X-ray mirrors for synchrotron radiation are often bent into a curved figure and work under grazing-incidence conditions due to the strong penetrating nature of X-rays to most materials. Mirrors of different cross sections have been recommended to reduce the mirror's slope inaccuracy and clamping difficulty in order to overcome mechanical tolerances. With the development of hard X-ray focusing, it is difficult to meet the needs of focusing mirrors with small slope error with the existing mirror processing technology. Deformable mirrors are adaptive optics that can produce a flexible surface figure. A method of using a deformable mirror as a phase compensator is described to enhance the focusing performance of an X-ray mirror. This paper presents an active piezoelectric plane X-ray focusing mirror with a linearly changing thickness that has the ability of phase compensation while focusing X-rays. Benefiting from its special structural design, the mirror can realize flexible focusing at different focusing geometries using a single input driving voltage. A prototype was used to measure its performance under one-dimension and two-dimension conditions. The results prove that, even at a bending magnet beamline, the mirror can easily achieve a single-micrometre focusing without a complicated bending mechanism or high-precision surface processing. It is hoped that this kind of deformable mirror will have a wide and flexible application in the synchrotron radiation field.

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.

Recently, there has been a high demand for elucidating kinetics and visualizing reaction processes under extreme dynamic conditions, such as chemical reactions under meteorite impact conditions, structural changes under non­equilibrium conditions, and in situ observations of dynamic changes. To accelerate material science studies and Earth science fields under dynamic conditions, a submillisecond in situ X-ray diffraction measurement system has been developed using a diamond anvil cell to observe reaction processes under rapidly changing pressure and temperature conditions replicating extreme dynamic conditions. The development and measurements were performed at the high-pressure beamline BL10XU/SPring-8 by synchronizing a high-speed hybrid pixel array detector, laser heating and temperature measurement system, and gas-pressure control system that enables remote and rapid pressure changes using the diamond anvil cell. The synchronized system enabled momentary heating and rapid cooling experiments up to 5000 K via laser heating as well as the visualization of structural changes in high-pressure samples under extreme dynamic conditions during high-speed pressure changes.

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.

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.

At-wavelength metrology of X-ray optics plays a crucial role in evaluating the performance of optics under actual beamline operating conditions, enabling in situ diagnostics and optimization. Techniques utilizing a wavefront random modulator have gained increasing attention in recent years. However, accurately mapping the measured wavefront slope to a curved X-ray mirror surface when the modulator is downstream of the mirror has posed a challenge. To address this problem, an iterative method has been developed in this study. The results demonstrate a significant improvement compared with conventional approaches and agree with offline measurements obtained from optical metrology. We believe that the proposed method enhances the accuracy of at-wavelength metrology techniques, and empowers them to play a greater role in beamline operation and optics fabrication.

Knife-edge imaging is a successful method for determining the wavefront distortion of focusing optics such as Kirkpatrick–Baez mirrors or compound refractive lenses. In this study, the wavefront error of an imperfect elliptical mirror is predicted by developing a knife-edge program using the SHADOW/OASYS platform. It is shown that the focusing optics can be aligned perfectly by minimizing the parabolic and cubic coefficients of the wavefront error. The residual wavefront error provides precise information about the figure/height errors of the focusing optics suggesting it as an accurate method for in situ optical metrology. A Python program is developed to design a customized wavefront refractive corrector to minimize the residual wavefront error. Uniform beam at and out of focus and higher peak intensity are achieved by the wavefront correction in comparison with ideal focusing. The developed code provides a quick way for wavefront error analysis and corrector design for non-ideal optics especially for the new-generation diffraction-limited sources, and saves considerable experimental time and effort.

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

Ion beam figuring (IBF) is a powerful technique for figure correction of X-ray mirrors to a high accuracy. Here, recent technical advancements in the IBF instrument developed at Diamond Light Source are presented and experimental results for figuring of X-ray mirrors are given. The IBF system is equipped with a stable DC gridded ion source (120 mm diameter), a four-axis motion stage to manipulate the optic, a Faraday cup to monitor the ion-beam current, and a camera for alignment. A novel laser speckle angular measurement instrument also provides on-board metrology. To demonstrate the IBF system's capabilities, two silicon X-ray mirrors were processed. For 1D correction, a height error of 0.08 nm r.m.s. and a slope error of 44 nrad r.m.s. were achieved. For 2D correction over a 67 mm × 17 mm clear aperture, a height error of 0.8 nm r.m.s. and a slope error of 230 nrad r.m.s. were obtained. For the 1D case, this optical quality is comparable with the highest-grade, commercially available, X-ray optics.

