Engineering neutron diffractometers are vital for non-destructive residual stress and texture analysis in bulk engineering components. Accurate data reduction and analysis software is essential for maximizing instrument capabilities. Here we present pyRS 2.0 , an upgraded open-source Python software package designed for the High Intensity Diffractometer for Residual Stress Analysis (HIDRA). Enhancements include a graphical user interface for detector calibration with advanced diagnostics, real-time reduction of live neutron event data, a new texture analysis module, and improved quality control features that flag and exclude poor data fits. The improved user experience and expanded functionality support the evolving needs of the HIDRA user community.
Motivated by the need for a convenient way to demonstrate the growth of crystals in glass plates by the lipid cubic phase method at crystallization workshops and courses, we developed a lightweight, portable, compact and inexpensive digital microscope device. The device is built around hand-held Wi-Fi and hardwired digital microscopes that are available commercially at low cost and that can use cell phones and personal computers for imaging without the need for unwieldy eyepieces. The device provides illumination from above and below the crystallization plate over a range of brightness levels. It can be used with regular white light and with polarized light to detect birefringent crystals. While not the focus of this study, the new device has been shown to also work with batch and vapour-diffusion plates. Remote monitoring of crystallization plates in a cold cabinet or walk-in refrigerator at 4 °C is possible with the Wi-Fi microscope. Crystals grown in lipid cubic phase and vapour-diffusion crystallization plates were harvested with the aid of the new device and used for diffraction data collection, leading to structure determination at high resolution. Most parts of the device were 3D printed in polylactic acid plastic. The corresponding STL files, included as part of this publication, can be used to make replicates of the current microscope and to produce bespoke devices suited to the specific needs of the user. We envision using the new device for outreach activities at primary, secondary and third-level schools, and at science fairs in support of the citizen scientist. Relatedly, in this study examples are included of recorded images of plant and animal tissue sections. One reveals birefringent materials in a tomato leaf. Another shows optically active crystals of calcium oxalate in onion tunic tissue.
Ultra-small-angle neutron scattering (USANS) measurements at the Spallation Neutron Source (SNS) at Oak Ridge require careful treatment of slit-geometry resolution effects and, in many cases, multiple scattering in complementary small-angle neutron scattering (SANS) data before meaningful structural interpretation can be made. We present a unified data-reduction framework that provides SNS USANS users with a systematic and reproducible workflow for obtaining intrinsic single-scattering intensities across the combined USANS–SANS Q range. The approach explicitly formulates the slit-geometry point-spread function for Bonse–Hart USANS, implements both analytical truncated Abel inversion and Bayesian Gaussian process regression for stable desmearing with uncertainty quantification, incorporates central-moment expansion for pinhole SANS resolution correction, and applies an orthonormal spectral method for probabilistic multiple-scattering removal. The ordered workflow ensures that instrumental resolution and multiple-scattering distortions are removed consistently prior to merging datasets, so that the resulting spectrum represents a physically meaningful resolution-free cross section. Experimental demonstrations on isotropic systems, uniaxially stretched materials and shear-induced anisotropic configurations illustrate both the applicability and the geometric limitations of anisotropic desmearing. This framework provides practical guidance for reliable SNS USANS data reduction and establishes a resolution-consistent foundation for quantitative structural analysis from nanometre to micrometre length scales.
One of the main advantages of Hirshfeld atom refinement (HAR), besides improved refinement statistics and reduced uncertainties of all derived parameters, is the possibility of refining anisotropic hydrogen atoms without any type of restriction to a correct distance. Notwithstanding this, there are still some problems that need attention for an accurate refinement of H atoms. For instance, X —H bond distances ( X = N, O) are typically underestimated when they participate in a strong hydrogen bond and the crystallographic environment is not accounted for in the refinement model. In this work, we propose the use of an embedding scheme to model bulk effects approximately, where a molecule or group of molecules is polarized by electrostatic potential (ESP)-derived charges. Quantum mechanics/molecular mechanics methods based on ESP-derived charges have been used successfully to reproduce band gaps or optical and electronic properties of crystalline systems. It is demonstrated that the H-atom refinement parameters obtained with this approach are comparable to those obtained from pure quantum mechanical models, but with a significantly lower computational cost. Thus, this embedded HAR method is suitable for performing refinements in reasonable time frames for large systems in which strong intermolecular interactions, such as hydrogen bonds, exist.
