Open-access and free articles in Journal of Applied Crystallography
Journal of Applied Crystallography covers a wide range of crystallographic topics from the viewpoints of both techniques and theory. The journal presents articles on the application of crystallographic techniques and on the related apparatus and computer software. For many years, Journal of Applied Crystallography has been the main vehicle for the publication of small-angle scattering articles and powder diffraction techniques. The journal is the primary place where crystallographic computer program information is published.
Copyright (c) 2026 International Union of Crystallography
Differences in hierarchical structural changes between unoriented P(3HB) and P(3HB-co-3HH) under stretching. Corrigendum
P(3HB); P(3HB-CO-3HH); CRYSTALLINE POLYMERS; USAXS; ULTRA-SMALL-ANGLE X-RAY SCATTERING; STRETCH-INDUCED DENSITY FLUCTUATIONS; IN SITU X-RAY SCATTERING
Lattice strain relaxation in thin Mo films grown heteroepitaxially on MgO single crystals
Mechanisms of the lattice strain relaxation in molybdenum thin films that were grown heteroepitaxially on (001)- and (011)-oriented MgO wafers using magnetron sputtering were studied using a combination of X-ray and electron diffraction and transmission electron microscopy. For the Mo film grown on (001)-oriented MgO, the X-ray diffraction pole figure measurements revealed (001)Mo ∥ (001)MgO & [110]Mo ∥ [100]MgO as the main orientation relationship. On the (011)-oriented MgO, the Mo film grew with the orientations (112)Mo ∥ (011)MgO & ±[110]Mo ∥ [100]MgO. In all cases, the stress generated by the lattice misfit exceeded the elastic deformation limit of Mo, which activated the lattice strain relaxation mechanisms, mainly the formation of dislocations and slip and twinning on the lattice planes {112}. The dominant relaxation mechanism depends on the mutual orientation between the film and the substrate, which defines the direction of the deformation force in the film. In the (001)-oriented film, the lattice strain produced by the lattice misfit was reduced by twinning and dislocations. In the film having the (112) orientation, the main relaxation mechanism was the formation of dislocations. In both cases, the deformation energy was additionally reduced by the small lateral size of the Mo crystallites.
HETEROEPITAXY; THIN FILMS; ORIENTATION RELATIONSHIPS; LATTICE MISFIT; STRESS RELAXATION; X-RAY DIFFRACTION; CRYSTALLITE GROUP METHOD; TRANSMISSION ELECTRON MICROSCOPY; ELECTRON DIFFRACTION
Describing neutron spin echo data from undulating lipid vesicles: recent advances
For almost 30 years, the Zilman–Granek stretched exponential [Zilman & Granek (1996). Phys. Rev. Lett. 77, 4788–4791] has been used to obtain bending rigidities of membranes in lipid and surfactant vesicles from neutron spin echo data. However, with the advent of improved spectrometers that can easily measure Fourier times up to some 100 ns and even 1 µs, more subtle effects become visible in the data, which requires a refined theory. Recently, we published a framework for analysing such neutron spin echo data [Granek et al. (2024). Eur. Phys. J. E 47, 12]. Here, we apply this framework to different model membranes. The purpose of this paper is twofold. We intend to elucidate some often overlooked parameters, such as vesicle diffusion, size, lamellarity and membrane tension, that limit the quantitative interpretation of bending modulus values from NSE data. We also present some future opportunities to better understand the membrane dynamics and major sources of dissipation at the nanoscale uniquely probed with NSE.
NEUTRON SPIN ECHO; MEMBRANE DYNAMICS; VESICLES
Impact of substrate curvature on grazing-incidence small-angle X-ray scattering signal: theory and example of Ag thin-film growth
Grazing-incidence small-angle X-ray scattering (GISAXS) is a technique of choice for providing information about the morphology of nano- and micro-structures at surfaces and interfaces, also in real time. The geometry of the sample, in particular its curvature, has an impact on the observed X-ray scattering signal. There are a multitude of systems with sophisticated geometries (including curvature), ranging from electronic devices on flexible substrates to biological membranes, for which GISAXS could provide valuable information. Therefore, in this work the effect of the sample geometry on the GISAXS signal is addressed. More specifically the influence of the substrate curvature and extent along the X-ray beam is considered. The analytical expressions accounting for the effects of those two geometrical parameters are provided, and the way to include them in the analysis of GISAXS patterns is described. The calculations reveal that no corrections are needed for small samples (length over distance to the detector ratio smaller than 1%) and radius of curvature |R| > 50 m. These results allow for a combination of GISAXS with substrate curvature measurements. The latter technique is a non-destructive in situ and real-time method providing information about the intrinsic stress in a thin film during its growth. Morphological information from GISAXS is supposed to complement this stress information. Herein this methodology is applied to the growth of Ag thin films deposited by magnetron sputtering with N2 plasma additive. The analysis of the GISAXS pattern obtained from the sample, which bends during the deposition, provided morphological parameters of the growing film. This methodology can be useful for understanding of the mechanisms at the nanoscale leading to the observed stress state. The ability to perform GISAXS on curved substrates enables its application to more complex systems.
GRAZING-INCIDENCE SMALL-ANGLE X-RAY SCATTERING; GISAXS; SUBSTRATE CURVATURE; THIN-FILM GROWTH; STRESS; REAL-TIME TECHNIQUES
Common misconceptions in crystallography and crystal optics
Did you know that an X-ray diffraction pattern is not a spectrum? However, one in five scientific papers showing X-ray diffraction patterns refers to them as `X-ray spectra'. Further, and in contrast to what is stated in many reference books, a triclinic substance could have a cubic-shaped cell. In crystal optics the terminology `parallel Nicols' is almost always misused, and in the frame of polarizing microscope observations zoning is sometimes mistaken for twinning. In this paper, six recurring misconceptions in crystallography, including several related to mineral and crystal optics, are analyzed. Their prevalence is assessed through statistical data on their persistent appearances in peer-reviewed scientific literature. The objective of this study is to promote the correction of these misconceptions in academic communication and teaching. Furthermore, and according to some learning theories, the explanation of well established misconceptions could be used by teachers as an educational resource, offering powerful learning opportunities and contributing to talent development.
MISCONCEPTIONS; X-RAY DIFFRACTION; CELL RESTRICTIONS; CRYSTAL OPTICS; XRD SPECTRA
pygid: a Python package for fast data reduction in grazing-incidence diffraction
Advances in X-ray and neutron sources, as well as in area-detector technologies, enable the recording of several terabytes of raw two-dimensional detector data in a single experiment. While several efficient integration and conversion tools are available for data collected in transmission geometry, analogous solutions for grazing-incidence diffraction (including grazing-incidence X-ray diffraction and grazing-incidence wide-angle X-ray scattering) experiments have not yet achieved the same level of efficiency. The development of new data analysis tools, including machine-learning-based software for X-ray data, necessitates the establishment of a standardized format for the converted data. To address these challenges, we have developed a new Python library, pygid, which is designed to facilitate fast data processing while providing compatibility with various raw data formats, a standardized data storage format and an intuitive interface for straightforward use. pygid supports three types of coordinate systems and both transmission and grazing-incidence geometries. It is capable of handling large datasets, performing one-dimensional line cuts and simulating expected Bragg peak positions for given structures. The package facilitates sample and experimental metadata curation in accordance with the FAIR principles. As an integral part of the broader mlgid pipeline, pygid serves as the initial step linking raw scattering patterns with machine learning tools for data analysis. The pygid package is accessible at https://github.com/mlgid-project.
PYTHON PACKAGES; DATA REDUCTION; DATA ANALYSIS; GRAZING-INCIDENCE X-RAY DIFFRACTION GIXD; GRAZING-INCIDENCE WIDE-ANGLE X-RAY SCATTERING GIWAXS; GRAZING-INCIDENCE SMALL-ANGLE X-RAY SCATTERING GISAXS; WIDE-ANGLE X-RAY SCATTERING WAXS; SMALL-ANGLE X-RAY SCAT
Evolution of crystallographic texture and material anisotropy effects resulting from uniaxial deformation for high-strength steels with high manganese content
Steels used in the automotive industry have seen significant improvements within the past few decades, as economic and environmental efficiency play major and increasing roles in current individual transportation. In particular, it has been possible to combine high formability with high strength, which contributes to passenger safety, vehicle performance and efficiency. Deep-drawing steels with higher manganese content play a special role in the class of automotive body sheet materials, in which the final mechanical properties are achieved, for example, through twinning-induced plasticity and/or transformation-induced plasticity effects. In this study, the deformation behavior of steels X40MnCrAlV-19-2.5-2, HCT690T and S355MC was investigated using laboratory X-ray diffraction analyses. The investigations cover the evolution of crystallographic texture and material anisotropy resulting from uniaxial deformation, as well as their influence on diffraction data, especially in the context of stress analyses. In contrast to the situation in the initial as-rolled state, the induced deformations up to the limit of uniform elongation lead to the formation of strong textures and a considerable impairment of the diffraction data due to material anisotropy. However, the formed crystallographic textures do not suffice to describe this impairment. Rather, this effect is mainly attributable to intergranular strains, which are caused by different degrees of deformation of individual crystallites within the elasto-plastic regime. These phenomena need to be considered, and this is demonstrated using the application example of a welded metal sheet. Correction approaches are proposed and their application is illustrated, with a focus on how readily the residual stresses can be evaluated.
TRIP/TWIP STEELS; ELASTIC ANISOTROPY; CRYSTALLOGRAPHIC TEXTURE; INTERGRANULAR STRAINS
Magnetic-lens-generated polarized neutron beam with enhanced intensity and Q resolution for small-angle neutron scattering
We installed a 30 mm-bore 3.2 m-long magnetic lens in the small-angle neutron scattering diffractometer (SANS-J) at the Japan Research Reactor 3 to focus the neutron beam near the sample position for measurements at Q > 0.1 nm−1. The focused beam at the sample position was over three times more intense than the standard non-focused beam, while the Q resolution was improved. The positive spin component of the neutron beam was focused near the sample, whereas the negative spin component was defocused and blocked by the slit just in front of the sample, producing a polarized beam. The 8 mm-diameter focusing polarized beam achieved a polarization of 0.95–0.96 and an intensity up to 22 times greater than that of a non-focusing polarized beam with the same collimation length. Using this beam with a remanent supermirror-coated spin analyser, we demonstrate that polarization analysis measurements of hydrogen-containing samples can be completed within tens of minutes.
NEUTRON MAGNETIC LENSES; POLARIZATION ANALYSIS; POLARIZED SMALL-ANGLE NEUTRON SCATTERING
From symmetry operations to dimensional restrictions: a mathematical formalization of unit-cell constraints for the seven crystal systems in crystallography
While the dimensional constraints of crystal systems are well documented in crystallography, chemistry and materials science textbooks, their pedagogical presentation predominantly relies on descriptive narratives lacking rigorous mathematical derivation, resulting in incomplete comprehension and persistent misconceptions among both instructors and learners. This study establishes a mathematical framework connecting symmetry operations with metrical restrictions through a systematic analysis of symmetry operation representation matrices. By developing transformation matrix derivations for the basis vectors, a, b and c, we demonstrate how dimensional constraints emerge inherently from rotational symmetry requirements. Our derivations rigorously confirm the conventional unit-cell dimensional constraints while providing critical arguments against the use of inequality constraints in non-cubic systems. Examples across representative non-cubic crystals with cubic metric specializations are provided to fulfill the conventional teaching paradigms. The formalization process offers a pedagogically understandable and accessible methodology to replace current approaches.
CRYSTALLOGRAPHIC CONSTRAINTS; UNIT-CELL GEOMETRY; SYMMETRY OPERATIONS; CRYSTAL SYSTEM CLASSIFICATION
Direct calculation of variable-resolution maps by fully analytic approximations to atomic images
Crystallographic maps are typically computed as Fourier series using complex-valued structure factors, with a single set of coefficients applied across the entire region and associating a single resolution value with the whole map. In cryo-electron microscopy, however, experimental maps often have variable local resolution. As a consequence, applying the same procedure to compute model maps for comparison with the respective experimental ones becomes complicated. An alternative strategy involves representing model maps as sums of atomic images. They are oscillatory functions of the distance from the atomic center and depend on atomic displacement parameters and local resolution. To calculate such maps, we propose a stand-alone program which uses the shell-function approximation of atomic images, making them analytic functions of all their parameters including the local resolution associated with each atom.
CRYO-EM; VARIABLE-RESOLUTION MAPS; DIRECT MAP CALCULATION; LOCAL RESOLUTION; SHELL FUNCTIONS; ANALYTIC APPROXIMATION; COMPUTER PROGRAMS
Adaptively coupled phase retrieval in multi-peak Bragg coherent diffraction imaging
Recent advances in Bragg coherent diffraction imaging (BCDI) experimental techniques permit routine measurement of multiple Bragg peaks from a single crystalline grain. The resulting images contain the full lattice distortion vector field which can be differentiated to provide lattice strain and rotation. With the advent of fourth-generation synchrotron light sources, such multi-peak datasets are produced at high rates, facilitating the need for rapid phase retrieval of the multiple peaks and subsequent image analysis. Here we describe and demonstrate a new implementation of a coupled phase retrieval technique for multi-peak BCDI which simultaneously treats each Bragg peak of the dataset and produces a three-dimensional image of the crystal's morphology and lattice distortion field. In addition, this method uses the redundant information contained in the various Bragg diffraction patterns to detect and suppress spurious signal appearing on the detector in a subset of the measurements. Compared with manual data editing, adaptive coupling produces a more consistent phase profile in reciprocal space and sharper surfaces in direct space, with no significant difference in computational cost. These improvements reduce the need for manual preprocessing and enable robust high-throughput analysis of multi-peak BCDI data, supporting near-real-time strain microscopy at modern synchrotron facilities.
X-RAY DIFFRACTION; STRAIN MICROSCOPY; BRAGG COHERENT DIFFRACTION IMAGING; PHASE RETRIEVAL
Scattering from `Babinet' particles (or not…): spherical particles made up of spheres and spherical particles with spherical voids
The small-angle scattering form factors of two classes of composite particles with contrasting internal architectures have been studied: one consisting of inclusions of smaller spheres embedded within a larger sphere, and the other comprising a solid sphere with randomly distributed spherical voids. These systems serve as material- and void-based analogues, providing a model framework for examining how internal material distribution in porous particles influences scattering signatures. Monte Carlo simulations were used to generate scattering curves across a range of volume fractions and polydispersities, which were then employed to benchmark analytically derived form factor expressions. Steric repulsion between, respectively, spheres and voids was taken as hard-sphere interactions. The results reveal that internal structural asymmetries, especially in spatial correlations and contrast topology, significantly affect scattering patterns, despite the particles having similar overall structures and volume fractions. In particular, spheres-of-spheres structures exhibit features in the scattering signal from internal modulations, while void-based particles display smoother shell-like scattering features. The analytical models show excellent agreement with the simulated data, capturing both the global shape and fine structural characteristics. These findings demonstrate that relatively simple analytical approaches, validated against numerical simulations, can reliably describe complex heterogeneous particles. This methodology provides a robust basis for interpreting scattering data from porous and composite materials across a wide range of applications.
SMALL-ANGLE SCATTERING; COMPOSITE PARTICLES; INTERNAL STRUCTURE; MONTE CARLO SIMULATIONS; ANALYTICAL FORM FACTORS; POLYDISPERSITY
X-ray data reconstruction from incomplete data sampling
For specific setups, a diffraction pattern can contain gaps or missing information. For example, that is the case when several detectors are used simultaneously, but a particular angular range is not covered between each detector. In this article, a procedure for the reconstruction of the missing signal is proposed. It is based on a modified Papoulis–Gerchberg algorithm that considers features of the diffraction pattern without loss of generality. The mathematical basis of the algorithm is presented, and several cases, simulated and experimental, are used to test the performance and robustness of the proposed solution.
X-RAY DIFFRACTION; SAMPLING; PAPOULIS-GERCHBERG
Anomalous X-ray diffraction on hybrid perovskite thin films: results and challenges
Anomalous X-ray diffraction has been applied for structure determination in both biological and inorganic systems. The ability to create elemental contrast by varying the X-ray energy around the absorption edge of a specific element makes it a viable tool to probe and locate specific elements within a crystal structure, providing valuable complementary information to standard X-ray diffraction. Considering the large amount of research on hybrid organic–inorganic perovskites for photovoltaic applications, it is surprising that anomalous diffraction experiments on these materials are rather under-explored. In recent years, hybrid lead halide perovskite materials have evolved as a promising material class for next-generation photovoltaic devices, as well as further applications. X-ray diffraction methods, including grazing-incidence and in situ techniques, are routinely implemented for structural investigations. This work presents anomalous diffraction studies on each component of hybrid metal halide perovskites, i.e. metal cation, halide anion and central cation, providing an overview of the opportunities and challenges associated with applying anomalous X-ray diffraction to hybrid metal halide perovskites. The results are consistent with model calculations on (pseudo-)cubic perovskite structures.
LEAD HALIDE PEROVSKITES; ANOMALOUS X-RAY DIFFRACTION; THIN FILMS; HYBRID MATERIALS
Room-temperature structure determination of vacuum-sensitive organic compounds by formvar encapsulation and serial electron diffraction
Samples used in electron microscopy are traditionally required to be stable under vacuum. However, many organic compounds with high vapor pressures readily sublime at room temperature, a process that is further accelerated under the high-vacuum conditions of an electron microscope. Here, we demonstrate for the first time the structure determination of vacuum-sensitive organic compounds in their solid state at room temperature using electron crystallography. Serial electron diffraction was employed to obtain sub-Å-resolution structures of anthracene and pyrene, two representative organic molecules which sublimate under the high-vacuum conditions of a transmission electron microscope. This was made possible by a simple sample preparation technique in which ultrathin crystals are encapsulated with a formvar layer to prevent sublimation under vacuum. By combining serial electron diffraction with formvar encapsulation, we demonstrate high-resolution structure determination of vacuum-sensitive samples at room temperature rather than cryogenic conditions. Moreover, by avoiding low-temperature phase transitions that can alter material properties, this method expands the accessible temperature range for studying the structural characteristics of vacuum-sensitive materials.
STRUCTURE DETERMINATION; TEM SAMPLE PREPARATION; TRANSMISSION ELECTRON MICROSCOPY; ELECTRON DIFFRACTION; ORGANIC MOLECULES; ROOM-TEMPERATURE DIFFRACTION STUDIES; FORMVAR
The moving-beam diffraction geometry: the DIAD application of a diffraction scanning probe
Understanding the interactions between microstructure, strain, phase and material behavior is crucial in scientific fields such as energy storage, carbon sequestration and biomedical engineering. However, quantifying these correlations is challenging, as it requires the use of multiple instruments and techniques, often separated by space and time. The Dual Imaging and Diffraction (DIAD) beamline at Diamond Light Source is designed to address this challenge. DIAD allows its users to visualize internal structures (in two and three dimensions), identify compositional/phase changes and measure strain. It enables in situ and operando experiments that require spatially correlated information. DIAD provides two independent beams combined at one sample position, allowing `quasi-simultaneous' X-ray computed tomography and X-ray powder diffraction. A unique functionality of the DIAD configuration is the ability to perform `image-guided diffraction', where the micrometre-sized diffraction beam is scanned over the complete area of the imaging field of view without moving the specimen. This moving-beam diffraction geometry enables the study of fast-evolving and motion-susceptible processes and samples. Here, we discuss the novel moving-beam diffraction geometry, presenting the latest findings on the reliability of both the geometry calibration and the data-reduction routines used. We provide a comprehensive quantitative assessment of the moving-beam diffraction geometry implemented at the DIAD beamline, which will serve as a reference for beamline users. Our measurements confirm that diffraction is most sensitive to the moving-beam geometry for the conventional transmission geometry of the detector. The observed data confirm that the motion of the Kirkpatrick–Baez mirror coupled with a fixed-aperture slit results in a rigid translation of the beam probe, without affecting the angle of the incident-beam path to the sample. Our measurements demonstrate that a nearest-neighbor calibration can achieve the same accuracy as a self-calibrated geometry when the distance between the calibrated and probed sample regions is smaller than or equal to the beam spot size. The absolute error of the moving-beam diffraction geometry at DIAD with typical calibration setup remains below 0.01%, which is the accuracy we observe for the beamline with stable beam operation.
