The success of experimental phasing in macromolecular crystallography relies primarily on the accurate locations of heavy atoms bound to the target crystal. To improve the process of substructure determination, a modified phase-retrieval algorithm built on the framework of the relaxed alternating averaged reflection (RAAR) algorithm has been developed. Importantly, the proposed algorithm features a combination of the π-half phase perturbation for weak reflections and enforces the direct-method-based tangent formula for strong reflections in reciprocal space. The proposed algorithm is extensively demonstrated on a total of 100 single-wavelength anomalous diffraction (SAD) experimental datasets, comprising both protein and nucleic acid structures of different qualities. Compared with the standard RAAR algorithm, the modified phase-retrieval algorithm exhibits significantly improved effectiveness and accuracy in SAD substructure determination, highlighting the importance of additional constraints for algorithmic performance. Furthermore, the proposed algorithm can be performed without human intervention under most conditions owing to the self-adaptive property of the input parameters, thus making it convenient to be integrated into the structural determination pipeline. In conjunction with the IPCAS software suite, we demonstrated experimentally that automatic de novo structure determination is possible on the basis of our proposed algorithm.

Single-particle cryo-electron microscopy (cryo-EM) has become an essential structural determination technique with recent hardware developments making it possible to reach atomic resolution, at which individual atoms, including hydrogen atoms, can be resolved. In this study, we used the enzyme involved in the penultimate step of riboflavin biosynthesis as a test specimen to benchmark a recently installed microscope and determine if other protein complexes could reach a resolution of 1.5 Å or better, which so far has only been achieved for the iron carrier ferritin. Using state-of-the-art microscope and detector hardware as well as the latest software techniques to overcome microscope and sample limitations, a 1.42 Å map of Aquifex aeolicus lumazine synthase (AaLS) was obtained from a 48 h microscope session. In addition to water molecules and ligands involved in the function of AaLS, we can observe positive density for ∼50% of the hydrogen atoms. A small improvement in the resolution was achieved by Ewald sphere correction which was expected to limit the resolution to ∼1.5 Å for a molecule of this diameter. Our study confirms that other protein complexes can be solved to near-atomic resolution. Future improvements in specimen preparation and protein complex stabilization may allow more flexible macromolecules to reach this level of resolution and should become a priority of study in the field.

The aberrant fibrillization of huntingtin exon 1 (Httex1) characterized by an expanded polyglutamine (polyQ) tract is a defining feature of Huntington's disease, a neurodegenerative disorder. Recent investigations underscore the involvement of a small EDRK-rich factor 1a (SERF1a) in promoting Httex1 fibrillization through interactions with its N terminus. By establishing an integrated approach with size-exclusion-column-based small- and wide-angle X-ray scattering (SEC-SWAXS), NMR, and molecular simulations using Rosetta, the analysis here reveals a tight binding of two NT17 fragments of Httex1 (comprising the initial 17 amino acids at the N terminus) to the N-terminal region of SERF1a. In contrast, examination of the complex structure of SERF1a with a coiled NT17-polyQ peptide (33 amino acids in total) indicates sparse contacts of the NT17 and polyQ segments with the N-terminal side of SERF1a. Furthermore, the integrated SEC-SWAXS and molecular-simulation analysis suggests that the coiled NT17 segment can transform into a helical conformation when associated with a polyQ segment exhibiting high helical content. Intriguingly, NT17-polyQ peptides with enhanced secondary structures display diminished interactions with SERF1a. This insight into the conformation-dependent binding of NT17 provides clues to a catalytic association mechanism underlying SERF1a's facilitation of Httext1 fibrillization.

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.

Reaching beyond the commonly used spherical atomic electron density model allows one to greatly improve the accuracy of hydrogen atom structural param­eters derived from X-ray data. However, the effects of atomic asphericity are less explored for electron diffraction data. In this work, Hirshfeld atom refinement (HAR), a method that uses an accurate description of electron density by quantum mechanical calculation for a system of interest, was applied for the first time to the kinematical refinement of electron diffraction data. This approach was applied here to derive the structure of ordinary hexagonal ice (Ih). The effect of introducing HAR is much less noticeable than in the case of X-ray refinement and it is largely overshadowed by dynamical scattering effects. It led to only a slight change in the O—H bond lengths (shortening by 0.01 Å) compared with the independent atom model (IAM). The average absolute differences in O—H bond lengths between the kinematical refinements and the reference neutron structure were much larger: 0.044 for IAM and 0.046 Å for HAR. The refinement results changed considerably when dynamical scattering effects were modelled – with extinction correction or with dynamical refinement. The latter led to an improvement of the O—H bond length accuracy to 0.021 Å on average (with IAM refinement). Though there is a potential for deriving more accurate structures using HAR for electron diffraction, modelling of dynamical scattering effects seems to be a necessary step to achieve this. However, at present there is no software to support both HAR and dynamical refinement.

