Three-dimensional electron diffraction (3D-ED) is a powerful technique for crystallographic characterization of nanometre-sized crystals that are too small for X-ray diffraction. For accurate crystal structure refinement, however, it is important that the Bragg diffracted intensities are treated dynamically. Bloch wave simulations are often used in 3D-ED, but can be computationally expensive for large unit cell crystals due to the large number of diffracted beams. Proposed here is an alternative method, the `scattering cluster algorithm' (SCA), that replaces the eigen-decomposition operation in Bloch waves with a simpler matrix multiplication. The underlying principle of SCA is that the intensity of a given Bragg reflection is largely determined by intensity transfer (i.e. `scattering') from a cluster of neighbouring diffracted beams. However, the penalty for using matrix multiplication is that the sample must be divided into a series of thin slices and the diffracted beams calculated iteratively, similar to the multislice approach. Therefore, SCA is more suitable for thin specimens. The accuracy and speed of SCA are demonstrated on tri-iso­propyl silane (TIPS) pentacene and rubrene, two exemplar organic materials with large unit cells.

The strong interaction of high-energy electrons with a crystal results in both dynamical elastic scattering and inelastic events, particularly phonon and plasmon excitation, which have relatively large cross sections. For accurate crystal structure refinement it is therefore important to uncover the impact of inelastic scattering on the Bragg beam intensities. Here a combined Bloch wave–Monte Carlo method is used to simulate phonon and plasmon scattering in crystals. The simulated thermal and plasmon diffuse scattering are consistent with experimental results. The simulations also confirm the empirical observation of a weaker unscattered beam intensity with increasing energy loss in the low-loss regime, while the Bragg-diffracted beam intensities do not change significantly. The beam intensities include the diffuse scattered background and have been normalized to adjust for the inelastic scattering cross section. It is speculated that the random azimuthal scattering angle during inelastic events transfers part of the unscattered beam intensity to the inner Bragg reflections. Inelastic scattering should not significantly influence crystal structure refinement, provided there are no artefacts from any background subtraction, since the relative intensity of the diffracted beams (which includes the diffuse scattering) remains approximately constant in the low energy loss regime.

Recent advances in quantum crystallography have shown that, beyond conventional charge density refinement, a one-electron reduced density matrix (1-RDM) satisfying N-representability conditions can be reconstructed using jointly experimental X-ray structure factors and directional Compton profiles (DCP) through semidefinite programming. So far, such reconstruction methods for 1-RDM, not constrained to idempotency, have been tested only on a toy model system (CO2). In this work, a new method is assessed on crystalline urea [CO(NH2)2] using static (0 K) and dynamic (50 K) artificial experimental data. An improved model, including symmetry constraints and frozen core-electron contribution, is introduced to better handle the increasing system complexity. Reconstructed 1-RDMs, deformation densities and DCP anisotropy are analysed, and it is demonstrated that the changes in the model significantly improve the reconstruction quality, even when there is insufficient information and data corruption. The robustness of the model and the strategy are thus shown to be well adapted to address the reconstruction problem from actual experimental scattering data.

Sorghum, a short-day tropical plant, has been adapted for temperate grain production, in particular through the selection of variants at the MATURITY loci (Ma1–Ma6) that reduce photoperiod sensitivity. Ma3 encodes phytochrome B (phyB), a red/far-red photochromic biliprotein photoreceptor. The multi-domain gene product, comprising 1178 amino acids, autocatalytically binds the phytochromobilin chromophore to form the photoactive holophytochrome (Sb.phyB). This study describes the development of an efficient heterologous overproduction system which allows the production of large quantities of various holoprotein constructs, along with purification and crystallization procedures. Crystals of the Pr (red-light-absorbing) forms of NPGP, PGP and PG (residues 1–655, 114–655 and 114–458, respectively), each C-terminally tagged with His6, were successfully produced. While NPGP crystals did not diffract, those of PGP and PG diffracted to 6 and 2.1 Å resolution, respectively. Moving the tag to the N-terminus and replacing phytochromobilin with phycocyanobilin as the ligand produced PG crystals that diffracted to 1.8 Å resolution. These results demonstrate that the diffraction quality of challenging protein crystals can be improved by removing flexible regions, shifting fusion tags and altering small-molecule ligands.

This work investigates the performance of the electrospray aerosol generator at the European X-ray Free Electron Laser (EuXFEL). This generator is, together with an aerodynamic lens stack that transports the particles into the X-ray interaction vacuum chamber, the method of choice to deliver particles for single-particle coherent diffractive imaging (SPI) experiments at the EuXFEL. For these experiments to be successful, it is necessary to achieve high transmission of particles from solution into the vacuum interaction region. Particle transmission is highly dependent on efficient neutralization of the charged aerosol generated by the electrospray mechanism as well as the geometry in the vicinity of the Taylor cone. We report absolute particle transmission values for different neutralizers and geometries while keeping the conditions suitable for SPI experiments. Our findings reveal that a vacuum ultraviolet ionizer demonstrates a transmission efficiency approximately seven times greater than the soft X-ray ionizer used previously. Combined with an optimized orifice size on the counter electrode, we achieve >40% particle transmission from solution into the X-ray interaction region. These findings offer valuable insights for optimizing electrospray aerosol generator configurations and data rates for SPI experiments.