MOVING-BEAM DIFFRACTION GEOMETRY; DIFFRACTION SCANNING PROBES; AREA-DETECTOR DIFFRACTION-GEOMETRY CALIBRATION; DIAD BEAMLINE; NEAREST-NEIGHBOR GEOMETRY CALIBRATION
A bond valence sum method to identify potential new fluoride ion conductors
The bond valence sum (BVS) method has been extensively used to probe the ionic diffusion pathways within solids possessing high ionic conductivities, both anionic and cationic. For the former, the presence of lone-pair cations such as Tl+, Sn2+, Pb2+, Sb3+ and Bi3+ is known to enhance the anionic conductivity of solids by promoting disorder within the anion substructure and lowering the energy barriers between lattice sites. However, the BVS formalism assumes spherical ions and does not include the possibility of the more irregular co­ordination environments associated with electron lone pairs. We present here a simple modification of the BVS approach, which has been implemented in the form of a Python program that permits the preferred F− diffusion pathways to be determined in fluoride ion conductors containing lone-pair cations. The method has been benchmarked by calculating energy barriers that broadly correlate with the F− ionic conductivities of known compounds, and successfully reproduces the F− distribution within the highly conducting compound β-PbSnF4 determined by neutron powder diffraction and molecular dynamics (MD) methods. Using this new approach, fluoride compounds within the Inorganic Crystal Structure Database that contain at least one lone-pair cation have been screened and several new potential F− ion conductors have been identified.
FLUORIDE CONDUCTORS; BOND VALENCE SUMS; LONE-PAIR ELECTRONS; IONIC DIFFUSION; MATERIALS DISCOVERY
Assessing the problem of excitation light scattering in high-viscosity jets used in serial crystallography sample delivery
Serial crystallography for time-resolved structural studies of light-triggered reactions often employs high-viscosity jets to deliver crystals into an X-ray beam. A potential complication is that pump light can scatter within the jet to unintentionally irradiate yet-to-be-probed portions of the jet – a problem known as light contamination. Importantly, by transporting light out of the nominal interaction region, light scattering can reduce the effective irradiation energy density experienced by the diffracting crystal. This issue, which can even jeopardize an experiment, has proven rather controversial. To provide direct insight, we performed custom femtosecond transient absorption experiments with spatially displaced pump and probe beams directed onto actual jets under realistic experimental conditions, allowing the distribution of excited molecules along the flowing jet to be mapped out explicitly. To characterize the underlying light scattering properties of commonly used jet media, the Kubelka–Munk formalism was utilized. Our results show that, in contrast to flat-cell geometries, which we found to exhibit minimal light contamination, the cylindrical geometry of jets can facilitate a degree of light spill-over. The excitation energy density loss due to the scattering is less than 30% in realistic experimental conditions. This highlights the importance of carefully selecting jet media and laser parameters to minimize light-scattering-induced artefacts when undertaking pump–probe serial crystallography experiments.
TIME-RESOLVED SERIAL CRYSTALLOGRAPHY; PUMP-PROBE EXPERIMENTS; PHOTOEXCITATION; LIGHT CONTAMINATION; LIGHT SCATTERING; HIGH-VISCOSITY JETS
Efficient detection of deformation-induced microstructural modifications in polycrystalline micropillars using scanning X-ray nanodiffraction
Microstructural characterization of polycrystalline micropillars remains a significant challenge, particularly under time constraints such as those encountered during in situ or other time-sensitive experimental conditions, where appropriate data checks might assist in taking the right decision and have influence on the outcome of the experiment. In this study, we present a fast and efficient method for estimating local structural properties using scanning X-ray nanodiffraction—a technique widely employed in various dynamic and static micro- and nanoscale material investigations. The analysis targets the strongest diffraction peaks within the scattering pattern to extract essential information on grain orientation, size and lattice strain, while excluding weaker signals to streamline processing. As a case study, a γ-TiAl-based micropillar (Ti–46.5Al–5Nb), fabricated via Xe+ plasma focused-ion-beam milling, was analyzed before and after 10% uniaxial compression. The micropillar's grain size significantly exceeded the X-ray beam size (∼300 nm2), and its known crystallographic orientation enabled accurate tracking of structural evolution. A direct point-to-point comparison between the undeformed and compressed states revealed localized microstructural changes associated with plastic deformation. This approach provides a rapid and reliable means of assessing microstructural evolution and demonstrates high potential for in situ and operando investigations of small-scale materials.
POLYCRYSTALLINE MICROPILLARS; X-RAY NANODIFFRACTION; X-RAY FLUORESCENCE; NANOMECHANICAL TESTING; X-RAY DATA ANALYSIS; DEFORMATION; MICROSTRUCTURE
Revisiting the structures and phase transitions of PrNiO3 nickelate using symmetry-mode analysis
We have investigated the complete sequence of temperature-induced structural phase transitions in PrNiO3 using high-angular-resolution synchrotron X-ray diffraction and symmetry-adapted distortion-mode analysis. By employing a high-purity sample synthesized under high pressure (3.5 GPa at 1073 K), we resolve the monoclinic (P21/n) → orthorhombic (Pbnm) → rhombohedral (R3c) evolution over an extended temperature range (10–900 K). Beyond confirming the role of oxygen stretching modes in the insulator–metal transition at ∼130 K, we show that these phonon modes also govern the high-temperature metallic–metallic transition at ∼750 K. This work provides a comprehensive mode-resolved picture of both insulator and metallic regimes in PrNiO3 and highlights the central role of phonon-mediated processes in driving charge disproportionation and lattice symmetry breaking across all the crystalline phases.
RNIO3 PEROVSKITES; PHASE TRANSITIONS; SYMMETRY-MODE ANALYSIS; METAL-INSULATOR TRANSITIONS
A simple goniometer-compatible flow cell for serial synchrotron X-ray crystallography. Corrigendum
SERIAL SYNCHROTRON X-RAY CRYSTALLOGRAPHY; MACROMOLECULAR CRYSTALLOGRAPHY; CYTOCHROME C OXIDASE; GONIOMETER-COMPATIBLE FLOW CELLS
Quantifying interflake ordering in graphene oxide films via wide-angle X-ray scattering analysis
We report a methodology based on wide-angle X-ray scattering (WAXS) to quantify the ordering between graphene oxide (GO) flakes in self-assembled films. By comparing WAXS signals of GO and graphite, we extract orientation distribution coefficients (S) from the GO 001 and (100) scattering features. To characterize the anisotropy in flake alignment, we define a ratio parameter (R) as the quotient of orientation distribution coefficients obtained under orthogonal orientations from the normal direction of the GO film with respect to the X-ray beam. This dimensionless ratio allows us to assess the degree of meso­structural anisotropy and condenses comparative orientation information into a single dimensionless metric, providing a new structural parameter for GO and related layered materials. In our measurements, R reached values of 0.11 for the GO 001 signal. These results demonstrate a metric for characterizing anisotropy in disordered 2D materials.
WIDE-ANGLE X-RAY SCATTERING; GRAPHENE OXIDE FILMS; ANISOTROPY QUANTIFICATION
Seismic noise in crystal neutron interferometry
We are involved in designing, constructing and operating a split-crystal interferometer that uses X-rays and neutrons simultaneously. Neutron interferometers are sensitive to seismic and acoustic noise due to the low speed, low flux and long detection time of thermal neutrons. The crystal splitting and the increased length and separation of the interferometer arms further heighten this sensitivity. To support the interferometer design and operation, we present an estimate of the root-mean-square phase noise when the interferometer is passively isolated from ground accelerations.
NEUTRON INTERFEROMETRY; INTERFERENCE VISIBILITY; SEISMIC NOISE; PHASE NOISE; SPLIT-CRYSTAL INTERFEROMETRY; INTERFERENCE FRINGES
Sample environment for simultaneous quasi-elastic neutron scattering and Raman spectroscopy experiments demonstrated on polymer films under changing humidity and temperature
Understanding the dynamic and structural properties of matter across different timescales and length scales is essential for elucidating their functionality. We focus here on soft-matter systems, which are typically particularly sensitive to relative humidity (RH) and temperature, necessitating well controlled experimental conditions. Quasi-elastic neutron scattering (QENS) and Raman spectroscopy offer complementary insights: QENS accesses diffusional dynamics, which are stochastic motions, while Raman spectroscopy provides information on periodic vibrational dynamics. To enable simultaneous QENS and Raman measurements on e.g. polymer films under controlled and variable RH and temperature, we have developed a dedicated sample environment (SE), which in the presented experiments covers an RH range of 5–85% and a temperature range of 20–50°C. This SE features a 3D-printed spherical chamber including a sample holder for films, a Raman spectrometer, a custom-built gas-flow system and a thermostat. The chamber can accommodate large samples (up to 5 × 5 cm) and provides space for additional measurement equipment. The 3D-printing technique allows the integration of channels into the chamber walls, which are used for cooling and heating, resulting in highly homogeneous temperature distributions. This is key to achieving a uniform humidity in the chamber. The chamber works with a variety of solvents and their mixtures, like heavy water or ethanol. We demonstrate the feasibility of this setup through simultaneous QENS and Raman measurements on poly(3,4-ethylene di­oxy­thio­phene):poly(styrene­sulfonate) films on Si substrates, confirming that the chamber provides a stable and low scattering background environment.
QUASI-ELASTIC NEUTRON SCATTERING; RAMAN SPECTROSCOPY; POLYMER FILMS; IN SITU HYDRATION; SAMPLE ENVIRONMENTS
Advancing small-angle X-ray scattering for complex metallic systems: Ti2Cu precipitation in a martensitic near-α Ti alloy
Small-angle X-ray scattering (SAXS) experiments performed at synchrotron radiation sources enable the in situ study of precipitation behaviour, providing crucial information for alloy design. Numerous studies have demonstrated the successful use of SAXS to investigate precipitation phenomena across a wide range of complex metallic systems. Nevertheless, despite its advantages, the application of SAXS remains often overlooked owing to the challenges associated with data analysis, especially under non-isothermal conditions in which a metal matrix is continuously evolving due to simultaneous phase transformations and microstructural coarsening. This work presents a novel SAXS modelling approach developed for the quantitative evaluation of precipitate formation in metallic systems exhibiting scattering signals superimposed on directionally streaked signals originating from the embedding matrix, as commonly found in martensitic microstructures. Two-dimensional synchrotron data recorded during a continuous in situ heating experiment on a Cu- and Si-containing near-α Ti alloy are used to demonstrate how the evolving SAXS signal can be separated into matrix- and precipitation-related contributions. A Guinier–Porod function linked to a grain coarsening model was used to describe the background signal from the matrix, while Ti2Cu precipitates were modelled using an ellipsoidal model function combined with a lognormal size distribution. This combined approach enabled the evaluation of precipitate volume fraction and size distribution throughout the heat treatment. The SAXS results were validated through complementary transmission electron microscopy and atom probe tomography experiments, showing excellent agreement in both size and phase fraction. The presented methodology allows the successful capture of early-stage precipitation and provides an adaptable solution to background modelling challenges in non-isothermal SAXS experiments. This approach expands the applicability of SAXS for precipitation studies in structurally complex alloy systems.
SMALL-ANGLE X-RAY SCATTERING; TITANIUM ALLOYS; PRECIPITATION KINETICS; MARTENSITIC MICROSTRUCTURE; METHODOLOGY
Automated and real-time structure solution using 3D electron diffraction
Three-dimensional electron diffraction (3D ED) has emerged as a powerful tool for solving the structures of small crystals down to nanometre-scale sizes. Despite advancements in automating data acquisition for 3D ED, the subsequent data processing and structure solution have largely relied on human intervention and have been mostly conducted offline. This reliance on expertise in electron crystallography and the lack of real-time feedback on data quality and structural information have limited the broader adoption of 3D ED. Here, we introduce Instamatic-solve, a fully automated, real-time structure solution pipeline for 3D ED deployed on a JEOL JEM 2100 transmission electron microscope. Instamatic-solve streamlines the entire process by automating the subsequent data processing and structure solution, providing real-time assessments of data quality and structural information. Moreover, the pipeline can handle offline 3D ED data acquired from various transmission electron microscope platforms. Using Instamatic-solve, we have successfully solved the crystal structures of diverse materials, including seven inorganic zeolites, two inorganic–organic hybrids and four organic molecules (including pharmaceuticals), all within 2 min. Instamatic-solve mimics the typical manual structure solution process, and its outcomes depend heavily on data quality. Our results indicate that a routine and reliable structure solution is achievable in most cases, provided that the data meet critical quality criteria, namely completeness ≥50% and resolution better than 1.0 Å. By enabling efficient, automated and real-time structure solution for crystalline materials, Instamatic-solve spans various scientific disciplines.
3D ELECTRON DIFFRACTION; AUTOMATED STRUCTURE SOLUTION; INSTAMATIC-SOLVE
Optimal ratio or historical convention: the use of methanol–ethanol mixtures as pressure-transmitting mediums
We employ a combined computational and experimental approach to systematically assess the hydrostatic properties of methanol–ethanol (MeOH–EtOH) mixtures of varying compositions, with the aim of evaluating their suitability as pressure-transmitting mediums (PTMs). PTMs are essential for enabling the characterization of materials properties at high pressure, perhaps most prominently in the context of diffraction measurements, to provide uniform compression and avoid strain on the sample. Molecular dynamics (MD) simulations indicate that the hydrostatic limit and several structural and dynamic properties of the widely used 4:1 MeOH–EtOH volume ratio do not exhibit any significant deviations from the monotonic trends observed as a function of MeOH content within the mixture. These findings are in agreement with X-ray pair distribution function measurements, which show no peculiar structural behaviour for the 4:1 composition. Experimental measurements of the hydrostatic limit confirm this result and demonstrate that, as previously reported, the role of ethanol is primarily to delay MeOH crystallization. However, we find that the same role can be fulfilled by other small molecules, such as propan-2-ol. Additional simulations of several MeOH–X binary mixtures suggest that these results might hold for a variety of similar mixtures. Thus, our findings indicate that the 4:1 ratio is neither peculiar nor optimal in terms of PTM performance; instead, its popularity seems to be mostly due to the influence of previous literature. Indeed, we find that the 9:1 MeOH–EtOH mixture is characterized by a hydrostatic limit which is superior (by nearly 1 GPa) to that observed for the 4:1 ratio. These findings offer a promising alternative PTM composition which is readily available, and pave the way towards future work aimed at the rational design of novel PTMs.
PRESSURE TRANSMITTING MEDIUMS; MOLECULAR DYNAMICS; HYDROSTATICITY; HIGH-PRESSURE CRYSTALLOGRAPHY
The AI-based phase-seeding (AI-PhaSeed) method: early applications and statistical analysis
The crystallographic challenge of structure determination is nowadays effectively supported by advanced computational methods, such as direct methods and Patterson techniques, implemented in sophisticated software. With the rapid expansion of artificial intelligence (AI) across diverse scientific domains, exploring its potential contribution to structure solution and its ability to overcome the limitations of traditional approaches has become increasingly compelling. This work builds upon and extends the findings of two recent studies on AI-driven phasing. The first, by Larsen et al. [Science (2024), 385, 522–528], focused on designing and applying a neural network architecture to solve small structures (with unit-cell volumes up to 1000 Å3), primarily within the most common centrosymmetric space group P21/c. The second, by Carrozzini et al. [Acta Cryst. (2025), A81, 188–201], introduced a novel phase-seeding method applicable to both centro­symmetric and non-centrosymmetric crystal structures of varying complexity, from small molecules to proteins. Although designed with AI integration in mind, this latter method had not yet been tested within an AI framework. In this paper, we apply the method proposed by Carrozzini et al. to cases where seed phases are generated by the AI network developed by Larsen et al. We demonstrate that this combined approach, termed AI-PhaSeed, successfully extends the applicability of Larsen's neural network to structures with unit-cell volumes exceeding 1000 Å3, even under conditions of limited experimental resolution. The proposed procedure has been extensively tested on a set of structures taken from the Crystallography Open Database, proving it to be a powerful and reliable tool for structure solution. We also provide insights into the use of AI for crystallographic phasing and introduce statistical tools to evaluate the robustness of the solution process based on AI-calculated phases.
CRYSTAL STRUCTURE SOLUTION; PHASE SEEDING; ARTIFICIAL INTELLIGENCE; AI PHASING
Physics-informed machine learning analysis for nanoscale grain mapping by synchrotron Laue microdiffraction
Understanding the grain morphology, orientation distribution and crystal structure of nanocrystals is essential for optimizing the mechanical and physical properties of functional materials. Synchrotron X-ray Laue microdiffraction is a powerful technique for characterizing crystal structures and orientation mapping using focused X-rays. However, when the grain sizes are smaller than the beam size, mixed peaks in the Laue pattern from neighboring grains limit the resolution of grain morphology mapping. We propose a physics-informed machine learning (PIML) approach that combines a convolutional neural network feature extractor with a physics-informed filtering algorithm to overcome the spatial resolution limits of X-rays, achieving nanoscale resolution for grain mapping. Our PIML method successfully resolves the grain size, orientation distribution and morphology of Au nanocrystals through synchrotron microdiffraction scans, showing good agreement with electron backscatter diffraction results. This PIML-assisted synchrotron microdiffraction analysis can be generalized to other diffraction-based probes, enabling the characterization of nanosized structures with micrometre-sized probes.
SYNCHROTRON LAUE MICRODIFFRACTION; PHYSICS-INFORMED MACHINE LEARNING; NANOCRYSTALS; GRAIN MAPPING; X-RAY CRYSTALLOGRAPHY
X-ray reflectivity from micrometre-scaled surfaces using nanobeams
Sample and diffractometer alignment for grazing-incidence X-ray measurements become ever more crucial once the beam and surface area of interest reach the nanometre scale. Here we show how a point of interest on a surface can be kept in the beam while measuring X-ray reflectivity, even if it is not in the centre of rotation, either because of systematic errors or additional unwanted angle-dependent sample movement. This can be achieved by a 1D trajectory scan varying the angle of incidence (θ), the detector angle (2θ) and the position of the sample along one axis in the scattering plane. As an example, we show the results of X-ray reflectivity measured from a 10 × 10 µm Au island using a 90 nm beam. Data analysis is presented which considers the angle-dependent X-ray beam footprint illuminating both the Au island and the surrounding support.
Structural analysis of co-sputtered Cu–Nb and Cu–Pd textured thin films
Structural characterization of nanoscale two-metal-phase systems, which exhibit partial, complete or no mixing when co-sputtered with a few percent of a minority element, is extremely challenging. Co-sputtering two metals at room temperature results in frozen disorder within the deposited films. Distinguishing the contribution of each metal phase, determining the distribution and self-organization of the second constituent element within the Cu matrix, accurately quantifying the extra element content, and assessing internal disorder through diffraction analysis are complex and require the development of a suitable model to fit diffraction patterns from various geometries. Here, we present a model to describe the structural distribution of alloy elements in magnetron-sputtered Cu thin films, exploring two contrasting cases: (1) with the mutually immiscible Nb and (2) with Pd, which has a negative heat of mixing with Cu, forming stable alloys. A comparison between X-ray diffraction data and energy-dispersive X-ray spectroscopy derived elemental distribution is discussed.
CO-SPUTTERING; X-RAY DIFFRACTION MODELING; THIN FILMS; MICROSTRUCTURE; SCANNING ELECTRON MICROSCOPY; ENERGY-DISPERSIVE SPECTROSCOPY; NANOSCALE TWO-METAL-PHASE SYSTEMS
The crystal structure of dypingite: understanding the long-range disorder
Dypingite, a hydrated magnesium carbonate hydroxide mineral [Mg5(CO3)4(OH)2·XH2O, X = 5–6], exhibits promising catalytic and purification properties. Although it was discovered 55 years ago, the crystal structure of this compound has remained unknown due to its aggregated morphology and structural disorder. This work investigates the origin of this phenomenon through a systematic analysis of synthetic and natural mineral samples, using synchrotron powder X-ray diffraction, thermogravimetric analysis and transmission electron microscopy. The findings reveal that ambient humidity significantly influences dypingite's structural properties at room temperature. High humidity (80% relative humidity at 22 °C) causes inhomogeneous expansion of the unit cell along the crystallographic c axis, leading to long-range structural disorder. Conversely, at 20% relative humidity at 22 °C, the mineral structure exhibits a shorter c lattice constant and reduced structural disorder. Chemical analysis reveals that samples kept at 80% and 20% relative humidity for 10 days differ by one molecule of water of hydration, yielding Mg5(CO3)4.5(2)(OH)0.96(3)·6.0(2)H2O and Mg5(CO3)4.5(2)(OH)1.02(4)·5.0(2)H2O, respectively. The results obtained demonstrate that the crystal structure of dehydrated dypingite [Mg5(CO3)4.5(2)(OH)1.02(4)·5.0(2)H2O] derives from hydro­magnesite's unit cell tripled along the a axis. The analysis of the mineral crystal structure provides insight into the role of humidity on the structural properties of dypingite, including unit-cell dimensions and long-range disorder.
