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 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.

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).

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.

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.

X-ray diffraction imaging (XDI) is utilized for visualizing the structures of non-crystalline particles in material sciences and biology. In the structural analysis, phase-retrieval (PR) algorithms are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X-rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small-angle regions and Poisson noise in X-ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non-crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity-score-selected maps is discussed.

In X-ray diffraction imaging (XDI), electron density maps of a targeted particle are reconstructed computationally from the diffraction pattern alone using phase-retrieval (PR) algorithms. However, the PR calculations sometimes fail to yield realistic electron density maps that approximate the structure of the particle. This occurs due to the absence of structure amplitudes at and near the zero-scattering angle and the presence of Poisson noise in weak diffraction patterns. Consequently, the PR calculation becomes a bottleneck for XDI structure analyses. Here, a protocol to efficiently yield realistic maps is proposed. The protocol is based on the empirical observation that realistic maps tend to yield low similarity scores, as suggested in our prior study [Sekiguchi et al. (2017), J. Synchrotron Rad. 24, 1024–1038]. Among independently and concurrently executed PR calculations, the protocol modifies all maps using the electron-density maps exhibiting low similarity scores. This approach, along with a new protocol for estimating particle shape, improved the probability of obtaining realistic maps for diffraction patterns from various aggregates of colloidal gold particles, as compared with PR calculations performed without the protocol. Consequently, the protocol has the potential to reduce computational costs in PR calculations and enable efficient XDI structure analysis of non-crystalline particles using synchrotron X-rays and X-ray free-electron laser pulses.

The use of hard X-ray transmission nano- and microdiffraction to perform in situ stress and strain measurements during deformation has recently been demonstrated and used to investigate many thin film systems. Here a newly commissioned sample environment based on a commercially available nanoindenter is presented, which is available at the NanoMAX beamline at the MAX IV synchrotron. Using X-ray nanoprobes of around 60–70 nm at 14–16 keV and a scanning step size of 100 nm, we map the strains, stresses, plastic deformation and fracture during nanoindentation of industrial coatings with thicknesses in the range of several micrometres, relatively strong texture and large grains. The successful measurements of such challenging samples illustrate broad applicability. The sample environment is openly accessible for NanoMAX beamline users through the MAX IV sample environment pool, and its capability can be further extended for specific purposes through additional available modules.

The X-ray emission spectrometer at SPring-8 BL07LSU has recently been upgraded with advanced modifications that enable the rotation of the spectrometer with respect to the scattering angle. This major upgrade allows the scattering angle to be flexibly changed within the range of 45–135°, which considerably simplifies the measurement of angle-resolved X-ray emission spectroscopy. To accomplish the rotation system, a sophisticated sample chamber and a highly precise spectrometer rotation mechanism have been developed. The sample chamber has a specially designed combination of three rotary stages that can smoothly move the connection flange along the wide scattering angle without breaking the vacuum. In addition, the spectrometer is rotated by sliding on a flat metal surface, ensuring exceptionally high accuracy in rotation and eliminating the need for any further adjustments during rotation. A control system that integrates the sample chamber and rotation mechanism to automate the measurement of angle-resolved X-ray emission spectroscopy has also been developed. This automation substantially streamlines the process of measuring angle-resolved spectra, making it far easier than ever before. Furthermore, the upgraded X-ray emission spectrometer can now also be utilized in diffraction experiments, providing even greater versatility to our research capabilities.

In this study, a combination of X-ray excited optical luminescence (XEOL), time-resolved XEOL (TR-XEOL) and the Hanbury-Brown and Twiss (HB-T) interferometer at the Taiwan Photon Source (TPS) 23A X-ray nanoprobe beamline for exploring quantum materials is demonstrated. On the basis of the excellent spatial resolution rendered using a nano-focused beam, emission distributions of artificial micro-diamonds can be obtained by XEOL maps, and featured emission peaks of a selected local area can be obtained by XEOL spectra. The hybrid bunch mode of the TPS not only provides a sufficiently high peak power density for experiments at each beamline but also permits high-quality temporal domain (∼200 ns) measurements for investigating luminescence dynamics. From TR-XEOL measurements, the decay lifetime of micro-diamonds is determined to be approximately 16 ns. Furthermore, the XEOL spectra of artificial micro-diamonds can be investigated by the HB-T interferometer to identify properties of single-photon sources. The unprecedented strategy of combining XEOL, TR-XEOL and the HB-T interferometer at the X-ray nanoprobe beamline will open new avenues with significant characterization abilities for unraveling the emission mechanisms of single-photon sources for quantum materials.