Ultrafast, high-intensity X-ray free-electron lasers can perform diffraction imaging of single protein molecules. Various algorithms have been developed to determine the orientation of each single-particle diffraction pattern and reconstruct the 3D diffraction intensity. Most of these algorithms rely on the premise that all diffraction patterns originate from identical protein molecules. However, in actual experiments, diffraction patterns from multiple different molecules may be collected simultaneously. Here, we propose a predicted model-aided one-step classification–multireconstruction algorithm that can handle mixed diffraction patterns from various molecules. The algorithm uses predicted structures of different protein molecules as templates to classify diffraction patterns based on correlation coefficients and determines orientations using a correlation maximization method. Tests on simulated data demonstrated high accuracy and efficiency in classification and reconstruction.

3D electron diffraction (3DED) is increasingly employed to determine molec­ular and crystal structures from micro-crystals. Indomethacin is a well known, marketed, small-molecule non-steroidal anti-inflammatory drug with eight known polymorphic forms, of which four structures have been elucidated to date. Using 3DED, we determined the structure of a new ninth polymorph, σ, found within an amorphous solid dispersion, a product formulation sometimes used for active pharmaceutical ingredients with poor aqueous solubility. Subsequently, we found that σ indomethacin can be produced from direct solvent evaporation using di­chloro­methane. These results demonstrate the relevance of 3DED within drug development to directly probe product formulations.

Conformational heterogeneity of biological macromolecules is a challenge in single-particle averaging (SPA). Current standard practice is to employ classification and filtering methods that may allow a discrete number of conformational states to be reconstructed. However, the conformation space accessible to these molecules is continuous and, therefore, explored incompletely by a small number of discrete classes. Recently developed heterogeneous reconstruction algorithms (HRAs) to analyse continuous heterogeneity rely on machine-learning methods that employ low-dimensional latent space representations. The non-linear nature of many of these methods poses a challenge to their validation and interpretation and to identifying functionally relevant conformational trajectories. These methods would benefit from in-depth benchmarking using high-quality synthetic data and concomitant ground truth information. We present a framework for the simulation and subsequent analysis with respect to the ground truth of cryo-EM micrographs containing particles whose conformational heterogeneity is sourced from molecular dynamics simulations. These synthetic data can be processed as if they were experimental data, allowing aspects of standard SPA workflows as well as heterogeneous reconstruction methods to be compared with known ground truth using available utilities. The simulation and analysis of several such datasets are demonstrated and an initial investigation into HRAs is presented.

The interaction of intense synchrotron radiation with molecular crystals frequently modifies the crystal structure by breaking bonds, producing fragments and, hence, inducing disorder. Here, a second-rank tensor of radiation-induced lattice strain is proposed to characterize the structural susceptibility to radiation. Quantitative estimates are derived using a linear response approximation from experimental data collected on three materials Hg(NO3)2(PPh3)2, Hg(CN)2(PPh3)2 and BiPh3 [PPh3 = triphenylphosphine, P(C6H5)3; Ph = phenyl, C6H5], and are compared with the corresponding thermal expansivities. The associated eigenvalues and eigenvectors show that the two tensors are not the same and therefore probe truly different structural responses. The tensor of radiative expansion serves as a measure of the susceptibility of crystal structures to radiation damage.

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

The molecule of anti-epileptic drug lamotrigine [LAM; 3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine] is capable of the formation of multicomponent solids. Such an enhanced tendency is related to the diverse functionalities of the LAM chemical groups able to form hydrogen bonds. Two robust synthons are recognized in the supramolecular structure of LAM itself formed via N—H⋯N hydrogen bond: homosynthon, so-called aminopyridine dimer or synthon 1 [R22(8)] and larger homosynthon 2 [R32(8)]. The synthetic procedures for a new hydrate and 11 solvates of LAM (in the series: with acetone, ethanol: two polymorphs: form I and form II, 2-propanol, n-butanol, tert-butanol, n-pentanol, benzonitrile, acetonitrile, DMSO and dioxane) were performed. The comparative solid state structural analysis of a new hydrate and 11 solvates of LAM has been undertaken in order to establish robustness of the supramolecular synthons 1 and 2 found in the crystal structure of LAM itself as well as LAM susceptibility to build methodical solid state supramolecular architecture in the given competitive surrounding of potential hydrogen bonds. The aminopyridine dimer homosynthon 1 [R22(8)] has been switched from para-para (P-P) topology to ortho-ortho (O-O) topology in all crystal structures, except in LAM:n-pentanol:water solvate where it remains P-P. Homosynthon 2 [R32(8)] of the LAM crystal structure imitates in the LAM solvates as a heterosynthon by replacing the triazine nitrogen proton acceptor atoms of LAM with the proton acceptors of solvates molecules.