A high-flux sub-micrometre focusing system was constructed using multilayer focusing mirrors in Kirkpatrick–Baez geometry for 100 keV X-rays. The focusing mirror system had a wide bandwidth of 5% and a high peak reflectivity of 74%. Performance was evaluated at the undulator beamline BL05XU of SPring-8, which produced an intense 100 keV X-ray beam with a bandwidth of 1%. When the light source was focused directly in both vertical and horizontal directions, the beam size was measured to be 0.32 µm (V) × 5.3 µm (H) with a flux of 1 × 1012 photons s−1. However, when a limited horizontal slit was used to form a secondary source, the focusing beam size decreased to 0.25 µm (V) × 0.26 µm (H) with a flux of 6 × 1010 photons s−1. The 200 nm line and space patterns of a Siemens star chart made of tantalum were clearly resolved by the absorption contrast of the focused beam. This 100 keV focusing system is applicable to various fields of nondestructive analyses with sub-micrometre resolutions.

Superconducting undulators (SCUs) can offer a much higher on-axis undulator field than state-of-the-art cryogenic permanent-magnet undulators with the same period and vacuum gap. The development of shorter-period and high-field SCUs would allow the free-electron laser and synchrotron radiation source community to reduce both the length of undulators and the dimensions of the accelerator. Magnetic measurements are essential for characterizing the magnetic field quality of undulators for operation in a modern light source. Hall probe scanning is so far the most mature technique for local field characterization of undulators. This article focuses on the systematic error caused by thermal contraction that influences Hall probe measurements carried out in a liquid helium cryostat. A novel procedure, based on the redundant measurement of the magnetic field using multiple Hall probes at known relative distance, is introduced for the correction of such systematic error.

Hard X-ray absorption spectroscopy is a valuable in situ probe for non-destructive diagnostics of metal sites. The low-energy interval of a spectrum (XANES) contains information about the metal oxidation state, ligand type, symmetry and distances in the first coordination shell but shows almost no dependency on the bridged metal–metal bond length. The higher-energy interval (EXAFS), on the contrary, is more sensitive to the coordination numbers and can decouple the contribution from distances in different coordination shells. Supervised machine-learning methods can combine information from different intervals of a spectrum; however, computational approaches for the near-edge region of the spectrum and higher energies are different. This work aims to keep all benefits of XANES and extend its sensitivity towards the interatomic distances in the first and second coordination shells. Using a binuclear bridged copper complex as a case study and cross-validation analysis as a quantitative tool it is shown that the first 170 eV above the edge are already sufficient to balance the contributions of Cu–O/N scattering and Cu–Cu scattering. As a more general outcome this work highlights the trivial but often overlooked importance of using `longer' energy intervals of XANES for structural refinement and machine-learning predictions. The first 200 eV above the absorption edge still do not require parametrization of Debye–Waller damping and can be calculated within full multiple scattering or finite difference approximations with only moderately increased computational costs.

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.

A reliable `in situ' method for wavefront sensing in the soft X-ray domain is reported, developed for the characterization of rotationally symmetric optical elements, like an ellipsoidal mirror shell. In a laboratory setup, the mirror sample is irradiated by an electron-excited (4.4 keV), micrometre-sized (∼2 µm) fluorescence source (carbon Kα, 277 eV). Substantially, the three-dimensional intensity distribution I(r) is recorded by a CCD camera (2048 × 512 pixels of 13.5 µm) at two positions along the optical axis, symmetrically displaced by ±21–25% from the focus. The transport-of-intensity equation is interpreted in a geometrical sense from plane to plane and implemented as a ray tracing code, to retrieve the phase Φ(r) from the radial intensity gradient on a sub-pixel scale. For reasons of statistical reliability, five intra-/extra-focal CCD image pairs are evaluated and averaged to an annular two-dimensional map of the wavefront error {cal W}. In units of the test wavelength (C Kα), an r.m.s. value sigma_{cal{W}} = ±10.9λ0 and a peak-to-valley amplitude of ±31.3λ0 are obtained. By means of the wavefront, the focus is first reconstructed with a result for its diameter of 38.4 µm, close to the direct experimental observation of 39.4 µm (FWHM). Secondly, figure and slope errors of the ellipsoid are characterized with an average of ±1.14 µm and ±8.8 arcsec (r.m.s.), respectively, the latter in reasonable agreement with the measured focal intensity distribution. The findings enable, amongst others, the precise alignment of axisymmetric X-ray mirrors or the design of a wavefront corrector for high-resolution X-ray science.