Transition-metal nitro­gen-doped carbons (TM-N-C) are emerging as a highly promising catalyst class for several important electrocatalytic processes, including the electrocatalytic CO2 reduction reaction (CO2RR). The unique local environment around the singly dispersed metal site in TM-N-C catalysts is likely to be responsible for their catalytic properties, which differ significantly from those of bulk or nanostructured catalysts. However, the identification of the actual working structure of the main active units in TM-N-C remains a challenging task due to the fluctional, dynamic nature of these catalysts, and scarcity of experimental techniques that could probe the structure of these materials under realistic working conditions. This issue is addressed in this work and the local atomistic and electronic structure of the metal site in a Co–N–C catalyst for CO2RR is investigated by employing time-resolved operando X-ray absorption spectroscopy (XAS) combined with advanced data analysis techniques. This multi-step approach, based on principal component analysis, spectral decomposition and supervised machine learning methods, allows the contributions of several co-existing species in the working Co–N–C catalysts to be decoupled, and their XAS spectra deciphered, paving the way for understanding the CO2RR mechanisms in the Co–N–C catalysts, and further optimization of this class of electrocatalytic systems.

The advent of diffraction-limited storage rings (DLSRs) has boosted the brilliance or coherent flux by one to two orders of magnitude with respect to the previous generation. One consequence of this brilliance enhancement is an increase in the flux density or number of photons per unit of area and time, which opens new possibilities for the spatiotemporal resolution of X-ray imaging techniques. This paper studies the time-resolved microscopy capabilities of such facilities by benchmarking the ForMAX beamline at the MAX IV storage ring. It is demonstrated that this enhanced flux density using a single harmonic of the source allows micrometre-resolution time-resolved imaging at 2000 tomograms per second and 1.1 MHz 2D acquisition rates using the full dynamic range of the detector system.

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.

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 ability to freely control the polarization of X-rays enables measurement techniques relying on circular or linear dichroism, which have become indispensable tools for characterizing the properties of chiral molecules or magnetic structures. Therefore, the demand for polarization control in X-ray free-electron lasers is increasing to enable polarization-sensitive dynamical studies on ultrafast time scales. The soft X-ray branch Athos of SwissFEL was designed with the aim of providing freely adjustable and arbitrary polarization by building its undulator solely from modules of the novel Apple X type. In this paper, the magnetic model of the linear inclined and circular Apple X polarization schemes are studied. The polarization is characterized by measuring the angular electron emission distributions of helium for various polarizations using cold target recoil ion momentum spectroscopy. The generation of fully linear polarized light of arbitrary angle, as well as elliptical polarizations of varying degree, are demonstrated.

Addressing the demand for high stability of beamline instruments at the SHINE facility, a high stability mirror regulating mechanism has been developed for mirror adjustments. Active mass damping was adopted to attenuate pitch angle vibrations of mirrors caused by structural vibrations. An internal absolute velocity feedback was used to reduce the negative impact of spillover effects and to improve performance. The experiment was conducted on a prototype structure of a mirror regulating mechanism, and results showed that the vibration RMS of the pitch angle was effectively attenuated from 47 nrad to 27 nrad above 1 Hz.

The inherent ambiguity in reconstructed images from coherent diffraction imaging (CDI) poses an intrinsic challenge, as images derived from the same dataset under varying initial conditions often display inconsistencies. This study introduces a method that employs the Noise2Noise approach combined with neural networks to effectively mitigate these ambiguities. We applied this methodology to hundreds of ambiguous reconstructed images retrieved from a single diffraction pattern using a conventional retrieval algorithm. Our results demonstrate that ambiguous features in these reconstructions are effectively treated as inter-reconstruction noise and are significantly reduced. The post-Noise2Noise treated images closely approximate the average and singular value decomposition analysis of various reconstructions, providing consistent and reliable reconstructions.

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.

Using a 1:1 cocrystal of (E)-N-(3,4-di­fluoro­phen­yl)-1-(pyridin-4-yl)methanimine with acetic acid, C12H8F2N2·C2H4O2, we investigate the influence of F atoms introduced to the aromatic ring on promoting π–π inter­actions. The cocrystal crystallizes in the triclinic space group P1. Through crystallographic analysis and com­putational studies, we reveal the mol­ecular arrangement within this co­crystal, demonstrating the presence of hydrogen bonding between the acetic acid mol­ecule and the pyridyl group, along with π–π inter­actions between the aromatic rings. Our findings highlight the importance of F atoms in promoting π–π inter­actions without necessitating full halogenation of the aromatic ring.