SnGe4N4O4 was synthesized at high pressure (16 and 20 GPa) and high temperature (1200 and 1500°C) in a large-volume press. Powder X-ray diffraction experiments using synchrotron radiation indicate that the derived samples are mixtures of known and unknown phases. However, the powder X-ray diffraction patterns are not sufficient for structural characterization. Transmission electron microscopy studies reveal crystals of several hundreds of nanometres in size with different chemical composition. Among them, crystals of a previously unknown phase with stoichiometry SnGe4N4O4 were detected and investigated using automated diffraction tomography (ADT), a three-dimensional electron diffraction method. Via ADT, the crystal structure could be determined from single nanocrystals in space group P63mc, exhibiting a nolanite-type structure. This was confirmed by density functional theory calculations and atomic resolution scanning transmission electron microscopy images. In one of the syntheses runs a rhombohedral 6R polytype of SnGe4N4O4 could be found together with the nolanite-type SnGe4N4O4. The structure of this polymorph was solved as well using ADT.

The structures of three multicomponent crystals formed with imidazole-based drugs, namely metronidazole, ketoconazole and miconazole, in conjunction with tri­thio­cyanuric acid are characterized. Each of the obtained adducts represents a different category of crystalline molecular forms: a cocrystal, a salt and a cocrystal of salt. The structural analysis revealed that in all cases, the N—H⋯N hydrogen bond is responsible for the formation of acid–base pairs, regardless of whether proton transfer occurs or not, and these molecular pairs are combined to form unique supramolecular motifs by centrosymmetric N—H⋯S interactions between acid molecules. The complex intermolecular forces acting in characteristic patterns are discussed from the geometric and energetic perspectives, involving Hirshfeld surface analysis, pairwise energy estimation, and natural bond orbital calculations.

In the title mol­ecule, C7H7N3O, the pyrimidine ring is essentially planar, with the propynyl group rotated out of this plane by 15.31 (4)°. In the crystal, a tri-periodic network is formed by N—H⋯O, N—H⋯N and C—H⋯O hydrogen-bonding and slipped π–π stacking inter­actions, leading to narrow channels extending parallel to the c axis. Hirshfeld surface analysis of the crystal structure reveals that the most important contributions for the crystal packing are from H⋯H (36.2%), H⋯C/C⋯H (20.9%), H⋯O/O⋯H (17.8%) and H⋯N/N⋯H (12.2%) inter­actions, showing that hydrogen-bonding and van der Waals inter­actions are the dominant inter­actions in the crystal packing. Evaluation of the electrostatic, dispersion and total energy frameworks indicates that the stabilization is dominated by the electrostatic energy contributions. The mol­ecular structure optimized by density functional theory (DFT) calculations at the B3LYP/6–311 G(d,p) level is compared with the experimentally determined structure in the solid state. The HOMO–LUMO behaviour was also elucidated to determine the energy gap.

Two new copper dimers, namely, bis­(dimethyl sulfoxide)­tetra­kis­(μ-pyrene-1-carboxyl­ato)dicopper(Cu—Cu), [Cu2(C17H9O2)4(C2H6OS)2] or [Cu2(pyr-COO−)4(DMSO)2] (1), and bis­(di­methyl­formamide)­tetra­kis­(μ-pyrene-1-carboxyl­ato)dicopper(Cu—Cu), [Cu2(C17H9O2)4(C3H7NO)2] or [Cu2(pyr-COO−)4(DMF)2] (2) (pyr = pyrene), were synthesized from the reaction of pyrene-1-carb­oxy­lic acid, copper(II) nitrate and tri­ethyl­amine from solvents DMSO and DMF, respectively. While 1 crystallized in the space group Poverline{1}, the crystal structure of 2 is in space group P21/n. The Cu atoms have octa­hedral geometries, with four oxygen atoms from carboxyl­ate pyrene ligands occupying the equatorial positions, a solvent mol­ecule coordinating at one of the axial positions, and a Cu⋯Cu contact in the opposite position. The packing in the crystal structures exhibits π–π stacking inter­actions and short contacts through the solvent mol­ecules. The Hirshfeld surfaces and two-dimensional fingerprint plots were generated for both compounds to better understand the inter­molecular inter­actions and the contribution of heteroatoms from the solvent ligands to the crystal packing. In addition, a Cu2+/Cu1+ quasi-reversible redox process was identified for compound 2 using cyclic voltammetry that accounts for a diffusion-controlled electron-donation process to the Cu dimer.