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

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

The structural and chemical evolution of battery electrodes at the nanoscale plays an important role in affecting the cell performance. Nano-resolution X-ray microscopy has been demonstrated as a powerful technique for characterizing the evolution of battery electrodes under operating conditions with sensitivity to their morphology, compositional distribution and redox heterogeneity. In real-world batteries, the electrode could deform upon battery operation, causing challenges for the image registration which is necessary for several experimental modalities, e.g. XANES imaging. To address this challenge, this work develops a deep-learning-based method for automatic particle identification and tracking. This approach was not only able to facilitate image registration with good robustness but also allowed quantification of the degree of sample deformation. The effectiveness of the method was first demonstrated using synthetic datasets with known ground truth. The method was then applied to an experimental dataset collected on an operating lithium battery cell, revealing a high degree of intra- and interparticle chemical complexity in operating batteries.

The results of a study of the structural and reflective characteristics of short-period multilayer X-ray mirrors based on Mo/B4C at wavelengths 1.54 Å, 9.89 Å and 17.59 Å are presented. The period of the samples varied in the range 8–35 Å. The average widths of the interfaces were ∼3.5 and 2.2 Å at one and the other boundaries, with a tendency for weak growth with any decrease in the period. The interlayer roughness was ∼1 Å. The research results indicate promising prospects for the use of multilayer Mo/B4C mirrors for synchrotron applications.

Alignment of each optical element at a synchrotron beamline takes days, even weeks, for each experiment costing valuable beam time. Evolutionary algorithms (EAs), efficient heuristic search methods based on Darwinian evolution, can be utilized for multi-objective optimization problems in different application areas. In this study, the flux and spot size of a synchrotron beam are optimized for two different experimental setups including optical elements such as lenses and mirrors. Calculations were carried out with the X-ray Tracer beamline simulator using swarm intelligence (SI) algorithms and for comparison the same setups were optimized with EAs. The EAs and SI algorithms used in this study for two different experimental setups are the Genetic Algorithm (GA), Non-dominated Sorting Genetic Algorithm II (NSGA-II), Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC). While one of the algorithms optimizes the lens position, the other focuses on optimizing the focal distances of Kirkpatrick–Baez mirrors. First, mono-objective evolutionary algorithms were used and the spot size or flux values checked separately. After comparison of mono-objective algorithms, the multi-objective evolutionary algorithm NSGA-II was run for both objectives – minimum spot size and maximum flux. Every algorithm configuration was run several times for Monte Carlo simulations since these processes generate random solutions and the simulator also produces solutions that are stochastic. The results show that the PSO algorithm gives the best values over all setups.

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

This work presents a detailed analysis of the performance of X-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) as a tool for vector reconstruction of magnetization. For this, 360° domain wall ring structures which form in a synthetic antiferromagnet are chosen as the model to conduct the quantitative analysis. An assessment is made of how the quality of the results is affected depending on the number of projections that are involved in the reconstruction process, as well as their angular distribution. For this a self-consistent error metric is developed which allows an estimation of the optimum azimuthal rotation angular range and number of projections. This work thus proposes XMCD-PEEM as a powerful tool for vector imaging of complex 3D magnetic structures.

Calculations and measurements of polarization-dependent soft X-ray scattering intensity are presented during a magnetic hysteresis cycle. It is confirmed that the dependence of the intensity on the magnetic moment can be linear, quadratic or a combination of both, depending on the polarization of the incident X-ray beam and the direction of the magnetic moment. With a linearly polarized beam, the scattered intensity will have a purely quadratic dependence on the magnetic moment when the magnetic moment is parallel to the scattering plane. However, with the magnetic moment perpendicular to the scattering plane, there is also a linear component. This means that, when measuring the hysteresis with linear polarization during a hysteresis cycle, the intensity will be an even function of the applied field when the change in the magnetic moment (and field) is confined within the scattering plane but becomes more complicated when the magnetic moment is out of the scattering plane. Furthermore, with circular polarization, the dependence of the scattered intensity on the moment is a combination of linear and quadratic. With the moment parallel to the scattering plane, the linear component changes with the helicity of the incident beam. Surprisingly, in stark contrast to absorption studies, even when the magnetic moment is perpendicular to the scattering plane there is still a dependence on the moment with a linear component. This linear component is completely independent of the helicity of the beam, meaning that the hysteresis loops will not be inverted with helicity.

