A seventh blind test of crystal structure prediction was organized by the Cambridge Crystallographic Data Centre featuring seven target systems of varying complexity: a silicon and iodine-containing molecule, a copper coordination complex, a near-rigid molecule, a cocrystal, a polymorphic small agrochemical, a highly flexible polymorphic drug candidate, and a polymorphic morpholine salt. In this first of two parts focusing on structure generation methods, many crystal structure prediction (CSP) methods performed well for the small but flexible agrochemical compound, successfully reproducing the experimentally observed crystal structures, while few groups were successful for the systems of higher complexity. A powder X-ray diffraction (PXRD) assisted exercise demonstrated the use of CSP in successfully determining a crystal structure from a low-quality PXRD pattern. The use of CSP in the prediction of likely cocrystal stoichiometry was also explored, demonstrating multiple possible approaches. Crystallographic disorder emerged as an important theme throughout the test as both a challenge for analysis and a major achievement where two groups blindly predicted the existence of disorder for the first time. Additionally, large-scale comparisons of the sets of predicted crystal structures also showed that some methods yield sets that largely contain the same crystal structures.

Hydraulic fracking exposes shale plays to acidic hydraulic fracking fluid (HFF), releasing toxic uranium (U) along with the desired oil and gas. With no existing methods to ensure U remains sequestered in the shale, this study sought to add organic ligands to HFF to explore potential U retention in shale plays. To test this possibility, incubations were set up in which uranyl acetate and one organic bipyridine ligand (either 2,2'-, 2,3'-, 2,4'-, or 4,4'-bipyridine) were added to pristine HFF as the crystallization medium. After several months and complete evaporation of all volatiles, bulk yellow crystalline material was obtained from the incubations, three of which yielded crystals suitable for single-crystal analysis, resulting in two novel structures and a high-quality structure of a previously described compound. The UO2VI acetate complexes bis(acetato-κ2O,O')(2,2'-bipyridine-κ2N,N')dioxidouranium(VI), [U(C2H3O2)2O2(C10H8N2)2] or [2,2'-bipyridine]UVIO2(CH3CO2)2, (I), and bis(acetato-κ2O,O')(2,4'-bipyridine-κN1')dioxidouranium(VI), [U(C2H3O2)2O2(C10H8N2)2] or [2,4'-bipyridine]2UVIO2(CH3CO2)2, (III), contain eight-coordinate UVI in a pseudo-hexagonal bipyramidal coordination geometry and are molecular, packing via weak C—H...O/N interactions, whereas catena-poly[bis(2,3'-bipyridinium) [di-μ-acetato-μ3-hydroxido-μ-hydroxido-di-μ3-oxido-hexaoxidotriuranium(VI)]–2,3'-bipyridine–water (1/1/1)], (C10H9N2)2[U3(C2H3O2)2O8(OH)2]·C10H8N2·H2O or {[2,3'-bipyridinium]2[2,3'-bipyridine][(UVIO2)3(O)2(OH)2(CH3CO2)2·H2O]}n, (II), forms an ionic one-dimensional polymer with seven-coordinate pentagonal bipyramidal UVI centers and hydrogen-bonding interactions within each chain. The formation of these crystals could indicate the potential for bipyridine to bind with U in shale during fracking, which will be explored in a future study via ICP-MS (inductively coupled plasma mass spectrometry) analyses of U concentration in HFF/bipyridine/shale incubations. The variation seen here between the molecular structures may indicate variance in the ability of bipyridine isomers to form complexes with U, which could impact their ability to retain U within shale in the context of fracking.

In electron diffraction, thermal atomic motion produces incoherent scattering over a relatively wide angular range, which appears as a diffuse background that is usually subtracted from measurements of Bragg spot intensities in structure solution methods. The transfer of electron flux from Bragg spots to diffuse scatter is modelled using complex scattering factors f + if' in the Bloch wave methodology. In a two-beam Einstein model the imaginary `absorptive' scattering factor f' can be obtained by the evaluation of an integral containing f over all possible scattering angles. While more sophisticated models of diffuse scatter are widely used in the electron microscopy community, it is argued in this paper that this simple model is appropriate for current structure solution and refinement methods. The two-beam model is a straightforward numerical calculation, but even this simplistic approach can become time consuming for simulations of materials with large numbers of atoms in the unit cell and/or many incident beam orientations. Here, a parameterized form of f' is provided for 103 elements as neutral, spherical atoms that reduces calculation time considerably.

