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.

This paper describes real-time statistical analysis of liquid jet images for SFX experiments at the European XFEL. This analysis forms one part of the automated jet re-alignment system for SFX experiments at the SPB/SFX instrument of European XFEL.

A neutron far-field interferometer is under development at NIST with the aim of enabling a multi-scale measurement combining the best of small-angle neutron scattering (SANS) and neutron imaging and tomography. We use the close relationship between SANS, ultra-SANS, spin-echo SANS and dark-field imaging and measurements of monodisperse spheres as a validation metric, highlighting the strengths and weaknesses of each of these neutron techniques.

Here, an open-source Python library for identifying and screening potential stacking fault models in crystalline materials with planar disorder is presented.

The symmetry groups of the weave patterns of the baskets, trays and mats of the Batak, an indigenous community in the Philippines, are discussed in this paper. The two-way twofold weaving technique is used by the Batak, and this study points to a total of 15 layer groups found in the Batak weaves out of the 80 layer groups known in crystallography.

The performance of a high-Z photon-counting detector for powder diffraction measurements at high (>50 keV) energies is characterized, and the appropriate corrections are described in order to obtain data of higher quality than have previously been obtained from 2D detectors in these energy ranges.

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 article presents a non-invasive nanoscale imaging technique that can be used in screening crystallization conditions for protein micro- and nanocrystals.

RAPID (RAtio method Pattern InDexing) is an ImageJ macro script developed for the quick determination of sample orientation and indexing of calibrated and uncalibrated zone axis aligned electron diffraction patterns from materials with a cubic crystal structure. In addition to SAED and NBED patterns, the program is also capable of handling zone axis TEM Kikuchi patterns and FFTs derived from HR(S)TEM images. The software enables users to rapidly determine whether materials are cubic, pseudo-cubic, or non-cubic, and to distinguish between P, I, and F Bravais lattices. It can also provide lattice parameters for material verification and aid in determining the camera constant of the instrument, thus making the program a convenient tool for on-site crystallographic analysis in the TEM laboratory.

This study proposes an operation optimization framework for impurity-free recycling of spent lithium-ion batteries. Using a hybrid population balance equation integrated with a data-driven condition classifier, the study firstly identifies the optimal batch and semi-batch operation conditions that significantly reduce the operation time with 100% purity of product; detailed guidelines are given for industrial applications.

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.

Here we describe TOMOMAN (TOMOgram MANager), an extensible open-sourced software package for handling cryo-electron tomography data preprocessing. TOMOMAN streamlines interoperability between a wide range of external packages and provides tools for project sharing and archival.

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.

Structures of tetra­pyridine­silver(I) hexa­fluoro­phosphate and tetra­pyridine silver(I) hexa­fluoro­anti­monate are reported from data collected at 300 K and 100 K.

The crystal structure of Cd5(TeO3)4(NO3)2 exhibits a distinct layered arrangement, whereas Cd4Te5O14 crystallizes with a framework structure.

In the complex, the ligand binds to the metal through an oxygen atom. The geometry of the seven-coordinate U atom is penta­gonal bipyramidal, with the uranyl O atoms in apical positions.

In the title compound, the tellurium(VI) and vanadium(V) atoms are statistically disordered over two of the ten metal-atom sites in the unprotonated [TeV9O28]5– heteropolyanion.

A chiral nickel(II) Schiff base complex derived from 2-hy­droxy­benzo­phenone and (1S,2S)-1,2-di­phenyl­ethyl­enedi­amine shows a λ conformation of the central di­amine chelate ring. The substituents on the C&z-dbnd;N carbon atoms significantly affect the circular dichroism spectra.

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.

Theoretical and experimental structural studies of the title compound were undertaken using X-ray and DFT methods. The inter­actions present in the crystal were analyzed using Hirshfeld surface and MEP surface analysis. Docking studies with a covid-19 main protease (PDB ID: 6LU7) as the target receptor indicate that the synthesized compound may be a potential candidate for pharmaceutical applications.

The crystal structure of the co-crystal salt solvate 1,10-phenanthrolinium violurate violuric acid penta­hydrate features a tri-periodic hydrogen-bonded network with the violurate and violuric acid residues each assembled into tapes and the phenanthrolinium cations residing in channels.

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

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.

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

The title compound is a non-liquid crystal mol­ecule. The mol­ecular crystal is consolidated by C—Br⋯O&z-dbnd;C type contacts running continuously along the [001] direction.

The mol­ecular and crystal structure of N-(4-meth­oxy­phen­yl)picolinamide were studied and Hirshfeld surfaces and fingerprint plots were generated to investigate various inter­molecular inter­actions.

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'.

Quantitative X-ray diffraction approaches require careful correction for sample transmission. Though this is a routine task at state-of-the-art small-angle X-ray scattering (SAXS), wide-angle X-ray scattering (WAXS) or diffraction beamlines at synchrotron facilities, the transmission signal cannot be recorded concurrently with SAXS/WAXS when using the small, sub-millimetre beamstops at many X-ray nanoprobes during SAXS/WAXS experiments due to the divergence-limited size of the beamstop and the generally tight geometry. This is detrimental to the data quality and often the only solution is to re-scan the sample with a PIN photodiode as a detector to obtain transmission values. In this manuscript, we present a simple yet effective solution to this problem in the form of a small beamstop with an inlaid metal target for optimal fluorescence yield. This fluorescence can be detected with a high-sensitivity avalanche photodiode and provides a linear counter to determine the sample transmission.

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.