Variable-temperature NMR (VT-NMR) spectroscopy was employed to investigate the rotational dynamics of (1,4-diacetoxy-3-methylnaphth-2-yl)diphenylphosphine oxide. The compound crystallizes in the centrosymmetric space group P 2 1 / n , featuring two distinct conformational states ( S1 and S2 ) coexisting within the crystal structure. Experimental kinetic analysis in deuterated dimethyl sulfoxide revealed a rotational barrier of approximately 20 kcal mol −1 (83.7 kJ mol −1 ) (coalescence at 105°C), which effectively restricts interconversion at ambient temperatures. Notably, while ωB97XD/SMD calculations predict an intrinsic barrier of only 4.8 kcal mol −1 (20.1 kJ mol −1 ), experimental results demonstrate that explicit solute–solvent interactions significantly reinforce the rotational hindrance. This nearly fourfold increase highlights the decisive role of solvent-induced stabilization in governing conformational dynamics. Our findings indicate that the observed conformational integrity is not solely an intrinsic feature of the molecule but is critically dependent on the chemical environment, allowing for the observation of conformers despite their subtle thermodynamic differences.
Total scattering models are essential for characterizing the structure and disorder of nanoscale materials. The Debye scattering equation (DSE) provides a rigorous route to elastic total scattering, but its direct evaluation is computationally demanding because pairwise contributions must be accumulated at every scattering vector, whereas common acceleration strategies based on binned pair-distance distributions or gridded fast Fourier transforms can introduce discretization and aliasing artifacts that compromise diffuse-scattering accuracy. Here, we present AES-Debye, an accuracy-preserving DSE framework that aggregates pair distances into a pair distribution function (PDF) using corrected bin centers and numerically robust accumulation to suppress discretization and summation errors. A data-locality-aware parallel design enables efficient execution on CPUs and GPUs. We demonstrate strong scalability by computing a high-resolution total scattering profile for a system of 90 million atoms, $(0.1,μ\mathrm{m})^{3}$, in minutes on a distributed-memory CPU platform. These capabilities extend accurate elastic total scattering calculations to large, complex systems while simultaneously providing high-resolution PDFs for downstream structural analysis.
The thermal expansion of natural FeWO4 (ferberite) and synthetic FeWO4:Fe2WO6 (7:1) was investigated over the 2-1123 K temperature range, combining single-crystal and powder X-ray diffraction together with neutron powder diffraction. High-precision lattice parameters were obtained for both samples. The temperature dependence of the unit-cell volume was analyzed using physically based thermodynamic models, including the Kroll and Berman approaches as implemented in EoSFit7-GUI. All datasets are well reproduced within their respective temperature intervals. However, significant differences are observed between the behavior of ferberite and FeWO4:Fe2WO6, which has a ∼40% smaller thermal expansion coefficient and a reduced reference volume. The possible origins of these differences, including microstructural and phase-coexistence effects, are discussed. The results provide a comprehensive description of the thermal expansion behavior of FeWO4 across a wide temperature range.
Porous and/or bicontinuous structures often display a pronounced correlation peak in their small-angle scattering that indicates a preferred domain spacing d. A first attempt to describe the full q dependence of small-angle scattering profiles has been formulated in a previous publication [Frielinghaus (2026) J. Appl. Cryst. 59, 837-844]. However, the diffuse scattering, i.e. the forward scattering, is often found to be lower than in this simple framework, while the correlation peak is rather broad. By adding one more parameter σ that stretches the correlation peak with respect to the residual features of the theory, a more general heuristic theoretical framework for porous and/or bicontinuous structures is obtained. The predominant conditions and their physical meaning are discussed in context with practical examples.