Small-angle X-ray scattering (SAXS) is widely used to analyze the shape and size of nanoparticles in solution. A multitude of models, describing the SAXS intensity resulting from nanoparticles of various shapes, have been developed by the scientific community and are used for data analysis. Choosing the optimal model is a crucial step in data analysis, which can be difficult and time-consuming, especially for non-expert users. An algorithm is proposed, based on machine learning, representation learning and SAXS-specific preprocessing methods, which instantly selects the nanoparticle model best suited to describe SAXS data. The different algorithms compared are trained and evaluated on a simulated database. This database includes 75 000 scattering spectra from nine nanoparticle models, and realistically simulates two distinct device configurations. It will be made freely available to serve as a basis of comparison for future work. Deploying a universal solution for automatic nanoparticle model selection is a challenge made more difficult by the diversity of SAXS instruments and their flexible settings. The poor transferability of classification rules learned on one device configuration to another is highlighted. It is shown that training on several device configurations enables the algorithm to be generalized, without degrading performance compared with configuration-specific training. Finally, the classification algorithm is evaluated on a real data set obtained by performing SAXS experiments on nanoparticles for each of the instrumental configurations, which have been characterized by transmission electron microscopy. This data set, although very limited, allows estimation of the transferability of the classification rules learned on simulated data to real data.

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.

In Part I of this series, all topologically possible 1-periodic infinite graphs (chain graphs) representing chains of tetrahedra with up to 6–8 vertices (tetrahedra) per repeat unit were generated. This paper examines possible restraints on embedding these chain graphs into Euclidean space such that they are compatible with the metrics of chains of tetrahedra in observed crystal structures. Chain-silicate minerals with T = Si4+ (plus P5+, V5+, As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+) have a grand nearest-neighbour 〈T–T〉 distance of 3.06±0.15 Å and a minimum T⋯T separation of 3.71 Å between non-nearest-neighbour tetrahedra, and in order for embedded chain graphs (called unit-distance graphs) to be possible atomic arrangements in crystals, they must conform to these metrics, a process termed equalization. It is shown that equalization of all acyclic chain graphs is possible in 2D and 3D, and that equalization of most cyclic chain graphs is possible in 3D but not necessarily in 2D. All unique ways in which non-isomorphic vertices may be moved are designated modes of geometric modification. If a mode (m) is applied to an equalized unit-distance graph such that a new geometrically distinct unit-distance graph is produced without changing the lengths of any edges, the mode is designated as valid (mv); if a new geometrically distinct unit-distance graph cannot be produced, the mode is invalid (mi). The parameters mv and mi are used to define ranges of rigidity of the unit-distance graphs, and are related to the edge-to-vertex ratio, e/n, of the parent chain graph. The program GraphT–T was developed to embed any chain graph into Euclidean space subject to the metric restraints on T–T and T⋯T. Embedding a selection of chain graphs with differing e/n ratios shows that the principal reason why many topologically possible chains cannot occur in crystal structures is due to violation of the requirement that T⋯T > 3.71 Å. Such a restraint becomes increasingly restrictive as e/n increases and indicates why chains with stoichiometry TO<2.5 do not occur in crystal structures.

