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 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.

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 X-ray diffraction measurements, the angular resolution has a detection limit due to the receiving size of the detector. In many cases this detection limit is too large and must be breached to obtain the desired information. A novel method is proposed here by making the detector simultaneously measuring and moving. Using the deconvolution algorithm to remove the convolution effect, the pixel size limitation is finally broken. The algorithm used is not a common one, and suppresses signals at high frequencies, ensuring the reliability of the peak shape after restoration. The feasibility of this method is verified by successfully measuring the crystal truncation rod signal of SrTiO3 single crystal, and the resolution is nearly ten times higher than that of a single pixel. Moreover, this method greatly reduces the noise and improves the signal-to-noise ratio.

During X-ray diffraction experiments on single crystals, the diffracted beam intensities may be affected by multiple-beam X-ray diffraction (MBD). This effect is particularly frequent at higher X-ray energies and for larger unit cells. The appearance of this so-called Renninger effect often impairs the interpretation of diffracted intensities. This applies in particular to energy spectra analysed in resonant experiments, since during scans of the incident photon energy these conditions are necessarily met for specific X-ray energies. This effect can be addressed by carefully avoiding multiple-beam reflection conditions at a given X-ray energy and a given position in reciprocal space. However, areas which are (nearly) free of MBD are not always available. This article presents a universal concept of data acquisition and post-processing for resonant X-ray diffraction experiments. Our concept facilitates the reliable determination of kinematic (MBD-free) resonant diffraction intensities even at relatively high energies which, in turn, enables the study of higher absorption edges. This way, the applicability of resonant diffraction, e.g. to reveal the local atomic and electronic structure or chemical environment, is extended for a vast majority of crystalline materials. The potential of this approach compared with conventional data reduction is demonstrated by the measurements of the Ta L3 edge of well studied lithium tantalate LiTaO3.

The Photoelectron-Related Image and Nano-Spectroscopy (PRINS) endstation located at the Taiwan Photon Source beamline 27A2 houses a photoelectron momentum microscope capable of performing direct-space imaging, momentum-space imaging and photoemission spectroscopy with position sensitivity. Here, the performance of this microscope is demonstrated using two in-house photon sources – an Hg lamp and He(I) radiation – on a standard checkerboard-patterned specimen and an Au(111) single crystal, respectively. By analyzing the intensity profile of the edge of the Au patterns, the Rashba-splitting of the Au(111) Shockley surface state at 300 K, and the photoelectron intensity across the Fermi edge at 80 K, the spatial, momentum and energy resolution were estimated to be 50 nm, 0.0172 Å−1 and 26 meV, respectively. Additionally, it is shown that the band structures acquired in either constant energy contour mode or momentum-resolved photoemission spectroscopy mode were in close agreement.

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

Large-bandwidth pulses produced by cutting-edge X-ray free-electron lasers (FELs) are of great importance in research fields like material science and biology. In this paper, a new method to generate high-power ultrashort FEL pulses with tunable spectral bandwidth with spectral coherence using a dielectric-lined waveguide without interfering operation of linacs is proposed. By exploiting the passive and dephasingless wakefield at terahertz frequency excited by the beam, stable energy modulation can be achieved in the electron beam and large-bandwidth high-intensity soft X-ray radiation can be generated. Three-dimensional start-to-end simulations have been carried out and the results show that coherent radiation pulses with duration of a few femtoseconds and bandwidths ranging from 1.01% to 2.16% can be achieved by changing the undulator taper profile.

The results of a study of the structural and reflective characteristics of short-period multilayer X-ray mirrors based on Mo/B4C at wavelengths 1.54 Å, 9.89 Å and 17.59 Å are presented. The period of the samples varied in the range 8–35 Å. The average widths of the interfaces were ∼3.5 and 2.2 Å at one and the other boundaries, with a tendency for weak growth with any decrease in the period. The interlayer roughness was ∼1 Å. The research results indicate promising prospects for the use of multilayer Mo/B4C mirrors for synchrotron applications.

The ForMAX beamline at the MAX IV Laboratory provides multiscale and multimodal structural characterization of hierarchical materials in the nanometre to millimetre range by combining small- and wide-angle X-ray scattering with full-field microtomography. The modular design of the beamline is optimized for easy switching between different experimental modalities. The beamline has a special focus on the development of novel fibrous materials from forest resources, but it is also well suited for studies within, for example, food science and biomedical research.

Various X-ray techniques are employed to investigate specimens in diverse fields. Generally, scattering and absorption/emission processes occur due to the interaction of X-rays with matter. The output signals from these processes contain structural information and the electronic structure of specimens, respectively. The combination of complementary X-ray techniques improves the understanding of complex systems holistically. In this context, we introduce a multiplex imaging instrument that can collect small-/wide-angle X-ray diffraction and X-ray emission spectra simultaneously to investigate morphological information with nanoscale resolution, crystal arrangement at the atomic scale and the electronic structure of specimens.

