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This work quantifies the core–shell structure of nano-confined CO 2 molecules under pressure in silica pores using in operando small-angle neutron scattering (SANS) measurements and molecular dynamics simulations.
A beam-normal single-spin asymmetry generated in the scattering of transversely polarized electrons from unpolarized nucleons is an observable related to the imaginary part of the two-photon exchange process. Here we report a 2% precision measurement of the beam-normal single-spin asymmetry in elastic electron-proton scattering with a mean scattering angle of θ lab = 7.9 ° and a mean energy of 1.149 GeV. The asymmetry result is B n = – 5.194 ± 0.067 ( stat ) ± 0.082 (syst) ppm. This is the most precise measurement of this quantity available to date and therefore provides a stringent test of two-photon exchange models at far-forward scattering angles ( θ lab → 0 ) where they should be most reliable.
Hypothesis Small-Angle Neutron Scattering (SANS) is a powerful technique for studying soft matter systems such as colloids, polymers, and lyotropic phases, providing nanoscale structural insights. However, its effectiveness is limited by low neutron flux, leading to long acquisition times and noisy data. Here, we hypothesize that Bayesian statistical inference using Gaussian Process Regression (GPR) can reconstruct high-fidelity scattering data from sparse measurements by leveraging intensity smoothness and continuity. Experiments and Simulations The method was benchmarked computationally and validated through SANS experiments on various soft matter systems, including wormlike micelles, colloidal suspensions, polymeric structures, and lyotropic phases. GPR-based inference was applied to both experimental and synthetic data to evaluate its effectiveness in noise reduction and intensity reconstruction. Findings GPR significantly enhances SANS data quality and therefore reducing measurement times by up to two orders of magnitude. This cost-effective approach maximizes experimental efficiency, enabling high-throughput studies and real-time monitoring of dynamic systems. It is particularly beneficial for weakly scattering and time-sensitive studies. Beyond SANS, this framework applies to other low-SNR techniques, including laboratory-based small-angle X-ray scattering and various dynamical scattering methods. Furthermore, it offers transformative potential for compact neutron sources, enhancing their viability for structural analysis in resource-limited settings.
Small angle scattering techniques have now been routinely used to quantitatively determine the potential of mean force in colloidal suspensions. However the numerical accuracy of data interpretation is often compounded by the approximations adopted by liquid state analytical theories. To circumvent this long standing issue, here we outline a machine learning strategy for determining the effective interaction in the condensed phases of matter using scattering. Via a case study of colloidal suspensions, we show that the effective potential can be probabilistically inferred from the scattering spectra without any restriction imposed by model assumptions. Comparisons to existing parametric approaches demonstrate the superior performance of this method in accuracy, efficiency, and applicability. This method can effectively enable quantification of interaction in highly correlated systems using scattering and diffraction experiments.
Biological small-angle neutron scattering (SANS) instruments facilitate critical analysis of the structure and dynamics of complex biological systems. However, with the growth of experimental demands and the advances in optical systems design, a new neutron optical concept is necessary to overcome the limitations of current instruments. This work presents an approach to include experimental objectives ( i.e. the science to be supported by a specific neutron scattering instrument) in the optimization of the neutron optical concept. The approach for a proposed SANS instrument at the Second Target Station of the Spallation Neutron Source at Oak Ridge National Laboratory, USA, is presented here. Further, the instrument is simulated with the McStas software package. The optimization process is driven by an evolutionary algorithm using McStas output data, which are processed to calculate an objective function designed to quantify the expected performance of the simulated neutron optical configuration for the intended purpose. Each McStas simulation covers the complete instrument, from source to detector, including realistic sample scattering functions. This approach effectively navigates a high-dimensional parameter space that is otherwise intractable; it allows the design of next-generation SANS instruments to address specific scientific cases and has the potential to increase instrument performance compared with traditional design approaches.
Bonse–Hart ultra-small-angle neutron scattering (USANS) provides access to micrometre-scale structure, but useful measurements often require long counting times. In this work, we test whether the expected smoothness of the scattering profile can be exploited to improve data quality at lower counting statistics. We apply a Gaussian-process-based method to Bonse–Hart USANS data and evaluate its performance on pseudo-measurements generated from high-statistics experiments under Poisson statistics. This provides a stringent test of how well the underlying I(Q) profile can be reconstructed when the available counts are substantially reduced. We further show that, in the counting-limited regime, the reconstruction error follows a universal scaling behaviour that differs from the usual independent-counting expectation. At higher counts, the improvement crosses over to a resolution-limited regime set by analyser-angle discretization and rocking-curve width. These results clarify when correlation-aware inference is useful in USANS and provide a practical basis for improving measurement efficiency and beam-time usage.