A series of animations, videos and 3D models that were developed, filmed or built to teach the symmetry properties of crystals are described. At first, these resources were designed for graduate students taking a basic crystallography course, coming from different careers, at the National Autonomous University of Mexico. However, the COVID-19 pandemic had the effect of accelerating the generation of didactic material. Besides our experience with postgraduate students, we have noted that 3D models attract the attention of children, and therefore we believe that these models are particularly useful for teaching children about the assembled arrangements of crystal structures.

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 continued advancement of complex materials often requires a deeper understanding of the structure–function relationship across many length scales, which quickly becomes an arduous task when multiple measurements are required to characterize hierarchical and inherently heterogeneous materials. Therefore, there are benefits in the simultaneous characterization of multiple length scales. At the National Institute of Standards and Technology, a new neutron far-field interferometer is under development that aims to enable a multi-scale measurement combining the best of small-angle neutron scattering (SANS) and neutron imaging and tomography. Spatially resolved structural information on the same length scales as SANS (0.001–1 µm) and ultra-small-angle neutron scattering (USANS, 0.1–10 µm) will be collected via dark-field imaging simultaneously with regular attenuation radiography (>10 µm). The dark field is analogous to the polarization loss measured in spin-echo SANS (SESANS) and is related to isotropic SANS through a Hankel transform. Therefore, we use this close relationship and analyze results from SANS, USANS, SESANS and dark-field imaging of monodisperse spheres as a validation metric for the interferometry measurements. The results also highlight the strengths and weaknesses of these neutron techniques for both steady-state and pulsed neutron sources. Finally, we present an example of the value added by the spatial resolution enabled by dark-field imaging in the study of more complex heterogeneous materials. This information would otherwise be lost in other small-angle scattering measurements averaged over the sample.

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.

BGaN epilayers with boron contents up to 5.6% were grown on SiC substrates by metal–organic chemical vapor deposition. The effects of boron incorporation on the structural and optical properties were studied by high-resolution X-ray diffraction (XRD), atomic force microscopy (AFM), Raman spectroscopy and photoluminescence (PL) spectroscopy. XRD reciprocal-space maps around the symmetric 0002 and asymmetric 11 {overline 2} 4 reflections allowed evaluation of the lattice constants and lattice mismatch with respect to the underlying substrate. XRD rocking curves and AFM measurements indicated the mosaic microstructure of the epilayer. The impact of boron content on crystallite size, tilt and twist is evaluated and the correlation with threading dislocation density is discussed. The deterioration of optical properties with increasing boron content was assessed by Raman and PL spectroscopy.

Nanometric precipitates in metallic alloys often have highly anisotropic shapes. Given the large grain size and non-random texture typical of these alloys, performing small- and wide-angle X-ray scattering (SAXS/WAXS) measurements on such samples for determining their characteristics (typically size and volume fraction) results in highly anisotropic and irreproducible data. Rotations of flat samples during SAXS/WAXS acquisitions are presented here as a solution to these anisotropy issues. Two aluminium alloys containing anisotropic precipitates are used as examples to validate the approach with a −45°/45° angular range. Clear improvements can be seen on the SAXS I(q) fitting and the consistency between the different SAXS/WAXS measurements. This methodology results in more reliable measurements of the precipitate's characteristics, and thus allows for time- and space-resolved measurements with higher accuracy.

The effect of an electric field on local domain structure near a 24° tilt grain boundary in a 200 nm-thick Pb(Zr0.2Ti0.8)O3 bi-crystal ferroelectric film was probed using synchrotron nanodiffraction. The bi-crystal film was grown epitaxially on SrRuO3-coated (001) SrTiO3 24° tilt bi-crystal substrates. From the nanodiffraction data, real-space maps of the ferroelectric domain structure around the grain boundary prior to and during application of a 200 kV cm−1 electric field were reconstructed. In the vicinity of the tilt grain boundary, the distributions of densities of c-type tetragonal domains with the c axis aligned with the film normal were calculated on the basis of diffracted intensity ratios of c- and a-type domains and reference powder diffraction data. Diffracted intensity was averaged along the grain boundary, and it was shown that the density of c-type tetragonal domains dropped to ∼50% of that of the bulk of the film over a range ±150 nm from the grain boundary. This work complements previous results acquired by band excitation piezoresponse force microscopy, suggesting that reduced nonlinear piezoelectric response around grain boundaries may be related to the change in domain structure, as well as to the possibility of increased pinning of domain wall motion. The implications of the results and analysis in terms of understanding the role of grain boundaries in affecting the nonlinear piezoelectric and dielectric responses of ferroelectric materials are discussed.

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

Besides traditional pinhole geometry, the multi-slit very small angle neutron scattering instrument (MS-VSANS) at the China Spallation Neutron Source also utilizes a multi-slit collimation system to focus neutrons. Using the special focusing structures, the minimum scattering vector magnitude (q) can reach 0.00028 Å−1. The special structures also lead to a significantly different smearing function. By comparing the results of theoretical calculations with experimental data, we have validated the feasibility of a smearing method based on a mature theory for slit smearing. We use the weight-averaged intensity of neutron wavelength as a representative to evaluate the effect from a broad wavelength distribution, concentrating on the effect from the geometry of the multi-slit structures and the detector. The consistency of the theoretical calculation of the smearing function with experimental VSANS scattering profiles for a series of polystyrene standards of different diameters proves the feasibility of the smearing method. This marks the inaugural use of real experimental data from an instrument employing a multi-slit collimation system.

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

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.

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