The phase problem in the context of focusing synchrotron beams with X-ray lenses is addressed. The feasibility of retrieving the surface error of a lens system by using only the intensity of the propagated beam at several distances is demonstrated. A neural network, trained with a few thousand simulations using random errors, can predict accurately the lens error profile that accounts for all aberrations. It demonstrates the feasibility of routinely measuring the aberrations induced by an X-ray lens, or another optical system, using only a few intensity images.

Two-directional beam-tracking (2DBT) is a method for phase-contrast imaging and tomography that uses an intensity modulator to structure the X-ray beam into an array of independent circular beamlets that are resolved by a high-resolution detector. It features isotropic spatial resolution, provides two-dimensional phase sensitivity, and enables the three-dimensional reconstructions of the refractive index decrement, δ, and the attenuation coefficient, μ. In this work, the angular sensitivity and the spatial resolution of 2DBT images in a synchrotron-based implementation is reported. In its best configuration, angular sensitivities of ∼20 nrad and spatial resolution of at least 6.25 µm in phase-contrast images were obtained. Exemplar application to the three-dimensional imaging of soft tissue samples, including a mouse liver and a decellularized porcine dermis, is also demonstrated.

In situ wavefront sensing plays a critical role in the delivery of high-quality beams for X-ray experiments. X-ray speckle-based techniques stand out among other in situ techniques for their easy experimental setup and various data acquisition modes. Although X-ray speckle-based techniques have been under development for more than a decade, there are still no user-friendly software packages for new researchers to begin with. Here, we present an open-source Python package, spexwavepy, for X-ray wavefront sensing using speckle-based techniques. This Python package covers a variety of X-ray speckle-based techniques, provides plenty of examples with real experimental data and offers detailed online documentation for users. We hope it can help new researchers learn and apply the speckle-based techniques for X-ray wavefront sensing to synchrotron radiation and X-ray free-electron laser beamlines.

The diagnostics of X-ray beam properties has a critical importance at the European X-ray Free-Electron Laser facility. Besides existing diagnostic components, utilization of a diamond sensor was proposed to achieve radiation-hard, non-invasive beam position and pulse energy measurements for hard X-rays. In particular, with very hard X-rays, diamond-based sensors become a useful complement to gas-based devices which lose sensitivity due to significantly reduced gas cross-sections. The measurements presented in this work were performed with diamond sensors consisting of an electronic-grade single-crystal chemical-vapor-deposition diamond with position-sensitive resistive electrodes in a duo-lateral configuration. The results show that the diamond sensor delivers pulse-resolved X-ray beam position data at 2.25 MHz with an uncertainty of less than 1% of the beam size. To our knowledge this is the first demonstration of pulse-resolved position measurements at the MHz rate using a transmissive diamond sensor at a free-electron laser facility. It can therefore be a valuable tool for X-ray free-electron lasers, especially for high-repetition-rate machines, enabling applications such as beam-based alignment and intra-pulse-train position feedback.

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.

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.

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.

The development of hard X-ray nanoprobe techniques has given rise to a number of experimental methods, like nano-XAS, nano-XRD, nano-XRF, ptychography and tomography. Each method has its own unique data processing algorithms. With the increase in data acquisition rate, the large amount of generated data is now a big challenge to these algorithms. In this work, an intuitive, user-friendly software system is introduced to integrate and manage these algorithms; by taking advantage of the loosely coupled, component-based design approach of the system, the data processing speed of the imaging algorithm is enhanced through optimization of the parallelism efficiency. This study provides meaningful solutions to tackle complexity challenges faced in synchrotron data processing.

Ultra-high-speed synchrotron-based hard X-ray (i.e. above 10 keV) imaging is gaining a growing interest in a number of scientific domains for tracking non-repeatable dynamic phenomena at spatio-temporal microscales. This work describes an optimized indirect X-ray imaging microscope designed to achieve high performance at micrometre pixel size and megahertz acquisition speed. The entire detector optical arrangement has an improved sensitivity within the near-ultraviolet (NUV) part of the emitted spectrum (i.e. 310–430 nm wavelength). When combined with a single-crystal fast-decay scintillator, such as LYSO:Ce (Lu2−xYxSiO5:Ce), it exploits the potential of the NUV light-emitting scintillators. The indirect arrangement of the detector makes it suitable for high-dose applications that require high-energy illumination. This allows for synchrotron single-bunch hard X-ray imaging to be performed with improved true spatial resolution, as herein exemplified through pulsed wire explosion and superheated near-nozzle gasoline injection experiments at a pixel size of 3.2 µm, acquisition rates up to 1.4 MHz and effective exposure time down to 60 ps.

The incommensurately modulated structure of (2S,3S)-2-amino-3-hy­droxy-3-methyl-4-phen­oxy­butanoic acid dihydrate (C11H15NO4·2H2O or I·2H2O) is described in the (3+1)-dimensional superspace group P212121(0β0)000 (β = 0.357). The loss of the three-dimensional periodicity is ascribed to the occupational modulation of one positionally disordered solvent water mol­ecule, where the two positions are related by a small translation [ca 0.666 (9) Å] and ∼168 (5)° rotation about one of its O—H bonds, with an average 0.624 (3):0.376 (3) occupancy ratio. The occupational modulation of this mol­ecule arises due to the com­petition between the different hy­dro­gen-bonding motifs associated with each position. The structure can be very well refined in the average approximation (all satellite reflections disregarded) in the space group P212121, with the water mol­ecule refined as disordered over two positions in a 0.625 (16):0.375 (16) ratio. The refinement in the commensurate threefold supercell approximation in the space group P1121 is also of high quality, with the six corresponding water mol­ecules exhibiting three different occupancy ratios averaging 0.635:0.365.