Small-angle neutron scattering (SANS) is a powerful tool for studying biological membranes and model lipid bilayer membranes. The length scales probed by SANS, being from 1 nm to over 100 nm, are well-matched to the relevant length scales of the bilayer, particularly when it is in the form of a vesicle. However, it is the ability of SANS to differentiate between isotopes of hydrogen as well as the availability of deuterium labeled lipids that truly enable SANS to reveal details of membranes that are not accessible with the use of other techniques, such as small-angle X-ray scattering. In this work, an overview of the use of SANS for studying unilamellar lipid bilayer vesicles is presented. The technique is briefly presented, and the power of selective deuteration and contrast variation methods is discussed. Approaches to modeling SANS data from unilamellar lipid bilayer vesicles are presented. Finally, recent examples are discussed. While the emphasis is on studies of unilamellar vesicles, examples of the use of SANS to study intact cells are also presented.
Spin-echo small-angle neutron scattering (SESANS) is a unique method to measure structures of materials in real space with length scales from ∼ 30 μm to ∼20 µm. As shown in Figure 1, the accessible length scale of SESANS is given by its ability to encode the momentum transfer into the Larmor phase, namely Φ = $\vec{𝛿}$ ⋅ $\vec{𝑄}$, where $\vec{𝑄}$ is the momentum transfer and $\vec{𝛿}$ is the encoding vector of the setup and its projection along Q (δQ) is called spin-echo length (SEL). The spin echo length, which is synonymous with the spatial correlation distance probed, is defined as the following 𝛿𝑄 ∝ 𝜆 2 𝐵𝐿cot𝜃 where 𝜆 is neutron wavelength, B is magnetic field, L is length of the parallelogram magnetic field region, and 𝜃 is the angle between the inclined magnetic field boundary and the beam direction, as shown in Figure 1. The result of the SESANS experiment is a Hankel transformation of the SANS scattering function I(Q), which yields the correlation function of the sample in real space.
Small-angle neutron scattering (SANS) and ultra-SANS (USANS) were employed to understand the aggregation behavior and observe the size reduction for nanoplastics (NPs) formed from a biodegradable mulch film, and microparticles of vermiculite (V), an artificial soil, suspended in water in the presence of low convective shear (ex situ stirring) prior to measurements. Neutron contrast matching was employed to minimize the signal of V (by 100-fold) and thereby isolate the signal due to NPs in the neutron beam, as the contrast match point (CMP) for V (67 vol% deuteration of water) differed from that of NPs by more than 20%. The original NPs' size distribution was bimodal: <200 nm and 500–1200 nm, referred to as small and large NPs, i.e., SNPs and LNPs, respectively. In the absence of V, SNPs formed homoaggregates at higher concentrations that decreased with stirring time, while the size of LNPs remained unchanged. The presence of V at 2-fold lower concentration than NPs did not change the size of SNPs but reduced the size of LNPs by nearly 2-fold as stirring time increased. Because the size of SNPs and LNPs did not differ substantially between CMP and 100% D 2 O solvents, it is evident that SNPs and LNPs are mainly composed of NPs and not V. In conclusion, the results suggest that LNPs are susceptible to size reduction through collisions with soil microparticles via convection, yielding SNPs near soil–water interfaces within vadose zones.
Binning in small-angle neutron scattering (SANS) is typically performed empirically, with fixed parameters chosen for convenience rather than statistical optimality. Such practices often fail to balance statistical precision and spatial resolution, leading to inconsistencies across instruments and datasets. Here we establish a correlation-aware framework that determines the optimal bin width from first principles by extending the classical Freedman–Diaconis (FD) rule to account for inter-bin correlations with a Gaussian process. In this formulation, the scattering intensity is treated as a smooth stochastic field whose statistical coherence is described by a covariance matrix. Analytical expressions of errors derived from this model yield closed-form criteria that separate the total deviation into contributions from counting noise, aliasing distortion and curvature-dependent correlation effects. Expressed in reduced variables, the resulting dimensionless error surface reveals a continuous transition from the uncorrelated FD regime to the correlation-dominated limit, providing a unified description of noise suppression and resolution control. Because the formulation depends only on the profile characteristics of scattering intensity I(Q), specifically its average intensity and first- and second-order derivatives, it applies generally to any SANS measurement regardless of sample, instrument or geometry. Experimental validation using small- and ultra-small-angle neutron scattering data confirms the predicted scaling behavior, demonstrating that correlation-aware inference systematically reduces mean-squared error and enables information-efficient reproducible data reduction across materials and instruments.