DYPINGITE; STRUCTURAL DISORDER; UNIAXIAL ELONGATION; MAGNESIUM HYDROXY CARBONATES; LONG-RANGE DISORDER
Laboratory three-dimensional X-ray micro-beam Laue diffraction
The development of 3D non-destructive X-ray characterization techniques in home laboratories is essential for enabling many more researchers to perform 3D characterization daily, overcoming the limitations imposed by competitive and scarce access to synchrotron facilities. Recent efforts have focused on techniques such as laboratory diffraction contrast tomography (LabDCT). LabDCT allows 3D characterization of recrystallized grains with sizes larger than 15–20 µm, offering a boundary resolution of approximately 5 µm using commercial X-ray computed tomography (CT) systems. To enhance the capa­bil­ities of laboratory instruments, we have developed a new laboratory-based 3D X-ray micro-beam diffraction (Lab-3DµXRD) technique. Lab-3DµXRD combines the use of a focused polychromatic beam with a scanning-tomographic data acquisition routine to enable depth-resolved crystallographic orientation characterization. This work presents the first realization of Lab-3DµXRD, including hardware development through the integration of a newly developed Pt-coated twin paraboloidal capillary X-ray focusing optics into a conventional X-ray micro-computed tomography (µCT) system, as well as the development of data acquisition and processing software. The results are validated through comparisons with LabDCT and synchrotron phase contrast tomography. The findings clearly demonstrate the feasibility of Lab-3DµXRD, particularly in detecting smaller grains and providing intragranular information. Finally, we discuss future directions for developing Lab-3DµXRD into a versatile tool for studying materials with smaller grain sizes and high defect densities, including the potential of combining it with LabDCT and µCT for multiscale and multimodal microstructural characterization.
THREE DIMENSIONAL X-RAY DIFFRACTION; 3DXRD; LABORATORY DIFFRACTION CONTRAST TOMOGRAPHY; LAUE MICRO-BEAM DIFFRACTION; SCANNING 3DXRD; INTRAGRANULAR ORIENTATION
Extending the depth range in energy-dispersive X-ray stress analysis by simultaneous multi-detector data acquisition in equatorial scattering geometry
A scattering geometry for depth-resolved energy-dispersive X-ray stress analysis on polycrystalline materials is introduced. Via simultaneous data acquisition during a sin2 ψ measurement using two detectors arranged in the horizontal diffraction plane, it aims to extend the accessible information depth to the free surface as well as deeper material zones. While data acquisition with the first detector takes place in a symmetrical configuration with regard to the incident and exit angles, αi and αe, respectively, the second detector runs in an asymmetrical mode, defined by αi < αe. Therefore, the scattering vectors assigned to the two diffraction geometries run in different tilt planes during a χ scan of the sample performed in the Eulerian cradle. Treatment of the data recorded in the asymmetric diffraction mode requires modifications of the fundamental equation of X-ray stress analysis, which are discussed using the example of measurements performed on a unidirectionally ground ferritic steel sample.
X-RAY STRESS ANALYSIS; ENERGY-DISPERSIVE DIFFRACTION; TWO-DETECTOR SETUPS; HORIZONTAL SCATTERING GEOMETRY; STRESS GRADIENTS; POLYCRYSTALLINE MATERIALS
DXRD: a user-friendly suite of two- and multiple-beam dynamical X-ray diffraction programs
The DXRD program suite consisting of a series of dynamical theory programs is introduced for computing dynamical X-ray diffraction from single crystals. Its interactive graphical user interfaces (GUIs) allow general users to make complicated calculations with minimal effort. It can calculate plane-wave Darwin curves of single crystals (or multiple crystals) for both the Bragg and Laue cases, including grazing-incidence diffraction and backward diffraction (with Bragg angles approaching 90°). It is also capable of simulating rocking curves for divergent incident X-ray beams with finite bandwidths. A unique feature of DXRD is that it provides a convenient GUI-based multiple-beam diffraction program that can accurately compute arbitrary N-beam diffraction of any geometry using a universal 4N × 4N matrix method. DXRD also provides a mapping program for plotting all the multiple-beam diffraction lines (monochromator glitches) in the azimuth–energy coordinate system. All these functions make DXRD a convenient and powerful software tool for designing crystal-based synchrotron/X-ray optics (monochromators, analyzers, polarizers, phase plates etc.) and for crystal characterization, X-ray spectroscopy and X-ray diffraction teaching.
X-RAY DYNAMICAL THEORY; MULTIPLE-BEAM DIFFRACTION; DARWIN CURVES; MONOCHROMATOR GLITCHES; BRAGG REFLECTION
Exploring humidity effects on polycrystalline human insulin–ligand complexes: preliminary crystallographic insights
This study investigates the effect of relative humidity (RH) on the crystal structures of human insulin (HI) complexes with organic ligands, m-cresol and m-nitro­phenol, using in situ X-ray powder diffraction (XRPD) with a controlled-humidity chamber. Co-crystallization at pH 7.5 produced hexagonal microcrystals (space group R3) for both protein–ligand complexes. The corresponding single-crystal X-ray diffraction structures were solved: HI–m-cresol (PDB entry 9ibb, 1.84 Å) and HI–m-nitro­phenol (PDB entry 9qld, 2.55 Å). Pawley analysis of the in situ XRPD data revealed structural stability up to 70% RH, with no phase transitions observed. At lower humidity levels, reduced diffraction intensities indicated loss of crystallinity, which was fully restored upon rehydration to 95% RH. Notably, each complex exhibited distinct changes in unit-cell parameters during dehydration–rehydration cycles. These results highlight the critical role of controlling environmental factors in structure-based drug design and pharmaceutical manufacturing, and demonstrate how organic ligands can enhance the stability of protein crystals, offering valuable insights for pharmaceutical development.
IN SITU X-RAY POWDER DIFFRACTION; XRPD; SINGLE-CRYSTAL X-RAY DIFFRACTION; SCXRD; PROTEIN CRYSTALLOGRAPHY; RELATIVE HUMIDITY EFFECTS; HUMAN INSULIN COMPLEXES; PHARMACEUTICAL CRYSTALLOGRAPHY; STRUCTURAL STABILITY; LIGAND BINDING; UNIT-CELL VARIATION; PROTEI
The study of crystallography and the introduction to X-ray structure analysis are generally regarded as tasks for universities and, even then, usually only in graduate studies. However, analysis of crystal structures in science classes at high schools offers a wide range of opportunities for illustrating and improving understanding of fundamental structural chemistry concepts. This article attempts to share some experiences with crystallographers who want to work with high school students on crystallographic topics. After presenting some preconditions for introducing students to crystallographic topics, such as the curricular situation, two levels of didactical reduction are suggested. Examples of the use of database structures from the Protein Data Bank and the Teaching Subset of the Cambridge Structural Database in chemistry lessons are presented. In the Göttingen experimental laboratory for young people, XLAB, high school students can carry out the essential steps of structure determination, structure solution and refinement of X-ray diffraction data themselves, using aspirin or citric acid as examples. Finally, a network scheme for promoting crystallographic topics in the classroom is proposed.
CRYSTALLOGRAPHY IN SCHOOL; DATABASE STRUCTURES; STRUCTURE DETERMINATION; TEACHING
In hospite and ex hospite architecture of photosynthetic thylakoid membranes in Symbiodinium spp. using small-angle neutron scattering
We demonstrate that small-angle neutron scattering (SANS) can resolve the architecture of photosynthetic thylakoid membranes in live symbiotic algal cells, both extracted from and living inside their respective hosts (ex hospite and in hospite, respectively). This enables a new non-destructive approach to probing thylakoid organization in coral symbioses, relevant to understanding the mechanisms of coral bleaching. A biologically realistic triple-vesicle model, guided by electron microscopy and established biochemical constraints, was fitted to SANS data from live Symbiodinium associated with both the coral analogue Aiptasia and the reef-building coral Acropora. The resulting compartment scattering length densities, together with established biochemical constraints, define a limited compositional range that supports the plausibility of the structural solution. These fits capture key scattering features and yield dimensional parameters, including inter-thylakoid (IT) gap widths, with uncertainties small enough to test models of stress-related membrane rearrangement. A focused covariance analysis shows that this SANS framework can resolve an IT-gap expansion of ∼2.4 nm with >7σ sensitivity, sufficient to distinguish structural changes proposed in thylakoid stress-response models. This provides a robust baseline for future live-cell studies.
SMALL-ANGLE NEUTRON SCATTERING; SANS; PHOTOSYNTHESIS; THYLAKOIDS; CORALS; SYMBIODINIUM; IN HOSPITE STUDIES
Model for small-angle scattering analysis of membranes with protein-like inclusions
Proteins are ubiquitous in biological membranes and have a significant impact on their scattering properties. In this contribution, we introduce a general mathematical construction to add proteins to any pre-existing membrane model and to calculate the resulting elastic and/or inelastic scattering cross section. The model is a low-resolution one, which describes the proteins as made up of regions of homogeneous scattering length density that extend through an arbitrary fraction of the membrane and possibly protrude out of it. In this construction, the protein characteristics that are relevant to scattering are their space and time correlation functions in the two-dimensional plane of the membrane. The results are particularized to a static bilayer model and to a Gaussian model of a fluctuating membrane. The models are then applied to the joint analysis of small-angle neutron and X-ray scattering of red blood cell membranes, of which transmembrane proteins constitute 25% of the volume, and to neutron spin–echo data measured on the same systems.
SMALL-ANGLE SCATTERING; NEUTRON SPIN-ECHO; MEMBRANES; PROTEINS
MUMOTT: a Python package for the analysis of multi-modal tensor tomography data
Small- and wide-angle X-ray scattering tensor tomography are powerful methods for studying anisotropic nanostructures in a volume-resolved manner and are becoming increasingly available to users of synchrotron facilities. The analysis of such experiments requires advanced procedures and algorithms, which creates a barrier for the wider adoption of these techniques. Here, in response to this challenge, we introduce the MUMOTT package. It is written in Python, with computationally demanding tasks handled via just-in-time compilation using both CPU and GPU resources. The package has been developed with a focus on usability and extensibility, while achieving a high computational efficiency. Following a short introduction to the common workflow, we review key features, outline the underlying object-oriented framework and demonstrate the computational performance. By developing the MUMOTT package and making it generally available, we hope to lower the threshold for the adoption of tensor tomography and to make these techniques accessible to a larger research community.
SMALL-ANGLE X-RAY SCATTERING; WIDE-ANGLE X-RAY SCATTERING; TENSOR TOMOGRAPHY; RECONSTRUCTION; SOFTWARE
Nematicity and structural strain: a tight connection in Fe-based superconductors
In the present work, the role of microstrain developing in the temperature range above the structural transition in Fe-based superconductors is analysed in depth. Reviewing the results obtained from different compositions, a similar behaviour emerges in all cases. In particular, using an accurate diffraction line broadening analysis it is demonstrated that the tetragonal-to-orthorhombic structural transition occurring on cooling is anticipated by a symmetry breaking developing on the local scale in the tetragonal plane. The increase in microstrain with decreasing temperature in the stability field of the tetragonal phase qualitatively mirrors the development of anisotropy measured in some physical properties, a behaviour ascribed to nematicity. These results demonstrate the tight and delicate interplay correlating structural features on the local scale with transport and magnetic properties.
SUPERCONDUCTOR MATERIALS; NEMATICITY; LINE PROFILE ANALYSIS
CrimsonCalc: a software tool for pressure determination based on ruby fluorescence spectra
CrimsonCalc is open-source software for processing ruby fluorescence spectra and calculating pressure from the shift of the R1 peak. It supports processing and plotting of an individual spectrum as well as batch processing of spectra from data in text or Bruker OPUS binary format. Core features include baseline correction, pseudo-Voigt peak fitting, automated detection of detector saturation, and pressure calculation using user-defined or automatically detected reference spectra. The software provides batch output in both human-readable and machine-readable formats. With an intuitive graphical user interface, CrimsonCalc is designed as a high-pressure research aid and includes additional tools such as a diamond Raman edge pressure calculator, an interferometry-based gasket thickness calculator and an estimator for the upper pressure limit based on diamond anvil culet diameter. The program can be easily adopted in high-pressure research laboratories to facilitate pressure readings directly from simple text data, and to generate the images and result files that enable straightforward report preparation.
HIGH-PRESSURE CALCULATOR; RUBY FLUORESCENCE; DIAMOND ANVIL CELLS
Operando anomalous X-ray powder diffraction interleaved with X-ray absorption spectroscopy using a scanning 2D imaging detector on the XMaS beamline: design, implementation and performance
We present a method for achieving high-quality anomalous X-ray powder diffraction, interleaved with transmission X-ray absorption spectroscopy, using a flat-panel imaging detector scanned over a large angular range. Anomalous X-ray powder diffraction is a technique that enables the highlighting of specific elements within a crystal structure and pinpointing the nature of active (or inactive) sites involved in specific reactions in situ or in an operando manner. This approach enables the collection of a Q range that is not attainable using static flat-panel detectors in the absorption energy regimes used (8.94–17.5 keV). We consider the advantages and limitations of such an approach compared with alternative methods and describe in detail how it is achieved, along with the data processing and workflow required for an accurate restoration of conventional X-ray powder diffraction and anomalous X-ray powder diffraction data from sequentially acquired images. We demonstrate the applicability and capacity of this method for the in situ/operando restoration of the positions and atomic arrangement of copper atoms in the elevated-temperature aerobic activation of a copper-ion-exchanged zeolite, Cu–mazzite.
SCANNING 2D IMAGING DETECTORS; ANOMALOUS X-RAY POWDER DIFFRACTION; AXRPD; TRANSMISSION X-RAY ABSORPTION SPECTROSCOPY; XAS; HETEROGENEOUS CATALYSIS; ZEOLITES
Detecting grain-scale plastic deformation events with time-resolved far-field high-energy diffraction microscopy
Far-field high-energy diffraction microscopy (ff-HEDM) bridges a critical gap between microscale and macroscale plasticity by enabling three-dimensional (3D) time-resolved observations of grain-scale deformation. It can be used to measure the grain-averaged elastic strain tensor, crystallographic orientation, centroid and relative volume of each individual grain. Researchers have also proposed methods to extract information about grain-scale plastic deformation from time-resolved ff-HEDM measurements, using e.g. signature changes in a grain's equivalent or resolved shear stress, orientation or diffraction peak width. However, the accuracy of these different methods is largely unexplored due to the absence of an independent ground truth, particularly for plastic deformation that occurs prior to the macroscopic yield point. In the present work, we evaluate four methods for detecting grain-scale plastic deformation events using ff-HEDM: (i) equivalent stress relaxation, (ii) resolved shear stress relaxation, (iii) orientation change and (iv) diffraction peak shape evolution. Using ff-HEDM data from room-temperature creep tests of a Ti–7Al alloy, we cross-validate these approaches. The achieved high validation rates support confidence in the identified events. Two types of stress relaxation are observed among the detected events – fast and large versus gradual and small – suggesting different deformation mechanisms. The spatiotemporal distribution of plastic events is also captured, revealing clustered activity and intergranular propagation. These findings open avenues for future studies to explore the initiation and propagation of plasticity among grains.
X-RAY CHARACTERIZATION; FAR-FIELD HIGH-ENERGY DIFFRACTION MICROSCOPY; PLASTIC DEFORMATION; TITANIUM-ALUMINIUM ALLOYS; CREEP LOADING
Solid solution quantification from full powder X-ray diffraction profile: novel application of multivariate calibration
Non-stochiometric crystals, such as solid solutions, represent a valid strategy for fine-tuning the properties of materials from inorganic pigments to active pharma­ceutical ingredients. The change is achieved by substitution of structurally similar compounds within the crystal structure, resulting in a minor variation of cell parameters, and it can be experimentally observed as a shift of the X-ray diffraction profile, with the shift depending on the substitutional amount. After proper alignment of the diffraction data, chemometric methods can detect the evolution of the solid solution profile and correlate it to the molar composition, creating rapid quantitative models. The solid solutions chosen for this work are NA2·FAxSA1−x and IN2·FAxSA1−x, i.e. co-crystals of nicotin­amide (NA) and isonicotinamide (IN) with fumaric acid (FA) and succinic acid (SA) in different proportions; they are used as model systems for the development of principal component regression and partial least-squares models for the quantification of solid solution composition. Different alignment strategies are presented, and the results obtained from test samples show the prediction efficacy of the proposed approach.
MULTIVARIATE ANALYSIS; POWDER X-RAY DIFFRACTION; QUANTITATIVE MODELS; PARTIAL LEAST-SQUARES REGRESSION; SOLID SOLUTIONS
A reference material for X-ray diffraction line profile analysis
A nanocrystalline Fe–1.8%Cr steel powder was tested as a reference material on more than five powder diffraction instruments and configurations, as well as with different data-analysis methodologies. The material, commercially available at low cost, was ground in a high-energy planetary mill to obtain homogeneous crystalline domain dimensions of 10 (2) nm, with size dispersion of 5 (1) nm and a nominal dislocation density of the order of 2.90 (2) × 1016 m−2. The powder is stable, easy to handle and suitable for preparing samples in any measurement geometry. It is well suited for testing the modelling of diffraction peak profiles, either individually or across the entire diffraction pattern, as in the Rietveld method. This paper reports the simple details for the production of the material and the analysis of the diffraction patterns collected with both laboratory and synchrotron beamline instruments, using X-rays of different energies. In particular, the screening of the data based on integral breadths (Williamson–Hall method), the analysis by whole powder pattern modelling and the analysis by the Rietveld method are shown. Aspects related to diffuse scattering and pair distribution function analysis are also discussed.
REFERENCE MATERIALS; STEEL; X-RAY DIFFRACTION; WHOLE POWDER PATTERN MODELLING; PAIR DISTRIBUTION FUNCTIONS; LINE PROFILE ANALYSIS; WILLIAMSON-HALL METHOD; RIETVELD METHOD; DIFFUSE SCATTERING
LibraEDT: a software solution for automated 3D-ED data acquisition
The LibraEDT software has been developed to enhance and automate 3D electron diffraction (3D-ED) experiments by addressing key challenges such as crystal tracking, low-fluence data acquisition and better data management. This tool significantly improves both the accuracy and efficiency of ED workflows, particularly when applied to beam-sensitive materials. The utility of this approach is demonstrated through the structural analysis of a known beam-sensitive organic crystal, as well as a novel and previously unreported zinc-based metal–organic framework incorporating protocatechuic acid.
CRYSTAL TRACKING; ELECTRON MICROSCOPY; THREE-DIMENSIONAL ELECTRON DIFFRACTION; 3D-ED
MagStREXS, a crystallographic computer program to determine magnetic structures through resonant elastic X-ray scattering data. I. Fundamental equations
Resonant elastic X-ray scattering (REXS) is an experimental technique that can be highly valuable for studying magnetic structures in certain scenarios. In this paper, we introduce MagStREXS, a crystallographic program designed to determine magnetic structures from REXS data. This software makes use of the key concepts and computational tools already established in the field of magnetic crystallography. Here, we present the fundamental equations implemented in MagStREXS, derived for the two methods used to describe magnetic models: the representation analysis and the symmetry-based approach. We illustrate the capabilities of MagStREXS with a case study. The software is under active development, with the aim of benefiting both specialists and non-specialists in the field.
RESONANT X-RAY MAGNETIC SCATTERING; REXS; MAGNETIC STRUCTURES; COMPUTER PROGRAMS
Ultimate sensitivity in X-ray diffraction: angular moments versus shot noise
The sensitivity towards Bragg peak parameters constitutes a crucial performance attribute of X-ray diffraction experiments. Diffraction peaks are frequently characterized by model-free angular moment analysis, which offers greater versatility compared with traditional model-based peak fitting. Here, we have theoretically determined the ultimate limit of the sensitivities of angular moments imposed by photon shot noise. These predictions have been validated by experimental data provided by three different setups. We have observed experimentally achieved sensitivities of the first moment below 1/1000th of a detector pixel and below 1 µrad. The formulae provided for the uncertainties of angular moments can now be used to rapidly determine experimentally achieved sensitivities from a single diffraction frame. Corresponding limitations (i.e. ultra-low photon counts and exceedingly high photon count rates) are identified and discussed.
X-RAY DIFFRACTION; BRAGG PEAK ANALYSIS; PHOTON SHOT NOISE; PHOTON COUNTING DETECTORS; ANGULAR MOMENTS
Coherent multiple scattering in small-angle scattering experiments: modeling approximations based on the Born expansion
We start from an analytical formulation for the coherent multiple scattering treatment – similar to Mie scattering – for spherical particles. Then, we revisit the Born approximation with an approximation for all higher-order terms. Finally, we draw conclusions from those calculations and formulate an approximative model to describe ultra-small-angle neutron scattering and ultra-small-angle X-ray scattering data. In all calculations, we can specify the conditions for coherent multiple scattering. Several examples are provided to show the quality of the simple approximation in comparison with exact calculations and experiments.