Following the work of Day & Hawthorne [Acta Cryst. (2022), A78, 212–233] and Day et al. [Acta Cryst. (2024), A80, 258–281], the program GraphT–T has been developed to embed graphical representations of observed and hypothetical chains of (SiO4)4− tetrahedra into 2D and 3D Euclidean space. During embedding, the distance between linked vertices (T–T distances) and the distance between unlinked vertices (T⋯T separations) in the resultant unit-distance graph are restrained to the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is restrained to be equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. The notional interactions between vertices are described by a 3D spring-force algorithm in which the attractive forces between linked vertices behave according to Hooke's law and the repulsive forces between unlinked vertices behave according to Coulomb's law. Embedding parameters (i.e. spring coefficient, k, and Coulomb's constant, K) are iteratively refined during embedding to determine if it is possible to embed a given graph to produce a unit-distance graph with T–T distances and T⋯T separations that are compatible with the observed T–T distances and T⋯T separations in crystal structures. The resultant unit-distance graphs are denoted as compatible and may form crystal structures if and only if all distances between linked vertices (T–T distances) agree with the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. If the unit-distance graph does not satisfy these conditions, it is considered incompatible and the corresponding chain of tetrahedra is unlikely to form crystal structures. Using GraphT–T, Day et al. [Acta Cryst. (2024), A80, 258–281] have shown that several topological properties of chain graphs influence the flexibility (and rigidity) of the corresponding chains of Si tetrahedra and may explain why particular compatible chain arrangements (and the minerals in which they occur) are more common than others and/or why incompatible chain arrangements do not occur in crystals despite being topologically possible.

The superstructure spots that appear in diffraction patterns of tilted perovskites are well documented and easily calculated using crystallographic software. Here, by considering a distortion mode as a perturbation of the prototype perovskite structure, it is shown how the structure-factor equation yields Boolean conditions for the presence of superstructure reflections. This approach may have some advantages for the analysis of electron diffraction patterns of perovskites.

Imaging scaffolds composed of designed protein cages fused to designed ankyrin repeat proteins (DARPins) have enabled the structure determination of small proteins by cryogenic electron microscopy (cryo-EM). One particularly well characterized scaffold type is a symmetric tetrahedral assembly composed of 24 subunits, 12 A and 12 B, which has three cargo-binding DARPins positioned on each vertex. Here, the X-ray crystal structure of a representative tetrahedral scaffold in the apo state is reported at 3.8 Å resolution. The X-ray crystal structure complements recent cryo-EM findings on a closely related scaffold, while also suggesting potential utility for crystallographic investigations. As observed in this crystal structure, one of the three DARPins, which serve as modular adaptors for binding diverse `cargo' proteins, present on each of the vertices is oriented towards a large solvent channel. The crystal lattice is unusually porous, suggesting that it may be possible to soak crystals of the scaffold with small (≤30 kDa) protein cargo ligands and subsequently determine cage–cargo structures via X-ray crystallography. The results suggest the possibility that cryo-EM scaffolds may be repurposed for structure determination by X-ray crystallography, thus extending the utility of electron-microscopy scaffold designs for alternative structural biology applications.

Fixed targets (`chips') offer efficient, high-throughput microcrystal delivery for serial crystallography at synchrotrons and X-ray free-electron lasers (XFELs). Within this family, sheet-on-sheet (SOS) chips offer noteworthy advantages in cost, adaptability, universality and ease of crystal loading. We describe our latest generation of SOS devices, which are now in active use at both synchrotrons and XFELs.

This review summarizes the methodological aspects of laboratory X-ray powder micro-diffraction and demonstrates the assets of the method in the research of painted artworks for evaluation of their provenance or diagnosing their degradation.

We present a demonstration of high-pressure grazing-incidence small-angle neutron scattering for soft matter thin films. The results suggest changes in water reorganization at different pressures.

A symmetry guide for the secondary structural degrees of freedom and related physical properties generated by tilts of BX6 octahedra in perovskites is proposed.

The electric field responses of the average and local lattice strains and polar nanoregions of relaxor ferroelectric PMN-30PT single crystals were revealed by multi-scale and time-resolved X-ray diffraction under DC and AC electric fields.

AnACor2.0 significantly accelerates the calculation of analytical absorption corrections in long-wavelength crystallography, achieving up to 175× speed improvements. This enhancement is achieved through innovative sampling techniques, bisection and gridding methods, and optimized CUDA implementations, ensuring efficient and accurate results.