Experimental characterization of the structural, electronic and dynamic properties of dilute systems in aqueous solvents, such as nanoparticles, molecules and proteins, are nowadays an open challenge. X-ray absorption spectroscopy (XAS) is probably one of the most established approaches to this aim as it is element-specific. However, typical dilute systems of interest are often composed of light elements that require extreme-ultraviolet to soft X-ray photons. In this spectral regime, water and other solvents are rather opaque, thus demanding radical reduction of the solvent volume and removal of the liquid to minimize background absorption. Here, we present an experimental endstation designed to operate a liquid flat jet of sub-micrometre thickness in a vacuum environment compatible with extreme ultraviolet/soft XAS measurements in transmission geometry. The apparatus developed can be easily connected to synchrotron and free-electron-laser user-facility beamlines dedicated to XAS experiments. The conditions for stable generation and control of the liquid flat jet are analyzed and discussed. Preliminary soft XAS measurements on some test solutions are shown.

Imaging energy filters in photoelectron microscopes and momentum microscopes use spherical fields with deflection angles of 90°, 180° and even 2 × 180°. These instruments are optimized for high energy resolution, and exhibit image aberrations when operated in high transmission mode at medium energy resolution. Here, a new approach is presented for bandpass-filtered imaging in real or reciprocal space using an electrostatic dodecapole with an asymmetric electrode array. In addition to energy-dispersive beam deflection, this multipole allows aberration correction up to the third order. Here, its use is described as a bandpass prefilter in a time-of-flight momentum microscope at the hard X-ray beamline P22 of PETRA III. The entire instrument is housed in a straight vacuum tube because the deflection angle is only 4° and the beam displacement in the filter is only ∼8 mm. The multipole is framed by transfer lenses in the entrance and exit branches. Two sets of 16 different-sized entrance and exit apertures on piezomotor-driven mounts allow selection of the desired bandpass. For pass energies between 100 and 1400 eV and slit widths between 0.5 and 4 mm, the transmitted kinetic energy intervals are between 10 eV and a few hundred electronvolts (full width at half-maximum). The filter eliminates all higher or lower energy signals outside the selected bandpass, significantly improving the signal-to-background ratio in the time-of-flight analyzer.

In situ and operando investigation of photocatalysts plays a fundamental role in understanding the processes of active phase formation and the mechanisms of catalytic reactions, which is crucial for the rational design of more efficient materials. Using a custom-made operando photocatalytic cell, an in situ procedure to follow the formation steps of Pd/TiO2 photocatalyst by synchrotron-based X-ray absorption spectroscopy (XAS) is proposed. The procedure resulted in the formation of ∼1 nm Pd particles with a much narrower size distribution and homogeneous spreading over TiO2 support compared with the samples generated in a conventional batch reactor. The combination of in situ XAS spectroscopy with high-angle annular dark-field scanning transmission electron microscopy demonstrated the formation of single-atom Pd(0) sites on TiO2 as the initial step of the photodeposition process. Palladium hydride particles were observed for all investigated samples upon exposure to formic acid solutions.

The differentially pumped rare-gas filter at the end of the VUV beamline of the Swiss Light Source has been adapted to house a windowless absorption cell for gases. Absorption spectra can be recorded from 7 eV to up to 21 eV photon energies routinely, as shown by a new water and nitrous oxide absorption spectrum. By and large, the spectra agree with previously published ones both in terms of resonance energies and absorption cross sections, but that of N2O exhibits a small shift in the { ilde{f D}} band and tentative fine structures that have not yet been fully described. This setup will facilitate the measurement of absorption spectra in the VUV above the absorption edge of LiF and MgF2 windows. It will also allow us to carry out condensed-phase measurements on thin liquid sheets and solid films. Further development options are discussed, including the recording of temperature-dependent absorption spectra, a stationary gas cell for calibration measurements, and the improvement of the photon energy resolution.

Multilayer gratings are increasingly popular optical elements at X-ray beamlines, as they can provide much higher photon flux in the tender X-ray range compared with traditional single-layer coated gratings. While there are several proprietary software tools that provide the functionality to simulate the efficiencies of such gratings, until now the X-ray community has lacked an open-source alternative. Here MLgrating is presented, a program for simulating the efficiencies of both multilayer gratings and single-layer coated gratings for X-ray applications. MLgrating is benchmarked by comparing its output with that of other software tools and plans are discussed for how the program could be extended in the future.