COHERENT MULTIPLE SCATTERING; MIE SCATTERING; USANS; ULTRA-SMALL-ANGLE NEUTRON SCATTERING; USAXS; ULTRA-SMALL-ANGLE X-RAY SCATTERING
Velocity gradient dependent structures of 12–2–12 wormlike micelles: insights from small-angle neutron scattering in the 1–2 shear plane
The velocity gradient dependent shear-induced structural evolution of wormlike micelles (WLMs) formed by a gemini-type cationic surfactant (12–2–12) in an aqueous solution was investigated using small-angle neutron scattering (SANS). To achieve this, a cell for observation in the velocity–velocity gradient (1–2) shear plane was constructed. SANS measurements were conducted at multiple positions across the gap of this 1–2 shear cell under various shear rates, covering both shear-thickening and shear-thinning regimes. During shear thickening at apparent shear rates of 70–200 s−1, a clear position-dependent alignment of WLMs was observed, with higher orientation near the rotor. In contrast, the intermicellar distance remained largely uniform across the gap. Neutron transmission measurements indicated no significant macroscopic concentration fluctuations. These results suggest that shear thickening is primarily driven by shear-induced micellar elongation and orientation, rather than the formation of concentration fluctuations. This study indicates the utility of SANS measurements in the 1–2 shear plane in revealing spatially resolved structural details, providing crucial insights into the 3D behavior of complex fluids under shear and complementing previous Rheo-SANS findings.
SMALL-ANGLE NEUTRON SCATTERING; SANS; RHEOLOGY; VELOCITY-VELOCITY GRADIENT
The Patterson function, P(u), is useful in many crystallographic applications, including experimental phasing, molecular replacement and the exploration of non-crystallographic symmetries. P(u) is defined as the autocorrelation of the electron density. Autocorrelation is often an unfamiliar concept for students of biological or biomedical fields of study. I present a freely available animated PowerPoint slide deck featuring 1D electron density plots and the corresponding autocorrelation resulting in the Patterson function that is readily interpretable as an interatomic distance map. The animation makes it easy to grasp the concept of autocorrelation in an intuitive manner.
PATTERSON FUNCTION; AUTOCORRELATION; GRAPHICAL ANIMATION; 1D ELECTRON DENSITY PLOTS
Cold versus thermal neutron source: assessment of performance of the KWS-2 SANS diffractometer of the Jülich Centre for Neutron Science at the FRM II reactor
The small-angle neutron scattering (SANS) diffractometer KWS-2 of the Jülich Centre for Neutron Science at the Heinz Maier-Leibnitz Zentrum, Garching, Germany, is a high-flux instrument based on the combination of a specially developed neutron guide system, which allows delivery of a high neutron intensity for a wide wavelength range λ between 2.8 and 20 Å to the instrument, and a versatile velocity selector, which allows an easy choice of wavelength spread Δλ/λ depending on whether the specific scientific goal is either improved resolution, i.e. Δλ/λ = 10%, or high intensity, i.e. Δλ/λ = 20%. Here we report an evaluation of KWS-2 performance by measurements and McStas simulations under the condition that only the thermal neutron source (TNS) is available at the FRM II reactor. According to the simulations, a flux decrease by a factor of 2.5 for λ = 2.8–3 Å and by a factor of 10 for λ ≥ 4.5 Å is expected if the reactor is operated only with the TNS compared with the established performance with cold neutrons provided by the cold neutron source. The flux decrease in TNS operation can be mitigated for λ ≥ 4.5 Å by using a low-resolution velocity selector which provides Δλ/λ = 20% for standard positioning and Δλ/λ = 35% when tilted at an angle ξi = −10° to the beam axis. According to measurements, this degradation of resolution for increasing intensity does not seem to be critical for the structural characterization of small biological morphologies, which would be one of the most investigated topics if only thermal neutrons were available at the FRM II. However, ordering effects in the scattering characteristics of lamellar soft or biophysical systems are barely observable when the resolution is relaxed to Δλ/λ ≥ 20%, which defines the performance limits of the experimental approach. Furthermore, by using MgF2 focusing lenses when working with large samples, an intensity gain on the sample of up to 12-fold is achieved while keeping the same Qmin resolution as with the standard pinhole mode, restoring the flux loss expected with thermal neutrons for λ ≥ 7 Å.
SANS; SMALL-ANGLE NEUTRON SCATTERING; NEUTRON SOURCES; PROTEIN STRUCTURE; MCSTAS SIMULATION; NEUTRON FOCUSING LENSES
Machine learning inversion from scattering for mechanically driven polymers
A machine learning inversion method is developed for analyzing scattering functions of mechanically driven polymers and extracting the corresponding feature parameters, which include energy parameters and conformation variables. The polymer is modeled as a chain of fixed-length bonds constrained by bending energy, and it is subject to external forces such as stretching and shear. We generate a data set consisting of random combinations of energy parameters, including bending modulus, stretching and shear force, along with Monte Carlo-calculated scattering functions and conformation variables such as end-to-end distance, radius of gyration and off-diagonal component of the gyration tensor. The effects of the energy parameters on the polymer are captured by the scattering function, and principal component analysis ensures the feasibility of the machine learning inversion. Finally, we train a Gaussian process regressor using part of the data set as a training set and validate the trained regressor for inversion using the rest of the data. The regressor successfully extracts the feature parameters.
SMALL-ANGLE SCATTERING; MACHINE LEARNING; GAUSSIAN PROCESS REGRESSORS; MONTE CARLO METHODS; POLYMERS
Solving disorder in (3D) real space: a comparative study of the three-dimensional difference pair distribution function and atomic resolution holography reconstructions
The quantitative analysis of local ordering principles in disordered crystalline systems has gained much attention over the past few years, as it is often considered crucial for optimizing material functionality. This development has been driven by significant advancements in computational and experimental methods, which have led to the establishment and widespread use of various analytical techniques. In this study, we perform model calculations to compare the effectiveness of atomic resolution holography and three-dimensional difference pair distribution function analysis (3D-ΔPDF). Using Cu3Au as a model system, we demonstrate an approach to derive local order parameters quantitatively and show that both techniques are well suited to quantifying chemical short-range order correlations and local bond-distance variations. By evaluating the strengths and limitations of both techniques, we advocate for their combined use to solve complex short-range order problems accurately.
DIFFUSE SCATTERING; THREE-DIMENSIONAL DIFFERENCE PAIR DISTRIBUTION FUNCTION ANALYSIS; 3D-[DELTA]PDF; ATOMIC RESOLUTION HOLOGRAPHY; DISORDER
Thermal expansion of LaB6 from 298 to 998 K
We propose LaB6 as a temperature calibration standard for high-temperature (HT) X-ray diffractometry owing to its high temperature stability. Such HT applications require a reliable HT lattice parameter or, equivalently, peak position data, which have not been readily accessible to the diffraction community to date. As such, the thermal expansion behavior of NIST SRM 660a LaB6 was assessed in the temperature range 298–998 K using HT Bragg–Brentano parafocusing θ:θ X-ray diffractometry in conjunction with Rietveld analysis. Data were collected in the 2θ range 20–150° at a data collection rate of 0.5° θ min−1 in air and at 1 atm. The temperature was stepped in 50 K increments. The cubic unit-cell lattice parameter [a(T)] of LaB6 in Å was found to vary as a(T) = 4.15678 (±0.00001) + Ξ(T − 298 K) + Ψ(T − 298 K)2, where Ξ = 2.4645 × 10−5 (±4.8904 × 10−8) Å K−1 and Ψ = 1.0325 × 10−8 (±6.7376 × 10−11) Å K−1. The isobaric volume thermal expansion coefficient (TEC) was obtained as αVP = (5.9291 × 10−6) + (4.9680 × 10−9)(T − 298 K) K−1, from which the corresponding linear TEC was obtained as αLP = (1.9764 × 10−6) + (1.6560 × 10−9)(T − 298 K) K−1. The 3 × 3 matrix representations of the single-crystal isobaric linear TEC and the volume expansivity were obtained for the cubic crystal class to which LaB6 belongs. Also, the temperature dependence of the lattice parameter data of this study was compared with past landmark studies on LaB6 by Dutchak et al. [Inorg. Mater. (1972), 8, 1877–1880] and Aivazov et al. [Inorg. Mater. (1979), 15, 1015–1016].
THERMAL EXPANSION; TEMPERATURE CALIBRATION; HIGH-TEMPERATURE X-RAY DIFFRACTOMETRY; LAB6 STANDARD MATERIAL
SUNBIM 4.0 software: new developments in small- and wide-angle X-ray scattering data analysis for scanning mode and grazing-incidence geometry
SUNBIM (supramolecular and submolecular nano- and biomaterials X-ray imaging) is a computer suite of integrated programs which, through a user-friendly graphical interface, is able to perform a number of functions for (grazing-incidence) small- and wide-angle X-ray scattering [(GI)SAXS and (GI)WAXS] data analysis. The software combines in the same package both originally developed algorithms and reliable methods documented in the literature. Recently, new tools have been added to the original program that are particularly devoted to data reduction. The release presented in this work, named SUNBIM 4.0, features a new interface to perform deeper data reduction for multi-scan SAXS/WAXS, including dark-current subtraction, background evaluation and subtraction, and normalization of scattering intensity against local sample thickness derived from absorption contrast maps. In SUNBIM 4.0, these functionalities have been made accessible for data sets in .edf, a data format commonly used by many next-generation X-ray detectors, thanks to a new guided procedure for converting entire multi-scan data sets into a format readable by the software. A new functionality in the single data analysis section has been implemented, consisting of a semi-automatic background subtraction from the 1D profile of the azimuthal integration, corrected for a flat-panel detector geometry, to enhance peak visibility at large scattering angles (WAXS/GIWAXS). This new SUNBIM release will include a Microsoft Windows installer, as in the previous version, and will also be available for Mac OSX. We are confident that the new features will enable a more accurate and comprehensive analysis of (GI)SAXS/(GI)WAXS data, addressing the issues and limitations of the previous release while also enhancing the extraction of structural information contained within the data.
SMALL- AND WIDE-ANGLE X-RAY SCATTERING; GRAZING-INCIDENCE SMALL- AND WIDE-ANGLE X-RAY SCATTERING; SAXS/WAXS; GISAXS/GIWAXS; COMPUTER PROGRAMS; IMAGING; MICROSCOPY
Oblique diffraction geometry for the observation of several non-coplanar Bragg reflections under identical illumination
A method to determine the strain tensor and local lattice rotation with dark-field X-ray microscopy is presented. Using a set of at least three non-coplanar symmetry-equivalent Bragg reflections, the illuminated volume of the sample can be kept constant for all reflections, facilitating easy registration of the measured lattice variations. This requires an oblique diffraction geometry, i.e. the diffraction plane is neither horizontal nor vertical. We derive a closed analytical expression that allows determination of the strain and lattice rotation from the deviation of experimental observables (e.g. goniometer angles) from their nominal values for an unstrained lattice.
X-RAY DIFFRACTION; STRAIN; DARK-FIELD X-RAY MICROSCOPY
High-energy diffuse X-ray scattering at ultra-small-angle grazing incidence for local structure study of single-crystalline thin films
We present a novel experimental approach employing high-energy X-ray scattering in ultra-small-angle grazing-incidence geometry to investigate local atomic structures in single-crystalline thin films. This non-destructive and non-invasive method overcomes the limitations of conventional moderate-energy grazing-incidence diffraction, achieving both high reciprocal-space resolution and coverage and high surface sensitivity. By leveraging high-energy X-ray diffraction, we enable quantitative analysis of local structures in the model system of ferroelectric PbTiO3 and dielectric SrTiO3 superlattices through three-dimensional difference pair distribution function analysis. The approach provides detailed insights into atomic structures in single-crystalline thin films with local order, capturing information on spatial correlations within and across unit cells.
DIFFUSE SCATTERING; SYNCHROTRON X-RAYS; HIGH-ENERGY STUDIES; SINGLE CRYSTALS; THIN FILMS; GRAZING INCIDENCE
Fundamental motifs and parity within the crystallographic point groups
This paper analyzes the Hasse diagram, or family tree, of the 3D crystal classes, also called geometric crystal classes. The 32 point-group classes are partitioned into seven crystal systems. In this paper, the structures of these systems are analyzed, leading to a new understanding of the relationships among and within them. The point groups, including their subgroups up to conjugacy, appear in six structural motifs in the Hasse diagram or family tree. Each motif has a parity – even or odd – that determines its structure. In three dimensions, the odd motifs are called monads, trigonals and cubics, and the even motifs are called dyads, tetragonals and hexagonals. Of the 32 classes of 3D point groups, 29 have a well defined parity, in that they appear in either an even or an odd motif. In contrast, the three monoclinic point groups are `ambidextrous', in that they appear in two motifs, one of each parity. An analysis of the ten 2D point groups reveals an analogous structure, except for the presence of an ambidextrous crystal system. The striking structural uniformity of the motifs across the Hasse diagram confirms that they are essential building blocks of the crystallographic point groups.
CRYSTALLOGRAPHIC POINT GROUPS; ABSTRACT GROUPS; CRYSTAL SYSTEMS; FAMILY TREES; HASSE DIAGRAMS; MOTIFS; SUBGROUPS; PARITY
On the use of beam precession for serial electron crystallography
During the past few years, serial electron crystallography (serial electron diffraction) has been gaining attention for the structure determination of crystalline compounds that are sensitive to irradiation by an electron beam. By recording a single electron diffraction pattern per crystal, indexing thousands to tens of thousands of such patterns and merging the reflection intensities of the successfully indexed patterns, one can retrieve crystal structure models with strongly mitigated beam damage contributions. However, one of the technique's bottlenecks is the need to obtain so many well indexed diffraction patterns, which leads to the collection of raw diffraction data in an automated way that usually yields low indexing rates. This work demonstrates how to overcome this limitation by performing the serial crystallography experiment following a semi-automated routine with a precessed electron beam (serial precession electron diffraction). The precession movement increases the number of reflections present in the diffraction patterns, and dynamical effects related to specific orientations of the crystals with respect to the electron beam are greatly minimized. This leads to more uniform reflection intensities across the serial data set, and a smaller number of patterns are required to merge the reflection intensities for good statistics. Furthermore, structure refinements based on the dynamical diffraction theory become possible due to the diffraction volume integration of beam precession, providing a novel approach for more accurate structure models. In this context, the use of beam precession is presented as an advantageous tool for serial electron crystallography, as it enables reliable crystal structure analysis with a lower amount of diffraction data.
PRECESSION ELECTRON DIFFRACTION; SERIAL CRYSTALLOGRAPHY; SERIALED; 3D ED; SCANNING TRANSMISSION ELECTRON MICROSCOPY
Small-angle X-ray scattering profile calculation for high-resolution models of biomacromolecules
We introduce a new approach to calculating small-angle X-ray scattering (SAXS) profiles from high-resolution atomic structures, which is realized in the open-source software AUSAXS. We employ an efficient implementation of the Debye equation, incorporating both accurate excluded volume models and a novel hydration shell model based on explicit dummy atoms. Two new excluded volume models are presented: (i) a simple, heterogeneous equivalent atom model, and (ii) a grid-based model. The two approaches reduce the risk of overfitting by either eliminating fitting parameters or introducing a safer volume scaling method. These models are compared with the traditional Gaussian sphere method, which is widely used in existing software. The comparisons reveal significant shortcomings in previously accepted methods, suggesting they may be more prone to overfitting than previously thought. This underscores the importance of a well tested and openly accessible baseline implementation like AUSAXS. AUSAXS is freely available at https://github.com/AUSAXS/AUSAXS.
SMALL-ANGLE X-RAY SCATTERING; BIOMACROMOLECULE SOLUTIONS; EXCESS SCATTERING; HYDRATION LAYERS; EXCLUDED VOLUME SCATTERING
Opportunities for near-surface small-angle neutron scattering to probe magnetic nanostructures within thin-film volumes
Near-surface small-angle neutron scattering (NS-SANS) is a highly versatile, yet under-utilized, technique in condensed matter research. It addresses the shortcomings of transmission SANS to enable the characterization of nano­structures within extremely small sample volumes in the thin-film limit. NS-SANS stands out in its capacity to resolve 1D, 2D or 3D structural, chemical and magnetic correlations beneath the surfaces of thin films with nanometre resolution. By varying the incident angle above the critical angle of reflection, NS-SANS delivers tuneable depth sensitivity across nano-confined volumes, effectively minimizing noise contributions from substrates while surpassing the surface-sensitive capabilities of grazing-incidence SANS. This perspective highlights the future potential of NS-SANS to study condensed matter thin films and heterostructures, with a special focus on nanoscale magnetic phenomena, such as topological skyrmion lattices, superconducting vortex lattices and chiral domain walls, which are of timely interest to the magnetism and quantum materials communities.
NEAR-SURFACE SMALL-ANGLE NEUTRON SCATTERING; GRAZING-INCIDENCE SMALL-ANGLE NEUTRON SCATTERING; MAGNETISM; THIN FILMS
A refinable three-parameter equation for phenomenological absorption in quantitative electron microscopy – determining the equation
A three-term equation for phenomenological absorption of electron beams in materials is derived for use in quantitative transmission electron microscopy simulations. This is motivated by differential quantitative convergent-beam electron diffraction (QCBED) using CBED patterns that have not been electron-optically energy filtered. As a starting point, this three-parameter function reproduces inelastic scattering factors generated by the ubiquitous ATOM subroutine of Bird & King [Acta Cryst. (1990), A46, 202–208] to within a few per cent, spanning elements Z = 1 to 98, Debye–Waller parameters from B = 0.05 Å2 to B = 2.0 Å2, scattering angles from s = 0 Å−1 to s = 6.0 Å−1 and electron energies from E0 = 1 keV to E0 = 1 MeV. As such, it is applicable to zero-energy-loss electron-optically filtered pattern matching for which the Bird and King ATOM subroutine was designed. Crucially, the coefficients of the three terms in the present equation can be refined to produce inelastic scattering factors with differing local and non-local contributions, which are better suited to unfiltered differential QCBED pattern matching.
PHENOMENOLOGICAL ABSORPTION; QUANTITATIVE CONVERGENT-BEAM ELECTRON DIFFRACTION; DIFFERENTIAL QCBED; QUANTITATIVE TRANSMISSION ELECTRON MICROSCOPY; ELECTRON SCATTERING CALCULATIONS; INELASTIC SCATTERING FACTORS
XRDlicious: an interactive web-based platform for online calculation of diffraction patterns and radial distribution functions from crystal structures
XRDlicious is an online computational tool for calculating powder X-ray diffraction and neutron diffraction patterns (diffractograms) and partial and total radial distribution functions [(P)RDFs] from crystal structures. It features a user-friendly browser-based interface that supports widely used structural file formats, such as CIF, POSCAR, XYZ and LMP. The structures can be either uploaded or retrieved directly from the Crystallography Open Database, Materials Project and Automatic FLOW databases via an integrated search interface. Uploaded structures can be modified and exported in CIF, POSCAR, LMP or XYZ formats. The tool also enables the conversion of experimental powder diffraction data between different wavelengths, to d-space or q-space representations, and between fixed or automatic divergence slits. By eliminating the need for software installation, this application ensures accessibility across various devices (including mobile phones and tablets) and different computer operating systems. Its ability to simultaneously plot diffraction patterns from multiple structures is particularly useful for comparing structures obtained from computational simulations. Beyond research applications, its intuitive interface also makes it suitable for educational purposes, allowing students to explore concepts such as diffraction patterns and (P)RDFs in an easily approachable way. XRDlicious is accessible at https://xrdlicious.com.
X-RAY DIFFRACTION; NEUTRON DIFFRACTION; RADIAL DISTRIBUTION FUNCTIONS; DIFFRACTION PATTERN SIMULATORS; WEB-BASED TOOLS; POWDER DIFFRACTION DATA CONVERSION
Mapping adsorption on ionic surfaces via a pairwise potential-based high-throughput approach
Understanding molecular adsorption on ionic surfaces is crucial for a variety of chemical applications, from heterogeneous catalysis to prebiotic chemistry. Traditional approaches for identifying adsorption sites often rely on computationally expensive methods such as density functional theory (DFT), which limits their applicability to chemically complex surfaces. In this work, we propose an automated high-throughput approach to obtain a complete picture of the adsorbate–surface interaction by means of pairwise Coulomb and Lennard–Jones potentials. Using a grid-based surface scan to calculate per-site potential energies of adsorption, this method efficiently predicts global adsorption minima and all potential binding modes of a surface–adsorbate system, with the only user input being the surface CIF. Our approach is validated by studying formaldehyde (H2CO) adsorption on forsterite (Mg2SiO4), a common silicate, and l-cysteine adsorption on cadmium sulfide (CdS). The predicted adsorption configurations and energies are compared with DFT values in the literature, showing good agreement and confirming the accuracy of our method. Our workflow provides a rapid means of exploring large configurational spaces and identifying stable adsorption structures, making it particularly useful for complex surfaces with multiple interaction sites. The simplicity of the model, combined with its accuracy, suggest it could be employed to discover new catalytic pathways on chemically complex ionic surfaces.