The title compound, C8H7NO2, crystallizes as prismatic colourless crystals in space group Poverline{1}, with one mol­ecule in the asymmetric unit. The pyridine ring is fused to acrylic acid, forming an almost planar structure with an E-configuration about the double bond with a torsion angle of −6.1 (2)°. In the crystal, strong O—H⋯N inter­actions link the mol­ecules, forming chains along the [101] direction. Weak C—H⋯O inter­actions link adjacent chains along the [100] direction, generating an R22(14) homosynthon. Finally, π–π stacking inter­actions lead to the formation of the three-dimensional structure. The supra­molecular analysis was supported by Hirshfeld surface and two-dimensional fingerprint plot analysis, indicating that the most abundant contacts are associated with H⋯H, O⋯H/H⋯O, N⋯H/H⋯N and C⋯H/H⋯C inter­actions.

The benzimidazole entity of the title mol­ecule, C17H21N5O, is almost planar (r.m.s. deviation = 0.0262 Å). In the crystal, bifurcated C—H⋯O hydrogen bonds link individual mol­ecules into layers extending parallel to the ac plane. Two weak C—H⋯π(ring) inter­actions may also be effective in the stabilization of the crystal structure. Hirshfeld surface analysis of the crystal structure reveals that the most important contributions for the crystal packing are from H⋯H (57.9%), H⋯C/C⋯H (18.1%) and H⋯O/O⋯H (14.9%) inter­actions. Hydrogen bonding and van der Waals inter­actions are the most dominant forces in the crystal packing. Evaluation of the electrostatic, dispersion and total energy frameworks indicate that the stabilization of the title compound is dominated via dispersion energy contributions. The mol­ecular structure optimized by density functional theory (DFT) at the B3LYP/6–311 G(d,p) level is compared with the experimentally determined mol­ecular structure in the solid state.

The structural characterization is reported of the supra­molecular complex between the tetra­quinoxaline-based cavitand 2,8,14,20-tetra­hexyl-6,10:12,16:18,22:24,4-O,O'-tetra­kis­(quinoxaline-2,3-di­yl)calix[4]resorcinarene (QxCav) with benzo­nitrile. The complex, of general formula C84H80N8O8·2C7H5N, crystallizes in the space group Poverline{1} with two independent mol­ecules in the asymmetric unit, displaying very similar geometrical parameters. For each complex, one of the benzo­nitrile mol­ecules is engulfed inside the cavity, while the other is located among the alkyl legs at the lower rim. The host and the guests mainly inter­act through weak C—H⋯π, C—H⋯N and dispersion inter­actions. These inter­actions help to consolidate the formation of supra­molecular chains running along the crystallographic b-axis direction.

The pyrazolo­pyrimidine moiety in the title mol­ecule, C13H12N4S, is planar with the methyl­sulfanyl substituent lying essentially in the same plane. The benzyl group is rotated well out of this plane by 73.64 (6)°, giving the mol­ecule an approximate L shape. In the crystal, C—H⋯π(ring) inter­actions and C—H⋯S hydrogen bonds form tubes extending along the a axis. Furthermore, there are π–π inter­actions between parallel phenyl rings with centroid-to-centroid distances of 3.8418 (12) Å. A Hirshfeld surface analysis of the crystal structure indicates that the most important contributions to the crystal packing are from H⋯H (47.0%), H⋯N/N⋯H (17.6%) and H⋯C/C⋯H (17.0%) inter­actions. The volume of the crystal voids and the percentage of free space were calculated to be 76.45 Å3 and 6.39%, showing that there is no large cavity in the crystal packing. Evaluation of the electrostatic, dispersion and total energy frameworks indicate that the cohesion of the crystal structure is dominated by the dispersion energy contributions.

The X-ray crystal structure data of 12-α-fluoro-3β-hy­droxy­olean-28,13β-olide methanol hemisolvate, 2C30H47FO3·CH3OH, (1), and 12-α-fluoro-3β-hy­droxy­taraxer-28,14β-olide methanol hemisolvate, 2C30H47FO3·CH3OH, (2), are described. The fluoro­lactonization of oleanolic acid using SelectfluorTM yielded a mixture of the six-membered δ-lactone (1) and the unusual seven-membered γ-lactone (2) following a 1,2-shift of methyl C-27 from C-14 to C-13.