A rigorous integral X-ray diffuse scattering (XRDS) method has been developed to experimentally determine separate densities and size distributions for interstitial- and vacancy-type dislocation loops in irradiated materials. Direct numerical calculations of the integral XRDS intensities for prismatic a 0 /2{111}-type dislocation loops around the tungsten (W) 110 Bragg reflection show for the first time that the opposite signs of the displacement fields surrounding interstitial and vacancy loops generate sufficiently asymmetric rocking curve intensity profiles to separate the size distributions of the two loop types. This capability is demonstrated using measurements of single-crystalline W after irradiation with 10.8 MeV self-ions near room temperature to 0.008 and 0.02 displacements per atom. Distinct size distributions are shown for interstitial and vacancy loops at both irradiation doses, and the densities of both loop types are shown to increase with higher dose. The comprehensive computational methods presented in this study enable integral XRDS intensity calculations to be rigorously tailored to specific measurement conditions and geometries. Moreover, these calculations can be applied to nearly any type of irradiation-induced defect cluster provided accurate modeling of the defect-induced strain field and atomic structure of the cluster is utilized. Combined with the new capability of distinguishing the interstitial/vacancy nature of dislocation loops presented in this study, these critical developments expand the utility of the technique significantly and establish a rigorous methodology for performing detailed studies of irradiation-induced defects using integral XRDS measurements.
The cubic space group P4332 has been previously reported for the multiferroic lithium ferrite (α-LiFe5O8, denoted LFO). Instead, results from the present study using PBEsol+U calculations with SSSP pseudopotentials suggest that the tetragonal space group P43212 is true for the ground state of LFO. Spin-resolved projected density of states analysis shows strong 3d electron localization of Fe3+ in FeO4 tetrahedra, mostly contributing to the high Hubbard energy U in the calculated tetragonal model. Its direct band gap of 2.050 eV is slightly lower than that of the cubic model (2.107 eV) in density of states calculations. The calculated ferrimagnetic ground state exhibits a collinear spin order along the crystallographic c axis in the tetragonal magnetic space group P4321'2', consistent with the group theoretical prediction. Decreasing ferromagnetic interactions and increasing antiferromagnetic interactions in the c direction, simultaneously, explain the origin of the tetragonality a/c > 1 with a = 8.3528 (2) Å and c = 8.3511 (1) Å. Strong Fe-O-Fe superexchange interactions contribute to the tetragonal lattice distortion of LFO as well.
A gas-controlled capillary spinner was developed for time-resolved powder X-ray diffraction measurements of crystalline materials under controlled atmospheres. This system enables continuous sample rotation with simultaneous gas control by integrating a gas-tight capillary cell, a magnetic fluid rotary feedthrough and a fast-response diaphragm valve, allowing diffraction measurements to be performed in rapidly changing environments. The system performance was evaluated using a standard Si powder sample, revealing that high-speed rotation significantly improves the uniformity of the diffraction peak intensity, with relative fluctuations reduced to <1% at speeds of ∼200 r min-1 even with millisecond-scale measurements. The applicability of the system was demonstrated by time-resolved diffraction measurements of a metal-organic framework during gas adsorption, in which structural changes were successfully tracked and quantitatively analyzed with a time resolution of 50 ms. These findings indicate that the developed system provides a reliable approach for in situ and operando diffraction studies under dynamic gas conditions.
Multi-domain proteins (MDPs) adopt diverse conformations arising from cooperative inter-domain motions, and such dynamics are coupled to their biological functions. Quantitative characterization of these motions is crucial for elucidating their functional mechanisms. Although small-angle X-ray scattering (SAXS) provides information on overall domain arrangement, the limited experimental constraints hinder reliable discrimination of conformational ensembles derived from molecular dynamics (MD) simulations. To address this limitation, complementary experimental constraints that offer domain-selective structural information are required. Inverse contrast-matching small-angle neutron scattering (iCM-SANS), combined with segmental deuteration, enables selective observation of individual domains and provides such complementary constraints. However, practical strategies for preparing segmentally deuterated MDPs have yet to be established. Here, we develop an experimental protocol that integrates controlled protein deuteration with high-efficiency multi-step protein ligation to generate a segmentally deuterated MDP. The combined use of SAXS and iCM-SANS yields complementary structural constraints that enhance discrimination of MD-derived conformational ensembles. This protocol expands the applicability of domain-selective observation, enabling analysis of dynamics in MDPs.