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

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

This study introduces a novel iterative Bragg peak removal with automatic intensity correction (IBR-AIC) methodology for X-ray absorption spectroscopy (XAS), specifically addressing the challenge of Bragg peak interference in the analysis of crystalline materials. The approach integrates experimental adjustments and sophisticated post-processing, including an iterative algorithm for robust calculation of the scaling factor of the absorption coefficients and efficient elimination of the Bragg peaks, a common obstacle in accurately interpreting XAS data, particularly in crystalline samples. The method was thoroughly evaluated on dilute catalysts and thin films, with fluorescence mode and large-angle rotation. The results underscore the technique's effectiveness, adaptability and substantial potential in improving the precision of XAS data analysis. While demonstrating significant promise, the method does have limitations related to signal-to-noise ratio sensitivity and the necessity for meticulous angle selection during experimentation. Overall, IBR-AIC represents a significant advancement in XAS, offering a pragmatic solution to Bragg peak contamination challenges, thereby expanding the applications of XAS in understanding complex materials under diverse experimental conditions.

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

The in situ measurement technique for a metal/metal-oxide mixture at extra-high temperature above 2000 K has been desired in the field of nuclear safety engineering. In the present study, we succeeded in simultaneous XAFS–XRD measurements of the Zr oxidation [Zr + O → Zr(O) + ZrO2] up to 1952 K and ZrO2–Y2O3 reaction from 1952 to 2519 K. The chemical shift during Zr oxidation was observed in the absorption spectra around the Zr K-edge, and the interatomic cation–cation and cation–oxygen distances obtained by the fitting analysis of EXAFS during the Y2O3–ZrO2 reaction are explained. Also, the temperature dependency of the anharmonic effect was investigated by comparing the fitted second- and third-order cumulants with the theoretical ones in which the Morse potential was applied as an interatomic potential, giving a good explanation about the local structure dynamics. Finally, the applicability of the developed system to investigation of nuclear fuel materials, such as UO2–Zr, is discussed.

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

Imaging energy filters in photoelectron microscopes and momentum microscopes use spherical fields with deflection angles of 90°, 180° and even 2 × 180°. These instruments are optimized for high energy resolution, and exhibit image aberrations when operated in high transmission mode at medium energy resolution. Here, a new approach is presented for bandpass-filtered imaging in real or reciprocal space using an electrostatic dodecapole with an asymmetric electrode array. In addition to energy-dispersive beam deflection, this multipole allows aberration correction up to the third order. Here, its use is described as a bandpass prefilter in a time-of-flight momentum microscope at the hard X-ray beamline P22 of PETRA III. The entire instrument is housed in a straight vacuum tube because the deflection angle is only 4° and the beam displacement in the filter is only ∼8 mm. The multipole is framed by transfer lenses in the entrance and exit branches. Two sets of 16 different-sized entrance and exit apertures on piezomotor-driven mounts allow selection of the desired bandpass. For pass energies between 100 and 1400 eV and slit widths between 0.5 and 4 mm, the transmitted kinetic energy intervals are between 10 eV and a few hundred electronvolts (full width at half-maximum). The filter eliminates all higher or lower energy signals outside the selected bandpass, significantly improving the signal-to-background ratio in the time-of-flight analyzer.

The demand for powder X-ray diffraction analysis continues to increase in a variety of scientific fields, as the excellent beam quality of high-brightness synchrotron light sources enables the acquisition of high-quality measurement data with high intensity and angular resolution. Synchrotron powder diffraction has enabled the rapid measurement of many samples and various in situ/operando experiments in nonambient sample environments. To meet the demands for even higher throughput measurements using high-energy X-rays at SPring-8, a high-throughput and high-resolution powder diffraction system has been developed. This system is combined with six sets of two-dimensional (2D) CdTe detectors for high-energy X-rays, and various automation systems, including a system for automatic switching among large sample environmental equipment, have been developed in the third experimental hutch of the insertion device beamline BL13XU at SPring-8. In this diffractometer system, high-brilliance and high-energy X-rays ranging from 16 to 72 keV are available. The powder diffraction data measured under ambient and various nonambient conditions can be analysed using Rietveld refinement and the pair distribution function. Using the 2D CdTe detectors with variable sample-to-detector distance, three types of scan modes have been established: standard, single-step and high-resolution. A major feature is the ability to measure a whole powder pattern with millisecond resolution. Equally important, this system can measure powder diffraction data with high Q exceeding 30 Å−1 within several tens of seconds. This capability is expected to contribute significantly to new research avenues using machine learning and artificial intelligence by utilizing the large amount of data obtained from high-throughput measurements.