A state-of-the-art multilayer deposition system with a 4200 mm-long linear substrate translator housed within an ultra-high vacuum chamber has been developed. This instrument is engineered to produce single and multilayer coatings, accommodating mirrors up to 2000 mm in length through the utilization of eight rectangular cathodes. To ensure the quality and reliability of the coatings, the system incorporates various diagnostic tools for in situ thickness uniformity and stress measurement. Furthermore, the system features an annealing process capable of heating up to 700°C within the load-lock chamber. The entire operation, including pump down, deposition and venting processes, is automated through user-friendly software. In addition, all essential log data, power of sputtering source, working pressure and motion positions are automatically stored for comprehensive data analysis. Preliminary commissioning results demonstrate excellent lateral film thickness uniformity, achieving 0.26% along the translation direction over 1500 mm in dynamic mode. The multilayer deposition system is poised for use in fabricating periodic, lateral-graded and depth-graded multilayers, specifically catering to the beamlines for diverse scientific applications at Diamond Light Source.

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

In the crystal structure of the title compound, {[Co(C11H9NSO5)(C10H9N3)]0.5C3H7NO·H2O}n or {[Co(dmtb)(dpa)]·0.5DMF·H2O}n (dmtb2– = 5-[(di­meth­yl­amino)­thioxometh­oxy]-1,3-benzene­dicarboxyl­ate and dpa = 4,4'-di­pyridyl­amine), an assembly of periodic [Co(C11H9NSO5)(C10H9N3)]n layers extending parallel to the bc plane is present. Each layer is constituted by distorted [CoO4N2] octa­hedra, which are connected through the μ2-coordination modes of both dmtb2– and dpa ligands. Occupationally disordered water and di­meth­yl­formamide (DMF) solvent mol­ecules are located in the voids of the network to which they are connected through hydrogen-bonding inter­actions.

In the title compound, [Mn(C68H44N12O4)(C5H8N2)]·2C6H5Cl, the central MnII ion is coordinated by four pyrrole N atoms of the porphyrin core in the basal sites and one N atom of the 2,5-di­methyl­imidazole ligand in the apical site. Two chloro­benzene solvent mol­ecules are also present in the asymmetric unit. Due to the apical imidazole ligand, the Mn atom is displaced out of the 24-atom porphyrin mean plane by 0.66 Å. The average Mn—Np (p = porphyrin) bond length is 2.143 (8) Å, and the axial Mn—NIm (Im = 2,5-di­methyl­imidazole) bond length is 2.171 (8) Å. The structure displays inter­molecular and intra­molecular N—H⋯O, N—H⋯N, C—H⋯O and C—H⋯N hydrogen bonding. The crystal studied was refined as a two-component inversion twin.

The title cobalt(II) complex, [Co(C2H3N)3(C9H21N3)](C24H20B)2 or [(tacn)Co(NCMe)3][BPh4]2, has been characterized by single-crystal X-ray diffraction. It incorporates the well-known macrocyclic tacn (1,4,7-trimethyl-1,4,7-tri­aza­cyclo­nona­ne) ligand, which is coordinated facially to the metal center. The complex crystallizes in space group P21/c with Z = 4. The divalent cobalt ion exhibits a six-coordinate octa­hedral geometry by one tacn and three aceto­nitrile ligands. Two non-coordinating tetra­phenyl­borate (BPh4−) anions are also present.

In the title compound, [Co(C8H6N3O2)Cl(C2H5OH)]n, the CoII atoms adopt octa­hedral trans-CoN2O4 and tetra­hedral CoCl2O2 coordination geometries (site symmetries overline{1} and m, respectively). The bridging μ3-O:O:N 2-(benzotriazol-1-yl)acetato ligands connect the octa­hedral cobalt nodes into (010) sheets and the CoCl2 fragments link the sheets into a tri-periodic network. The structure displays O—H⋯O hydrogen bonding and the ethanol mol­ecule is disordered over two orientations.

The title coordination polymer, [Co(N3)2(C9H8N2)]n, was synthesized solvothermally. The CoII atom exhibits a distorted octa­hedral [CoN6] coordination geometry with a bidentate 8-amino­quinoline ligand and four azide ligands. Bridging azide ligands result in chains extending along [100]. N—H⋯N hydrogen bonds join the chains to give an extended structure with sheets parallel to (002).

The structures of five ammonium salt forms of mono­sulfonated azo dyes, derivatives of 4-(2-phenyldiazen-1-yl)benzenesulfonate, with the general formula [NH4][O3S(C6H4)NN(C6H3)RR']·XH2O [R = OH, NH2 or N(C2H4OH)2; R' = H or OH] are presented. All form simple layered structures with alternating hydro­phobic (organic) and hydro­philic (cation, solvent and polar groups) layers. To assess for isostructural behaviour of the ammonium cation with M+ ions, the packing of these structures is compared with literature examples. To aid this comparison, the corresponding structures of four potassium salt forms of the mono­sulfonated azo dyes are also presented herein. Of the five ammonium salts it is found that three have isostructural equivalents. In two cases this equivalent is a potassium salt form and in one case it is a rubidium salt form. The isostructurality of ion packing and of unit-cell symmetry and dimensions tolerates cases where the ammonium ions form somewhat different inter­action types with coformer species than do the potassium or rubidium ions. No sodium salt forms are found to be isostructural with any ammonium equivalent. However, similarities in the anion packing within a single hydro­phobic layer are found for a group that consists of the ammonium and rubidium salt forms of one azo anion species and the sodium and silver salt forms of a different azo species.