The benzimidazole moiety in the title mol­ecule, C19H25N5O, is almost planar and oriented nearly perpendicular to the triazole ring. In the crystal, C—H⋯O hydrogen bonds link the mol­ecules into a network structure. There are no π–π inter­actions present but two weak C—H⋯π(ring) inter­actions are observed. A Hirshfeld surface analysis of the crystal structure indicates that the most important contributions for the crystal packing are from H⋯H (62.0%), H⋯C/C⋯H (16.1%), H⋯N/N⋯H (13.7%) and H⋯O/O⋯H (7.5%) inter­actions. Evaluation of the electrostatic, dispersion and total energy frameworks indicate that the stabilization is dominated via the dispersion energy contributions in the title compound.

The title mol­ecule, C25H23BrN2O2, adopts a cup shaped conformation with the distinctly ruffled imidazolidine ring as the base. In the crystal, weak C—H⋯O hydrogen bonds and C—H⋯π(ring) inter­actions form helical chains of mol­ecules extending along the b-axis direction that are linked by additional weak C—H⋯π(ring) inter­actions across inversion centres. The Hirshfeld surface analysis of the crystal structure indicates that the most important contributions for the crystal packing are from H⋯H (51.0%), C⋯H/H⋯C (21.3%), Br⋯H/H⋯Br (12.8%) and O⋯H/H⋯O (12.4%) inter­actions. The volume of the crystal voids and the percentage of free space were calculated to be 251.24 Å3 and 11.71%, respectively, showing that there is no large cavity in the crystal packing. Evaluation of the electrostatic, dispersion and total energy frameworks indicate that the stabilization is dominated by the dispersion energy.

A host–guest supra­molecular inclusion complex was obtained from the co-crystallization of A1/A2-bromo­but­oxy-hy­droxy difunctionalized pillar[5]arene (PilButBrOH) with adipo­nitrile (ADN), C47H53.18Br0.82O10·C6H8N2. The adipo­nitrile guest is stabilized within the electron-rich cavity of the pillar[5]arene host via multiple C—H⋯O and C—H⋯π inter­actions. Both functional groups on the macrocyclic rim are engaged in supra­molecular inter­actions with an adjacent inclusion complex via hydrogen-bonding (O—H⋯N or C—H⋯Br) inter­actions, resulting in the formation of a supra­molecular dimer in the crystal structure.

Through numerical optimization of cooling lengths and cooling groove positions for the first reflection mirror of a free-electron laser [OK?], the root mean square of the height error of the mirror's thermal deformation was minimized. The optimized mirror design effectively mitigated stray light and enhanced the peak intensity of the focus spot at the sample, thereby enhancing the optical performance of the high-heat-load mirror under high repetition rates at beamline FEL-II of the SHINE facility.

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

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.

Low-energy electron diffraction patterns contain precise information about the structure of the surface studied. However, retrieving the real space lattice periodicity from complex diffraction patterns is challenging, especially when the modeled patterns originate from superlattices with large unit cells composed of several symmetry-equivalent domains without a simple relation to the substrate. This work presents ProLEED Studio software, built to provide simple, intuitive and precise modeling of low-energy electron diffraction patterns. The interactive graphical user interface allows real-time modeling of experimental diffraction patterns, change of depicted diffraction spot intensities, visualization of different diffraction domains, and manipulation of any lattice points or diffraction spots. The visualization of unit cells, lattice vectors, grids and scale bars as well as the possibility of exporting ready-to-publish models in bitmap and vector formats significantly simplifies the modeling process and publishing of results.

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.

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.

This work introduces X-Ray Calc (XRC), an open-source software package designed to simulate X-ray reflectivity (XRR) and address the inverse problem of reconstructing film structures on the basis of measured XRR curves. XRC features a user-friendly graphical interface that facilitates interactive simulation and reconstruction. The software employs a recursive approach based on the Fresnel equations to calculate XRR and incorporates specialized tools for modeling periodic multilayer structures. This article presents the latest version of the X-Ray Calc software (XRC3), with notable improvements. These enhancements encompass an automatic fitting capability for XRR curves utilizing a modified flight particle swarm optimization algorithm. A novel cost function was also developed specifically for fitting XRR curves of periodic structures. Furthermore, the overall user experience has been enhanced by developing a new single-window interface.

X-ray reflectometry (XRR) is a powerful tool for probing the structural characteristics of nanoscale films and layered structures, which is an important field of nanotechnology and is often used in semiconductor and optics manufacturing. This study introduces a novel approach for conducting quantitative high-resolution millisecond monochromatic XRR measurements. This is an order of magnitude faster than in previously published work. Quick XRR (qXRR) enables real time and in situ monitoring of nanoscale processes such as thin film formation during spin coating. A record qXRR acquisition time of 1.4 ms is demonstrated for a static gold thin film on a silicon sample. As a second example of this novel approach, dynamic in situ measurements are performed during PMMA spin coating onto silicon wafers and fast fitting of XRR curves using machine learning is demonstrated. This investigation primarily focuses on the evolution of film structure and surface morphology, resolving for the first time with qXRR the initial film thinning via mass transport and also shedding light on later thinning via solvent evaporation. This innovative millisecond qXRR technique is of significance for in situ studies of thin film deposition. It addresses the challenge of following intrinsically fast processes, such as thin film growth of high deposition rate or spin coating. Beyond thin film growth processes, millisecond XRR has implications for resolving fast structural changes such as photostriction or diffusion processes.