The contrast-variation method in small-angle neutron scattering (SANS) is a uniquely powerful technique for determining the structure of individual components in biomolecular systems containing regions of different neutron scattering length density ρ . By altering the ρ of the target solute and the solvent through judicious incorporation of deuterium, the scattering of desired solute features can be highlighted. Most contrast-variation methods focus on highlighting specific bulk solute elements, but not on how the scattering at specific scattering vectors q , which are associated with specific structural distances, changes with contrast. Indeed, many systems exhibit q -dependent contrast effects. Here, a method is presented for calculating both bulk contrast-match points and q -dependent contrast using 3D models with explicit solute and solvent atoms and SASSENA , an explicit-atom SANS calculator. The method calculates the bulk contrast-match points within 2.4% solvent D 2 O accuracy for test protein–nucleic acid and lipid nanodisc systems. The method incorporates a general model for the incorporation of deuterium at non-exchangeable sites that was derived by performing mass spectrometry on green fluorescent protein. The method also decomposes the scattering profile into its component parts and identifies structural features that change with contrast. The method is readily applicable to a variety of systems, will expand the understanding of q -dependent contrast matching and will aid in the optimization of next-generation neutron scattering experiments.
This study demonstrates how the large concentration fluctuations of polymeric liquids under deformation and flow can be quantitatively studied by applying the spherical harmonic expansion technique to small-angle neutron scattering. Using a series of binary polymer blends, it is shown that the emergence of the so-called butterfly patterns is caused by the change of sign in the leading anisotropic component of the small-angle spectrum, when the scattering is dominated by intermolecular correlation associated with flow-induced demixing. The increasing spatial fluctuations of concentration are evidenced by the enhancement of the isotropic component of the scattering spectrum in the zero-angle limit and peak shift of the leading anisotropic coefficients toward low Q. Additionally, the spherical harmonic expansion framework permits real-space analysis of anisotropic scattering length density correlation in a convenient form. The methodology described in this work provides a concrete venue for quantitative studies of phase behavior of fluids under deformation and flow via small-angle scattering techniques, where mainly qualitative approaches were previously employed.
CENTAUR has been selected as one of the eight initial instruments to be built at the Second Target Station (STS) of the Spallation Neutron Source at Oak Ridge National Laboratory. It is a small-angle neutron scattering (SANS) and wide-angle neutron scattering (WANS) instrument with diffraction and spectroscopic capabilities. This instrument will maximally leverage the high brightness of the STS source, the state-of-the-art neutron optics, and a suite of detectors to deliver unprecedented capabilities that enable measurements over a wide range of length scales with excellent resolution, measurements on smaller samples, and time-resolved investigations of evolving structures. Notably, the simultaneous WANS and diffraction capability will be unique among neutron scattering instruments in the United States. This instrument will provide much needed capabilities for soft matter and polymer sciences, geology, biology, quantum condensed matter, and other materials sciences that need in situ and operando experiments for kinetic and/or out-of-equilibrium studies. Beam polarization and a high-resolution chopper will enable detailed structural and dynamical investigations of magnetic and quantum materials. CENTAUR’s excellent resolution makes it ideal for low-angle diffraction studies of highly ordered large-scale structures, such as skyrmions, shear-induced ordering in colloids, and biomembranes. Additionally, the spectroscopic mode of this instrument extends to lower momentum transfers than are currently possible with existing spectrometers, thereby providing a unique capability for inelastic SANS studies.
Here, we show the implementation of superconducting magnetic Wollaston prisms for spin echo small-angle neutron scattering. Two calibration methods for the spin echo length are presented: one utilizing spin echo modulated small-angle neutron scattering and the other based on the neutron refraction by quartz wedge crystals. Our experimental results with polystyrene nano-particle colloids showcase the system’s efficacy in measuring both dilute and concentrated colloidal systems. Additionally, investigations into the pore diameter and pitch of a nano-porous alumina membrane demonstrate its capability in analyzing nano-porous materials. Furthermore, we discuss potential optimizations to further extend the accessible spin echo length.
Understanding and improving hydrocarbon yields during enhanced oil recovery (EOR) in unconventional reservoirs is complicated by the intrinsic mineralogical and geochemical heterogeneity of shale formations. Here, in this study, we utilized small-angle neutron scattering (SANS) and ultra-small-angle neutron scattering (USANS) to investigate the degree of oil retention and its location in the nanoporous shale matrix for two mineralogically distinct shale samples. The two samples, dubbed “dark” and “light” based on their color, were taken from adjacent strata in a Wolfcamp shale core. While both samples contained kerogen, the dark sample contained more kerogen and clay (43.7 wt %) while the light sample contained more calcite (54.9 wt %). Samples were presaturated with decane, a model hydrocarbon, prior to pressure cycling with methane. Results showed significantly more retention of decane in 1.5–10 nm radius pores of both, likely indicating that oil is retained within kerogen nanopores. Although the dark sample had a higher porosity of 8.7%, versus 3.3% for the light sample, more pores were accessible to decane and a higher percentage of the imbibed decane was removable from the light sample compared to the dark sample. The majority of decane was not recoverable for the dark sample, indicating that EOR with methane can be challenging. These new findings can help to model expected recoveries of in-place oil from heterogeneous shale formations, as well as inform improved EOR strategies.