Macromolecular crystallography generally requires the recovery of missing phase information from diffraction data to reconstruct an electron-density map of the crystallized molecule. Most recent structures have been solved using molecular replacement as a phasing method, requiring an a priori structure that is closely related to the target protein to serve as a search model; when no such search model exists, molecular replacement is not possible. New advances in computational machine-learning methods, however, have resulted in major advances in protein structure predictions from sequence information. Methods that generate predicted structural models of sufficient accuracy provide a powerful approach to molecular replacement. Taking advantage of these advances, AlphaFold predictions were applied to enable structure determination of a bacterial protein of unknown function (UniProtKB Q63NT7, NCBI locus BPSS0212) based on diffraction data that had evaded phasing attempts using MIR and anomalous scattering methods. Using both X-ray and micro-electron (microED) diffraction data, it was possible to solve the structure of the main fragment of the protein using a predicted model of that domain as a starting point. The use of predicted structural models importantly expands the promise of electron diffraction, where structure determination relies critically on molecular replacement.

Complex I (proton-pumping NADH:ubiquinone oxidoreductase) is the first component of the mitochondrial respiratory chain. In recent years, high-resolution cryo-EM studies of complex I from various species have greatly enhanced the understanding of the structure and function of this important membrane-protein complex. Less well studied is the structural basis of complex I biogenesis. The assembly of this complex of more than 40 subunits, encoded by nuclear or mitochondrial DNA, is an intricate process that requires at least 20 different assembly factors in humans. These are proteins that are transiently associated with building blocks of the complex and are involved in the assembly process, but are not part of mature complex I. Although the assembly pathways have been studied extensively, there is limited information on the structure and molecular function of the assembly factors. Here, the insights that have been gained into the assembly process using cryo-EM are reviewed.

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.

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

Histidine can be protonated on either or both of the two N atoms of the imidazole moiety. Each of the three possible forms occurs as a result of the stereochemical environment of the histidine side chain. In an atomic model, comparing the possible protonation states in situ, looking at possible hydrogen bonding and metal coordination, it is possible to predict which is most likely to be correct. A more direct method is described that uses quantum-mechanical methods to calculate, also in situ, the minimum geometry and energy for comparison, and therefore to more accurately identify the most likely proton­ation state.

For protein crystals in which more than two thirds of the volume is occupied by solvent, the featureless nature of the solvent region often generates a constraint that is powerful enough to allow direct phasing of X-ray diffraction data. Practical implementation relies on the use of iterative projection algorithms with good global convergence properties to solve the difficult nonconvex phase-retrieval problem. In this paper, some aspects of phase retrieval using iterative projection algorithms are systematically explored, where the diffraction data and density-value distributions in the protein and solvent regions provide the sole constraints. The analysis is based on the addition of random error to the phases of previously determined protein crystal structures, followed by evaluation of the ability to recover the correct phase set as the distance from the solution increases. The properties of the difference-map (DM), relaxed–reflect–reflect (RRR) and relaxed averaged alternating reflectors (RAAR) algorithms are compared. All of these algorithms prove to be effective for crystallographic phase retrieval, and the useful ranges of the adjustable parameter which controls their behavior are established. When these algorithms converge to the solution, the algorithm trajectory becomes stationary; however, the density function continues to fluctuate significantly around its mean position. It is shown that averaging over the algorithm trajectory in the stationary region, following convergence, improves the density estimate, with this procedure outperforming previous approaches for phase or density refinement.

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

Carbonic anhydrase (CA) was among the first proteins whose X-ray crystal structure was solved to atomic resolution. CA proteins have essentially the same fold and similar active centers that differ in only several amino acids. Primary sulfonamides are well defined, strong and specific binders of CA. However, minor variations in chemical structure can significantly alter their binding properties. Over 1000 sulfonamides have been designed, synthesized and evaluated to understand the correlations between the structure and thermodynamics of their binding to the human CA isozyme family. Compound binding was determined by several binding assays: fluorescence-based thermal shift assay, stopped-flow enzyme activity inhibition assay, isothermal titration calorimetry and competition assay for enzyme expressed on cancer cell surfaces. All assays have advantages and limitations but are necessary for deeper characterization of these protein–ligand interactions. Here, the concept and importance of intrinsic binding thermodynamics is emphasized and the role of structure–thermodynamics correlations for the novel inhibitors of CA IX is discussed – an isozyme that is overexpressed in solid hypoxic tumors, and thus these inhibitors may serve as anticancer drugs. The abundant structural and thermodynamic data are assembled into the Protein–Ligand Binding Database to understand general protein–ligand recognition principles that could be used in drug discovery.