Fragment-based drug design using X-ray crystallography is a powerful technique to enable the development of new lead compounds, or probe molecules, against biological targets. This study addresses the need to determine fragment binding orientations for low-occupancy fragments with incomplete electron density, an essential step before further development of the molecule. Halogen atoms play multiple roles in drug discovery due to their unique combination of electronegativity, steric effects and hydrophobic properties. Fragments incorporating halogen atoms serve as promising starting points in hit-to-lead development as they often establish halogen bonds with target proteins, potentially enhancing binding affinity and selectivity, as well as counteracting drug resistance. Here, the aim was to unambiguously identify the binding orientations of fragment hits for SARS-CoV-2 nonstructural protein 1 (nsp1) which contain a combination of sulfur and/or chlorine, bromine and iodine substituents. The binding orientations of carefully selected nsp1 analogue hits were focused on by employing their anomalous scattering combined with Pan-Dataset Density Analysis (PanDDA). Anomalous difference Fourier maps derived from the diffraction data collected at both standard and long-wavelength X-rays were compared. The discrepancies observed in the maps of iodine-containing fragments collected at different energies were attributed to site-specific radiation-damage stemming from the strong X-ray absorption of I atoms, which is likely to cause cleavage of the C—I bond. A reliable and effective data-collection strategy to unambiguously determine the binding orientations of low-occupancy fragments containing sulfur and/or halogen atoms while mitigating radiation damage is presented.

For cryo-electron tomography (cryo-ET) of beam-sensitive biological specimens, a planar sample geometry is typically used. As the sample is tilted, the effective thickness of the sample along the direction of the electron beam increases and the signal-to-noise ratio concomitantly decreases, limiting the transfer of information at high tilt angles. In addition, the tilt range where data can be collected is limited by a combination of various sample-environment constraints, including the limited space in the objective lens pole piece and the possible use of fixed conductive braids to cool the specimen. Consequently, most tilt series are limited to a maximum of ±70°, leading to the presence of a missing wedge in Fourier space. The acquisition of cryo-ET data without a missing wedge, for example using a cylindrical sample geometry, is hence attractive for volumetric analysis of low-symmetry structures such as organelles or vesicles, lysis events, pore formation or filaments for which the missing information cannot be compensated by averaging techniques. Irrespective of the geometry, electron-beam damage to the specimen is an issue and the first images acquired will transfer more high-resolution information than those acquired last. There is also an inherent trade-off between higher sampling in Fourier space and avoiding beam damage to the sample. Finally, the necessity of using a sufficient electron fluence to align the tilt images means that this fluence needs to be fractionated across a small number of images; therefore, the order of data acquisition is also a factor to consider. Here, an n-helix tilt scheme is described and simulated which uses overlapping and interleaved tilt series to maximize the use of a pillar geometry, allowing the entire pillar volume to be reconstructed as a single unit. Three related tilt schemes are also evaluated that extend the continuous and classic dose-symmetric tilt schemes for cryo-ET to pillar samples to enable the collection of isotropic information across all spatial frequencies. A fourfold dose-symmetric scheme is proposed which provides a practical compromise between uniform information transfer and complexity of data acquisition.

Serial electron diffraction (SerialED), which applies a snapshot data acquisition strategy for each crystal, was introduced to tackle the problem of radiation damage in the structure determination of beam-sensitive materials by three-dimensional electron diffraction (3DED). The snapshot data acquisition in SerialED can be realized using both transmission and scanning transmission electron microscopes (TEM/STEM). However, the current SerialED workflow based on STEM setups requires special external devices and software, which limits broader adoption. Here, we present a simplified experimental implementation of STEM-based SerialED on Thermo Fisher Scientific STEMs using common proprietary software interfaced through Python scripts to automate data collection. Specifically, we utilize TEM Imaging and Analysis (TIA) scripting and TEM scripting to access the STEM functionalities of the microscope, and DigitalMicrograph scripting to control the camera for snapshot data acquisition. Data analysis adapts the existing workflow using the software CrystFEL, which was developed for serial X-ray crystallography. Our workflow for STEM SerialED can be used on any Gatan or Thermo Fisher Scientific camera. We apply this workflow to collect high-resolution STEM SerialED data from two aluminosilicate zeolites, zeolite Y and ZSM-25. We demonstrate, for the first time, ab initio structure determination through direct methods using STEM SerialED data. Zeolite Y is relatively stable under the electron beam, and STEM SerialED data extend to 0.60 Å. We show that the structural model obtained using STEM SerialED data merged from 358 crystals is nearly identical to that using continuous rotation electron diffraction data from one crystal. This demonstrates that accurate structures can be obtained from STEM SerialED. Zeolite ZSM-25 is very beam-sensitive and has a complex structure. We show that STEM SerialED greatly improves the data resolution of ZSM-25, compared with serial rotation electron diffraction (SerialRED), from 1.50 to 0.90 Å. This allows, for the first time, the use of standard phasing methods, such as direct methods, for the ab initio structure determination of ZSM-25.