A new processing technique for synchrotron scanning 3D X-ray diffraction data is introduced, utilizing symmetric Bragg reflections hkl and hkl, known as Friedel pairs. This technique is designed to tackle the difficulties associated with large, highly deformed, polyphase materials, especially geological samples.

This study examines the quality of charge density obtained by fitting the multipole model to wavefunctions in different basis sets. The complex analysis reveals that changing the basis set quality from double- to triple-zeta can notably improve the charge density related properties of a multipole model.

Combined 100 ms resolved grazing-incidence small/wide-angle X-ray scattering and optical interferometry reveal that the additive diiodooctane can significantly double the solvent evaporation rate, thereby effectively suppressing the rapid spinodal decomposition process in the early stage of spin-coasting, favouring slow phase segregation kinetics with nucleation and growth.

The position- and time-resolved monitoring of a mechanochemical reaction using synchrotron powder X-ray diffraction revealed a position-independent increase rate of product in the jar of a shaker mill.

The L-edge EXAFS of the entire set of lanthanide oxides were collected and modeled, taking into consideration the aggregation of inequivalent absorbing sites, geometric parameterization of the crystal lattice and multielectron excitation removal.

For the first time, a multimodal reconstruction of a magnetic thin-film structure has been found using polarised neutron reflectivity. This has been achieved by implementing the Bayesian approach in combination with error correction based on the maximum likelihood method and instrument function optimization.

This article describes the implementation of GRIP as a module of GRASP, enabling the fully three-dimensional visualization and analysis of data collected on small-angle neutron scattering instruments.

This article reports an investigation into the effects of specific radiation damage to halogenated ligands in crystal structures of protein-inhibitor complexes.

We explain analysis of RIXS, HERFD and XR-HERFD data to discover new physical processes in manganese and manganese-containing materials, by applying our new technique XR-HERFD, developed from high resolution RIXS and HERFD.

The impact of sample thickness and experimental noise on angular correlation analysis from scanning electron nanobeam diffraction patterns of disordered carbon are investigated and analyzed regarding the interpretability of the analysis results.

The crystal structure of a metabolite of the insecticide/acaricide etoxazole, designated R13 is presented along with a Hirshfeld surface analysis of inter­molecular inter­actions present in the crystal structure.

In the title compound, [Cu2(L)2]·2CH2Cl2, the CuII ions coordinate two (S,O)-chelating aroyl­thio­urea moieties of doubly deprotonated furan-2,5-di­carbonyl­bis­(N,N-di­ethyl­thio­urea) (H2L) ligands. The coordination geometry of the metal centers is best described as a flat isosceles trapezoid with a cis arrangement of the donor atoms.

N-terminally hexahistidine-tagged O. volvulus macrophage migration inhibitory factor-1 has a unique jellyfish-like structure with the prototypical macrophage migration inhibitory factor trimer as the `head' and a C-terminal extension as the `tail'.

Analytical absorption corrections are employed in scaling diffraction data for highly absorbing samples, such as those used in long-wavelength crystallography, where empirical corrections pose a challenge. AnACor2.0 is an accelerated software package developed to calculate analytical absorption corrections. It accomplishes this by ray-tracing the paths of diffracted X-rays through a voxelized 3D model of the sample. Due to the computationally intensive nature of ray-tracing, the calculation of analytical absorption corrections for a given sample can be time consuming. Three experimental datasets (insulin at λ = 3.10 Å, thermolysin at λ = 3.53 Å and thaumatin at λ = 4.13 Å) were processed to investigate the effectiveness of the accelerated methods in AnACor2.0. These methods demonstrated a maximum reduction in execution time of up to 175× compared with previous methods. As a result, the absorption factor calculation for the insulin dataset can now be completed in less than 10 s. These acceleration methods combine sampling, which evaluates subsets of crystal voxels, with modifications to standard ray-tracing. The bisection method is used to find path lengths, reducing the complexity from O(n) to O(log2 n). The gridding method involves calculating a regular grid of diffraction paths and using interpolation to find an absorption correction for a specific reflection. Additionally, optimized and specifically designed CUDA implementations for NVIDIA GPUs are utilized to enhance performance. Evaluation of these methods using simulated and real datasets demonstrates that systematic sampling of the 3D model provides consistently accurate results with minimal variance across different sampling ratios. The mean difference of absorption factors from the full calculation (without sampling) is at most 2%. Additionally, the anomalous peak heights of sulfur atoms in the Fourier map show a mean difference of only 1% compared with the full calculation. This research refines and accelerates the process of analytical absorption corrections, introducing innovative sampling and computational techniques that significantly enhance efficiency while maintaining accurate results.