The unambiguous identification of all crystallographic faces and directions, including those associated with plastic bending, is a prerequisite for establishing reliable structure–property relationships in flexible organic crystals. Conventional face indexing via single-crystal X-ray diffraction (SCXRD) is often compromised by the morphological imperfections typical for these materials and the technical limitations of diffractometer on-axis optical microscopes. This work introduces and validates an integrated analytical protocol that synergistically combines computational morphology prediction, precise interfacial angle measurement via scanning electron and optical microscopy, and directed SCXRD indexing enhanced by internal (crystal bend) and external (mount) geometric standards. Applied to the plastically bendable crystals of α-pyrazinamide, 1,3,5-trichlorobenzene and L-leucinium hydrogen maleate, this multi-technique framework conclusively resolved their bending geometries, identifying the primary bending faces and directions as (002)/[100], {011}/[100] and (20 1 )/[010], respectively. Crucially, while the bending plane can be identified via SCXRD standards alone, the full protocol is mandatory for determining all morphological faces, providing the complete dataset essential for computational analysis and predictive model building. This workflow overcomes the ambiguities inherent to any single method and provides a robust, generalizable framework for the reliable morphology characterization of mechanically flexible molecular crystals.
We report on the temperature evolution of magnetic satellites associated with the incommensurate magnetic ordering of Dy3+ ions in DyFeO3 below 4.1 K. Using high-resolution neutron diffraction, incommensurate magnetic reflections, satellites of the 001 reflection with odd harmonics up to the seventh order, were observed and their temperature dependence quantified. Key parameters, such as the modulation length, FWHM and integrated intensities, were analysed across the measured temperature range. The results were compared with a previous study of the soliton lattice in TbFeO3 which appears under an applied magnetic field. Possible microscopic models underlying the magnetic order of Dy3+ are discussed in this context.
Pair distance distribution functions (PDDFs) similar to those obtained by indirect Fourier transformation of small-angle scattering data from interacting prolate and oblate ellipsoids have been simulated using a Monte Carlo approach. Interactions were modelled with a square-well or square-wall potential combined with a non-overlapping core, and spanned from a maximum attraction of -1.5 kT per pair of particles to a repulsion of +1.5 kT. Volume fractions ranged from 1% to 10%, with an extension to 20% for systems in which particles interacted solely via non-overlapping cores, without further attraction or repulsion. The data were also transformed into scattering curves and analysed using the generalized indirect Fourier transformation (GIFT). The results show that rules of thumb for interpreting PDDFs can be misleading. GIFT removes most interaction effects and allows correct identification of the ellipsoidal shape; however, axis lengths are often underestimated. Attractive interactions are more challenging than repulsive ones and may go unnoticed without additional information.
We propose a Shannon sampling based approach for the analysis of laboratory and synchrotron small-angle X-ray scattering (SAXS) data. This method avoids calculation of the pair distance distribution function P(r), which is typically used as an alternative to the model-dependent fitting of SAXS data for determining the size and shape of the scattering object. Using this new approach it is also possible to skip any model-dependent fit of the SAXS data. The method has been tested on SAXS data collected from Polysorbate 20, d-α-tocopheryl polyethyl-ene glycol 1000 succinate spheroidal core-shell micelles and relevant well known proteins (lysozyme, apoferritin, carbonic anhydrase 2) of different molecular weights. The results confirm the potential of the approach, even for laboratory scattering data and in the presence of polydispersity. The method allows the reliable derivation of maximum size, mass, volume, polar/equatorial asymmetry, hydration fraction, shell thickness and core/shell electron-density differences for core-shell structures, directly in the q domain, working on SAXS data measured from dilute samples for which interparticle structure factors are negligible.