The influence of the crystal synthesis method on the crystallographic structure of caffeine–citric acid co­crystals was analyzed thanks to the synthesis of a new polymorphic form of the cocrystal. In order to com­pare the new form to the already known forms, the crystal structure of the new cocrystal (C8H10N4O2·C6H8O7) was solved by powder X-ray diffraction thanks to synchrotron experiments. The structure determination was performed using `GALLOP', a recently developed hybrid approach based on a local optimization with a particle swarm optimizer, particularly powerful when applied to the structure resolution of materials of pharmaceutical inter­est, com­pared to classical Monte-Carlo simulated annealing. The final structure was obtained through Rietveld refinement, and first-principles density functional theory (DFT) calculations were used to locate the H atoms. The symmetry is triclinic with the space group Poverline{1} and contains one mol­ecule of caffeine and one mol­ecule of citric acid per asymmetric unit. The crystallographic structure of this cocrystal involves different hydrogen-bond associations com­pared to the already known structures. The analysis of these hydrogen bonds indicates that the cocrystal obtained here is less stable than the co­crystals already identified in the literature. This analysis is confirmed by the determination of the melting point of this cocrystal, which is lower than that of the previously known co­crystals.

The salt ammonium 2-am­ino­mal­on­ate (systematic name: ammonium 2-aza­niumyl­propane­dioate), NH4+·C3H4NO4−, was synthesized in diethyl ether from the starting materials malonic acid, ammonia and bromine. The salt was recrystallized from water as colourless blocks. In the solid state, intra­molecular medium–strong N—H⋯O, weak C—H⋯O and weak C—H⋯N hydrogen bonds build a three-dimensional network.

A series of organotin heterocycles of general formula [{Me2C(C6H3CH2)2O}SnR2] [R = methyl (Me, 4), n-butyl (n-Bu, 5), benzyl (Bn, 6) and phenyl (Ph, 7)] was easily synthesized by a Barbier-type reaction assisted by the sonochemical activation of metallic magnesium. The 119Sn{1H} NMR data for all four com­pounds confirm the presence of a central Sn atom in a four-coordinated environment in solution. Single-crystal X-ray diffraction studies for 17,17-dimethyl-7,7-di­phenyl-15-oxa-7-stanna­tetra­cyclo­[11.3.1.05,16.09,14]hepta­deca-1,3,5(16),9(14),10,12-hexa­­ene, [Sn(C6H5)2(C17H16O)], 7, at 100 and 295 K con­firmed the formation of a mono­nuclear eight-membered heterocycle, with a conformation depicted as boat–chair, resulting in a weak Sn⋯O inter­action. The Sn and O atoms are surrounded by hydro­phobic C—H bonds. A Hirshfeld surface analysis of 7 showed that the eight-membered heterocycles are linked by weak C—H⋯π, π–π and H⋯H noncovalent inter­actions. The pairwise inter­action energies showed that the cohesion between the heterocycles are mainly due to dispersion forces.

Treating the amide acetanilide (N-phenyl­acetamide, C8H9NO) with aqueous strong acids allowed the structures of five hemi-protonated salt forms of acetanilide to be elucidated. N-(1-Hy­droxy­ethyl­idene)anilinium chloride–N-phenyl­acetamide (1/1), [(C8H9NO)2H][Cl], and the bromide, [(C8H9NO)2H][Br], triiodide, [(C8H9NO)2H][I3], tetra­fluoro­borate, [(C8H9NO)2H][BF4], and di­iodo­bromide hemi(diiodine), [(C8H9NO)2H][I2Br]·0.5I2, analogues all feature centrosymmetric dimeric units linked by O—H⋯O hy­dro­gen bonds that extend into one-dimensional hy­dro­gen-bonded chains through N—H⋯X inter­actions, where X is the halide atom of the anion. Protonation occurs at the amide O atom and results in systematic lengthening of the C=O bond and a corresponding shortening of the C—N bond. The size of these geometric changes is similar to those found for hemi-protonated paracetamol structures, but less than those in fully protonated paracetamol structures. The bond angles of the amide fragments are also found to change on protonation, but these angular changes are also influenced by conformation, namely, whether the amide group is coplanar with the phenyl ring or twisted out of plane.