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

Evidence that the electronic structure of atoms persists in molecules to a much greater extent than has been usually admitted is presented. This is achieved by resorting to N-electron real-space descriptors instead of one- or at most two-particle projections like the electron or exchange-correlation densities. Here, the 3N-dimensional maxima of the square of the wavefunction, the so-called Born maxima, are used. Since this technique is relatively unknown to the crystallographic community, a case-based approach is taken, revisiting first the Born maxima of atoms in their ground state and then some of their excited states. It is shown how they survive in molecules and that, beyond any doubt, the distribution of electrons around an atom in a molecule can be recognized as that of its isolated, in many cases excited, counterpart, relating this fact with the concept of energetic promotion. Several other cases that exemplify the applicability of the technique to solve chemical bonding conflicts and to introduce predictability in real-space analyses are also examined.

X-ray scattering/diffraction tensor tomography techniques are promising methods to acquire the 3D texture information of heterogeneous biological tissues at micrometre resolution. However, the methods suffer from a long overall acquisition time due to multi-dimensional scanning across real and reciprocal space. Here, a new approach is introduced to obtain 3D reciprocal information of each illuminated scanning volume using mathematic modeling, which is equivalent to a physical scanning procedure for collecting the full reciprocal information required for voxel reconstruction. The virtual reciprocal scanning scheme was validated by a simulated 6D wide-angle X-ray diffraction tomography experiment. The theoretical validation of the method represents an important technological advancement for 6D diffraction tensor tomography and a crucial step towards pervasive applications in the characterization of heterogeneous materials.

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

In the folded state, biomolecules exchange between multiple conformational states crucial for their function. However, most structural models derived from experiments and computational predictions only encode a single state. To represent biomolecules accurately, we must move towards modeling and predicting structural ensembles. Information about structural ensembles exists within experimental data from X-ray crystallography and cryo-electron microscopy. Although new tools are available to detect conformational and compositional heterogeneity within these ensembles, the legacy PDB data structure does not robustly encapsulate this complexity. We propose modifications to the macromolecular crystallographic information file (mmCIF) to improve the representation and interrelation of conformational and compositional heterogeneity. These modifications will enable the capture of macromolecular ensembles in a human and machine-interpretable way, potentially catalyzing breakthroughs for ensemble–function predictions, analogous to the achievements of AlphaFold with single-structure prediction.

A series of events underscoring the significant advancements in micro-crystallization and in vivo crystallography were held during the 26th IUCr Congress in Melbourne, positioning microcrystallography as a pivotal field within structural biology. Through collaborative discussions and the sharing of innovative methodologies, these sessions outlined frontier approaches in macromolecular crystallography. This review provides an overview of this rapidly moving field in light of the rich dialogues and forward-thinking proposals explored during the congress workshop and microsymposium. These advances in microcrystallography shed light on the potential to reshape current research paradigms and enhance our comprehension of biological mechanisms at the molecular scale.

Traditional X-ray methods are extensively applied to commercial cement samples in order to determine their physical and chemical properties. Powder patterns are routinely used to quantify the composition of these phase mixtures, but structure determination becomes difficult because of reflection overlapping caused by the high number of different crystal structures. The fast-growing 3D electron diffraction technique and its related automated acquisition protocols arise as a potentially very interesting tool for the cement industry, since they enable the fast and systematic acquisition of diffraction data from individual particles. In this context, electron diffraction has been used in the investigation of the different crystalline phases present in various commercial clinkers for cement. Automated data collection procedures and subsequent data processing have enabled the structural characterization of the different crystal structures from which the α'H polymorph of Ca2SiO4 (belite) exhibited satellite reflections. Its average crystal structure has been known since 1971 and satellite reflections have been reported previously, yet the modulation was never fully described by means of the superspace formalism. Here, the incommensurately modulated structure is solved and refined using harmonic and crenel functions in the superspace group Pnma(α00)0ss, showing the potential of 3D electron diffraction for systematic crystallographic characterizations of cement. A full description of the different belite polymorphs is provided considering this modulated structure.

A few real case examples are presented on how to report magnetic structures, with precise step-by-step explanations, following the guidelines of the IUCr Commission on Magnetic Structures [Perez-Mato et al. (2024). Acta Cryst. B80, 219–234]. Four examples have been chosen, illustrating different types of single-k magnetic orders, from the basic case to more complex ones, including odd-harmonics, and one multi-k order. In addition to acquainting researchers with the process of communicating commensurate magnetic structures, these examples also aim to clarify important concepts, which are used throughout the guidelines, such as the transformation to a standard setting of a magnetic space group.