During beam time at a research facility, alignment and optimization of instrumentation, such as spectrometers, is a time-intensive task and often needs to be performed multiple times throughout the operation of an experiment. Despite the motorization of individual components, automated alignment solutions are not always available. In this study, a novel approach that combines optimisers with neural network surrogate models to significantly reduce the alignment overhead for a mobile soft X-ray spectrometer is proposed. Neural networks were trained exclusively using simulated ray-tracing data, and the disparity between experiment and simulation was obtained through parameter optimization. Real-time validation of this process was performed using experimental data collected at the beamline. The results demonstrate the ability to reduce alignment time from one hour to approximately five minutes. This method can also be generalized beyond spectrometers, for example, towards the alignment of optical elements at beamlines, making it applicable to a broad spectrum of research facilities.

The New Advanced Telescope for High ENergy Astrophysics (NewAthena) will be the largest space-based X-ray observatory ever built. It will have an effective area above 1.1 m2 at 1 keV, which corresponds to a polished mirror surface of about 300 m2 due to the grazing incidence. As such a mirror area is not achievable with an acceptable mass even with nested shells, silicon pore optics (SPO) technology will be utilized. In the PTB laboratory at BESSY II, two dedicated beamlines are in use for their characterization with monochromatic radiation at 1 keV and a low divergence well below 2 arcsec: the X-ray Pencil Beam Facility (XPBF 1) and the X-ray Parallel Beam Facility (XPBF 2.0), where beam sizes up to 8 mm × 8 mm are available while maintaining low beam divergence. This beamline is used for characterizing mirror stacks and controlling the focusing properties of mirror modules (MMs) – consisting of four mirror stacks – during their assembly at the beamline. A movable CCD based camera system 12 m from the MM registers the direct and the reflected beams. The positioning of the detector is verified by a laser tracker. The energy-dependent reflectance in double reflection through the pores of an MM with an Ir coating was measured at the PTB four-crystal monochromator beamline in the photon energy range 1.75 keV to 10 keV, revealing the effects of the Ir M edges. The measured reflectance properties are in agreement with the design values to achieve the envisaged effective area.

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

The differentially pumped rare-gas filter at the end of the VUV beamline of the Swiss Light Source has been adapted to house a windowless absorption cell for gases. Absorption spectra can be recorded from 7 eV to up to 21 eV photon energies routinely, as shown by a new water and nitrous oxide absorption spectrum. By and large, the spectra agree with previously published ones both in terms of resonance energies and absorption cross sections, but that of N2O exhibits a small shift in the { ilde{f D}} band and tentative fine structures that have not yet been fully described. This setup will facilitate the measurement of absorption spectra in the VUV above the absorption edge of LiF and MgF2 windows. It will also allow us to carry out condensed-phase measurements on thin liquid sheets and solid films. Further development options are discussed, including the recording of temperature-dependent absorption spectra, a stationary gas cell for calibration measurements, and the improvement of the photon energy resolution.

A broadband online X-ray spectrometer has been designed and commissioned at the SUD beamline of the Shanghai Soft X-ray Free-Electron Laser Facility, which can deliver both SASE and seeded FEL pulses to user experiments, spanning the photon energy range of 50–620 eV. The resolving powers of the spectrometer calibrated via online measurement at 92 eV and 249 eV are ∼20000 and ∼15000, respectively, and the absolute photon energy is characterized by an electron time-of-flight spectrometer. The high energy resolution provided by the spectrometer can differentiate the fine structure in the FEL spectrum, to determine its pulse length.

A 1D imaging soft X-ray spectrometer installed on the small quantum systems (SQS) scientific instrument of the European XFEL is described. It uses movable cylindrical constant-line-spacing gratings in the Rowland configuration for energy dispersion in the vertical plane, and Wolter optics for simultaneous 1D imaging of the source in the horizontal plane. The soft X-ray fluorescence spectro-imaging capability will be exploited in pump–probe measurements and in investigations of propagation effects and other nonlinear phenomena.