The synthesis and structural characterization of four novel supra­molecular hy­dro­gen-bonded arrangements based on self-assembly from mol­ecular `[Cu(2,2'-bi­imid­az­ole)]' modules and malonate anions are pre­sent­ed, namely, tetra­kis­(2,2'-bi­imid­az­ole)di-μ-chlorido-dimal­on­atotricopper(II) penta­hydrate, [Cu3(C3H2O4)2Cl2(C6H6N4)4]·5H2O or [Cu(H2biim)2(μ-Cl)Cu0.5(mal)]2·5H2O, aqua­(2,2'-bi­imid­az­ole)­mal­on­atocopper(II) dihydrate, [Cu(C3H2O4)(C6H6N4)(H2O)]·2H2O or [Cu(H2biim)(mal)(H2O)]·2H2O, bis­[aqua­bis­(2,2'-bi­imid­az­ole)­cop­per(II)] di­mal­on­atodi­perchloratocopper(II) 2.2-hydrate, [Cu(C6H6N4)2(H2O)]2[Cu(C3H2O4)(ClO4)2]·2.2H2O or [Cu(H2biim)2(H2O)]2[Cu(mal)2(ClO4)2]·2.2H2O, and bis­(2,2'-bi­imid­az­ole)­copper(II) bis­[bis­(2,2'-bi­imid­az­ole)(2-carb­oxy­acetato)mal­on­atocopper(II)] tridecahydrate, [Cu(C6H6N4)2][Cu(C3H2O4)(C3H3O4)(C6H6N4)2]·13H2O or [Cu(H2biim)2][Cu(H2biim)2(Hmal)(mal)]2·13H2O. These as­sem­blies are characterized by self-com­plementary donor–acceptor mol­ecular inter­actions, demonstrating a recurrent and distinctive pattern of hy­dro­gen-bonding preferences among the carboxyl­ate, carb­oxy­lic acid and N—H groups of the coordinated 2,2'-bi­imid­az­ole and malonate ligands. Additionally, co­or­din­ation of the carboxyl­ate group with the metallic centre helps sustain re­mark­able supra­molecular assemblies, such as layers, helices, double helix columns or 3D channeled architectures, including mixed-metal com­plexes, into a single structure.

The crystal structure of the salt calcium (2R,3R)-tar­trate tetra­hydrate {sys­tem­atic name: poly[[di­aqua­[μ4-(2R,3R)-2,3-di­hydroxy­butane­dioato]calcium(II)] di­hydrate]}, {[Ca(C4H8O8)(H2O)2]·2H2O}n, is reported. The absolute configuration of the crystal was established unambiguously using anomalous dispersion effects in the diffraction patterns. High-quality data also allowed the location and free refinement of all the H atoms, and therefore to a careful analysis of the hy­dro­gen-bond inter­actions.

Fatty acid-derivative prodrugs have been utilized extensively to improve the physicochemical, biopharmaceutical and pharmacokinetic properties of active pharmaceutical ingredients. However, to our knowledge, the crystallization behavior of prodrugs modified with different fatty acids has not been explored. In the present work, a series of paliperidone aliphatic prodrugs with alkyl chain lengths ranging from C4 to C16 was investigated with respect to crystal structure, crystal morphology and crystallization kinetics. The paliperidone derivatives exhibited isostructural crystal packing, despite the different alkyl chain lengths, and crystallized with the dominant (100) face in both melt and solution. The rate of crystallization for paliperidone derivatives in the melt increases with alkyl chain length owing to greater molecular mobility. In contrast, the longer chains prolong the nucleation induction time and reduce the crystal growth kinetics in solution. The results show a correlation between difficulty of nucleation in solution and the interfacial energy. This work provides insight into the crystallization behavior of paliperidone aliphatic prodrugs and reveals that the role of alkyl chain length in the crystallization behavior has a strong dependence on the crystallization method.

As an important characterization method, pair distribution function (PDF) has been extensively used in structural analysis of nanomaterials, providing key insights into the degree of crystallinity, atomic structure, local disorder etc. The collection of scattering signals with good statistics is necessary for a reliable structural analysis. However, current conventional electron diffraction experiments using PDF (ePDF) are limited in their ability to acquire continuous diffraction rings for large nanoparticles. Herein, a new method – tilt-ePDF – is proposed to improve the data quality and compatibility of ePDF by a combination of electron diffraction and specimen tilting. In the present work, a tilt-series of electron diffraction patterns was collected from gold nanoparticles with three different sizes and a standard sample polycrystalline aluminium film for ePDF analysis. The results show that tilt-ePDF can not only enhance the continuity of diffraction rings, but can also improve the signal-to-noise ratio in the high scattering angle range. As a result, compared with conventional ePDF data, tilt-ePDF data provide structure parameters with a better accuracy and lower residual factors in the refinement against the crystal structure. This method provides a new way of utilizing ePDF to obtain accurate local structure information from nanoparticles.

Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235–244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740–751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92–109; Jha et al. (2021). J. Appl. Cryst. 54, 1234–1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyl­uracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.