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.

Here, the novel technique of extended-range high-energy-resolution fluorescence detection (XR-HERFD) has successfully observed the n = 2 satellite in manganese to a high accuracy. The significance of the satellite signature presented is many hundreds of standard errors and well beyond typical discovery levels of three to six standard errors. This satellite is a sensitive indicator for all manganese-containing materials in condensed matter. The uncertainty in the measurements has been defined, which clearly observes multiple peaks and structure indicative of complex physical quantum-mechanical processes. Theoretical calculations of energy eigenvalues, shake-off probability and Auger rates are also presented, which explain the origin of the satellite from physical n = 2 shake-off processes. The evolution in the intensity of this satellite is measured relative to the full Kα spectrum of manganese to investigate satellite structure, and therefore many-body processes, as a function of incident energy. Results demonstrate that the many-body reduction factor S02 should not be modelled with a constant value as is currently done. This work makes a significant contribution to the challenge of understanding many-body processes and interpreting HERFD or resonant inelastic X-ray scattering spectra in a quantitative manner.

Light–oxygen–voltage (LOV) domains are small photosensory flavoprotein modules that allow the conversion of external stimuli (sunlight) into intra­cellular signals responsible for various cell behaviors (e.g. phototropism and chloro­plast relocation). This ability relies on the light-induced formation of a covalent thio­ether adduct between a flavin chromophore and a reactive cysteine from the protein environment, which triggers a cascade of structural changes that result in the activation of a serine/threonine (Ser/Thr) kinase. Recent developments in time-resolved crystallography may allow the activation cascade of the LOV domain to be observed in real time, which has been elusive. In this study, we report a robust protocol for the production and stable delivery of microcrystals of the LOV domain of phototropin Phot-1 from Chlamydomonas reinhardtii (CrPhotLOV1) with a high-viscosity injector for time-resolved serial synchrotron crystallography (TR-SSX). The detailed process covers all aspects, from sample optimization to data collection, which may serve as a guide for soluble protein preparation for TR-SSX. In addition, we show that the crystals obtained preserve the photoreactivity using infrared spectroscopy. Furthermore, the results of the TR-SSX experiment provide high-resolution insights into structural alterations of CrPhotLOV1 from Δt = 2.5 ms up to Δt = 95 ms post-photoactivation, including resolving the geometry of the thio­ether adduct and the C-terminal region implicated in the signal transduction process.

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

Mineral identification and quantification are key to the understanding and, hence, the capacity to predict material properties. The method of choice for mineral quantification is powder X-ray diffraction (XRD), generally using a Rietveld refinement approach. However, a successful Rietveld refinement requires preliminary identification of the phases that make up the sample. This is generally carried out manually, and this task becomes extremely long or virtually impossible in the case of very large datasets such as those from synchrotron X-ray diffraction computed tomography. To circumvent this issue, this article proposes a novel neural network (NN) method for automating phase identification and quantification. An XRD pattern calculation code was used to generate large datasets of synthetic data that are used to train the NN. This approach offers significant advantages, including the ability to construct databases with a substantial number of XRD patterns and the introduction of extensive variability into these patterns. To enhance the performance of the NN, a specifically designed loss function for proportion inference was employed during the training process, offering improved efficiency and stability compared with traditional functions. The NN, trained exclusively with synthetic data, proved its ability to identify and quantify mineral phases on synthetic and real XRD patterns. Trained NN errors were equal to 0.5% for phase quantification on the synthetic test set, and 6% on the experimental data, in a system containing four phases of contrasting crystal structures (calcite, gibbsite, dolomite and hematite). The proposed method is freely available on GitHub and allows for major advances since it can be applied to any dataset, regardless of the mineral phases present.