The paper considers the possibility of using the diamond-silicon carbide composite Skeleton® with a technological coating of polycrystalline silicon as a substrate for X-ray mirrors used with powerful synchrotron radiation sources (third+ and fourth generation). Samples were studied after polishing to provide the following surface parameters: root-mean-square flatness ≃ 50 nm, micro-roughness on the frame 2 µm × 2 µm σ ≃ 0.15 nm. The heat capacity, thermal conductivity and coefficient of linear thermal expansion were investigated. For comparison, a monocrystalline silicon sample was studied under the same conditions using the same methods. The value of the coefficient of linear thermal expansion turned out to be higher than that of monocrystalline silicon and amounted to 4.3 × 10−6 K−1, and the values of thermal conductivity (5.0 W cm−1 K−1) and heat capacity (1.2 J K−1 g−1) also exceeded the values for Si. Thermally induced deformations of both Skeleton® and monocrystalline silicon samples under irradiation with a CO2 laser beam have also been experimentally studied. Taking into account the obtained thermophysical constants, the calculation of thermally induced deformation under irradiation with hard (20 keV) X-rays showed almost three times less deformation of the Skeleton® sample than of the monocrystalline silicon sample.

MuscleX is an integrated, open-source computer software suite for data reduction of X-ray fiber diffraction patterns from striated muscle and other fibrous systems. It is written in Python and runs on Linux, Microsoft Windows or macOS. Most modules can be run either from a graphical user interface or in a `headless mode' from the command line, suitable for incorporation into beamline control systems. Here, we provide an overview of the general structure of the MuscleX software package and describe the specific features of the individual modules as well as examples of applications.

Advances in physics have been significantly driven by state-of-the-art technology, and in photonics and X-ray science this calls for the ability to manipulate the characteristics of optical beams. Orbital angular momentum (OAM) beams hold substantial promise in various domains such as ultra-high-capacity optical communication, rotating body detection, optical tweezers, laser processing, super-resolution imaging etc. Hence, the advancement of OAM beam-generation technology and the enhancement of its technical proficiency and characterization capabilities are of paramount importance. These endeavours will not only facilitate the use of OAM beams in the aforementioned sectors but also extend the scope of applications in diverse fields related to OAM beams. At the FERMI Free-Electron Laser (Trieste, Italy), OAM beams are generated either by tailoring the emission process on the undulator side or, in most cases, by coupling a spiral zone plate (SZP) in tandem with the refocusing Kirkpatrick–Baez active optic system (KAOS). To provide a robust and reproducible workflow to users, a Hartmann wavefront sensor (WFS) is used for both optics tuning and beam characterization. KAOS is capable of delivering both tightly focused and broad spots, with independent control over vertical and horizontal magnification. This study explores a novel non-conventional `near collimation' operational mode aimed at generating beams with OAM that employs the use of a lithographically manufactured SZP to achieve this goal. The article evaluates the mirror's performance through Hartmann wavefront sensing, offers a discussion of data analysis methodologies, and provides a quantitative analysis of these results with ptychographic reconstructions.

Errors in variable subscripts, equations and Fig. 8 in Section 3.2 of the article by Lotze et al. [(2024). J. Synchrotron Rad. 31, 42–52] are corrected.

The Keck-PAD (pixel array detector) was developed at Cornell as a burst-rate imager capable of recording images from successive electron bunches (153 ns period) from the Advanced Photon Source (APS). Both Si and hole-collecting Schottky CdTe have been successfully bonded to this ASIC (application-specific integrated circuit) and used with this frame rate. The facility upgrades at the APS will lower the bunch period to 77 ns, which will require modifications to the Keck-PAD electronics to image properly at this reduced period. In addition, operation at high X-ray energies will require a different sensor material having a shorter charge collection time. For the target energy of 40 keV for this project, simulations have shown that electron-collecting CdTe should allow >90% charge collection within 35 ns. This collection time will be sufficient to sample the signal from one frame and prepare for the next. 750 µm-thick electron-collecting Schottky CdTe has been obtained from Acrorad and bonded to two different charge-integrating ASICs developed at Cornell, the Keck-PAD and the CU-APS-PAD. Carrier mobility has been investigated using the detector response to single X-ray bunches at the Cornell High Energy Synchrotron Source and to a pulsed optical laser. The tests indicate that the collection time will meet the requirements for 77 ns imaging.