Thio­phosgene is one of the principal C=S building blocks in synthetic chemistry. At room temperature, thio­phosgene is a red liquid. While its properties in the liquid and gaseous states are well known, a comprehensive characterization of thio­phosgene in its solid state is presented here. Differential scanning calorimetry shows that thio­phosgene forms a supercooled melt before rapidly crystallizing. Its melting point is 231.85 K (−41.3 °C). At 80 K, thio­phosgene crystallizes in space group P63/m [No. 174, a = b = 5.9645 (2), c = 6.2835 (3) Å, V = 193.59 (2) Å3]. The molecule shows a distinct rotational disorder: all S and Cl positions are of mixed occupancy and the disorder does not resolve at temperatures as low as 10 K, as was shown by neutron powder diffraction. Infrared, Raman and inelastic neutron scattering spectra were collected and assigned with the aid of quantum chemical calculations. A larger ordered structural model allowed for better agreement between the measured and calculated spectra, further indicating that disorder is an inherent feature of solid-state thio­phosgene.

A CuII coordination polymer, catena-poly[[[aqua­copper(II)]-bis­(μ-4-amino­benz­o­ato)-κ2N:O;κ2O:N] monohydrate], {[Cu(pABA)2(H2O)]·H2O}n (pABA = p-amino­benzoate, C7H4NO2−), was synthesized and characterized. It exhibits a one-dimensional chain structure extended into a three-dimensional supra­molecular assembly through hydrogen bonds and π–π inter­actions. While the twinned crystal shows a metrically ortho­rhom­bic lattice and an apparent space group Pbcm, the true symmetry is monoclinic (space group P2/c), with disordered Cu atoms and mixed roles of water mol­ecules (aqua ligand/crystallization water). The luminescence spectrum of the complex shows an emission at 345 nm, cf. 349 nm for pABAH.

The complex, tri­chlorido­(1,4,11-tri­aza-8-azonia­tetra­cyclo­[6.6.2.04,16.011,15]hexa­decane 1-oxide-κO)zinc(II) monohydrate, [ZnCl3(C12H23N4O)]·H2O, (I), has monoclinic symmetry (space group P21/n) at 120 K. The zinc(II) center adopts a slightly distorted tetra­hedral coordination geometry and is coordinated by three chlorine atoms and the oxygen atom of the oxidized tertiary amine of the tetra­cycle. The amine nitro­gen atom, inside the ligand cleft, is protonated and forms a hydrogen bond to the oxygen of the amine oxide. Additional hydrogen-bonding inter­actions involve the protonated amine, the water solvate oxygen atom, and one of the chloro ligands.

In the title mol­ecule, C21H23N3O3, the imidazolidine ring slightly deviates from planarity and the morpholine ring exhibits the chair conformation. In the crystal, N—H⋯O and C—H⋯O hydrogen bonds form helical chains of mol­ecules extending parallel to the c axis that are connected by C—H⋯π(ring) inter­actions. A Hirshfeld surface analysis reveals that the most important contributions for the crystal packing are from H⋯H (55.2%), H⋯C/C⋯H (22.6%) and H⋯O/O⋯H (20.5%) inter­actions. The volume of the crystal voids and the percentage of free space were calculated to be 236.78 Å3 and 12.71%, respectively. Evaluation of the electrostatic, dispersion and total energy frameworks indicates that the stabilization is dominated by the nearly equal electrostatic and dispersion energy contributions. The DFT-optimized mol­ecular structure at the B3LYP/6-311 G(d,p) level is compared with the experimentally determined mol­ecular structure in the solid state. Moreover, the HOMO–LUMO behaviour was elucidated to determine the energy gap.

This title compound, C20H26O2, was isolated from the benzene fraction of the stem bark of Staudtia kamerunensis Warb. (Myristicaceae) using column chromatography techniques over silica gel. The compound was fully characterized by single-crystal X-ray diffraction, one and two-dimensional NMR spectroscopy, IR and MS spectrometry. The compound has two fused cyclo­hexane rings attached to a benzene ring, with a carb­oxy­lic acid on C-4. This cyclo­hexene ring has a chair conformation while the other adopts a half-chair conformation. The benzene ring is substituted with a propenyl moiety. The structure is characterized by inter­molecular O—H⋯O hydrogen bonds, two C—H⋯O intra­molecular hydrogen bonds and two C—H⋯π inter­actions. The mol­ecular structure confirms previous studies carried out by spectroscopic techniques.