Owing to their exceptional properties, hard materials such as advanced ceramics, metals and composites have enormous economic and societal value, with applications across numerous industries. Understanding their microstructural characteristics is crucial for enhancing their performance, materials development and unleashing their potential for future innovative applications. However, their microstructures are unambiguously hierarchical and typically span several length scales, from sub-ångstrom to micrometres, posing demanding challenges for their characterization, especially for in situ characterization which is critical to understanding the kinetic processes controlling microstructure formation. This review provides a comprehensive description of the rapidly developing technique of ultra-small angle X-ray scattering (USAXS), a nondestructive method for probing the nano-to-micrometre scale features of hard materials. USAXS and its complementary techniques, when developed for and applied to hard materials, offer valuable insights into their porosity, grain size, phase composition and inhomogeneities. We discuss the fundamental principles, instrumentation, advantages, challenges and global status of USAXS for hard materials. Using selected examples, we demonstrate the potential of this technique for unveiling the microstructural characteristics of hard materials and its relevance to advanced materials development and manufacturing process optimization. We also provide our perspective on the opportunities and challenges for the continued development of USAXS, including multimodal characterization, coherent scattering, time-resolved studies, machine learning and autonomous experiments. Our goal is to stimulate further implementation and exploration of USAXS techniques and inspire their broader adoption across various domains of hard materials science, thereby driving the field toward discoveries and further developments.

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.

Ultrahigh-resolution structures provide unprecedented details about protein dynamics, hydrogen bonding and solvent networks. The reported 0.70 Å, room-temperature crystal structure of crambin is the highest-resolution ambient-temperature structure of a protein achieved to date. Sufficient data were collected to enable unrestrained refinement of the protein and associated solvent networks using SHELXL. Dynamic solvent networks resulting from alternative side-chain conformations and shifts in water positions are revealed, demonstrating that polypeptide flexibility and formation of clathrate-type structures at hydro­phobic surfaces are the key features endowing crambin crystals with extraordinary diffraction power.

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.

MltG, a membrane-bound lytic transglycosyl­ase, has roles in terminating glycan polymerization in peptidoglycan and incorporating glycan chains into the cell wall, making it significant in bacterial cell-wall biosynthesis and remodeling. This study provides the first reported MltG structure from Mycobacterium abscessus (maMltG), a superbug that has high antibiotic resistance. Our structural and biochemical analyses revealed that MltG has a flexible peptidoglycan-binding domain and exists as a monomer in solution. Further, the putative active site of maMltG was disclosed using structural analysis and sequence comparison. Overall, this study contributes to our understanding of the transglycosyl­ation reaction of the MltG family, aiding the design of next-generation antibiotics targeting M. abscessus.

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.

Ion radii are derived here from the characteristic (grand mean) bond lengths for (i) 135 ions bonded to oxygen in 459 configurations (on the basis of coordination number) using 177 143 bond lengths extracted from 30 805 ordered coordination polyhedra from 9210 crystal structures; and (ii) 76 ions bonded to nitro­gen in 137 configurations using 4048 bond lengths extracted from 875 ordered coordination polyhedra from 434 crystal structures. There are two broad categories of use for ion radii: (1) those methods which use the relative sizes of cation and anion radii to predict local atomic arrangements; (2) those methods which compare the radii of different cations (or the radii of different anions) to predict local atomic arrangements. There is much uncertainty with regard to the relative sizes of cations and anions, giving rise to the common failure of type (1) methods, e.g. Pauling's first rule which purports to relate the coordination adopted by cations to the radius ratio of the constituent cation and anion. Conversely, type (2) methods, which involve comparing the sizes of different cations with each other (or different anions with each other), can give very accurate predictions of site occupancies, physical properties etc. Methods belonging to type (2) can equally well use the characteristic bond lengths themselves (from which the radii are derived) in place of radii to develop correlations and predict crystal properties. Extensive quantum-mechanical calculations of electron density in crystals in the literature indicate that the radii of both cations and anions are quite variable with local arrangement, suggesting significant problems with any use of ion radii. However, the dichotomy between the experimentally derived ion radii and the quantum-mechanical calculations of electron density in crystals is removed by the recognition that ion radii are pr­oxy variables for characteristic bond lengths in type (2) relations.

It is pointed out that many authors are unaware that the particular choice of unit-cell origin determines the irreducible representations to which octahedral tilts in perovskites belong. Furthermore, a recommendation is made that the preferred option is with the origin at the B-cation site rather than that of the A site.