AUTOMATION; INTERACTIONS; POTENTIAL ENERGIES; HIGH-THROUGHPUT TECHNIQUES; SURFACES
Visual Studio Code (VS Code) is a popular text editor and integrated development environment commonly used in software development. The crystallographic information file (CIF) language extension makes syntax highlighting, auto completion, error checking and hover information available for crystallographers reading and editing CIFs. The language extension features are available for all files following the CIF syntax, including CIF dictionary files. The design and features of the VS Code CIF extension are presented.
CRYSTALLOGRAPHIC INFORMATION FILES; CIF DICTIONARY; CIF PARSER; VISUAL STUDIO CODE
The {010} form of polar brushite (CaHPO4·2H2O) deposits as an epi-growing crystal on a non-polar {010} substrate of gypsum (CaSO4·2H2O)
The mechanisms of crystal growth from solution are more complicated than those from vapor or melt growth. These mechanisms are important in bio­mineralization (bones, teeth, shells) and in the characterization of optically non-linear crystals, perfectly crystallized proteins, nucleic acids and complex viruses. This motivated studies on new basic phenomena, including the crystal interfaces of biological macromolecules and those of low-solubility inorganic salts. Generalization of the Gibbs–Thomson effect has been questioned when describing isotropic (circular) or anisotropic (polygonized) spiral steps spreading onto a crystal face. This work focuses on the brushite crystal (CaHPO4·2H2O) since it can grow freely or as a deposit on a gypsum (CaSO4·2H2O) substrate. Brushite looks like a 2D crystal built by a flat {010} form limited by {h0l} polar and thin faces running as straight steps. Moreover, it is worth investigating the {010} gypsum to {010} brushite transformation since mineralogy and geochemistry play an important role in the crystal growth. Here, we study the freely growing brushite and, subsequently, its {010} form arising from gypsum. The epitaxy {010} gypsum/{010} brushite is also examined because brushite twins are involved. A new way of thinking about the epi-relations is proposed, along with more rigorous constraints; this new approach emphasizes the physical importance of the adhesion energy connected to every epitaxy.
CYSTAL GROWTH; GYPSUM/BRUSHITE PINACOIDS; GYPSUM/BRUSHITE TRANSFORMATION EPITAXY; SPECIFIC ADHESION ENERGY
A systematic approach for quantitative orientation and phase fraction analysis of thin films through grazing-incidence X-ray diffraction
Grazing-incidence X-ray diffraction (GIXD) is widely used for the structural characterization of thin films, particularly for analyzing phase composition and the orientation distribution of crystallites. While various tools exist for qualitative evaluation, a widely applicable systematic procedure to obtain quantitative information has not yet been developed. This work presents a first step in that direction, allowing accurate quantitative information to be obtained through the evaluation of radial line profiles from GIXD data. An algorithm is introduced for computing radial line profiles based on the crystal structure of known compounds. By fitting experimental data with calculated line profiles, accurate quantitative information about orientation distribution and phase composition is obtained, along with additional parameters such as mosaicity and total crystal volume. The approach is demonstrated using three distinct thin film systems, highlighting the broad applicability of the algorithm. This method provides a systematic and general approach to obtaining quantitative information from GIXD data.
GRAZING-INCIDENCE X-RAY DIFFRACTION; GRAZING-INCIDENCE WIDE-ANGLE X-RAY SCATTERING; QUANTITATIVE ORIENTATION ANALYSIS; QUANTITATIVE PHASE FRACTION ANALYSIS; ANTHRAQUINONE; ZIF-8; BINAPHTHALENE
Kinetics of light-induced mesophase transitions in azo­benzene amphiphiles containing lyotropic liquid crystals
This study focuses on the kinetics of light-induced mesophase transitions in lyotropic liquid crystals containing a mixture of phospho­lipids and azo­benzene amphiphiles. Lipid membranes organize in a wide range of morphologies, directly influencing their functionality and the efficiency of associated components such as proteins. Transitions between mesophases occur naturally during membrane fusion and can also be triggered by multiple factors, such as pH, salinity, temperature and light. Employing light to isomerize artificial photoswitchable lipids in mixed model membranes containing 1,2-dipalmitoyl­phos­pha­tidylcholine or 1,2-didecanoyl­phosphatidylcholine revealed light-induced structural changes including mesophase transitions from a lamellar to a cubic Pn3m phase. Performing time-resolved small-angle X-ray scattering measurements, the kinetics of the change in membrane repeat distance and the transition from a lamellar to a bicontinuous cubic phase could be captured on the timescale of tens of seconds. The results demonstrate new possibilities for investigating intermediate states during mesophase transitions that are important to understand membrane fusion, and they highlight the potential of photoswitchable lipids for designing bespoke drug delivery systems.
KINETICS; PHOTOSWITCHING; AZOBENZENE; LIPID MESOPHASES; VESICLES; SMALL-ANGLE X-RAY SCATTERING; STRUCTURE DETERMINATION; SOLUTION SCATTERING; STRUCTURAL BIOLOGY
Superstability of micrometre jets surrounded by a polymeric shell
We have produced superstable compound liquid microjets with a 3D-printed coaxial flow-focusing injector. The aqueous jet core is surrounded by a shell, a few hundred nanometres in thickness, of a low-concentration aqueous solution of a low-molecular-weight polymer. Due to the stabilizing effect of the polymeric shell, the minimum liquid flow rate leading to stable flow-focusing is decreased by one order of magnitude, resulting in much thinner and longer jets. Possible applications of this technique for serial femtosecond X-ray crystallography are discussed.
SERIAL FEMTOSECOND CRYSTALLOGRAPHY; FLOW-FOCUSING; VISCOELASTIC JETS
Inversion of the X-ray restrained wavefunction equations: a first step towards the development of exchange–correlation functionals based on X-ray data
The X-ray restrained wavefunction (XRW) method is a quantum crystallographic technique that enables the determination of wavefunctions compatible with experimental X-ray diffraction data. Extensive research has demonstrated that this strategy inherently captures electron correlation and polarization effects on the electron density, while also providing consistent electron distributions. These findings suggest that the approach could be valuable in the development of new exchange–correlation (xc) functionals for density functional theory (DFT) calculations. This is particularly relevant in light of recent observations and recommendations by Medvedev et al. [Science (2017), 355, 49–52], who stressed the importance that xc functionals give both accurate energy values and exact electron densities, in line with the original spirit of DFT. Motivated by this perspective, this paper presents a preliminary investigation that aims at extracting and visualizing for the first time the perturbation potentials arising from the use of X-ray diffraction data as restraints in XRW calculations. In the present work, these potentials are simply obtained as orbital-averaged potentials through straightforward inversions of the XRW equations, where theoretical or high-quality experimental X-ray structure factors are employed in XRW computations at the restricted Hartree–Fock level for atoms (neon, argon and krypton) and simple molecules (dilithium and urea). Features and limitations of the resulting preliminary potentials are illustrated, while future perspectives on the use of the XRW method for the development of xc functionals are also discussed.
QUANTUM CRYSTALLOGRAPHY; X-RAY RESTRAINED WAVEFUNCTIONS; X-RAY CONSTRAINED WAVEFUNCTIONS; DENSITY FUNCTIONAL THEORY; EXCHANGE-CORRELATION FUNCTIONALS; ELECTRON DENSITY; ORBITAL-AVERAGED POTENTIALS
Powder diffraction data beyond the pattern: a practical review
We share personal experience in the fields of materials science and high-pressure research, discussing which parameters, in addition to positions of peak maxima and intensities, may be important to control and to document in order to make deposited powder diffraction data reusable, reproducible and replicable. We discuss, in particular, which data can be considered as `raw' and some challenges of revisiting deposited powder diffraction data. We consider procedures such as identifying (`fingerprinting') a known phase in a sample, solving a bulk crystal structure from powder data, and analyzing the size of coherently scattering domains, lattice strain, the type of defects or preferred orientation of crystallites. The specific case of characterizing a multi-phase multi-grain sample following in situ structural changes during mechanical treatment in a mill or on hydrostatic compression is also examined. We give examples of when revisiting old data adds a new knowledge and comment on the challenges of using deposited data for machine learning.
POWDER DIFFRACTION; FAIR DATA; RAW DATA; 2D TO 1D CONVERSION; METADATA; PARTICLE STATISTICS; IMAGES; MATERIALS; MINERALS; HIGH-PRESSURE DATA; IN SITU MECHANOCHEMICAL STUDIES
Differentiating the solution structures and stability of transthyretin tetramer complexed with tolcapone and tafamidis using SEC-SWAXS and NMR
Human transthyretin (TTR) is a homotetrameric protein involved in transporting thyroxine (T4) and retinol-binding protein within serum and cerebrospinal fluid. The disassociation of TTR's tetrameric structure can lead to the formation of biologically toxic TTR amyloid fibrils. Tolcapone, a small molecule currently under clinical trial, has shown potential as a TTR stabilizer and may act as an alternative to tafamidis, the conventional therapeutic agent used to prevent TTR dissociation. Using size-exclusion-chromatography-based small- and wide-angle X-ray scattering (SEC-SWAXS) complemented by nuclear magnetic resonance (NMR) spectroscopy, this study reveals the solution conformations of Apo-TTR and TTR complexed with tolcapone and tafamidis. Our results indicate that both compounds can bind similarly to the two T4 sites of TTR, leading to a small increase in the radius of gyration from 24.3 ± 0.1 Å (Apo-TTR) to 25.8 ± 0.1 Å. Consequently, both compounds largely stabilize the TTR against dissociation, denaturation and oligomerization up to 8 M urea, whereas Apo-TTR starts to denature at this concentration and forms larger oligomers at 8 M urea. Additionally, under a reduced TTR–drug mixing ratio of 1:1, which targets only one T4 site, tafamidis more effectively stabilizes the TTR tetrameric conformation at 8 M urea, a difference attributed to its higher affinity for the first T4 site. These results illustrate an effective strategy for investigating protein–drug interactions by examining the solution conformations of protein–drug complexes under physiological conditions, providing structural hints to the design of therapeutic agents targeting TTR.
HUMAN TRANSTHYRETIN; TOLCAPONE; TAFAMIDIS; SOLUTION STRUCTURE; SMALL- AND WIDE-ANGLE X-RAY SCATTERING; SWAXS; NMR
Optimization of magnetic reference layer for neutron reflectometry
Neutron reflectivity is a powerful technique for probing density profiles in films, with applications across physics, chemistry and biology. However, challenges arise when dealing with samples characterized by high roughness, unknown scattering length density (SLD) with low contrast, very thin layers or complex multi-layered structures that cannot be uniquely resolved due to the phase problem. Incorporating a magnetic reference layer (MRL) and using polarized neutron reflectivity improves the sensitivity and modelling accuracy by providing complementary information. In this study, we introduce a quantitative means of comparing MRL systems in a model-free way. We apply this approach to demonstrate that CoTi alloys offer a superior solution as MRLs compared with the commonly used Fe or Ni MRLs. The low nuclear and magnetic scattering length densities of CoTi significantly enhance sensitivity, making it particularly advantageous for soft-matter research. Furthermore, the tunable Co versus Ti ratio allows for optimization of the SLD to achieve maximum sensitivity, establishing CoTi as a highly effective choice for MRL applications. The applied simulation framework for optimizing MRL sensitivity to a specific materials system and research question is a generic approach that can be used prior to growing the MRL for a given experiment.
MAGNETIC REFERENCE LAYERS; THIN FILMS; REFLECTOMETRY; NEUTRON SCATTERING; SENSITIVITY
Small-angle scattering studies on diverse peptide-based nanotube and helical ribbon structures reveal distinct form and structure factors
Peptide-based nanotubes are bio-based self-assembled nanostructures with intriguing structural and functional properties. The structure of such nanotubes can be probed in detail using small-angle scattering experiments due to the typical length scales, i.e. diameter and wall thickness of the nanotubes, which span the range accessible in small-angle X-ray scattering (SAXS) or small-angle neutron scattering (SANS) studies. Here, we present SAXS data for several classes of peptide and lipopeptide systems previously studied by our group, as well as newly reported data for model short lysine-sequence lipopeptides. Previous data are re-examined using more accurate models for data plotted on Kratky plots, which emphasizes fine details of nanotube structure. In some cases, consideration of structure-factor effects is necessary to allow for the coexisting structures, and a lamellar structure factor is used to describe this. In other cases, such as several examples of surfactant-like peptides, only a form factor has to be considered to accurately fit the measured SAXS data. In these cases, a form factor for hollow nanotubes with a Gaussian bilayer profile to represent the layered peptide ordering in the nanotube walls is used to model the data. A general expression for the cross section scattering form factor is provided, which can be used for any scattering density profile (electron density for SAXS or scattering length density for SANS) across the wall. This is analysed along with the form factor for multishell (multiwall) nanotube structures with a series of slabs to represent the scattering density profile. For lipopeptides C16-KFK and C16-K (C16 indicates a hexa­decyl lipid chain), SAXS data show aperiodicity in the form-factor oscillations, as well as apparent broad structure-factor peaks. These features cannot be fitted using solely nanotube form-factor models, this being ascribed to the presence of coexisting structures. Lastly, for comparison, the form factors for helical ribbon and cochleate (scroll) structures are evaluated for several examples, since in many cases electron microscopy of peptide- and lipopeptide-based nanotube systems reveals the coexistence of nanotubes with such structures, related to nanotubes.
SMALL-ANGLE SCATTERING; NANOTUBES; PEPTIDES; FORM FACTORS; STRUCTURE FACTORS
Practical neutron detection modalities for industrial use available at a time-of-flight small-angle scattering instrument
We report the latest advances of the iMATERIA instrument, namely, time-of-flight small-angle neutron scattering (SANS) specifically for measurements in the manufacturing and energy industries. Observations are available that are multi-scale (from a minimum qmin = 0.007 Å−1 to a maximum q = 30 Å−1), multi-time domain (>0.5 s) and multi-contrast by dynamical nuclear polarization. Multi-angle (or stereo) observation of film specimens can bridge between conventional SANS and reflectivity measurements. For multi-analysis, we have developed real-time simultaneous SANS and neutron radiography (NR), targeting polymer electrolyte fuel cells. In the future, we plan to establish simultaneous triple-analysis combining SANS, NR and prompt γ-ray analysis. By scanning with a beam of 1 mm2 in size, such analysis enables the mapping of structural parameters determined by SANS and elemental composition determined by prompt γ-ray analysis on the image obtained by NR.
INDUSTRIAL USE SMALL-ANGLE NEUTRON SCATTERING; SANS; NEUTRON RADIOGRAPHY; REFLECTIVITY; PROMPT [GAMMA]-RAYS; MULTI-MEASUREMENT
Two metrics for quantifying systematic errors in diffraction experiments: systematic errors in the variance of the observed intensities and agreement factor gap
The increase in the weighted agreement factor due to systematic errors in single-crystal X-ray and neutron diffraction experiments can be quantified precisely, provided the estimated standard uncertainties of the observed intensities, s.u.(Iobs), are sufficiently accurate. The increase in the weighted agreement factor quantifies the `costs' of the systematic errors. This is achieved by comparison with the lowest possible weighted agreement factor for the specific data set. Application to 314 published data sets from inorganic, metal–organic and organic compounds shows that systematic errors increase the weighted agreement factor by a surprisingly large factor of g = 3.31 (or more) in 50% of the small-molecule data sets from the sample. Examples of twinning, disorder, neglect of bonding densities and low-energy contamination are taken from the literature and examined with respect to the increase in the weighted agreement factor, which is typically less than three. The large value g = 3.31 for the supposedly simple case of rather small molecules, as opposed to macromolecules, is interpreted as a warning sign that there are not only the expected remaining systematic errors, like not-modelled disorder, unrecognized twinning or neglect of bonding electrons or similar errors, but additionally a common systematic error of insufficiently accurate s.u.(Iobs). Inadequate s.u.(Iobs) may not just compromise the model parameters and model parameter errors; they are also a threat to the whole data quality evaluation procedure that relies crucially on adequate s.u.(Iobs).
SYSTEMATIC ERRORS; METRICS; TWINNING; DISORDER
Accounting for instrument resolution in the pair distribution functions obtained from total scattering data using Hermite functions
The use of Hermite functions to describe pair distribution functions (PDFs) from total scattering data was previously proposed by Krylov & Vvedenskii [J. Non-Cryst. Solids (1995), 192–193, 683–687]. Hermite functions have a suitable form for describing both the total scattering data and the PDF, and have the useful feature that they are eigenfunctions of the Fourier transform operation. We demonstrate that, by fitting Hermite functions to total scattering data, it is possible to take into account the effects of experimental resolution when deriving the PDF from the scattering data. This is particularly advantageous for neutron time-of-flight data, where different banks of detectors have different resolution functions and the resolution widths vary with the size of the scattering vector. A number of technical points are discussed and illustrated using examples of synthetic data, including both amorphous and crystalline materials. These include a solution to the problem of handling the sharp Bragg peaks, and how to scale the scattering function and PDF to match the scale of the Hermite functions. A number of examples using real scattering data, both synchrotron X-ray and spallation neutron data, are also shown. To account for uncertainties in the levels of the scattering functions, we have modified a method of Billinge & Farrow [J. Phys. Condens. Matter (2013), 25, 454202] to remove backgrounds by fitting with low-order orthogonal (Chebyshev) functions.
PAIR DISTRIBUTION FUNCTIONS; TOTAL SCATTERING; RESOLUTION; HERMITE FUNCTIONS
PRINSAS 2.0: a Python-based graphical user interface tool for fitting polydisperse spherical pore models in small-angle scattering analysis of porous materials
Despite the growing use of small- and ultra-small-angle scattering (SAS/USAS) across various fields, data processing remains challenging due to the complexity of SAS analysis and the limited accessibility of existing analysis software. These issues are addressed with PRINSAS 2.0, a portable Python-based tool with an intuitive graphical user interface. It enables efficient fitting of the polydisperse spherical pore model to SAS data and is specifically designed for porous materials often encountered in geoscience. This paper outlines the scientific and mathematical foundations of the software, along with its numerical implementation, to provide users with theoretical context and to support future development. The software was tested and validated using data from a range of geological and engineered porous samples measured at various neutron scattering facilities, ensuring broad compatibility. Additional validation using synthetic data sets, along with comparisons with existing pore size distribution fitting tools, confirmed its robustness in recovering predefined pore size distributions. PRINSAS 2.0 offers wide accessibility while ensuring that the fit results adhere closely to the underlying theoretical model, making it a practical tool for non-specialist users of SAS techniques. It also integrates seamlessly with larger Python-based SAS analysis frameworks, while remaining fully functional as a standalone application.
SMALL-ANGLE SCATTERING; POLYDISPERSE SPHERICAL PORE MODELS; POROUS MEDIA; DATA ANALYSIS SOFTWARE; PRINSAS 2.0
Desmearing small-angle scattering data by central moment expansions of instrument resolution
This study introduces an enhanced numerical technique tailored specifically for refining 1D small-angle scattering (SAS) intensity profiles affected by smearing. Our primary objective is to address the resolution blurring commonly encountered in SAS data, particularly in systems with clearly defined correlation peaks whose spread aligns with the width of the resolution function at corresponding Q positions. Unlike previous approaches that expanded the SAS intensity using central moment expansion, the new method focuses on expanding the resolution function itself, thus eliminating artificial oscillations observed in smeared spectra due to limitations inherent in our earlier algorithm. This method is straightforward to implement, computationally efficient and consistently performs well in numerical benchmarking. To illustrate its effectiveness, we present a case study of a lamellar phase characterized by distinct peaks in its small-angle neutron scattering intensities.