In the structure of the title salt, {[Ba(μ3-C3H2N3O2)2(μ-H2O)(H2O)]·H2O}n, the barium ion and all three oxygen atoms of the water mol­ecules reside on a mirror plane. The hydrogen atoms of the bridging water and the solvate water mol­ecules are arranged across a mirror plane whereas all atoms of the monodentate aqua ligand are situated on this mirror plane. The distorted ninefold coord­ination of the Ba ions is completed with four nitroso-, two carbonyl- and three aqua-O atoms at the distances of 2.763 (3)–2.961 (4) Å and it is best described as tricapped trigonal prism. The three-dimensional framework structure is formed by face-sharing of the trigonal prisms, via μ-nitroso- and μ-aqua-O atoms, and also by the bridging coordination of the anions via carbonyl-O atoms occupying two out of the three cap positions. The solvate water mol­ecules populate the crystal channels and facilitate a set of four directional hydrogen bonds. The principal Ba–carbamoyl­cyano­nitro­somethanido linkage reveals a rare example of the inherently polar binodal six- and three-coordinated bipartite topology (three-letter notation sit). It suggests that small resonance-stabilized cyano­nitroso anions can be utilized as bridging ligands for the supra­molecular synthesis of MOF solids. Such an outcome may be anti­cipated for a broader range of hard Lewis acidic alkaline earth metal ions, which perfectly match the coordination preferences of highly nucleophilic nitroso-O atoms. Thermal analysis reveals two-stage dehydration of the title compound (383 and 473 K) followed by decomposition with release of CO2, HCN and H2O at 558 K.

The major principles and requirements of asymmetric and inclined double-crystal monochromators are re-examined and presented to guide their design and development for significantly reducing heat load density and gradient on the monochromators of fourth-generation synchrotron light sources and X-ray free-electron lasers.

Recently, we introduced the liquid application method for time-resolved analyses (LAMA). The time-consuming cleaning cycles required for the substrate solution exchange and storage of the sensitive droplet-dispenser nozzles present practical challenges. In this work, a dispenser cleaning system for the semi-automated cleaning of the piezo-actuator-driven picolitre-droplet dispensers required for LAMA is introduced to streamline typical workflows.

Scintillator-based ZnS:Ag/6LiF neutron detectors have been under development at ISIS for more than three decades. Continuous research and development aim to improve detector capabilities, achieve better performance and meet the increasingly demanding requirements set by neutron instruments. As part of this program, a high-efficiency 2D position-sensitive scintillator detector with wavelength-shifting fibres has been developed for neutron-diffraction applications. The detector consists of a double scintillator-fibre layer to improve detection efficiency. Each layer is made up of two orthogonal fibre planes placed between two ZnS:Ag/6LiF scintillator screens. Thin reflective foils are attached to the front and back scintillators of each layer to minimize light cross-talk between layers. The detector has an active area of 192 × 192 mm with a square pixel size of 3 × 3 mm. As part of the development process of the double-layer detector, a single-layer detector was built, together with a prototype detector in which the two layers of the detector could be read out separately. Efficiency calculations and measurements of all three detectors are discussed. The novel double-layer detector has been installed and tested on the SXD diffractometer at ISIS. The detector performance is compared with the current scintillator detectors employed on SXD by studying reference crystal samples. More than a factor of 3 improvement in efficiency is achieved with the double-layer wavelength-shifting-fibre detector. Software routines for further optimizations in spatial resolution and uniformity of response have been implemented and tested for 2D detectors. The methods and results are discussed in this manuscript.

Small-angle X-ray tensor tomography and the related wide-angle X-ray tensor tomography are X-ray imaging techniques that tomographically reconstruct the anisotropic scattering density of extended samples. In previous studies, these methods have been used to image samples where the scattering density depends slowly on the direction of scattering, typically modeling the directionality, i.e. the texture, with a spherical harmonics expansion up until order ℓ = 8 or lower. This study investigates the performance of several established algorithms from small-angle X-ray tensor tomography on samples with a faster variation as a function of scattering direction and compares their expected and achieved performance. The various algorithms are tested using wide-angle scattering data from an as-drawn steel wire with known texture to establish the viability of the tensor tomography approach for such samples and to compare the performance of existing algorithms.

For a reliable characterization of materials and systems featuring multiple structural levels, a broad length scale from a few ångström to hundreds of nanometres must be analyzed and an extended Q range must be covered in X-ray and neutron scattering experiments. For certain samples or effects, it is advantageous to perform such characterization with a single instrument. Neutrons offer the unique advantage of contrast variation and matching by D-labeling, which is of great value in the characterization of natural or synthetic polymers. Some time-of-flight small-angle neutron scattering (TOF-SANS) instruments at neutron spallation sources can cover an extended Q range by using a broad wavelength band and a multitude of detectors. The detectors are arranged to cover a wide range of scattering angles with a resolution that allows both large-scale morphology and crystalline structure to be resolved simultaneously. However, for such analyses, the SANS instruments at steady-state sources operating in conventional monochromatic pinhole mode rely on additional wide-angle neutron scattering (WANS) detectors. The resolution must be tuned via a system of choppers and a TOF data acquisition option to reliably measure the atomic to mesoscale structures. The KWS-2 SANS diffractometer at Jülich Centre for Neutron Science allows the exploration of a wide Q range using conventional pinhole and lens focusing modes and an adjustable resolution Δλ/λ between 2 and 20%. This is achieved through the use of a versatile mechanical velocity selector combined with a variable slit opening and rotation frequency chopper. The installation of WANS detectors planned on the instrument required a detailed analysis of the quality of the data measured over a wide angular range with variable resolution. This article presents an assessment of the WANS performance by comparison with a McStas [Willendrup, Farhi & Lefmann (2004). Physica B, 350, E735–E737] simulation of ideal experimental conditions at the instrument.