Grazing-incidence small-angle scattering (GISAS) is a relatively young technique with important applications in thin-film technology and untapped potential when it comes to 2D analysis on an absolute intensity scale. Approaching standardization and reference methods early is foundational for reproducibility and comparability across laboratories and reduction of systematic error sources. It underpins trust in data obtained and accelerates innovation by ensuring that scientists work from a common methodological baseline. Accordingly, obtaining reproducible results from different GISAS instruments requires an agreement on how measurements are performed, instruments calibrated and terms defined. To pave the way for standardization and reference methods, we surveyed GISAS practitioners on what comes before an experiment: hardware, software, sample alignment and instrument calibration. Twenty-two questions were designed to elucidate the state of the art, which can be used for the development of reference methods. Our data on 27 instruments provide the basis for standardization. With very few exceptions, we found laboratories prepared to implement future reference methods, but no consensus emerges naturally for sample alignment and instrument calibration. We, that is the GISAS community, are thus in a position to embark on the journey of standardization.
We accelerate synchrotron X-ray reflectometry (XRR) by more than an order of magnitude and demonstrate the acquisition of full reflectivity curves within 213 µs over a q z range of 0.05 to 0.35 Å-1 at 0.001 Å-1 resolution. This is achieved by rapidly sweeping the incidence angle with a high-speed galvanometer and recording the reflected beam on an area detector. The method preserves a monochromatic parallel-beam geometry, requires only straightforward geometric and exposure time corrections, and yields quantitative agreement with standard XRR in thickness, density and roughness. At the shortest acquisition times, the photon statistics enter the low-count Poisson regime, where conventional least-squares fitting becomes biased. We show that applying an Anscombe variance-stabilizing transform restores near-Gaussian error behavior and significantly improves fitting robustness. Our approach benefits not only ultrafast XRR but reflectometry data in general at large q z , where count rates are intrinsically low. This advance enables time-resolved studies of thin-film growth, diffusion, photoswitching and other rapid kinetic processes.
In this study we use Fisher information within the software HOGBEN to optimize the structure of magnetic reference layers to maximize the information gained from polarized neutron reflectometry (PNR) measurements on soft-matter and biological samples. Our approach is based on simulating the reflectivity from an experimentally determined dataset of a supported lipid bilayer. A set of reflectivity curves is calculated by varying parameters associated with the substrate assembly containing a magnetic reference layer. For each of the calculated reflectivity curves, we quantified the sensitivity of the simulated data to the sample structure. Our Fisher information analysis predicts that decreasing the thickness of the capping layer combined with increasing the magnetic scattering length density of the magnetic reference layer will reduce measurement time of similar PNR experiments by up to a factor of 5.6 or, equivalently, reduce parameter uncertainties at fixed beam time by the same factor relative to the reference experiment. Within a practically realizable SiO2 capping layer window of 200-400 Å, the predicted gain remains substantial (G ≈ 2.7). Because the parameters determining reflectivity curves are often correlated, such information is difficult to obtain in any other way. Experimental validation of these predictions on substrate assemblies synthesized according to the proposed designs is the natural next step. We established a theoretical method that can also be implemented within the context of other neutron reflectometry experiment. The approach allows the optimization of PNR experiments and will enable more straightforward and robust extraction of relevant parameters as well as more efficient use of neutron beam time.
In a recent paper [Frielinghaus & Gommes (2025), J. Appl. Cryst. 58, 1553-1570] the appearance of coherent multiple scattering was discussed, whereby surface scattering takes over against the classical bulk scattering. This effect has been overlooked in the past and happens in a transition region between the classical bulk scattering that involves the first-order Born approximation and the quantum mechanical limit where the projected shadow of the structure is observed. This paper discusses a new example emerging from small-angle light scattering and describes it with surface scattering from the Teubner-Strey model that is also used to describe porous materials.