This work presents observations of symmetry breakages in the intensity distributions of near-zone-axis convergent-beam electron diffraction (CBED) patterns that can only be explained by the symmetry of the specimen and not the symmetry of the unit cell describing the atomic structure of the material. The specimen is an aluminium–copper–tin alloy containing voids many tens of nanometres in size within continuous single crystals of the aluminium host matrix. Several CBED patterns where the incident beam enters and exits parallel void facets without the incident beam being perpendicular to these facets are examined. The symmetries in their intensity distributions are explained by the specimen morphology alone using a geometric argument based on the multislice theory. This work shows that it is possible to deduce nanoscale morphological information about the specimen in the direction of the electron beam – the elusive third dimension in transmission electron microscopy – from the inspection of CBED patterns.

Due to the ambiguity related to the lack of phase information, determining the physical parameters of multilayer thin films from measured neutron and X-ray reflectivity curves is, on a fundamental level, an underdetermined inverse problem. This ambiguity poses limitations on standard neural networks, constraining the range and number of considered parameters in previous machine learning solutions. To overcome this challenge, a novel training procedure has been designed which incorporates dynamic prior boundaries for each physical parameter as additional inputs to the neural network. In this manner, the neural network can be trained simultaneously on all well-posed subintervals of a larger parameter space in which the inverse problem is underdetermined. During inference, users can flexibly input their own prior knowledge about the physical system to constrain the neural network prediction to distinct target subintervals in the parameter space. The effectiveness of the method is demonstrated in various scenarios, including multilayer structures with a box model parameterization and a physics-inspired special parameterization of the scattering length density profile for a multilayer structure. In contrast to previous methods, this approach scales favourably when increasing the complexity of the inverse problem, working properly even for a five-layer multilayer model and a periodic multilayer model with up to 17 open parameters.

X-ray crystallography is an established tool to probe the structure of macromolecules with atomic resolution. Compared with alternative techniques such as single-particle cryo-electron microscopy and micro-electron diffraction, X-ray crystallography is uniquely suited to room-temperature studies and for obtaining a detailed picture of macromolecules subjected to an external electric field (EEF). The impact of an EEF on proteins has been extensively explored through single-crystal X-ray crystallography, which works well with larger high-quality protein crystals. This article introduces a novel design for a 3D-printed in situ crystallization plate that serves a dual purpose: fostering crystal growth and allowing the concurrent examination of the effects of an EEF on crystals of varying sizes. The plate's compatibility with established X-ray crystallography techniques is evaluated.

The capillary wave model of a liquid surface predicts both the X-ray specular reflection and the diffuse scattering around it. A quantitative method is presented to obtain the X-ray reflectivity (XRR) from a liquid surface through the diffuse scattering data around the specular reflection measured using a grazing incidence X-ray off-specular scattering (GIXOS) geometry at a fixed horizontal offset angle with respect to the plane of incidence. With this approach the entire Qz-dependent reflectivity profile can be obtained at a single, fixed incident angle. This permits a much faster acquisition of the profile than with conventional reflectometry, where the incident angle must be scanned point by point to obtain a Qz-dependent profile. The XRR derived from the GIXOS-measured diffuse scattering, referred to in this paper as pseudo-reflectivity, provides a larger Qz range compared with the reflectivity measured by conventional reflectometry. Transforming the GIXOS-measured diffuse scattering profile to pseudo-XRR opens up the GIXOS method to widely available specular XRR analysis software tools. Here the GIXOS-derived pseudo-XRR is compared with the XRR measured by specular reflectometry from two simple vapor–liquid interfaces at different surface tension, and from a hexadecyltri­methyl­ammonium bromide monolayer on a water surface. For the simple liquids, excellent agreement (beyond 11 orders of magnitude in signal) is found between the two methods, supporting the approach of using GIXOS-measured diffuse scattering to derive reflectivities. Pseudo-XRR obtained at different horizontal offset angles with respect to the plane of incidence yields indistinguishable results, and this supports the robustness of the GIXOS-XRR approach. The pseudo-XRR method can be extended to soft thin films on a liquid surface, and criteria are established for the applicability of the approach.

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.