Full-field transmission X-ray microscopy has been recently implemented at the hard X-ray ROCK–SOLEIL quick-EXAFS beamline, adding micrometre spatial resolution to the second time resolution characterizing the beamline. Benefiting from a beam size versatility due to the beamline focusing optics, full-field hyperspectral XANES imaging has been successfully used at the Fe K-edge for monitoring the pressure-induced spin transition of a 150 µm × 150 µm Fe(o-phen)2(NCS)2 single crystal and the charge of millimetre-sized LiFePO4 battery electrodes. Hyperspectral imaging over 2000 eV has been reported for the simultaneous monitoring of Fe and Cu speciation changes during activation of a FeCu bimetallic catalyst along a millimetre-sized catalyst bed. Strategies of data acquisition and post-data analysis using Jupyter notebooks and multivariate data analysis are presented, and the gain obtained using full-field hyperspectral quick-EXAFS imaging for studies of functional materials under process conditions in comparison with macroscopic information obtained by non-spatially resolved quick-EXAFS techniques is discussed.

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

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

The extraction and purification procedures, crystallization and crystal structure refinement (single-crystal X-ray data) of germacrone type II, C15H22O, are presented. The structural results are compared with a previous powder X-ray synchrotron study [Kaduk et al. (2022). Powder Diffr. 37, 98–104], revealing significant improvements in terms of accuracy and precision. Hirshfeld atom refinement (HAR), as well as Hirshfeld surface analysis, give insight into the inter­molecular inter­actions of germacrone type II.

The title compound, C19H30O2Si, has triclinic (Poverline{1}) symmetry at 100 K. The O atom of the epoxide group has a pseudoaxial orientation and the dihedral angle between the cyclo­hexyl and benzene rings is 85.80 (8)°. The C—O—Si—Ct (t = tert-but­yl) torsion angle is −177.40 (14)°. In the crystal, pairwise C—H⋯O links connect the mol­ecules into inversion dimers featuring R22(8) loops.

In the title compound, C14H14O3, the dihedral angle between the aromatic rings is 39.76 (9)°. In the crystal, the mol­ecules associate to form centrosymmetric acid–acid dimers linked by pairwise O—H⋯O hydrogen bonds. The precision of the geometric parameters in the present single-crystal study is about an order of magnitude better than the previous powder diffraction study [Chattopadhyay et al. (2013). CrystEngComm, 15, 1077–1085].

In the title compound, C21H27BF2N2O4, a highly fluorescent boron–dipyrromethene dye, the methyl­propionate moieties have different conformations. In the crystal, weak C—H⋯F and C—H⋯O inter­actions link the mol­ecules. Some optical properties are presented.

The crystal structure of a new 1:1 cocrystal of carbamazepine and S-naproxen (C15H12N2O·C14H14O3) was solved from powder X-ray diffraction (PXRD). The PXRD pattern was measured at the high-resolution beamline CRISTAL at synchrotron SOLEIL (France). The structure was solved using Monte Carlo simulated annealing, then refined with Rietveld refinement. The positions of the H atoms were obtained from density functional theory (DFT) ground-state calculations. The symmetry is ortho­rhom­bic with the space group P212121 (No. 19) and the following lattice parameters: a = 33.5486 (9), b = 26.4223 (6), c = 5.3651 (10) Å and V = 4755.83 (19) Å3.

Beauveriolides, including the main beauveriolide I {systematic name: (3R,6S,9S,13S)-9-benzyl-13-[(2S)-hexan-2-yl]-6-methyl-3-(2-methyl­prop­yl)-1-oxa-4,7,10-tri­aza­cyclo­tridecane-2,5,8,11-tetrone, C27H41N3O5}, are a series of cyclo­depsipeptides that have shown promising results in the treatment of Alzheimer's disease and in the prevention of foam cell formation in atherosclerosis. Their crystal structure studies have been difficult due to their tiny crystal size and fibre-like morphology, until now. Recent developments in 3D electron diffraction methodology have made it possible to accurately study the crystal structures of submicron crystals by overcoming the problems of beam sensitivity and dynamical scattering. In this study, the absolute structure of beauveriolide I was determined by 3D electron diffraction. The cyclo­dep­si­peptide crystallizes in the space group I2 with lattice parameters a = 40.2744 (4), b = 5.0976 (5), c = 27.698 (4) Å and β = 105.729 (6)°. After dynamical refinement, its absolute structure was determined by comparing the R factors and calculating the z-scores of the two possible enanti­omorphs of beauveriolide I.