SMALL-ANGLE SCATTERING; DESMEARING; CENTRAL MOMENT EXPANSIONS; INSTRUMENT RESOLUTION EFFECT; SOFT MATTER
Structure refinement and anisotropic atomic displacement parameters of 1M Illite: Rietveld and pair distribution function analysis using synchrotron X-ray radiation
Illite, a widespread clay mineral, plays a pivotal role in geological processes, notably as an indicator in diagenetic and hydro­thermal alteration environments, and possesses significant industrial relevance in applications including ceramics, construction and catalysis. However, challenges including its nanoscale crystallinity, structural disorder and frequent interstratification with other clay minerals have hindered detailed structural characterization using conventional X-ray diffraction (XRD) techniques. This study employs integrated synchrotron XRD and pair distribution function (PDF) analysis to elucidate the crystal structure of the 1M illite polytype, yielding the first determination of its anisotropic atomic displacement parameters (Uaniso). These Uaniso parameters provide critical insights into atomic dynamics and static disorder within the structure, enabling a more refined understanding of structure–property relationships. This integrated approach, combining synchrotron XRD, Rietveld refinement and PDF analysis, yields a comprehensive structural characterization, capturing both average crystallographic and local atomic arrangements. Considering illite's widespread geological occurrence and industrial importance, this high-precision structural dataset, especially the determined Uaniso values, provides a crucial benchmark for future modeling and simulation efforts targeting accurate prediction of its physicochemical behavior.
ILLITE; SYNCHROTRON X-RAY RADIATION; RIETVELD REFINEMENT; PAIR DISTRIBUTION FUNCTION ANALYSIS; ANISOTROPIC ATOMIC DISPLACEMENT PARAMETERS
Machine learning assisted nanobeam X-ray diffraction based analysis on hydride vapor-phase epitaxy GaN
Nanobeam X-ray diffraction (nanoXRD) is a powerful tool for collecting in situ crystal structure information with high spatial resolution and data acquisition rate. However, analyzing the enormous amount of data produced by these high-throughput experiments for defect recognition or discovering hidden structural features becomes challenging. Machine learning (ML) methods have become attractive recently due to their outstanding performance in analyzing large data sets. This research utilizes an ML algorithm, uniform manifold approximation and projection (UMAP), to enhance the nanoXRD-based crystal structure analysis of a cross-sectional hydride vapor-phase epitaxy GaN wafer. Compared with the results obtained by conventional fitting, UMAP gives a more precise categorization of crystal structure based on the raw three-dimensional ω–2θ–φ diffraction patterns. The property that UMAP embeds the high-dimensional data while retaining the data structure is valuable in guiding the analysis of nanoXRD profiles. This research also demonstrates the capability of UMAP in analyzing other spectroscopic or diffraction data sets to guide crystal structure investigations.
HYDRIDE VAPOR-PHASE EPITAXY FILMS; HVPE GAN WAFERS; MACHINE LEARNING; X-RAY DIFFRACTION; NANOXRD; CRYSTAL GROWTH
Incorporating the direct derivation method and molecular scattering power method into the Rietveld quantitative phase analysis routine in TOPAS
The equations of the direct derivation method (DDM) and the unit-cell scattering power method are reviewed in this report. Their relationships and connections to the conventional Rietveld quantitative phase analysis (QPA) are revealed, leading to the development of the Ck-corrected DDM and the molecular scattering power (MSP) method. Both methods can be seamlessly integrated into the conventional Rietveld QPA routine as hybrid QPA, i.e. they enable fitting phases of partially or no known crystal structure simultaneously with conventional crystal structure modelling of other known crystalline phases. The accuracies of these hybrid QPA methods are evaluated using a calculated X-ray diffraction pattern for a mixture, the IUCr round robin CPD-1 dataset and synthetic mixtures of disordered source clay minerals (kaolinite KGa-2, chlorite CCa-2) with corundum, using both Launch Mode and Graphical User Interface (GUI) Mode of the TOPAS software. Although the accuracies of these hybrid QPA methods are slightly lower than that of conventional Rietveld QPA, their absolute deviations from weighed percentages are scarcely larger than 3 wt%. Compared with the original DDM, the Ck correction enhances QPA accuracy, particularly for mixtures containing phases of large differences in average atomic number. An advantage over the original unit-cell scattering power method is that the proposed MSP method eliminates the need to know the lattice parameters, unit-cell volume or number of molecules in the unit cell.
DIRECT DERIVATION METHOD; MOLECULAR SCATTERING POWER; RIETVELD; QUANTITATIVE PHASE ANALYSIS; QPA; TOPAS
A model for out-of-phase boundary induced X-ray diffraction peak profile changes in Aurivillius oxide thin films
Layered crystal structures, such as the Ruddlesden–Popper and Aurivillius families of layered perovskites, have long been studied for their diverse range of functionalities. The Aurivillius family has been extensively studied for its ferroelectric properties and potential applications in various fields, including multiferroic memories. A new analytical model is presented here that explains how out-of-phase boundaries (OPBs) in epitaxial thin films of layered materials affect X-ray diffraction (XRD) peak profiles. This model predicts which diffraction peaks will split and the degree of splitting in terms of simple physical parameters that describe the nanostructure of the OPBs, specifically the structural displacement perpendicular to the layers when moving across the OPB, the angle made by the OPB at the thin-film–substrate interface, and the OPB periodicity and its statistical distribution. The model was applied to epitaxial thin films of two Aurivillius oxides, SrBi2(Ta,Nb)O9 (SBTN) and Bi4Ti3O12 (BiT), and its predictions were compared with experimental XRD data for these materials. The results showed good agreement between the predicted and observed peak splitting as a function of OPB periodicity for SBTN and for an XRD profile taken from a BiT thin film containing a well characterized distribution of OPBs. These results have proven the model's validity and accuracy. The model provides a new framework for analysing and characterizing this class of defect structures in layered systems containing OPBs.
AURIVILLIUS PHASES; PEROVSKITES; LAYERED STRUCTURES; THIN FILMS; DEFECTS; MODELLING; OUT-OF-PHASE BOUNDARIES; X-RAY DIFFRACTION; PEAK SPLITTING
How X-ray dark-field imaging relates to small-angle X-ray scattering measurements
Dark-field (DF) imaging is a recent X-ray imaging modality which is promising because it gives access to information not resolved in conventional transmission X-ray imaging. The DF technique was first introduced as a loss of visibility of the grating interferometry modulations. DF signal is now measured with all the different X-ray phase contrast setups such as beam tracking or modulation-based imaging. Using a dedicated setup [Magnin et al. (2023). Opt. Lett. 48, 5839–5842], we present in the present article combined measurements of small-angle X-ray scattering and DF signal on the same material. We confirm that DF imaging is sensitive to multiple refraction from a sample, as can be found in the literature on lung imaging, but we show that the DF signal is also sensitive to scattering events. Finally, we measure a porous membrane that creates both types of signal (scattering and refraction), showing that, contrary to existing models, it is difficult to be quantitative about DF.
DARK-FIELD IMAGING; SMALL-ANGLE X-RAY SCATTERING; MULTIPLE REFRACTION
Pydidas: a tool for automated X-ray diffraction data analysis
The processing and analysis of X-ray diffraction (XRD) data at synchrotrons is often left to the user groups, which limits the user base to groups with a background in analyzing XRD data. Pydidas is a new Python package for processing XRD data. It provides an easy and intuitive interface and versatile processing options with the aim of being accessible to non-experts in XRD analysis. A graphical user interface (GUI) allows users to perform the full pipeline of data browsing, experiment calibration, workflow setup, processing and visualization in a single tool. In addition, pydidas' logic is decoupled from the GUI and it can be fully used from within scripts or embedded into other processing pipelines. The pydidas processing pipeline is assembled from individual plugins which perform specific processing steps. This modular design allows for very versatile pipelines covering a wide range of applications. To improve the usability even further, custom plugins can be integrated in the pydidas workflow to allow specialized processing steps.
X-RAY DIFFRACTION; XRD ANALYSIS; SOFTWARE
SAXS-A-FOLD: a website for fast ensemble modeling optimizing the fit of AlphaFold or user-supplied protein structures with flexible regions to SAXS data
AI programs such as AlphaFold (AF) are having a major impact on structural biology. However, predicted unstructured regions, the arrangement of linker-connected domains and their conformational changes in response to environmental variables present challenges that are not easily dealt with on purely computational grounds. An approach that uses predicted (or solved) protein modules/domains linked by potentially unstructured regions and that generates ensembles of models optimized against small-angle X-ray scattering (SAXS) data has been recently described [Brookes et al. (2023). J. Appl. Cryst. 56, 910–926]. Its implementation on a public-domain website, SAXS-A-FOLD (https://saxsafold.genapp.rocks), is presented here. User-supplied SAXS experimental intensity I(q) versus scattering vector magnitude q and the derived pair-wise distance distribution function P(r) versus r are first uploaded. An AF or user-supplied structure (currently only single chains without prosthetic groups) is then uploaded and displayed, and its SAXS I(q) and P(r) profiles are computed and compared with the experimental data. If uploaded from AF, the structure is color-coded by the associated confidence level: on this basis, the website automatically proposes potential flexible regions that can be user modified. For user-supplied structures, these regions have to be directly entered. A starting pool of typically 10–50 × 103 conformations is generated using a Monte Carlo method that samples backbone dihedral angles along the chosen segments of potential flexibility in the protein structures. The initial pool is reduced to obtain a tractable set of models, for which P(r) and I(q) are computed with fast established methods. A global fit is performed using non-negatively constrained least-squares (NNLS) versus original data. The P(r) and I(q) NNLS results are then displayed, showing both the reconstructed curves and the contributing model curves, with their percentage contributions. A WAXSiS (https://waxsis.uni-saarland.de) implementation is utilized to calculate an I(q) for each selected model. These sets can be enhanced by adding a user-defined number of models generated before and after each selected model in the original Monte Carlo pool, ensuring the inclusion of nearby models that might better fit the data. Finally, NNLS is used on the WAXSiS-generated I(q) set versus the original I(q) data, with the results displaying the contributing models and their I(q). Aside from being representative of contributing conformations, the models selected by SAXS-A-FOLD could constitute a set of starting structures for more advanced MD simulations.
SMALL-ANGLE X-RAY SCATTERING; SAXS; ALPHAFOLD; ENSEMBLE MODELING; PROTEIN STRUCTURES; STRUCTURAL FLEXIBILITY
Comparison of time-of-flight and MIEZE neutron spectroscopy of H2O
We report a comparison of modulation of intensity with zero effort (MIEZE), a neutron spin–echo technique, and neutron time-of-flight (ToF) spectroscopy, a conventional neutron scattering method. The evaluation of the respective recorded signals, which can be described by the intermediate scattering function I(Q, τ) (MIEZE) and the dynamic structure factor S(Q, E) (ToF), involves a Fourier transformation that requires detailed knowledge of the detector efficiency, instrumental resolution, signal background and range of validity of the spin–echo approximation. It is demonstrated that data obtained from pure water align well within the framework presented here, thereby extending the applicability of the MIEZE technique beyond the spin–echo approximation and emphasizing the complementarity of the two methods. Computational methods, such as molecular dynamics simulations, are highlighted as essential for enhancing the understanding of complex systems. Together, MIEZE and ToF provide a powerful framework for investigating dynamic processes across different time and energy domains, with particular attention required to ensure identical sample geometries for meaningful comparisons.
NEUTRON SPIN-ECHO SPECTROSCOPY; NEUTRON TIME-OF-FLIGHT SPECTROSCOPY; MODULATION OF INTENSITY WITH ZERO EFFORT; MIEZE; DATA ANALYSIS
Three-point bending behavior of individual ZnO nanowires studied by in situ Laue microdiffraction
The mechanical behavior of piezoelectric semiconductor ZnO nanowires was studied in three-point bending configuration using the custom-built atomic force microscope SFINX coupled with in situ Laue microdiffraction. Besides bending, torsion of the nanowires was shown during mechanical loading. A fracture strength of up to 3 GPa was demonstrated, which is about one order of magnitude higher than that for bulk ZnO. In the case of a piezoelectric material like ZnO, this fracture strength represents the maximum elastic strain that could eventually be converted into electrical energy by the piezoelectric effect. The significantly increased fracture strength found for nanowires compared with bulk ZnO thus offers increased energy-harvesting potential from material flexing. While bulk ZnO is a brittle material, plasticity with the storage of dislocations in the basal plane was shown in the three-point bent ZnO nanowires.
ZNO; LAUE DIFFRACTION; NANOMECHANICS; DISLOCATIONS; NANOWIRES; PIEZOELECTRICS; SEMICONDUCTORS; FRACTURE STRENGTH; THREE-POINT BENDING; TORSION; PLASTICITY
Changes of the lipid membrane structures caused by chain-length-dependent doxorubicin embedment in PEGylated liposomes
Poly(ethyl­ene glycol)-grafted (PEGylated) liposomes receive increasingly more attention due to their practical applications in delivering vaccines, nutrients and drug molecules such as doxorubicin (DOX). PEGylated liposomes have been well documented for their capability in carrying DOX as rod-like crystallites enclosed inside the unilamellar vesicles. This study addresses the previously unresolved question of whether DOX intercalates into liposome bilayers by employing simultaneous small- and wide-angle X-ray scattering (SWAXS), complemented by an integrated asymmetric flow field-flow fractionation system coupled with multi-angle light scattering, dynamic light scattering and refractive index detection. The DOX-loaded PEGylated liposomes used are composed of phosphatidylcholine (N:0 PC) lipids, with different lipid chain lengths N = 18, 20 and 22, and a fixed molar ratio of lipid:cholesterol:DSPE-PEG2000 of 45:50:5. SWAXS analysis reveals that rod-like DOX nanocrystallites—approximately 70–95 nm in length and 14 nm in diameter—are encapsulated within the PEGylated liposomes across all three lipid types, with each exhibiting distinct membrane structural responses to DOX incorporation. Notably, 22:0 PC liposomes demonstrate significant DOX-induced disruption of lipid chain packing, accompanied by enhanced alignment of phosphate headgroups in the outer leaflet. Consistently, cryo-EM imaging reveals pronounced faceted membrane morphologies in DOX-loaded 22:0 PC liposomes. This faceting phenomenon is attributed to the accumulation of DOX within the excess hydro­phobic core regions created by the extended aliphatic chains beyond the cholesterol saturation limit. These DOX-enriched domains locally stiffen the membrane, promoting the formation of rigid, faceted structures.
PEGYLATED LIPOSOMES; LIPID CHAIN LENGTHS; BILAYER STRUCTURE; ASYMMETRIC FLOW FIELD-FLOW FRACTIONATION; AF4; SIMULTANEOUS SMALL- AND WIDE-ANGLE X-RAY SCATTERING; SWAXS
A multiscale in situ time-resolved study of the nano- to millisecond structural dynamics during protein crystallization
Protein crystallization is key to determining the structure of proteins at atomic resolution. It can occur naturally, including in pathological pathways, for instance with aquaporin and γ-crystallin proteins. A fundamental understanding of the underlying crystallization process is both technologically and biologically relevant. A multitechnique approach is employed here to investigate protein crystallization in situ, allowing us to assess the evolution of the liquid suspension and crystallite structure as well as protein diffusion during the crystallization process. The wide range of methods probe the sample on ångström to millimetre length scales, accessing nanosecond to millisecond dynamics information while acquiring data with minute-timescale kinetic resolution during crystallization. This process takes several hours from an initial state of monomers or small clusters until the presence of large crystallites. Employing neutron spectroscopy allows us to distinguish different crystallization pathways and to reveal the presence of coexisting clusters during the entire crystallization process. We demonstrate the multitechnique approach on human serum albumin (HSA) proteins crystallized from aqueous solution in the presence of LaCl3. For this system, the crystallization kinetics can be consistently described by a sigmoid function across all methods, and the kinetics can be controlled by the salt concentration. Moreover, we compare the HSA–LaCl3 model system with the crystallization behavior of β-lactoglobulin–CdCl2, which includes a metastable intermediate state.
IN SITU PROTEIN CRYSTALLIZATION; DIFFUSION; STRUCTURAL DYNAMICS; SMALL-ANGLE NEUTRON SCATTERING; NEUTRON SPECTROSCOPY
Simulation of bright and dark diffuse multiple scattering lines in high-flux synchrotron X-ray experiments
We present a theoretical framework for understanding diffuse multiple scattering (DMS) in single crystals, focusing on diffuse scattering Bragg channels. These channels, when probed with high-flux low-divergence monochromatic synchrotron X-rays, provide well defined visualizations of Bragg cones. Our main contribution lies in modelling the intensity distribution along these lines by considering diffuse scattering (DS) around individual reciprocal-lattice nodes. The model incorporates contributions from both general DS and mosaicity, elucidating their connection to second-order scattering events. This comprehensive approach advances our understanding of DMS phenomena, enabling their use as probes for complex material behaviour, particularly under extreme conditions.
DIFFUSE SCATTERING; DEFECTS IN CRYSTALS; SYNCHROTRON X-RAYS; MULTIPLE DIFFRACTION; STRUCTURE PROPERTIES
The in crystallo optical spectroscopy toolbox
Over the past ten years, there has been a surge in the demand for in crystallo optical spectroscopy (icOS), since optical spectroscopy is one of the few biophysical characterization methods applicable to both protein solutions and crystals. Historically, icOS has been used to compare the state of proteins in crystals and in solution, and to assess their functionality by determining the redox state of metal ions, cofactors or chromophores. The recent rejuvenation of time-resolved crystallography experiments has sparked a renewed interest in optical spectroscopy as a bridge between kinetic studies in solution and in the crystalline state. The method of icOS can be defined as the ensemble of spectroscopic techniques in the UV–visible–infrared range that can be applied to crystals. It has also been instrumental in understanding specific X-ray radiation damage to redox-sensitive parts of proteins. Spectra recorded from crystals are affected by crystal orientation, shape or position due to various optical phenomena. Fortunately, these can be modelled and their effect can be corrected. The icOS laboratory at the European Synchrotron Radiation Facility (ESRF) specializes in recording UV–Vis absorption, fluorescence emission and Raman spectra from protein crystals. Here, we present a suite of utilities that streamline the analysis and correction of UV–Vis absorption icOS data, encased in a graphical interface. This was originally developed for the icOS laboratory at ESRF but is available as a standalone package, with the aim of making icOS more accessible.
IN CRYSTALLO SPECTROSCOPY; MACROMOLECULAR CRYSTALLOGRAPHY; TIME-RESOLVED CRYSTALLOGRAPHY; OPTICAL SPECTROSCOPY; ABSORPTION SPECTROSCOPY; PROTEIN CRYSTALS
Enhanced estimation method for partial scattering functions in contrast variation small-angle neutron scattering via Gaussian process regression with prior knowledge of smoothness
Contrast variation small-angle neutron scattering (CV-SANS) is a powerful tool for evaluating the structure of multi-component systems. In CV-SANS, the scattering intensities I(Q) measured with different scattering contrasts are de­com­posed into partial scattering functions S(Q) of the self- and cross-correlations between components. Since the measurement has a measurement error, S(Q) must be estimated statistically from I(Q). If no prior knowledge about S(Q) is available, the least-squares method is best, and this is the most popular estimation method. However, if prior knowledge is available, the estimation can be improved using Bayesian inference in a statistically authorized way. In this paper, we propose a novel method to improve the estimation of S(Q), based on Gaussian process regression using prior knowledge about the smoothness and flatness of S(Q). We demonstrate the method using synthetic core–shell and experimental polyrotaxane SANS data.
CONTRAST VARIATION SMALL-ANGLE NEUTRON SCATTERING; CV-SANS; PARTIAL SCATTERING FUNCTIONS; MULTI-COMPONENT SYSTEMS; STATISTICAL METHODS; BAYESIAN INFERENCE; CONTRAST VARIATION; GAUSSIAN PROCESS REGRESSION
Machine-learning-informed scattering correlation analysis of sheared colloids
We have carried out theoretical analysis, Monte Carlo simulations and machine-learning analysis to quantify microscopic rearrangements of dilute dispersions of spherical colloidal particles from coherent scattering intensity. Both monodisperse and polydisperse dispersions of colloids were created and underwent a rearrangement consisting of an affine simple shear and non-affine rearrangement using the Monte Carlo method. We calculated the coherent scattering intensity of the dispersions and the correlation function of intensity before and after the rearrangement and generated a large data set of angular correlation functions for varying system parameters, including number density, polydispersity, shear strain and non-affine rearrangement. Singular value decomposition of the data set shows the feasibility of machine-learning inversion from the correlation function for the polydispersity, shear strain and non-affine rearrangement using only three parameters. A Gaussian process regressor is then trained on the data set and can retrieve the affine shear strain, non-affine rearrangement and polydispersity with relative errors of 3%, 1% and 6%, respectively. Altogether, our model provides a framework for quantitative studies of both steady and non-steady microscopic dynamics of colloidal dispersions using coherent scattering methods.
