymmetry). Here the equations which rule peak splitting are elaborated for the six minimal symmetry transitions, showing that the resulting split peaks are generally broader and asymmetric, and suffer an hkl-dependent displacement with respect to the high-symmetry parent peak. These results will be of help in Rietveld refinement of pseudosymmetric structures where an exact interpretation of peak deformation is required.

The crystal structure uniformity is numerically estimated as the standard deviation of the crystal space quantizer 〈G3〉. This criterion has been applied to explore the uniformity of ionic sublattices in 21465 crystal structures of inorganic ionic compounds. In most cases, at least one kind of sublattice (whole ionic lattice, cationic or anionic sublattice) was found to be highly uniform with a small 〈G3〉 value. Non-uniform structures appeared to be either erroneous or essentially non-ionic. As a result, a set of uniformity criteria is proposed for the estimation of the stability of ionic crystal structures.

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.

This article describes the diffraction pattern (2-periodic Fourier transform) from the vertices of a large patch of the recently discovered `Spectre' tiling – a strictly chiral aperiodic monotile. It was reported recently that the diffraction pattern of the related weakly chiral aperiodic `Hat' monotile was 2-periodic with chiral plane-group symmetry p6 [Kaplan et al. (2024). Acta Cryst. A80, 72–78]. The diffraction periodicity arises because the Hat tiling is a systematic aperiodic deletion of vertices from the 2-periodic hexagonal mta tiling. Despite the similarity of the Hat and Spectre tilings, the Spectre tiling is not aligned with a 2-periodic lattice, and its diffraction pattern is non-periodic with chiral point symmetry 6 about the origin.

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.

Painted artworks represent a significant group of cultural heritage artifacts, which are primarily admired because of their aesthetic quality. Nevertheless, the value of each particular painting depends also on what is known about it. Material investigation of paintings is one of the most reliable sources of information. Materials in painted artworks (i.e. panel, easel and miniature paintings, wall paintings, polychromed sculptures etc.) represent an extensive set of inorganic and organic phases, which are often present in complicated mixtures and exhibit characteristics reflecting their geological genesis (mineral pigments), manufacturing technology (artificial pigments), diverse biological nature (binders or dyes) or secondary changes (degradation or intentional later interventions). The analyses of paintings are often made challenging by the heterogeneous nature and minute size of micro-samples or, in some cases, even by the impossibility of sampling due to the preciousness, fragility or small dimensions of the artwork. This review demonstrates the successful implementation of laboratory X-ray powder micro-diffraction for material investigation of paintings, illustrating its efficiency for mineralogical analysis of (i) earth-based materials indicating the provenance of paintings, (ii) copper-based pigments pointing to their origin, and (iii) products of both salt corrosion and saponification enabling one to reveal the deterioration and probable original appearance of artworks.

Serial crystallography (SX) efficiently distributes over many crystals the radiation dose absorbed during diffraction data acquisition, enabling structure determination of samples at ambient temperature. SX relies on the rapid and reliable replacement of X-ray-exposed crystals with fresh crystals at a rate commensurate with the data acquisition rate. `Solid supports', also known as `fixed targets' or `chips', offer one approach. These are microscopically thin solid panes into or onto which crystals are deposited to be individually interrogated by an X-ray beam. Solid supports are generally patterned using photolithography methods to produce a regular array of features that trap single crystals. A simpler and less expensive alternative is to merely sandwich the microcrystals between two unpatterned X-ray-transparent polymer sheets. Known as sheet-on-sheet (SOS) chips, these offer significantly more versatility. SOS chips place no constraint on the size or size distribution of the microcrystals or their growth conditions. Crystals ranging from true nanocrystals up to microcrystals can be investigated, as can crystals grown in media ranging from low viscosity (aqueous solution) up to high viscosity (such as lipidic cubic phase). Here, we describe our two SOS devices. The first is a compact and lightweight version designed specifically for synchrotron use. It incorporates a standard SPINE-type magnetic base for mounting on a conventional macromolecular crystallography goniometer. The second and larger chip is intended for both X-ray free-electron laser and synchrotron use and is fully compatible with the fast-scanning XY-raster stages developed for data collection with patterned chips.

The dualism between direct and reciprocal space is at the origin of well known relations between basis vectors in the two spaces. It is shown that when a coordinate system corresponding to a non-primitive unit cell is adopted, this dualism has to be handled with care. In particular, the reciprocal of a non-primitive unit cell is not a unit cell but a region in reciprocal space that does not represent a unit of repetition by translation. The basis vectors do not correspond to reciprocal-space cell lengths, contrary to what is stated even in the core CIF dictionary. The corresponding unit cell is a multiple of this region. The broken correspondence between basis vectors and unit cell is at the origin of the integral reflection conditions.

In the family of perovskite materials, the tilts of BX6 octahedra are the most common type of structural distortion. Conventionally, the formation of low-symmetry perovskite phases with tilted octahedra is analyzed by considering only primary order parameters. However, octahedral tilting also gives rise to secondary order parameters which contribute to additional atomic displacements, ordering and lattice distortions. Our study highlights the significant impact of secondary order parameters on the structural formation and emergent physical properties of perovskites. Through group-theoretical and crystallographic analyses, we have identified all secondary order parameters within Glazer-type tilt systems and clarified their physical manifestations. We explore the fundamental symmetry relationships among various structural degrees of freedom in perovskites, including tilt-induced ferroelasticity, correlations between displacements and ordering of atoms occupying different positions, and the potential for rigid unit rotations and unconventional octahedral tilts. Particular emphasis is placed on the emergence of secondary order parameters and their coupling with primary order parameters, as well as their symmetry-based hierarchy, illustrated through a modified Bärnighausen tree. We applied our theoretical insights to elucidate phase transitions in well known perovskites such as CaTiO3 and RMnO3 (where R = La and lanthanide ions), thereby demonstrating the significant influence of secondary order parameters on crystal structure formation. Our results serve as a symmetry-based guide for the design, identification and structural characterization of perovskites with tilted octahedra, and for understanding tilt-induced physical properties.

In the conventional crucible structure for AlN crystal growth by physical vapor transport, owing to the long molecular transport path of Al vapor and the disruption of the gas flow by the presence of a deflector, the Al vapor easily forms polycrystals in the growth domain. The result is increased internal stress in the crystals and increased difficulty in growing large-sized crystals. On this basis, with the help of finite element simulations, a novel crucible structure is designed. This crucible not only optimizes the gas transport but also increases the radial gradient of the AlN crystal surface, making the enhanced growth rate in the central region more obvious. The thermal stresses between the deflector and the crystal are also reduced. High-quality AlN crystals with an FWHM of 79 arcsec were successfully grown with this structure, verifying the accuracy of finite element simulation of the growth of AlN crystals. Our work has important guiding significance for the growth of high-quality AlN crystals.

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.

Structure refinement with reverse Monte Carlo (RMC) is a powerful tool for interpreting experimental diffraction data. To ensure that the under-constrained RMC algorithm yields reasonable results, the hybrid RMC approach applies interatomic potentials to obtain solutions that are both physically sensible and in agreement with experiment. To expand the range of materials that can be studied with hybrid RMC, we have implemented a new interatomic potential constraint in RMCProfile that grants flexibility to apply potentials supported by the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) molecular dynamics code. This includes machine learning interatomic potentials, which provide a pathway to applying hybrid RMC to materials without currently available interatomic potentials. To this end, we present a methodology to use RMC to train machine learning interatomic potentials for hybrid RMC applications.