Using the well known Rn ratio method, a protocol has been elaborated for determining the lattice direction for the 15 most common cubic zone axis spot patterns. The method makes use of the lengths of the three shortest reciprocal-lattice vectors in each pattern and the angles between them. No prior pattern calibration is required for the method to work, as the Rn ratio method is based entirely on geometric relationships. In the first step the pattern is assigned to one of three possible pattern types according to the angles that are measured between the three reciprocal-lattice vectors. The lattice direction [uvw] and possible Bravais type(s) and Laue indices of the corresponding reflections can then be determined by using lookup tables. In addition to determining the lattice direction, this simple geometric analysis allows one to distinguish between the P, I and F Bravais lattices for spot patterns aligned along [013], [112], [114] and [233]. Moreover, the F lattice can always be uniquely identified from the [011] and [123] patterns.

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.

Structural modelling of operando pair distribution function (PDF) data of complex functional materials can be highly challenging. To aid the understanding of complex operando PDF data, this article demonstrates a toolbox for PDF analysis. The tools include denoising using principal component analysis together with the structureMining, similarityMapping and nmfMapping apps available through the online service `PDF in the cloud' (PDFitc, https://pdfitc.org/). The toolbox is used for both ex situ and operando PDF data for 3 nm TiO2-bronze nanocrystals, which function as the active electrode material in a Li-ion battery. The tools enable structural modelling of the ex situ and operando PDF data, revealing two pristine TiO2 phases (bronze and anatase) and two lithiated LixTiO2 phases (lithiated versions of bronze and anatase), and the phase evolution during galvanostatic cycling is characterized.

The first Federation of European Biochemical Societies Advanced Course on macromolecular crystallization was launched in the Czech Republic in October 2004. Over the past two decades, the course has developed into a distinguished event, attracting students, early career postdoctoral researchers and lecturers. The course topics include protein purification, characterization and crystallization, covering the latest advances in the field of structural biology. The many hands-on practical exercises enable a close interaction between students and teachers and offer the opportunity for students to crystallize their own proteins. The course has a broad and lasting impact on the scientific community as participants return to their home laboratories and act as nuclei by communicating and implementing their newly acquired knowledge and skills.

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

X-ray scattering has become a major tool in the structural characterization of nanoscale materials. Thanks to the widely available experimental and computational atomic models, coordinate-based X-ray scattering simulation has played a crucial role in data interpretation in the past two decades. However, simulation of real-space pair distance distribution functions (PDDFs) from small- and wide-angle X-ray scattering, SAXS/WAXS, has been relatively less exploited. This study presents a comparison of PDDF simulation methods, which are applied to molecular structures that range in size from β-cyclo­dextrin [1 kDa molecular weight (MW), 66 non-hydrogen atoms] to the satellite tobacco mosaic virus capsid (1.1 MDa MW, 81 960 non-hydrogen atoms). The results demonstrate the power of interpretation of experimental SAXS/WAXS from the real-space view, particularly by providing a more intuitive method for understanding of partial structure contributions. Furthermore, the computational efficiency of PDDF simulation algorithms makes them attractive as approaches for the analysis of large nanoscale materials and biological assemblies. The simulation methods demonstrated in this article have been implemented in stand-alone software, SolX 3.0, which is available to download from https://12idb.xray.aps.anl.gov/solx.html.

Understanding the structure–property relationship in electrocatalysts under working conditions is crucial for the rational design of novel and improved catalytic materials. This paper presents the Aarhus University reactor for electrochemical studies using X-rays (AUREX) operando electrocatalytic flow cell, designed as an easy-to-use versatile setup with a minimal background contribution and a uniform flow field to limit concentration polarization and handle gas formation. The cell has been employed to measure operando total scattering, diffraction and absorption spectroscopy as well as simultaneous combinations thereof on a commercial silver electrocatalyst for proof of concept. This combination of operando techniques allows for monitoring of the short-, medium- and long-range structure under working conditions, including an applied potential, liquid electrolyte and local reaction environment. The structural transformations of the Ag electrocatalyst are monitored with non-negative matrix factorization, linear combination analysis, the Pearson correlation coefficient matrix, and refinements in both real and reciprocal space. Upon application of an oxidative potential in an Ar-saturated aqueous 0.1 M KHCO3/K2CO3 electrolyte, the face-centered cubic (f.c.c.) Ag gradually transforms first to a trigonal Ag2CO3 phase, followed by the formation of a monoclinic Ag2CO3 phase. A reducing potential immediately reverts the structure to the Ag (f.c.c.) phase. Following the electrochemical-reaction-induced phase transitions is of fundamental interest and necessary for understanding and improving the stability of electrocatalysts, and the operando cell proves a versatile setup for probing this. In addition, it is demonstrated that, when studying electrochemical reactions, a high energy or short exposure time is needed to circumvent beam-induced effects.