X-ray and neutron crystallography, as well as cryogenic electron microscopy (cryo-EM), are the most common methods to obtain atomic structures of biological macromolecules. A feature they all have in common is that, at typical resolutions, the experimental data need to be supplemented by empirical restraints, ensuring that the final structure is chemically reasonable. The restraints are accurate for amino acids and nucleic acids, but often less accurate for substrates, inhibitors, small-molecule ligands and metal sites, for which experimental data are scarce or empirical potentials are harder to formulate. This can be solved using quantum mechanical calculations for a small but interesting part of the structure. Such an approach, called quantum refinement, has been shown to improve structures locally, allow the determination of the protonation and oxidation states of ligands and metals, and discriminate between different interpretations of the structure. Here, we present a new implementation of quantum refinement interfacing the widely used structure-refinement software Phenix and the freely available quantum mechanical software ORCA. Through application to manganese superoxide dismutase and V- and Fe-nitro­genase, we show that the approach works effectively for X-ray and neutron crystal structures, that old results can be reproduced and structural discrimination can be performed. We discuss how the weight factor between the experimental data and the empirical restraints should be selected and how quantum mechanical quality measures such as strain energies should be calculated. We also present an application of quantum refinement to cryo-EM data for particulate methane monooxygenase and show that this may be the method of choice for metal sites in such structures because no accurate empirical restraints are currently available for metals.

The accuracy of the information in the Protein Data Bank (PDB) is of great importance for the myriad downstream applications that make use of protein structural information. Despite best efforts, the occasional introduction of errors is inevitable, especially where the experimental data are of limited resolution. A novel protein structure validation approach based on spotting inconsistencies between the residue contacts and distances observed in a structural model and those computationally predicted by methods such as AlphaFold2 has previously been established. It is particularly well suited to the detection of register errors. Importantly, this new approach is orthogonal to traditional methods based on stereochemistry or map–model agreement, and is resolution independent. Here, thousands of likely register errors are identified by scanning 3–5 Å resolution structures in the PDB. Unlike most methods, the application of this approach yields suggested corrections to the register of affected regions, which it is shown, even by limited implementation, lead to improved refinement statistics in the vast majority of cases. A few limitations and confounding factors such as fold-switching proteins are characterized, but this approach is expected to have broad application in spotting potential issues in current accessions and, through its implementation and distribution in CCP4, helping to ensure the accuracy of future depositions.

The embedded call to a special version of the web-based Bilbao Crystallographic Server tool k-SUBGROUPSMAG from within GSAS-II to form a list of all possible commensurate magnetic subgroups of a parent magnetic grey group is described. It facilitates the selection and refinement of the best commensurate magnetic structure model by having all the analysis tools including Rietveld refinement in one place as part of GSAS-II. It also provides the chosen magnetic space group as one of the 1421 possible standard Belov–Neronova–Smirnova forms or equivalent non-standard versions.

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

Van Vleck modes describe all possible displacements of octahedrally coordinated ligands about a core atom. They are a useful analytical tool for analysing the distortion of octahedra, particularly for first-order Jahn–Teller distortions, but determination of the Van Vleck modes of an octahedron is complicated by the presence of angular distortion of the octahedron. This problem is most commonly resolved by calculating the bond distortion modes (Q2, Q3) along the bond axes of the octahedron, disregarding the angular distortion and losing information on the octahedral shear modes (Q4, Q5 and Q6) in the process. In this paper, the validity of assuming bond lengths to be orthogonal in order to calculate the Van Vleck modes is discussed, and a method is described for calculating Van Vleck modes without disregarding the angular distortion. A Python package for doing this, VanVleckCalculator, is introduced and some examples of its use are given. Finally, it is shown that octahedral shear and angular distortion are often, but not always, correlated, and a parameter η is proposed as the shear fraction. It is demonstrated that η can be used to predict whether the values will be correlated when varying a tuning parameter such as temperature or pressure.

Characterization of a material structure with pair distribution function (PDF) analysis typically involves refining a structure model against an experimental data set, but finding or constructing a suitable atomic model for PDF modelling can be an extremely labour-intensive task, requiring carefully browsing through large numbers of possible models. Presented here is POMFinder, a machine learning (ML) classifier that rapidly screens a database of structures, here polyoxometallate (POM) clusters, to identify candidate structures for PDF data modelling. The approach is shown to identify suitable POMs from experimental data, including in situ data collected with fast acquisition times. This automated approach has significant potential for identifying suitable models for structure refinement to extract quantitative structural parameters in materials chemistry research. POMFinder is open source and user friendly, making it accessible to those without prior ML knowledge. It is also demonstrated that POMFinder offers a promising modelling framework for combined modelling of multiple scattering techniques.