This article presents a Python-based program, DFT2FEFFIT, to regress theoretical extended X-ray absorption fine structure (EXAFS) spectra calculated from density functional theory structure models against experimental EXAFS spectra. To showcase its application, Ce-doped fluorapatite [Ca10(PO4)6F2] is revisited as a representative of a material difficult to analyze by conventional multi-shell least-squares fitting of EXAFS spectra. The software is open source and publicly available.

Metal–organic frameworks (MOFs) have garnered significant attention in recent years owing to their exceptional properties. Understanding the intricate relationship between the structure of a material and its properties is crucial for guiding the synthesis and application of these materials. (Scanning) Transmission electron microscopy (S)TEM imaging stands out as a powerful tool for structural characterization at the nanoscale, capable of detailing both periodic and aperiodic local structures. However, the high electron-beam sensitivity of MOFs presents substantial challenges in their structural characterization using (S)TEM. This paper summarizes the latest advancements in low-dose high-resolution (S)TEM imaging technology and its application in MOF material characterization. It covers aspects such as framework structure, defects, and surface and interface analysis, along with the distribution of guest molecules within MOFs. This review also discusses emerging technologies like electron ptychography and outlines several prospective research directions in this field.

High-pressure neutron powder diffraction data from PbNCN were collected on the high-pressure diffraction beamline SNAP located at the Spallation Neutron Source (SNS) of Oak Ridge National Laboratory (Tennessee, USA). The diffraction data were analyzed using the novel method of multidimensional (two dimensions for now, potentially more in the future) Rietveld refinement and, for comparison, employing the conventional Rietveld method. To achieve two-dimensional analysis, a detailed description of the SNAP instrument characteristics was created, serving as an instrument parameter file, and then yielding both cell and spatial parameters as refined under pressure for the first time for solid-state cyanamides/carbodi­imides. The bulk modulus B0 = 25.1 (15) GPa and its derivative B'0 = 11.1 (8) were extracted for PbNCN following the Vinet equation of state. Surprisingly, an internal transition was observed beyond 2.0 (2) GPa, resulting from switching the bond multiplicities (and bending direction) of the NCN2− complex anion. The results were corroborated using electronic structure calculation from first principles, highlighting both local structural and chemical bonding details.

Here, it is investigated how optical properties of single scatterers in interacting multi-particle systems influence measurable structure factors. Both particles with linear gradients of their scattering length density and core–shell structures evoke characteristic deviations between the weighted sum 〈S(Q)〉 of partial structure factors in a multi-component system and experimentally accessible measurable structure factors SM(Q). While 〈S(Q)〉 contains only the structural information of self-organizing systems, SM(Q) is additionally influenced by the optical properties of their constituents, resulting in features such as changing amplitudes, additional peaks in the low-wavevector region or splitting of higher-order maxima, which are not related to structural reasons. It is shown that these effects can be systematically categorized according to the qualitative behaviour of the form factor in the Guinier region, which enables assessing the suitability of experimentally obtained structure factors to genuinely represent the microstructure of complex systems free from any particular model assumption. Hence, a careful data analysis regarding size distribution and optical properties of single scatterers is mandatory to avoid a misinterpretation of measurable structure factors.

We enumerate the 55083357 iso-edge subdivisions of six-dimensional translational lattices. We report on the use of the method of canonical forms that allows us to apply hashing techniques used in modern databases.

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After 16 years of dedicated planning and engineering, scientists at the U.S. Department of Energy's (DOE) Brookhaven National Laboratory have completed a 3.2 gigapixel sensor array for the camera that will be used in the Large Synoptic Survey Telescope (LSST), a massive telescope that will observe the universe like never before. The digital sensor array is composed of about 200 16-megapixel sensors, divided into 21 modules called "rafts." Each raft can function on its own, but when combined, they will view an area of sky that can fit more than 40 full moons in a single image. Researchers will stitch these images together to create a time-lapse movie of the complete visible universe accessible from Chile. Currently under construction on a mountaintop in Chile, LSST is designed to capture the most complete images of our universe that have ever been achieved. The project to build the telescope facility and camera is a collaborative effort among more than 30 institutions from around the world, and it is primarily funded by DOE's Office of Science and the National Science Foundation.

Image credit: SLAC National Accelerator Laboratory

Floating point arithmetic doesn't get the respect it deserves. Many people consider it mysterious, fuzzy, unpredictable. These misgivings often occur in discussion of vector sums. Our provocatively named SuperSum is intended to calm these fears.... read more >>

I didn't know anything about these topics until a couple of weeks ago. Now I can't stop thinking about them.... read more >>