SMALL-ANGLE SCATTERING; MACHINE LEARNING; GAUSSIAN PROCESS REGRESSION; MONTE CARLO SIMULATIONS; COLLOIDS
Phase behavior of silica-PNIPAm nanogels under high hydrostatic pressure
The structure and dynamics of concentrated silica-PNIPAm (poly-N-iso­prop­yl­acrylamide) nanogels are studied as a function of hydrostatic pressure up to 3500 bar. A combination of X-ray photon correlation spectroscopy and small-angle X-ray scattering shows similar characteristics of the dynamics for both temperature- and pressure-induced volume phase transitions of PNIPAm nanogels. Upon increasing the pressure and depending on the initial particle volume fraction, a transition from a liquid or glass state to a colloidal gel is observed for pressures p ≃ 1500 bar at a temperature of 293 K. Time-dependent analysis of the dynamics shows aging in glass and gel samples which is absent in the liquid state. This indicates stress-dominated dynamics upon pressure changes that equilibrate after a few hundred seconds.
X-RAY PHOTON CORRELATION SPECTROSCOPY; XPCS; PNIPAM NANOGELS; HIGH PRESSURE; SMALL-ANGLE X-RAY SCATTERING; SAXS; VOLUME PHASE TRANSITIONS
Shielded magnetic small-angle neutron scattering for characterization of radioactive samples
The development of a Pb-shielded fixture for the execution of a small-angle neutron scattering (SANS)-based workflow for interrogation of highly irradiated nuclear materials has been explored. The Pb shielding was specially designed to reduce the detected radioactivity from the specimen during SANS experiments, and the overall configuration is termed shielded magnetic SANS (SM-SANS). Two FeCrAl-based alloys, C35M and 125YF, were examined with the SM-SANS technique using a free-form size distribution locally monodisperse model in both the as-received and irradiated states. Quantitative values derived from the free-form size distribution were compared with atom probe tomography experiments. Microstructural and compositional parameters determined using the two characterization techniques were complements of each other. The results demonstrate that the SM-SANS technique is an effective means of characterizing nanoscale clustering in irradiated material systems and provides new avenues for investigating radioactive material microstructures.
FECRAL; SMALL-ANGLE NEUTRON SCATTERING; SANS; MAGNETIC SCATTERING; RADIOACTIVE MATERIALS CHARACTERIZATION
Classification and statistical analysis of structural disorder in crystalline materials
Approximately 50% of entries in the Inorganic Crystal Structure Database (ICSD; https://www.fiz-karlsruhe.de/en) exhibit some form of structural disorder. This work aims to provide a thorough analysis of structurally disordered materials within the ICSD, using data extracted from crystallographic information files. To achieve this, we derive a classification of structurally disordered crystalline materials described by their spatially averaged structures and introduce a range of quantitative measures of structural disorder. The overarching aim of this classification and analysis is to facilitate high-throughput and machine learning studies of disordered materials. To demonstrate the application of our approach, we perform statistical analysis of the disordered compounds reported in the ICSD to identify general trends in the distribution of disorder across different chemical elements, structures and classes of materials.
DISORDER CLASSIFICATION; CIFS; ENTROPY CALCULATION; MIXING ENTROPY; CONFIGURATIONAL ENTROPY
Analyzer-based X-ray phase contrast imaging using the forward-diffracted o-beam in a few-millimetre-thick Bragg-case asymmetrically cut crystal
An analyzer-based X-ray phase contrast imaging experiment employing the forward-diffracted o-beam in a few-millimetre-thick Bragg-case asymmetrically cut analyzer crystal has been implemented and tested in a geometry similar to that used in conventional radiography. The high angular stability requirements were overcome using specially designed crystals and a closed-loop feedback intensity system, monitoring the intensity of the diffracted h-beam. Analyzer-based images (ABis) taken at different angular positions on the forward-diffracted o-beam rocking curve show different contrasts, as expected. However, the ABis did not show sharp borders. This was closely investigated by X-ray topography and Δd/d mapping and was attributed to the stresses caused by the analyzer crystal's own weight in the bulk. Further investigation of the crystal design using finite element analysis coupled with dynamical theory of X-ray diffraction is envisaged.
ENHANCED ANOMALOUS TRANSMISSION; ANALYZER-BASED X-RAY PHASE CONTRAST IMAGING; FORWARD-DIFFRACTED O-BEAM; THICK CRYSTALS
Rheo-SAXS study on electrically responsive hydro­gels with shear-induced conductive micellar networks for on-demand drug release
This study presents a novel approach to creating electrically responsive hydro­gels utilizing a poly(ethyl­ene oxide)–poly(propyl­ene oxide)–poly(ethyl­ene oxide) (PEO100–PPO65–PEO100) triblock copolymer, functionalized with benzene­sulfonate end groups to form sF127. This functionalization allows the incorporation of sF127 into F127 micelles, resulting in tailored micelles designated as F18S2P when combined with poly(3,4-ethyl­ene­dioxy­thio­phene):poly(benzene­sulfonate) (PEDOT:PSS). For comparison, a control system using non-functionalized PEDOT:PSS/F127 micelles, designated F20S0P, was also developed. Using piroxicam as a model hydro­phobic drug, we evaluated the hydro­gel's drug encapsulation efficiency and electrical responsiveness. The functionalized F18S2P hydro­gel demonstrated superior performance of electrically stimulated drug release, especially when prepared with a blade-coating process. In situ rheological small-angle X-ray scattering (rheo-SAXS) measurements under large amplitude oscillatory shear revealed that function­alization facilitates crystal plane sliding, leading to the formation of a randomly hexagonal close-packed (rHCP) sliding layer structure. This behavior contrasts with the face-centered cubic to rHCP phase transition observed in the unfunctionalized hydro­gel. In situ SAXS analysis under applied electric fields (E-SAXS) further confirmed the electroresponsive micellar deformation. By integrating the rheo-SAXS and E-SAXS findings with blade-coating processing insights, we identify a clear structure–function relationship that governs the performance of these hydro­gels. The enhanced drug delivery of the function­al­ized F18S2P hydro­gel is attributed to the electrostatic attraction between the positively charged PEDOT and the negatively charged benzene­sulfonate-functionalized micelles. This interaction creates conductive nanonetworks within the hydro­gel, significantly improving its ability to release drugs in response to electrical stimulation. This work highlights the potential of electrically responsive hydro­gels for precise, localized drug delivery applications.
MICELLAR CRYSTALS; HYDROGELS; ELECTRICALLY STIMULATED DRUG RELEASE; RHEO-SAXS
Interface densification in a microphase-separated diblock copolymer resolved by small-angle X-ray scattering
In block copolymers exhibiting lower critical ordering transition behavior, the segregation strength increases with temperature due to the significantly different thermal expansivities of the constituent blocks. Using synchrotron small-angle X-ray scattering, we reveal a phenomenon of segmental densification at the microdomain interface in this type of system, where the local electron density in a specific region of the interface surpasses that of the denser domain. As a result, the interfacial electron density profile deviates significantly from the hyperbolic tangent function expected for an incompressible melt. This unique densification effect can be attributed to the negative volume of mixing at the interface between the dissimilar segments and emerges when the electron densities of the constituent blocks are similar.
BLOCK COPOLYMERS; INTERFACES; LOWER CRITICAL ORDERING TRANSITIONS; ELECTRON DENSITY PROFILES; SEGMENTAL DENSIFICATION
Individual dislocation identification in dark-field X-ray microscopy
Dark-field X-ray microscopy (DFXM) has recently been introduced for 3D mapping of dislocations and their strain fields in bulk samples and with high angular resolution (10−4°). In this work, we investigate the minimum information needed to identify the type of an isolated dislocation, parameterized by its Burgers vector, line direction and slip plane. Forward projections of DFXM weak-beam images are generated for a face-centred cubic symmetry using geometrical optics simulations with realistic noise levels. Cross correlating one DFXM image with similar images representing all possible combinations of dislocation types, we find that the cross-correlation values for all non-identical images are below 0.7, clearly demonstrating the feasibility of this method of identification. Experimental DFXM images of isolated dislocations are compared with forward-modelled ones. Complete identification is demonstrated, with the exception of the sign of the Burgers vector. The performance improvement obtained by acquiring data from a 3D volume is explored. This work verifies the use of geometrical optics to simulate DFXM weak-beam images and supports the interfacing of DFXM data with discrete dislocation dynamics simulations.
DIFFRACTION MICROSTRUCTURE IMAGING; X-RAY IMAGING; X-RAY MICROSCOPY; GEOMETRICAL OPTICS; DISLOCATION IDENTIFICATION
A SAXS/WAXD beamline with laboratory SAXS apparatus at NanoTerasu
NanoTerasu is a new 3 GeV synchrotron radiation facility in Sendai, Japan, which began user operation in April 2024. A station for small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD) has been built at the wiggler beamline BL08W. The station was built in a branch for which an X-ray beam is provided by Bragg reflection from two Si crystals. The X-ray energy is 8.0 or 13.1 keV using either an Si(111) or an Si(220) crystal, respectively. The beam is focused with an Ru-coated bent cylindrical mirror. In the SAXS station, an Anton Paar SAXSpoint 5.0 laboratory X-ray apparatus has been installed. The original X-ray generator and focusing mirror in the laboratory equipment were removed and four-quadrant slits and an ion chamber have been installed. Low-scatter slits in SAXSpoint 5.0 are used as guard slits in front of the sample. The X-ray detector is a DECTRIS Eiger2 1M. The slits, sample and detector are enclosed in a vacuum chamber to reduce scattering from the air. The detector can be moved along the X-ray axis under vacuum to change the sample-to-detector distance between 53 and 1610 mm. The X-ray flux at 8.0 keV is 1.0 × 1011 cps with a ring current of 200 mA, shortening the exposure time by nearly 1000 times compared with the original laboratory X-ray source. The purpose of employing SAXSpoint 5.0 is to provide a user-friendly SAXS/WAXD system. Anton Paar's measurement control system is employed in user operations. Many users utilize a multi-sample holder onto which 20 samples are fixed and measured in turn as programmed. The data analysis software is also provided by Anton Paar, but data can optionally be stored in TIFF format to be processed by any software that users are familiar with. Among the various sample attachments available from Anton Paar, a goniometer stage for grazing-incidence SAXS/WAXD is employed by many users.
SMALL-ANGLE X-RAY SCATTERING; WIDE-ANGLE X-RAY DIFFRACTION; NANOTERASU; BRANCH BEAMLINES
Forward-model-based grain reconstruction to improve the tolerance of diffraction contrast tomography for increased sample deformation
To extend the applicability of synchrotron diffraction contrast tomography (DCT) towards more plastically deformed materials, we have developed a forward-model-based reconstruction method. This allows us to reconstruct grain shapes and local orientations in materials exhibiting levels of intragranular orientation spread that can no longer be handled with the conventional Friedel-pair-based indexing and tomographic reconstruction approach. This method consists of seed and regional indexing, in which an exhaustive searching and fitting of orientations is first performed to index the seed orientation, and then a regional indexing by testing a list of local orientations around the seed orientation is carried out to maximize the completeness. The capability of this novel method was benchmarked and compared with reconstructions based on the conventional Friedel-pair-matching and tomographic reconstruction method using samples made from fully recrystallized Al–Cu alloy, moderately deformed α-Ti alloy and 10% creep-ruptured Fe–Au alloy. The results show that this method has the potential to overcome the deformation constraint and can reconstruct reasonably well the intragranular orientations. It is also suitable for multi-phase reconstruction and both box-beam and line-beam acquisition geometries. The implementation has been made flexible to support the use of single or multiple GPU machines. The strengths and weaknesses of the current forward-model-based reconstruction are discussed in detail with respect to the conventional Friedel-pair-matching method. To fully exploit and complement the strengths of the two methods, the code to implement the current forward-model-based reconstruction has been fully integrated with the existing DCT code and is open source for beamline data processing.
DIFFRACTION CONTRAST TOMOGRAPHY; GRAIN MAPPING; FORWARD MODEL RECONSTRUCTION; SYNCHROTRON X-RAY DIFFRACTION; INTRAGRANULAR ORIENTATION
New features in ATSAS-4, a program suite for small-angle scattering data analysis
The ATSAS release 4 series introduces substantial architectural updates and enhanced user-friendly tools for analyzing biological macromolecules and nanostructured objects. In particular, highly requested project support for graphical user interfaces (GUIs) has been implemented. Here the state of the main window of each GUI application can be saved as a project and then restored to continue or extend analyses. All GUI applications now share a common framework, enabling various plot annotations and export as figures or text for easy data exchange with other plotting applications. The main interactive data processing and interpretation program, PRIMUS, has been significantly expanded with new features and integrated analysis modules. A new GUI for the program PEAK allows for multiple fitting functions, including Gaussian, Lorentzian and pseudo-Voigt. The online chromatography analysis program CHROMIXS supports multiple frame selections and subtractions, along with a newly included EFAMIX module for resolving partially overlapping components. The new ATSAS application LAUNCHER provides user-friendly wizards to configure and run command-line applications. Wherever feasible, operations like file reading and calculations have been parallelized to take advantage of available local compute resources. Command-line interfaces of many applications have been updated, e.g. with renaming and unification of common options. Improved readers/writers are implemented for Protein Data Bank and macromolecular CIF (mmCIF) file handling. The program MIXTURES now combines the functionalities of BILMIX, LIPMIX and MIXTURE, offering simplified and more versatile analyses for polydisperse systems of different shapes, also with single- or multi-layered organization. Installer packages of ATSAS are available for the latest versions of Windows, frequently used Linux distributions and recent macOS releases, both for Intel and ARM architectures, and are free for academic use.
SMALL-ANGLE SCATTERING; DATA ANALYSIS; BIOLOGICAL MACROMOLECULES; NANOSTRUCTURE; STRUCTURAL MODELING; ATSAS
A simple cryotransfer method for 3D electron diffraction measurements of highly sensitive samples
The accurate characterization of highly sensitive materials using 3D electron diffraction (3D ED) is often challenged by sample degradation caused by exposure to moisture, air, temperature variations and high vacuum during the transfer and introduction into the transmission electron microscope (TEM). A cryogenic sample-transfer protocol is presented here, designed to enable the safe and effective transfer of reactive samples into the TEM, ensuring an inert and moisture-free environment throughout the process. The protocol was validated by redetermining the crystal structures of the moisture-sensitive, strongly oxidizing and highly reactive compounds XeF2, XeF4 and XeF2·XeF4 cocrystal. Crystal structures of all three compounds were successfully solved ab initio and dynamically refined, yielding results that showed good agreement with the previously reported X-ray and neutron diffraction structures. This approach holds significant promise for advancing the study of other reactive and moisture-sensitive samples, enabling precise structural characterization in cases where traditional TEM sample preparation is unsuitable.
3D ELECTRON DIFFRACTION; CRYOTRANSFER; XENON FLUORIDES; NOBLE-GAS COMPOUNDS
Prediction of the space group and cell volume by training a convolutional neural network with primitive `ideal' diffraction profiles and its application to `real' experimental data
This study describes a deep learning approach to predict the space group and unit-cell volume of inorganic crystals from their powder X-ray diffraction profiles. Using an inorganic crystallographic database, convolutional neural network (CNN) models were successfully constructed with the δ-function-like `ideal' X-ray diffraction profiles derived solely from the intrinsic properties of the crystal structure, which are dependent on neither the incident X-ray wavelength nor the line shape of the profiles. We examined how the statistical metrics (e.g. the prediction accuracy, precision and recall) are influenced by the ensemble averaging technique and the multi-task learning approach; six CNN models were created from an identical data set for the former, and the space group classification was coupled with the unit-cell volume prediction in a CNN architecture for the latter. The CNN models trained in the `ideal' world were tested with `real' X-ray profiles for eleven materials such as TiO2, LiNiO2 and LiMnO2. While the models mostly fared well in the `real' world, the cases at odds were scrutinized to elucidate the causes of the mismatch. Specifically for Li2MnO3, detailed crystallographic considerations revealed that the mismatch can stem from the state of the specific material and/or from the quality of the experimental data, and not from the CNN models. The present study demonstrates that we can obviate the need for emulating experimental diffraction profiles in training CNN models to elicit structural information, thereby focusing efforts on further improvements.
SPACE GROUP CLASSIFICATION; DEEP LEARNING; POWDER X-RAY DIFFRACTION; ENSEMBLE AVERAGING; MULTI-TASK LEARNING
Differences in hierarchical structural changes between unoriented P(3HB) and P(3HB-co-3HH) under stretching
Poly[(R)-3-hy­droxy­butyrate] [P(3HB)] is a promising environmentally friendly polymer. However, P(3HB) exhibits brittle fracture, and the brittleness makes P(3HB) unsuitable for practical application. To improve the brittleness, 3-hy­droxy­hexano­ate (3HH) is introduced as a second monomer into P(3HB). The random copolymer P(3HB-co-3HH) shows a reduction in brittleness. In this paper, we investigate the changes in the hierarchical structures in unoriented P(3HB) and P(3HB-co-11mol%-3HH) during uniaxial stretching using in situ ultra-small-angle, small-angle and wide-angle X-ray scattering to clarify the effects of the introduction of 3HH. We reveal that the introduction of amorphous component units to P(3HB) not only suppresses crystallization and reduces crystal thickness on the nanometre scale but also destabilizes the crystal structure. We observed stretch-induced density fluctuations near the yield point by in situ X-ray scattering, showing heterogeneous deformation on scales from slightly larger than the lamellae to submicrometres in P(3HB) and on the submicrometre scale in its copolymer under uniaxial stretching. The enhancement of density fluctuations in the copolymer was smaller than that in P(3HB) because stress dispersion was caused by the hierarchical structure formed with the suppression of crystallization.
Optimal weights and priors in simultaneous fitting of multiple small-angle scattering datasets
Small-angle X-ray and neutron scattering (SAXS and SANS) are powerful techniques in materials science and soft matter. This study addressed how multiple SAXS or SANS datasets are best weighted when performing simultaneous fitting. Three weighting schemes were tested: (1) equal weighting of all datapoints, (2) equal weighting of each dataset through normalization with the number of datapoints and (3) weighting proportional to the information content. The weighting schemes were assessed by model refinement against synthetic data under numerous conditions. The first weighting scheme led to the most accurate parameter estimation, especially when one dataset substantially outnumbered the other(s). Furthermore, it was demonstrated that inclusion of Gaussian priors significantly improves the accuracy of the refined parameters, as compared with common practice, where each parameter is constrained uniformly within an allowed interval.
CO-REFINEMENT; SMALL-ANGLE SCATTERING; SAXS; SANS; SIMULTANEOUS FITTING; BAYESIAN REFINEMENT; WEIGHTING SCHEMES; PRIORS
Structure factors of random hard disk packing in 2D by explicit modeling
This paper describes a method that can (1) generate random packing of hard disks in 2D using Monte Carlo simulation, (2) extract the corresponding pair distribution function using normalization by disk line picking probability and (3) convert it to the structure factor. The generated structure factor agrees well with the analytical form based on the Percus–Yevick equation at a low area fraction (that is, within 1% at an area fraction below 0.2 and 2% at an area fraction of 0.3) but differs at a higher area fraction with more pronounced peaks and oscillations. Above an area fraction of 0.69, the hexagonal packing feature appears as sharp peaks at low Q, which are absent in the analytical solution. The structure factors up to an area fraction of 0.65 as a function of QR and the area fraction are stored in table form. The structure factor table can be combined with the cylinder form factors to simulate the X-ray/neutron scattering intensity of wood cell wall scattering.
STRUCTURE FACTORS; RANDOM PACKING; PARALLEL CYLINDERS; X-RAY/NEUTRON SCATTERING INTENSITY SIMULATION
A machine-learning-driven data labeling pipeline for scientific analysis in MLExchange
This study introduces a novel labeling pipeline to accelerate the labeling process of scientific data sets by using artificial intelligence (AI)-guided tagging techniques. This pipeline includes a set of interconnected web-based graphical user interfaces (GUIs), where Data Clinic and MLCoach enable the preparation of machine learning (ML) models for data reduction and classification, respectively, while Label Maker is used for label assignment. Throughout this pipeline, data can be accessed through a direct connection to a file system or through Tiled for access through Hypertext Transfer Protocol (HTTP). Our experimental results present three use cases where this labeling pipeline has been instrumental for the study of large X-ray scattering data sets in the area of pattern recognition, the remote analysis of resonant soft X-ray scattering data and the fine-tuning process of foundation models. These use cases highlight the labeling capabilities of this pipeline, including the ability to label large data sets in a short period of time, to perform remote data analysis while minimizing data movement and to enhance the fine-tuning process of complex ML models with human involvement.
X-RAY SCATTERING; DATA LABELING; MACHINE LEARNING; USER INTERFACES; FEATURE EXTRACTION
Strain-induced density fluctuations in linear low-density polyethyl­ene
In our previous study [Kishimoto et al. (2020). Macromolecules, 53, 9097–9107], density fluctuations were induced on the submicrometre scale in polyethyl­ene (PE) during strain and led to the generation of voids. The strength of the induction was found to increase with the amplitude of the spatial inhomogeneity of the stress field. In this work, we investigated how comonomer species and content affect the behaviors of the strain-induced density fluctuations in linear low-density PE. We found that the strength of the induction decreased with an increase in the spatial homogeneity before stretching and the mechanical melting during strain and that the degree of spatial homogeneity and mechanical melting depend on the species and content of the comonomer.