Grazing-incidence small-angle neutron scattering (GISANS) under pressure (HP-GISANS) at the solid (Si)–liquid (D2O) interface is demonstrated for the pressure-induced lateral morphological characterization of the nanostructure in thin (<100 nm) soft matter films. We demonstrate feasibility by investigating a hydrophobic {poly[(2,2,3,3,4,4,5,5-octafluoro)pentyl methacrylate]} (POFPMA)–hydrophilic {poly[2-(dimethylamino)ethyl methacrylate]} (PDMAEMA) brush mixture of strong incompatibility between the homopolymers, anchored on Si, at T = 45°C for two pressures, P = 1 bar and P = 800 bar. Our GISANS results reveal nanostructural rearrangements with increasing P, underlining P-induced effects in tethered polymer brush layers swollen with bulk solvent.

We investigated the position and time dependence of a mechanochemical reaction induced by ball milling using in situ synchrotron powder X-ray diffraction with changing X-ray irradiation position. The mechanochemical reduction of AgCl with Cu was monitored in situ with the X-rays incident at two different vertical positions on the jar. Our previously developed multi-distance Rietveld method was applied to analyze the in situ diffraction data with a 1 min resolution. Both the vertical and the horizontal sample positions were determined using the sample-to-detector distances from the in situ data. Position dependence was found in the powder spreading and induction time. We reveal that the increase rate of the product is independent of the sample position when measured with a 1 min time resolution, confirming the validity of in situ monitoring of part of the space in a milling jar for a gradual mechanochemical reaction.

The present study introduces a processing strategy for synchrotron scanning 3D X-ray diffraction (s3DXRD) data, aimed at addressing the challenges posed by large, highly deformed, polyphase materials such as crystalline rocks. Leveraging symmetric Bragg reflections known as Friedel pairs, our method enables diffraction events to be precisely located within the sample volume. This method allows for fitting the phase, crystal structure and unit-cell parameters at the intra-grain scale on a voxel grid. The processing workflow incorporates several new modules, designed to (i) efficiently match Friedel pairs in large s3DXRD datasets containing up to 108 diffraction peaks; (ii) assign phases to each pixel or voxel, resolving potential ambiguities arising from overlap in scattering angles between different crystallographic phases; and (iii) fit the crystal orientation and unit cell locally on a point-by-point basis. We demonstrate the effectiveness of our technique on fractured granite samples, highlighting the ability of the method to characterize complex geological materials and show their internal structure and mineral composition. Additionally, we include the characterization of a metal gasket made of a commercial aluminium alloy, which surrounded the granite sample during experiments. The results show the effectiveness of the technique in recovering information about the internal texture and residual strain of materials that have undergone high levels of plastic deformation.

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

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

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

Lead-based relaxor ferroelectrics exhibit giant piezoelectric properties owing to their heterogeneous structures. The average and local structures measured by single-crystal X-ray diffraction under DC and AC electric fields are reviewed in this article. The position-dependent local lattice strain and the distribution of polar nanodomains and nanoregions show strong electric field dependence, which contributes to the giant piezoelectric properties.