The scattering of massless waves of helicity |$h$| = $0$, $\frac{1}{2}$, $1$ in Schwarzschild and Kerr backgrounds is revisited in the long-wavelength regime. Using a novel description of such backgrounds in terms of gravitating massive particles, we compute classical wave scattering in terms of 2 → 2 QFT amplitudes in flat space, to all orders in spin. The results are Newman-Penrose amplitudes which are in direct correspondence with solutions of the Regge-Wheeler/Teukolsky equation. By introducing a precise prescription for the point-particle limit, in Part I of this work we show how both agree for $h$ = 0 at finite values of the scattering angle and arbitrary spin orientation. Associated classical observables such as the scattering cross sections, wave polarizations and time delay are studied at all orders in spin. The effect of the spin of the black hole on the polarization and helicity of the waves is found in agreement with previous analysis at linear order in spin. In the particular limit of small scattering angle, we argue that wave scattering admits a universal, point-particle description determined by the eikonal approximation. We show how our results recover the scattering eikonal phase with spin up to second post-Minkowskian order, and match it to the effective action of null geodesics in a Kerr background. Using this correspondence we derive classical observables such as polar and equatorial scattering angles. This study serves as a preceding analysis to Part II, where the Gravitational Wave ($h$ = 2) case will be studied in detail.
Here, we used grazing-incidence small-angle neutron scattering (GISANS) to probe the depth-dependent orientation of self-assembled morphologies of block copolymers. A hydrophobic–hydrophobic block copolymer, poly(solketal methacrylate)-block-polystyrene (PSM-b-PS), was synthesized and spin-coated into films tens of nanometers in thickness where the polymers adopted a disordered state. PSM-b-PS was then hydrolyzed by exposing the polymer thin film to trifluoroacetic acid vapor or embedding a photoacid generator in the film during spin coating, followed by exposure to UV light. The hydrolysis converted the block copolymer into a hydrophilic–hydrophobic block copolymer, poly(glycerol monomethacrylate)-block-polystyrene (PGM-b-PS), significantly increasing the segmental interaction parameter (χ) and causing microphase separation of the copolymers. GISANS was used to study the depth-dependent structure of the films and revealed that the orientation of the microphase-separated structure differed at the polymer–air and polymer–substrate interfaces. In the regions where the lamellae were parallel to the interfaces, the orientation propagated into the film from the interfaces. However, in the areas where the lamellae were perpendicular to the interfaces, the orientation did not persist with increasing distance from the interfaces.
PDBx/mmCIF, Protein Data Bank Exchange (PDBx) macromolecular Crystallographic Information Framework (mmCIF), has become the data standard for structural biology. With its early roots in the domain of small-molecule crystallography, PDBx/mmCIF provides an extensible data representation that is used for deposition, archiving, remediation, and public dissemination of experimentally determined three-dimensional (3D) structures of biological macromolecules by the Worldwide Protein Data Bank (wwPDB, wwpdb.org). Extensions of PDBx/mmCIF are similarly used for computed structure models by ModelArchive (modelarchive.org), integrative/hybrid structures by PDB-Dev (pdb-dev.wwpdb.org), small angle scattering data by Small Angle Scattering Biological Data Bank SASBDB (sasbdb.org), and for models computed generated with the AlphaFold 2.0 deep learning software suite (alphafold.ebi.ac.uk). Community-driven development of PDBx/mmCIF spans three decades, involving contributions from researchers, software and methods developers in structural sciences, data repository providers, scientific publishers, and professional societies. Having a semantically rich and extensible data framework for representing a wide range of structural biology experimental and computational results, combined with expertly curated 3D biostructure data sets in public repositories, accelerates the pace of scientific discovery. Herein, we describe the architecture of the PDBx/mmCIF data standard, tools used to maintain representations of the data standard, governance, and processes by which data content standards are extended, plus community tools/software libraries available for processing and checking the integrity of PDBx/mmCIF data. Use cases exemplify how the members of the Worldwide Protein Data Bank have used PDBx/mmCIF as the foundation for its pipeline for delivering Findable, Accessible, Interoperable, and Reusable (FAIR) data to many millions of users worldwide.