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

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

Data collection at X-ray free electron lasers has particular experimental challenges, such as continuous sample delivery or the use of novel ultrafast high-dynamic-range gain-switching X-ray detectors. This can result in a multitude of data artefacts, which can be detrimental to accurately determining structure-factor amplitudes for serial crystallography or single-particle imaging experiments. Here, a new data-classification tool is reported that offers a variety of machine-learning algorithms to sort data trained either on manual data sorting by the user or by profile fitting the intensity distribution on the detector based on the experiment. This is integrated into an easy-to-use graphical user interface, specifically designed to support the detectors, file formats and software available at most X-ray free electron laser facilities. The highly modular design makes the tool easily expandable to comply with other X-ray sources and detectors, and the supervised learning approach enables even the novice user to sort data containing unwanted artefacts or perform routine data-analysis tasks such as hit finding during an experiment, without needing to write code.

The suitability of point focus X-ray beam and area detector techniques for the determination of the uniaxial symmetry axis (fibre texture) of the natural mineral satin spar is demonstrated. Among the various diffraction techniques used in this report, including powder diffraction, 2D pole figures, rocking curves looped on φ and 2D X-ray diffraction, a single simple symmetric 2D scan collecting the reciprocal plane perpendicular to the apparent fibre axis provided sufficient information to determine the crystallographic orientation of the fibre axis. A geometrical explanation of the `wing' feature formed by diffraction spots from the fibre-textured satin spar in 2D scans is provided. The technique of wide-range reciprocal space mapping restores the `wing' featured diffraction spots on the 2D detector back to reciprocal space layers, revealing the nature of the fibre-textured samples.

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

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

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

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

With the emergence of ultrafast X-ray sources, interest in following fast processes in small molecules and macromolecules has increased. Most of the current research into ultrafast structural dynamics of macromolecules uses X-ray free-electron lasers. In parallel, small-scale laboratory-based laser-driven ultrafast X-ray sources are emerging. Continuous development of these sources is underway, and as a result many exciting applications are being reported. However, because of their low flux, such sources are not commonly used to study the structural dynamics of macromolecules. This article examines the feasibility of time-resolved powder diffraction of macromolecular microcrystals using a laboratory-scale laser-driven ultrafast X-ray source.

High-energy X-ray diffraction methods can non-destructively map the 3D microstructure and associated attributes of metallic polycrystalline engineering materials in their bulk form. These methods are often combined with external stimuli such as thermo-mechanical loading to take snapshots of the evolving microstructure and attributes over time. However, the extreme data volumes and the high costs of traditional data acquisition and reduction approaches pose a barrier to quickly extracting actionable insights and improving the temporal resolution of these snapshots. This article presents a fully automated technique capable of rapidly detecting the onset of plasticity in high-energy X-ray microscopy data. The technique is computationally faster by at least 50 times than the traditional approaches and works for data sets that are up to nine times sparser than a full data set. This new technique leverages self-supervised image representation learning and clustering to transform massive data sets into compact, semantic-rich representations of visually salient characteristics (e.g. peak shapes). These characteristics can rapidly indicate anomalous events, such as changes in diffraction peak shapes. It is anticipated that this technique will provide just-in-time actionable information to drive smarter experiments that effectively deploy multi-modal X-ray diffraction methods spanning many decades of length scales.

This article demonstrates the feasibility of obtaining accurate pair distribution functions of thin amorphous films down to 80 nm, using modern laboratory-based X-ray sources. The pair distribution functions are obtained using a single diffraction scan without the requirement of additional scans of the substrate or of the air. By using a crystalline substrate combined with an oblique scattering geometry, most of the Bragg scattering of the substrate is avoided, rendering the substrate Compton scattering the primary contribution. By utilizing a discriminating energy filter, available in the latest generation of modern detectors, it is demonstrated that the Compton intensity can further be reduced to negligible levels at higher wavevector values. Scattering from the sample holder and the air is minimized by the systematic selection of pixels in the detector image based on the projected detection footprint of the sample and the use of a 3D-printed sample holder. Finally, X-ray optical effects in the absorption factors and the ratios between the Compton intensity of the substrate and film are taken into account by using a theoretical tool that simulates the electric field inside the film and the substrate, which aids in planning both the sample design and the measurement protocol.