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

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

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

Small-angle X-ray scattering (SAXS) is a widely used method for nanoparticle characterization. A common approach to analysing nanoparticles in solution by SAXS involves fitting the curve using a parametric model that relates real-space parameters, such as nanoparticle size and electron density, to intensity values in reciprocal space. Selecting the optimal model is a crucial step in terms of analysis quality and can be time-consuming and complex. Several studies have proposed effective methods, based on machine learning, to automate the model selection step. Deploying these methods in software intended for both researchers and industry raises several issues. The diversity of SAXS instrumentation requires assessment of the robustness of these methods on data from various machine configurations, involving significant variations in the q-space ranges and highly variable signal-to-noise ratios (SNR) from one data set to another. In the case of laboratory instrumentation, data acquisition can be time-consuming and there is no universal criterion for defining an optimal acquisition time. This paper presents an approach that revisits the nanoparticle model selection method proposed by Monge et al. [Acta Cryst. (2024), A80, 202–212], evaluating and enhancing its robustness on data from device configurations not seen during training, by expanding the data set used for training. The influence of SNR on predictor robustness is then assessed, improved, and used to propose a stopping criterion for optimizing the trade-off between exposure time and data quality.

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

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

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

A plug-flow fixed-bed cell for synchrotron powder X-ray diffraction (PXRD) and X-ray absorption fine structure (XAFS) idoneous for the study of heterogeneous catalysts at high temperature, pressure and under gas flow is designed, constructed and demonstrated. The operating conditions up to 1000°C and 50 bar are ensured by a set of mass flow controllers, pressure regulators and two infra-red lamps that constitute a robust and ultra-fast heating and cooling method. The performance of the system and cell for carbon dioxide hydrogenation reactions under specified temperatures, gas flows and pressures is demonstrated both for PXRD and XAFS at the P02.1 (PXRD) and the P64 (XAFS) beamlines of the Deutsches Elektronen-Synchrotron (DESY).

In the realm of X-ray ptychography experiments, a considerable amount of ptychography scans are typically performed within a field of view encompassing the target sample. While it is crucial to obtain overlapping scans in small increments over the region of interest for achieving high-resolution sample reconstruction, a significant number of these scans often redundantly measure the empty background within the wide field of view. To address this inefficiency, an innovative algorithm is proposed that introduces automatic guidance for data acquisition. The algorithm first directs the scan point to actively search for the object of interest within the field of view. Subsequently, it intelligently scans along the perimeter of the sample, strategically acquiring measurements exclusively within the boundary of the region of interest. By employing this approach, a reduction in the number of measurements required to obtain high-resolution reconstruction images is demonstrated, as compared with conventional raster scanning methods. Furthermore, the automatic guidance provided by the algorithm offers the added advantage of saving valuable time during the reconstruction process. Through practical implementation on real experiments, these findings showcase the efficacy of the proposed algorithm in enhancing the efficiency and accuracy of X-ray ptychography experiments. This novel approach holds immense potential for advancing sample analysis and imaging techniques in various scientific disciplines.

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

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

Bone material contains a hierarchical network of micro- and nano-cavities and channels, known as the lacuna-canalicular network (LCN), that is thought to play an important role in mechanobiology and turnover. The LCN comprises micrometer-sized lacunae, voids that house osteocytes, and submicrometer-sized canaliculi that connect bone cells. Characterization of this network in three dimensions is crucial for many bone studies. To quantify X-ray Zernike phase-contrast nanotomography data, deep learning is used to isolate and assess porosity in artifact-laden tomographies of zebrafish bones. A technical solution is proposed to overcome the halo and shade-off domains in order to reliably obtain the distribution and morphology of the LCN in the tomographic data. Convolutional neural network (CNN) models are utilized with increasing numbers of images, repeatedly validated by `error loss' and `accuracy' metrics. U-Net and Sensor3D CNN models were trained on data obtained from two different synchrotron Zernike phase-contrast transmission X-ray microscopes, the ANATOMIX beamline at SOLEIL (Paris, France) and the P05 beamline at PETRA III (Hamburg, Germany). The Sensor3D CNN model with a smaller batch size of 32 and a training data size of 70 images showed the best performance (accuracy 0.983 and error loss 0.032). The analysis procedures, validated by comparison with human-identified ground-truth images, correctly identified the voids within the bone matrix. This proposed approach may have further application to classify structures in volumetric images that contain non-linear artifacts that degrade image quality and hinder feature identification.