X-ray and electron diffraction methods independently identify the S-enanti­omer of Berkecoumarin [systematic name: (S)-8-hy­droxy-3-(2-hy­droxy­prop­yl)-6-meth­oxy-2H-chromen-2-one]. Isolated from Berkeley Pit Lake Penicillium sp., Berkecoumarin is a natural product with a light-atom com­position (C13H14O5) that challenges in-house absolute structure determination by anomalous scattering. This study further demonstrates the utility of dynamical refinement of electron-diffraction data for absolute structure determination.

The synthesis and structural characterization of three families of coordination com­plexes synthesized from 4'-phenyl-2,2':6',2''-terpyridine (8, Ph-TPY), 4'-(4-chloro­phen­yl)-2,2':6',2''-terpyridine (9, ClPh-TPY) and 4'-(4-meth­oxy­phen­yl)-2,2':6',2''-terpyridine (10, MeOPh-TPY) ligands with the divalent metals Co2+, Fe2+, Mn2+ and Ni2+ are reported. The com­pounds were synthesized from a 1:2 mixture of the metal and ligand, resulting in a series of com­plexes with the general formula [M(R-TPY)2](ClO4)2 (where M = Co2+, Fe2+, Mn2+ and Ni2+, and R-TPY = Ph-TPY, ClPh-TPY and MeOPh-TPY). The general formula and structural and supra­molecular features were determinated by single-crystal X-ray diffraction for bis­(4'-phenyl-2,2':6',2''-terpyridine)­nickel(II) bis­(per­chlo­rate), [Ni(C21H15N3)2](ClO4)2 or [Ni(Ph-TPY)2](ClO4)2, bis­[4'-(4-meth­oxy­phen­yl)-2,2':6',2''-terpyridine]­manganese(II) bis­(per­chlo­rate), [Mn(C22H17N3O)2](ClO4)2 or [Mn(MeOPh-TPY)2](ClO4)2, and bis­(4'-phenyl-2,2':6',2''-ter­py­ridine)­manganese(II) bis­(per­chlo­rate), [Mn(C21H15N3)2](ClO4)2 or [Mn(Ph-TPY)2](ClO4)2. In all three cases, the com­plexes present distorted octa­hedral coordination polyhedra and the crystal packing is determined mainly by weak C—H⋯π inter­actions. All the com­pounds (except for the Ni derivatives, for which FT–IR, UV–Vis and thermal analysis are reported) were fully characterized by spectroscopic (FT–IR, UV–Vis and NMR spectroscopy) and thermal (TGA–DSC, thermogravimetric analysis–differential scanning calorimetry) methods.

Geminal and vicinal bis­(tri­fluoro­methane­sulfonate) esters are highly reactive alkyl­ene synthons used as potent electrophiles in the macrocyclization of imid­azoles and the transformation of bypyridines to diquat derivatives via nucleophilic substitution reactions. Herein we report the crystal structures of methyl­ene (C3H2F6O6S2) and ethyl­ene bis­(tri­fluoro­methane­sulfonate) (C4H4F6O6S2), the first examples of a geminal and vicinal bis­(tri­fluoro­methane­sulfonate) ester characterized by single-crystal X-ray diffraction (SC-XRD). With melting points slightly below ambient temperature, both reported bis­(tri­fluoro­methane­sulfonate)s are air- and moisture-sensitive oils and were crys­tallized at 277 K to afford two-com­ponent non-merohedrally twinned crystals. The dominant inter­actions present in both com­pounds are non-classical C—H⋯O hydrogen bonds and inter­molecular C—F⋯F—C inter­actions between tri­fluoro­methyl groups. Mol­ecular electrostatic potential (MEP) cal­culations by DFT-D3 helped to qu­antify the polarity between O⋯H and F⋯F contacts to rationalize the self-sorting of both bis­(tri­fluoro­methane­sulfonate) esters in polar (non-fluorous) and non-polar (fluorous) domains within the crystal structure.