A neutron time-of-flight (TOF) powder diffractometer with a continuous wide-angle array of detectors can be electronically focused to make a single pseudo-constant wavelength diffraction pattern, thus facilitating angle-dependent intensity corrections. The resulting powder diffraction peak profiles are affected by the neutron source emission profile and resemble the function currently used for TOF diffraction.

VMXm joins the suite of operational macromolecular crystallography beamlines at Diamond Light Source. It has been designed to optimize rotation data collections from protein crystals less than 10 µm and down to below 1 µm in size. The beamline has a fully focused beam of 0.3 × 2.3 µm (vertical × horizontal) with a tuneable energy range (6–28 keV) and high flux (1.6 × 1012 photons s−1 at 12.5 keV). The crystals are housed within a vacuum chamber to minimize background scatter from air. Crystals are plunge-cooled on cryo-electron microscopy grids, allowing much of the liquid surrounding the crystals to be removed. These factors improve the signal-to-noise during data collection and the lifetime of the microcrystals can be prolonged by exploiting photoelectron escape. A novel in vacuo sample environment has been designed which also houses a scanning electron microscope to aid with sample visualization. This combination of features at VMXm allows measurements at the physical limits of X-ray crystallography on biomacromolecules to be explored and exploited.

High-repetition-rate free-electron lasers impose stringent requirements on the thermal deformation of beamline optics. The Shanghai HIgh-repetition-rate XFEL aNd Extreme light facility (SHINE) experiences high average thermal power and demands wavefront preservation. To deeply study the thermal field of the first reflection mirror M1 at the FEL-II beamline of SHINE, thermal analysis under a photon energy of 400 eV was executed by fluid and solid heat transfer method. According to the thermal analysis results and the reference cooling water temperature of 30 °C, the temperature of the cooling water at the flow outlet is raised by 0.15 °C, and the wall temperature of the cooling tube increases by a maximum of 0.5 °C. The maximum temperature position of the footprint centerline in the meridian direction deviates away from the central position, and this asymmetrical temperature distribution will directly affect the thermal deformation of the mirror and indirectly affect the focus spot of the beam at the sample.

Geological samples are inherently multi-scale. Understanding their bulk physical and chemical properties requires characterization down to the nano-scale. A powerful technique to study the three-dimensional microstructure is X-ray tomography, but it lacks information about the chemistry of samples. To develop a methodology for measuring the multi-scale 3D microstructure of geological samples, correlative X-ray micro- and nanotomography were performed on two rocks followed by scanning electron microscopy with energy-dispersive spectroscopy (SEM-EDS) analysis. The study was performed in five steps: (i) micro X-ray tomography was performed on rock sample cores, (ii) samples for nanotomography were prepared using laser milling, (iii) nanotomography was performed on the milled sub-samples, (iv) samples were mounted and polished for SEM analysis and (v) SEM imaging and compositional mapping was performed on micro and nanotomography samples for complimentary information. Correlative study performed on samples of serpentine and basalt revealed multiscale 3D structures involving both solid mineral phases and pore networks. Significant differences in the volume fraction of pores and mineral phases were also observed dependent on the imaging spatial resolution employed. This highlights the necessity for the application of such a multiscale approach for the characterization of complex aggregates such as rocks. Information acquired from the chemical mapping of different phases was also helpful in segmentation of phases that did not exhibit significant contrast in X-ray imaging. Adoption of the protocol used in this study can be broadly applied to 3D imaging studies being performed at the Advanced Light Source and other user facilities.

We present first hard X-ray photoelectron spectroscopy (HAXPES) results of aqueous salt solutions and dispersions of gold nanoparticles in liquid cells equipped with specially designed microfabricated thin silicon nitride membranes, with thickness in the 15–25 nm range, mounted in a high-vacuum-compatible environment. The experiments have been performed at the HAXPES endstation of the GALAXIES beamline at the SOLEIL synchrotron radiation facility. The low-stress membranes are fabricated from 100 mm silicon wafers using standard lithography techniques. Platinum alignment marks are added to the chips hosting the membranes to facilitate the positioning of the X-ray beam on the membrane by detecting the corresponding photoemission lines. Two types of liquid cells have been used, a static one built on an Omicron-type sample holder with the liquid confined in the cell container, and a circulating liquid cell, in which the liquid can flow in order to mitigate the effects due to beam damage. We demonstrate that the membranes are mechanically robust and able to withstand 1 bar pressure difference between the liquid inside the cell and vacuum, and the intense synchrotron radiation beam during data acquisition. This opens up new opportunities for spectroscopic studies of liquids.