The title compound, [Co(NCS)2(C6H7NO)]n or Co(NCS)2(2-methyl­pyridine N-oxide), was prepared by the reaction of Co(NCS)2 and 2-methyl­pyridine N-oxide in methanol. All crystals obtained by this procedure show reticular pseudo-merohedric twinning, but after recrystallization, one crystal was found that had a minor component with only a very few overlapping reflections. The asymmetric unit consists of one CoII cation, two thio­cyanate anions and one 2-methyl­pyridine N-oxide coligand in general positions. The CoII cations are octa­hedrally coordinated by two O-bonding 2-methyl­pyridine N-oxide ligands, as well as two S- and two N-bonding thio­cyanate anions, and are connected via μ-1,3(N,S)-bridging thio­cyanate anions into chains that are linked by μ-1,1(O,O) bridging coligands into layers. No pronounced directional inter­molecular inter­actions are observed between the layers. The 2-methyl­pyridine coligand is disordered over two orientations and was refined using a split model with restraints. Powder X-ray diffraction (PXRD) indicates that a pure sample was obtained and IR spectroscopy confirms that bridging thio­cyanate anions are present. Thermogravimetry and differential thermoanalysis (TG-DTA) shows one poorly resolved mass loss in the TG curve that is accompanied by an exothermic and an endothermic signal in the DTA curve, which indicate the decomposition of the 2-methyl­pyridine N-oxide coligands.

Syntheses of the acyclic amidinium salts, morpholino­formamidinium hexa­fluorido­phosphate [OC4H8N—CH=NH2]PF6 or C5H11N2O+·PF6−, 1, and pyrrolidinoformamidinium hexa­fluorido­phosphate [C4H8N—CH= NH2]PF6 or C5H11N2+·PF6−, 2, were carried out by heating either morpholine or pyrrolidine with triethyl orthoformate and ammonium hexa­fluorido­phosphate. Crystals of 1 obtained directly from the reaction mixture contain one cation and one anion in the asymmetric unit. The structure involves cations linked in chains parallel to the b axis by N—H⋯O hydrogen bonds in space group Pbca, with glide-related chains pointing in opposite directions. Crystals of 1 obtained by recrystallization from ethanol, however, showed a similar unit cell and the same basic structure, but unexpectedly, there was positional disorder [occupancy ratio 0.639 (4):0.361 (4)] in one of the cation chains, which lowered the crystal symmetry to the non-centrosymmetric space group Pca21, with two cations and anions in the asymmetric unit. In the pyrrolidino compound, 2, cations and anions are ordered and are stacked separately, with zigzag N—H⋯F hydrogen-bonding between stacks, forming ribbons parallel to (101), extended along the b-axis direction. Slight differences in the delocalized C=N distances between the two cations may reflect the inductive effect of the oxygen atom in the morpholino compound.

Reaction of CoBr2 with 2-methyl­pyridine N-oxide in n-butanol leads to the formation of the title compound, [CoBr2(C6H7NO)2] or [CoBr2(2-methyl­pyridine N-oxide)2]. Its asymmetric unit consists of one CoII cation as well as two bromide anions and two 2-methyl­pyridine N-oxide coligands in general positions. The CoII cations are tetra­hedrally coordinated by two bromide anions and two 2-methyl­pyridine N-oxides, forming discrete complexes. In the crystal structure, these complexes are linked predominantly by weak C–H⋯Br hydrogen bonding into chains that propagate along the crystallographic a-axis. Powder X-ray diffraction (PXRD) measurements indicate that a pure phase was obtained. Thermoanalytical investigations prove that the title compound melts before decomposition; before melting, a further endothermic signal of unknown origin was observed that does not correspond to a phase transition.

The reaction of Co(NCS)2 with 4-methyl­pyridine N-oxide (C6H7NO) leads to the formation of two compounds, namely, tetra­kis­(4-methyl­pyridine N-oxide-κO)bis­(thio­cyanato-κN)cobalt(II), [Co(NCS)2(C6H7NO)4] (1), and tris­(4-methyl­pyridine N-oxide-κO)bis­(thio­cyanato-κN)cobalt(II), [Co(NCS)2(C6H7NO)3] (2). The asymmetric unit of 1 consists of one CoII cation located on a centre of inversion, as well as one thio­cyanate anion and two 4-methyl­pyridine N-oxide coligands in general positions. The CoII cations are octa­hedrally coordinated by two terminal N-bonding thio­cyanate anions in trans positions and four 4-methyl­pyridine N-oxide ligands. In the extended structure, these complexes are linked by C—H⋯O and C—H⋯S inter­actions. In compound 2, two crystallographically independent complexes are present, which occupy general positions. In each of these complexes, the CoII cations are coordinated in a trigonal–bipyramidal manner by two terminal N-bonding thio­cyanate anions in axial positions and by three 4-methyl­pyridine N-oxide ligands in equatorial positions. In the crystal, these complex mol­ecules are linked by C—H⋯S inter­actions. For compound 2, a nonmerohedral twin refinement was performed. Powder X-ray diffraction (PXRD) reveals that 2 was nearly obtained as a pure phase, which is not possible for compound 1. Differential thermoanalysis and thermogravimetry data (DTA–TG) show that compound 2 start to decompose at about 518 K.