DENSITY FLUCTUATIONS; MECHANICAL MELTING; X-RAY SCATTERING; LINEAR LOW-DENSITY POLYETHYLENE; SPATIAL HOMOGENEITY
Linearization routines for the parameter space concept to determine crystal structures without Fourier inversion
We present the elaboration and first generally applicable linearization routines of the parameter space concept (PSC) for determining one-dimensionally projected structures of m independent scatterers. This crystal determination approach does not rely on Fourier inversion but rather considers all structure parameter combinations consistent with available diffraction data in a parameter space of dimension m. The method utilizes m structure-factor amplitudes or intensities represented by piecewise analytic hyper-surfaces to define the acceptable parameter regions. The coordinates of the point scatterers are obtained through the intersection of multiple isosurfaces. This approach allows for the detection of all possible solutions for the given structure-factor amplitudes in a single derivation. Taking the resonant contrast into account, the spatial resolution achieved by the presented method may exceed that of traditional Fourier inversion, and the algorithms can be significantly optimized by exploiting the symmetry properties of the isosurfaces. The applied one-dimensional projection demonstrates the efficiency of the PSC linearization approach based on fewer reflections than Fourier sums. Monte Carlo simulations, using the projections of various random two- and three-atom structure examples, are presented to illustrate the universal applicability of the proposed method. Furthermore, ongoing efforts aim to enhance the efficiency of data handling and to overcome current constraints, promising further advancements in the capabilities and accuracy of the PSC framework.
CRYSTAL STRUCTURE DETERMINATION; CENTROSYMMETRIC STRUCTURES; TWO- AND THREE-DIMENSIONAL PARAMETER SPACE; LINEARIZATION; PARAMETER SPACE CONCEPT; MONTE CARLO SIMULATION; ONE-DIMENSIONAL PROJECTION; X-RAY DIFFRACTION
Optimal st-PMMA/C60 helical inclusion complexes via tunable energy landscapes for the application of an Ag SERS-active substrate
In bio-inspired systems, the hierarchical structures of biomolecules are mimicked to impart desired functions to self-assembled materials. However, these hierarchical architectures are based on multicomponent systems, which require not only a well defined primary structure of functional molecules but also the programming of self-assembly pathways. In this study, we investigate pathway complexity in the energy landscape of the syndiotactic poly(methyl methacrylate) (st-PMMA)/C60/toluene complex system, where C60 and toluene serve as guests in the st-PMMA helical host. Structural characterization revealed that st-PMMA preferentially wraps around C60, forming a thermodynamically favorable helical inclusion complex (HIC). However, during the preparation of the st-PMMA/C60 HIC, a lengthy guest-exchange pathway was discovered, where the st-PMMA/toluene HIC transformed into the st-PMMA/C60 HIC. This pathway complexity may hinder the formation of the st-PMMA/C60 HIC within a feasible timeframe. Given that the energy landscape can be modulated by temperature, the st-PMMA host can directly wrap around C60 in higher temperature ranges, thereby bypassing the guest-exchange process and increasing the st-PMMA/C60 HIC formation efficiency. Additionally, after self-assembly programming, the st-PMMA/C60 HIC can serve as an excellent photochemical reduction site. The well dispersed nanodomains of the st-PMMA/C60 HICs act as nanoparticle templates for surface-enhanced Raman scattering (SERS) hotspot fabrication. We successfully utilized these HIC templates to synthesize self-assembled SERS-active silver nanoparticle arrays, demonstrating their potential for use in chemical sensing applications. In summary, a clear energy landscape can guide supramolecular engineering to achieve the desired supramolecular architectures by selecting appropriate self-assembly pathways.
SUPRAMOLECULAR CHEMISTRY; INCLUSION COMPLEXES; HELICAL POLYMERS; C60; RAMAN SPECTROSCOPY
Synthesis and quantum crystallographic evaluation of WYLID: YLID's red rival
The synthesis and characterization of WYLID [2-(di­methyl-λ4-sulfane­ylidene)-[1,2′-bi­indenyl­idene]-1′,3,3′(2H)-trione], a side product that appears during the synthesis of YLID, is presented in this study. Quantum crystallographic insights into the bonding situation in WYLID are provided on the basis of Hirshfeld atom refinement (HAR), multipolar modelling and X-ray restrained wavefunction fitting. We compare these results with theoretical calculations on a gas-phase optimized density functional theory and a Hartree–Fock calculation based on the geometry obtained by HAR. The S—C bond in WYLID is best described as an ylid-type bond and the SMe2 fragment does not affect the nearest C—O carbonyl/enolate equilibrium. This work may contribute to an ongoing debate in the quantum crystallography community about the bonding situation in YLID and provides a routine for distinguishing between carbonyls and enolates.
QUANTUM CRYSTALLOGRAPHY; SYNTHESIS; CHEMICAL CRYSTALLOGRAPHY; COMPLEMENTARY BOND ANALYSIS
Local orthorhombic phase in zirconium oxide nanocrystals: insights from X-ray pair distribution function analysis
Zirconium dioxide (ZrO2) and hafnium dioxide (HfO2) have emerged as promising alternatives to conventional ferroelectric materials. Understanding the crystal phases of these oxides under different conditions is crucial for optimizing their properties. There are several theories for the (anti)ferroelectric properties; however, comprehensive analysis, particularly at the local structure level, is lacking. In this study, we investigate the local structure of ZrO2 nanocrystals using X-ray pair distribution function (PDF) analysis, revealing an unexpected local orthorhombic distortion irrespective of crystallite size. This finding suggests the potential existence of an intermediate orthorhombic phase during the microscopic switching pathway observed in previous studies. Additionally, we explore the influence of crystallite size and surface effects on the PDF. These results contribute to a deeper understanding of the structural dynamics in ZrO2 and offer insights for the design of next-generation ferroelectric materials.
LOCAL STRUCTURE; NANOCRYSTALS; ZIRCONIUM OXIDE; TOTAL SCATTERING; PAIR DISTRIBUTION FUNCTION; FERROELECTRICS
Reliability of pair distribution function analysis in in situ experiments
In situ and operando pair distribution function (PDF) studies are becoming commonly used to study chemical reactions, nucleation and growth of nanoparticles, or structural changes during the operation of batteries, catalysts, thermoelectric devices etc. However, repeated time-resolved total scattering experiments and subsequent PDF analysis are often not prioritized due to the scarce synchrotron beam time available. This means that the experimental uncertainty and reproducibility of the experimental methods are unknown, and the full potential of in situ PDF experiments may not be exploited. Here, we quantify the experimental uncertainty of the PDF technique in an in situ study of the hydro­thermal synthesis of ZrO2 nanoparticles. Systematic variation of the parameters used to obtain the PDF shows that the user-defined parameters can potentially affect the chemical conclusions obtained from the time-resolved experiment. We found that comparable results are best obtained using the same input parameters across different experiments. We also compare different PDF algorithms to examine whether the processing algorithm influences the chemical analysis.
PAIR DISTRIBUTION FUNCTIONS; IN SITU STUDIES; NANOCRYSTAL NUCLEATION; NANOCRYSTAL GROWTH; TIME-RESOLVED EXPERIMENTS
Solvent-annealing-induced microphase separation in polyether polyurethane: a small-angle X-ray scattering study
This study investigated the effects of solvent vapor annealing on the microphase separation structure of polyurethane (PU) using small-angle X-ray scattering (SAXS) and complementary techniques. Solvent annealing, as an alternative to thermal annealing, offers a lower-temperature method to refine the microstructure of PU. We examined the impact of methyl ethyl ketone (MEK), acetone and toluene vapors on a commercial polyether PU, focusing on changes in microphase structure, adsorption kinetics and thermal stability. The SAXS data, analyzed by a polydisperse hard-sphere model, indicated that the degree of phase separation increased upon solvent annealing, and the order of influence exerted by the solvent vapors on the microphase structure follows MEK > acetone > toluene. The in situ variable-temperature SAXS results showed that the solvent-annealed sample had superior thermal stability to the quenched sample. Compared with high-temperature annealing, solvent annealing induced a higher degree of phase separation but did not lead to significant growth of the hard-urethane-segment-rich domains. These findings provide valuable insights into optimizing solvent annealing processes, allowing for advanced applications of PUs where excessive heat may lead to degradation or other undesirable changes.
POLYURETHANE; SOLVENT ANNEALING; MICROPHASE SEPARATION; SMALL-ANGLE X-RAY SCATTERING; SAXS
Upgrade of the KWS-2 high-intensity/extended-Q-range SANS diffractometer of JCNS for soft matter and biophysics: in situ SEC, controlled in situ RH/T variation and WANS detection
The KWS-2 small-angle neutron scattering (SANS) diffractometer operated by Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum, Garching, Germany, is dedicated to the investigation of mesoscopic multi-scale structures and structural changes due to rapid kinetic processes in soft condensed matter and biophysical systems. Following requests from the user community, it has been repeatedly upgraded with respect to the most important methodological parameters of an instrument of this type, namely the intensity on the sample, the instrumental resolution and the minimum scattering variable Qmin. Here we report on further specific improvements to the sample environment and detection capabilities which have just been completed or are being implemented. Complementary size-exclusion chromatography (SEC) for in situ protein purification was developed and optimized at KWS-2 to provide the instrument with biological samples of controlled quality. The instrument is also currently being equipped with a wide-angle neutron scattering (WANS) detector which will allow it to bridge the atomic and mesoscale, benefiting from the instrument's adjustable resolution down to Δλ/λ = 2%. For controlled relative humidity and temperature (RH/T) on ionic conductive samples for energy applications or biomembranes for biophysical and health applications, a precise dew point generator has recently been characterized and commissioned; this offers great versatility with regard to varying the contrast in situ in the beam on hydrated samples.
SANS; SMALL-ANGLE NEUTRON SCATTERING; WANS; WIDE-ANGLE NEUTRON SCATTERING; SIZE-EXCLUSION CHROMATOGRAPHY; SEC-SANS; SEMI-CRYSTALLINE POLYMERS
Complete online database of maximal subgroups of subperiodic groups at the Bilbao Crystallographic Server
The section of the Bilbao Crystallographic Server (https://www.cryst.ehu.es) dedicated to subperiodic groups includes the program MAXSUB, which gives online access to the complete database of maximal subgroups of subperiodic groups. All maximal non-isotypic subgroups as well as all maximal isotypic subgroups of indices up to 9 are listed individually, together with the series of maximal isotypic subgroups of subperiodic groups. These data were compared with those of Litvin [(2013), Magnetic group tables, 1-, 2- and 3-dimensional subperiodic groups and magnetic space groups], which revealed several differences, discussed here in detail.
SUBPERIODIC GROUPS; MAXIMAL SUBGROUPS; BILBAO CRYSTALLOGRAPHIC SERVER; SERIES OF MAXIMAL SUBGROUPS
Texture tomography with high angular resolution utilizing sparsity
We demonstrate an approach to the reconstruction of scanning probe X-ray diffraction tomography data with anisotropic polycrystalline samples. The method involves reconstructing a voxel map containing an orientation distribution function in each voxel of a bulk 3D sample. By choosing a particular kind of basis functions, we can effectively utilize non-negativity in orientation space for samples with sparse texture. This enables us to achieve stable solutions at high angular resolutions where the problem would otherwise be underdetermined. This method differs from established approaches by not relying on a peak-finding step. It is therefore applicable to sample systems consisting of small and highly mosaic crystalline domains that are not handled well by these methods. We demonstrate the new approach using data from a shot-peened martensite sample where we are able to map the twinning microstructure in the interior of a bulk sample without resolving the individual lattice domains. We also demonstrate the approach on a piece of gastropod shell with a mosaic microstructure. The results suggest that, by utilizing the sparsity of the texture, the experiment can be carried out using only a single rotation axis, unlike previous demonstrations of texture and tensor tomography.
TOMOGRAPHY; TEXTURE ANALYSIS; XRD-CT; X-RAY DIFFRACTION COMPUTED TOMOGRAPHY; 3D-XRD; 3D X-RAY DIFFRACTION
A critical step toward far-field laboratory diffraction contrast tomography in Laue focusing geometry
Recent simulations have demonstrated the promising potential of far-field laboratory diffraction contrast tomography (FF-LabDCT) in the Laue focusing geometry for 3D mapping of grain-averaged deviatoric strain tensors, achieving a strain uncertainty as low as 1 × 10−4 [Lindkvist & Zhang (2022). J. Appl. Cryst. 55, 21–32]. The present work takes a critical step towards realizing this tool. It presents the first attempt at implementing FF-LabDCT using a Zeiss Xradia 520 Versa X-ray microscope, including both hardware and software development. A new algorithm, LabDBB, which adapts the previously developed dictionary-based branch and bound (DBB) principles, is implemented for indexing FF-LabDCT data. The performance of LabDBB is evaluated by comparing the indexed grain crystallographic orientations and center of mass positions with those obtained using near-field LabDCT within the same gauge volume of a fully recrystallized iron sample. Finally, the challenges related to fitting the grain-averaged deviatoric strain tensor using the current FF-LabDCT setup are identified. The strain analysis suggests that, once these challenges are addressed, a strain uncertainty as low as 2 × 10−4 could potentially be achieved. This work demonstrates the possibility for developing a tool capable of 3D grain-scale strain analysis with high strain precision in home laboratories.
FAR-FIELD LABORATORY DIFFRACTION CONTRAST TOMOGRAPHY; DICTIONARY-BASED BRANCH AND BOUND METHODS; GRAIN INDEXING; STRAIN ANALYSIS
If you cannot see it, is it still there?
Protein crystallographers rely on electron density to build atomic models of molecular structures, yet flexible regions often remain unseen in electron density and are omitted. We suggest that ensemble refinement can be used to visualize and analyse the conformational landscape of such `invisible' protein segments, which is particularly useful in cases where molecular flexibility plays a functional role. Using ensemble refinement on multiple crystal forms of the fungal methyl­transferase PsiM as an example, we illustrate the dynamic nature of a key substrate recognition loop, demonstrating its potential role in substrate binding and release. Ensemble refinement provides a persuasive visualization of biologically relevant flexible regions and can be a powerful tool for exploring molecular plasticity and aiding the modelling of dynamic protein components.
ENSEMBLE REFINEMENT; MODELLING; INVISIBLE PROTEIN SEGMENTS; FLEXIBILITY; MISSING ELECTRON DENSITY; PROTEIN CRYSTALLOGRAPHY
Probing the out-of-equilibrium dynamics of driven colloids by X-ray photon correlation spectroscopy
The high brilliance of fourth-generation synchrotron sources coupled with advanced X-ray detectors enables a wide range of dynamic studies of colloids and other soft-matter systems. In particular, the higher fraction of coherent flux provided by these new sources is a major boost for X-ray photon correlation spectroscopy (XPCS). As a result, not only can equilibrium dynamics be accessed but also relatively fast out-of-equilibrium processes can be investigated by XPCS. This article briefly recalls the statistical properties of coherent scattering and then demonstrates a case study of non-equilibrium fluctuations in a driven colloidal system. A simple example is the resuspension of colloids by vigorous shaking, where the inhomogeneous flow generates local variations in number density of particles leading to strong velocity fluctuations. The Brownian motion of the particles homogenizes the suspension with time and the system gradually returns to pure diffusive dynamics. On the other hand, in a uniformly sheared suspension of particles, such concentration gradients do not form and upon cessation of shear the return to Brownian dynamics is rapid. These transient non-equilibrium effects can inadvertently influence micrometre-range particle size measurement by means of dynamic scattering methods.
X-RAY PHOTON CORRELATION SPECTROSCOPY; XPCS; ULTRA-SMALL-ANGLE X-RAY SCATTERING; USAXS; COLLOIDS; OUT-OF-EQUILIBRIUM DYNAMICS; NON-EQUILIBRIUM FLUCTUATIONS
In situ small-angle X-ray scattering measurement at the Very Small Angle Neutron Scattering Instrument at the China Spallation Neutron Source
Small-angle X-ray and neutron scattering (SAXS and SANS) offer complementary insights into multi-scale and multiphase structures. Efforts have been made to integrate SAXS into SANS instruments, with only D22 at the Institut Laue–Langevin successfully implementing a SAXS setup; this was constrained to a horizontal geometry due to space limitations and high radiation noise. Here, we introduce an in situ vertical SAXS setup at beamline 14, Very Small Angle Neutron Scattering (VSANS) instrument, at the China Spallation Neutron Source. The compact vertical SAXS instrument without a beam stop, measuring 87 cm × 93 cm × 240 cm (W × L × H) and featuring a hoisting frame, can be easily installed in the VSANS sample room within 5 h. Utilizing a 50 mm-diameter neutron collimation guide, we can simultaneously detect X-rays from below and neutrons from behind, with the backboard of the SAXS chamber coated in a boron–aluminium alloy to reduce neutron background interference. Through testing with standard samples like deuterated and hydrogenated PEG, silver behenate, LaB6, and glass carbon, we demonstrate that concurrent neutron and X-ray measurements are successful.
VERY SMALL ANGLE X-RAY SCATTERING; SAXS; VSANS; VERTICAL GEOMETRY; CHINA SPALLATION NEUTRON SOURCE
XRDplayground: a Python-based educational tool for interactive learning of powder X-ray diffraction crystallography
One of the barriers to learning crystallography through the powder X-ray diffraction (PXRD) technique is the understanding and visualization of the crystal structure and its effects on the diffraction pattern. To enhance learning through visualization, we present XRDplayground, an open-source software developed in Python that can simultaneously simulate the unit cell and its PXRD pattern. It features a graphical user interface where all the structural parameters of the crystal, such as lattice parameters and atomic positions inside the unit cell, are adjustable via sliders. The PXRD pattern is simulated by taking into consideration the X-ray energy and the crystallite size using Scherer's equation. XRDplayground is an educational tool to make PXRD crystallography more engaging and enhance learning and understanding of the concepts rather than mathematical treatment and/or superficial memorization.
XRDPLAYGROUND; POWDER X-RAY DIFFRACTION; PXRD; SIMULATION; XRD FUNDAMENTALS; TEACHING
SAStutorials.org – online tutorials on small-angle scattering data analysis
Small-angle X-ray and neutron scattering (SAXS and SANS) are versatile techniques for studying the structure of various materials and particles, enabling investigations of structures from a few to hundreds of nanometres. However, interpreting SAXS or SANS data can be challenging, hence the need for effective training. Here, we present the website SAStutorials.org, which offers tutorials on small-angle scattering (SAS) data analysis. The website serves as a learning platform that supports active learning both in the classroom and through self-study. The tutorials cover basic concepts, advanced modelling and theoretical aspects of SAS. Each tutorial follows a structure based on the principle of SOLO taxonomy, guiding learners from minimal or no knowledge in a given area to the ability to tackle real-world problems. SAStutorials.org has been developed as a community tool, providing tutorials that encompass a broad range of data analysis types, leveraging various programs and investigating different materials. Moreover, the website and all its data are open source, encouraging contributions from the community.
SMALL-ANGLE SCATTERING; SAXS; SANS; TEACHING; SIMULATION; DIDACTICS; ACTIVE LEARNING; TUTORIALS
Benchmarking deep learning for automated peak detection on GIWAXS data
Recent advancements in X-ray sources and detectors have dramatically increased data generation, leading to a greater demand for automated data processing. This is particularly relevant for real-time grazing-incidence wide-angle X-ray scattering (GIWAXS) experiments which can produce hundreds of thousands of diffraction images in a single day at a synchrotron beamline. Deep learning (DL)-based peak-detection techniques are becoming prominent in this field, but rigorous benchmarking is essential to evaluate their reliability, identify potential problems, explore avenues for improvement and build confidence among researchers for seamless integration into their workflows. However, the systematic evaluation of these techniques has been hampered by the lack of annotated GIWAXS datasets, standardized metrics and baseline models. To address these challenges, we introduce a comprehensive framework comprising an annotated experimental dataset, physics-informed metrics adapted to the GIWAXS geometry and a competitive baseline – a classical, non-DL peak-detection algorithm optimized on our dataset. Furthermore, we apply our framework to benchmark a recent DL solution trained on simulated data and discover its superior performance compared with our baseline. This analysis not only highlights the effectiveness of DL methods for identifying diffraction peaks but also provides insights for further development of these solutions.
DEEP LEARNING; GRAZING-INCIDENCE WIDE-ANGLE X-RAY SCATTERING; GIWAXS; PEAK DETECTION; CONVOLUTIONAL NEURAL NETWORKS; FASTER R-CNN