The crystal structure of the tetra­ethyl­ammonium salt of the non-steroidal anti-inflammatory drug nimesulide (polymorph II) (systematic name: tetra­ethyl­ammonium N-methane­sulfonyl-4-nitro-2-phen­oxy­anilinide), C8H20N+·C13H11N2O5S−, was determined using single-crystal X-ray diffraction. The title compound crystallizes in the monoclinic space group P21/c with one tetra­ethyl­ammonium cation and one nimesulide anion in the asymmetric unit. In the crystal, the ions are linked by C—H⋯N and C—H⋯O hydrogen bonds and C—H⋯π inter­actions. There are differences in the geometry of both the nimesulide anion and the tetra­ethyl­ammonium cation in polymorphs I [Rybczyńska & Sikorski (2023). Sci. Rep. 13, 17268] and II of the title compound.

The crystal structure of the sodium salt of mesotrione, namely, catena-poly[[sodium-μ3-2-[(4-methane­sulfonyl-2-nitro­phen­yl)carbon­yl]-3-oxo­cyclo­hex-1-en-1-olato] ethanol monosolvate], {[Na(C14H12NO7S)]C2H5OH}n, is described. The X-ray structural analysis results reveal that the coordination sphere is established by two chelating O atoms, the O atom of the coordinated ethanol mol­ecule, and an O atom from the methyl­sulfonyl group of a neighboring mol­ecule. Simultaneously, an O atom of the cyclo­hexane fragment serves as a bridge to a neighboring sodium ion, forming a flat Na–O–Na–O quadrangle, thereby forming a mono-periodic polymer. The structure displays O—H⋯O hydrogen bonds and C—H⋯O short contacts. Thermogravimetric analysis (TGA) data indicate that the sodium salt of mesotrione decomposes in four stages.

Reaction of Co(NCS)2 with 2-methyl­pyridine N-oxide in a 1:3 ratio in n-butanol leads to the formation of crystals of tris­(2-methyl­pyridine N-oxide-κO)bis­(thio­cyanato-κN)cobalt(II), [Co(NCS)2(C6H7NO)3]. The asymmetric unit of the title compound consists of one CoII cation two thio­cyanate anions and three crystallographically independent 2-methyl­pyridine N-oxide coligands in general positions. The CoII cations are trigonal–bipyramidally coordinated by two terminal N-bonding thio­cyanate anions in the trans-positions and three 2-methyl­pyridine N-oxide coligands into discrete complexes. These complexes are linked by inter­molecular C–H⋯S inter­actions into double chains that elongate in the c-axis direction. Powder X-ray diffraction (PXRD) measurements prove that all batches are always contaminated with an additional and unknown crystalline phase. Thermogravimetry and differential analysis of crystals selected by hand reveal that the title compound decomposes at about 229°C in an exothermic reaction. At about 113°C a small endothermic signal is observed that, according to differential scanning calorimetry (DSC) measurements, is irreversible. PXRD measurements of the residue prove that a poorly crystalline and unknown phase has formed and thermomicroscopy indicates that some phase transition occurs that is accompanied with a color change of the title compound.

Reaction of Co(NCS)2 with 4-methyl­pyridine N-oxide in methanol leads to the formation of crystals of the title compound, [Co2(NCS)4(C6H7NO)4(CH4O)2] or Co2(NCS)4(4-methyl­pyridine N-oxide)4(methanol)2. The asymmetric unit consist of one CoII cation, two thio­cyanate anions, two 4-methyl­pyridine N-oxide coligands and one methanol mol­ecule in general positions. The H atoms of one of the methyl groups are disordered and were refined using a split model. The CoII cations octa­hedrally coordinate two terminal N-bonded thio­cyanate anions, three 4-methyl­pyridine N-oxide coligands and one methanol mol­ecule. Each two CoII cations are linked by pairs of μ-1,1(O,O)-bridging 4-methyl­pyridine N-oxide coligands into dinuclear units that are located on centers of inversion. Powder X-ray diffraction (PXRD) investigations prove that the title compound is contaminated with a small amount of Co(NCS)2(4-meth­yl­pyridine N-oxide)3. Thermogravimetric investigations reveal that the methanol mol­ecules are removed in the beginning, leading to a compound with the composition Co(NCS)2(4-methyl­pyridine N-oxide), which has been reported in the literature and which is of poor crystallinity.

The title compound, [Co(C3H4N2)(C30H30N10)](BF4)2, is a five-coordinate CoII complex based on the neutral ligands tris­[(1-benzyl­triazol-4-yl)meth­yl]amine (tbta) and imidazole. It exhibits a distorted trigonal bipyramidal geometry in which the equatorial positions are occupied by the three N-atom donors from the triazole rings of the tripodal tbta ligand. The apical amine N-atom donor of tbta and the N-atom donor of the imidazole ligand occupy the axial positions of the coordination sphere. Two tetra­fluoro­borate anions provide charge balance in the crystal.