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A data-efficient and trustworthy machine learning approach is developed for automated inverse analysis of small angle scattering data.
Lamellar phases are essential in various soft matter systems, with topological defects significantly influencing their mechanical properties. In this report, we present a machine-learning approach for quantitatively analyzing the structure and dynamics of distorted lamellar phases using scattering techniques. By leveraging the mathematical framework of Kolmogorov–Arnold networks, we demonstrate that the conformations of these distorted phases – expressed as superpositions of complex waves – can be reconstructed from small-angle scattering intensities. Through the contour analysis of wave field phase singularities, we obtain the statistics of the spatial distribution of topological defects. Furthermore, we establish that the temporal evolution of these defects can be derived from the time-dependent traveling wave field, informed by the dispersion relation of spectral components. This method opens new avenues for investigating the dynamics of distorted lamellar phases using various dynamic scattering techniques such as neutron spin echo and X-ray photon correlation spectroscopy. These findings enhance our microscopic understanding of how defects influence the physical properties of lamellar materials, with implications for both equilibrium and non-equilibrium states in general lamellar systems.
Methods to prepare and characterize neutron helical waves carrying orbital angular momentum (OAM) were recently demonstrated at small-angle neutron scattering (SANS) facilities. These methods enable access to the neutron orbital degree of freedom which provides new avenues of exploration in fundamental science experiments as well as in material characterization applications. However, it remains a challenge to recover phase profiles from SANS measurements. We introduce and demonstrate a novel neutron interferometry technique for extracting phase information that is typically lost in SANS measurements. An array of reference beams, with complementary structured phase profiles, are put into a coherent superposition with the array of object beams, thereby manifesting the phase information in the far-field intensity profile. We demonstrate this by resolving petal-structure signatures of helical wave interference for the first time: an implementation of the long-sought recovery of phase information from small-angle scattering measurements.
In this work, the initial formation stages of surfactant-templated silica thin films which grow at the air–water interface were studied using combined spin–echo modulated small-angle neutron scattering (SEMSANS) and small-angle neutron scattering (SANS). The films are formed from either a cationic surfactant or nonionic surfactant (C 16 EO 8 ) in a dilute acidic solution by the addition of tetramethoxysilane. Previous work has suggested a two stage formation mechanism with mesostructured particle formation in the bulk solution driving film formation at the solution surface. From the SEMSANS data, it is possible to pinpoint accurately the time associated with the formation of large particles in solution that go on to form the film and to show their emergence is concomitant with the appearance of Bragg peaks in the SANS pattern, associated with the two-dimensional hexagonal order. The combination of SANS and SEMSANS allows a complete depiction of the steps of the synthesis that occur in the subphase.
We outline a machine learning strategy for quantitively determining the conformation of AB-type diblock copolymers with excluded volume effects using small angle scattering. Complemented by computer simulations, a correlation matrix connecting conformations of different copolymers according to their scattering features is established on the mathematical framework of a Gaussian process, a multivariate extension of the familiar univariate Gaussian distribution. We show that the relevant conformational characteristics of copolymers can be probabilistically inferred from their coherent scattering cross sections without any restriction imposed by model assumptions. This work not only facilitates the quantitative structural analysis of copolymer solutions but also provides the reliable benchmarking for the related theoretical development of scattering functions.
The propagation of photons in a medium with strongly anisotropic scattering is a problem with a considerable history. Like the propagation of electrons in metal foils, it may be solved in the small-angle scattering approximation by the use of Fourier-transform techniques. In certain limiting cases, one may even obtain analytic expressions. This paper presents some of these results in a model-independent form and also illustrates them by the use of four different phase-function models. Sample calculations are provided for comparison purposes
We develop Monte Carlo simulations for uniformly charged polymers and a machine learning algorithm to interpret the intra-polymer structure factor of the charged polymer system, which can be obtained from small-angle scattering experiments. The polymer is modeled as a chain of fixed-length bonds, where the connected bonds are subject to bending energy, and there is also a screened Coulomb potential for charge interaction between all joints. The bending energy is determined by the intrinsic bending stiffness, and the charge interaction depends on the interaction strength and screening length. All three contribute to the stiffness of the polymer chain and lead to longer and larger polymer conformations. The screening length also introduces a second length scale for the polymer besides the bending persistence length. To obtain the inverse mapping from the structure factor to these polymer conformation and energy-related parameters, we generate a large data set of structure factors by running simulations for a wide range of polymer energy parameters. We use principal component analysis to investigate the intra-polymer structure factors and determine the feasibility of the inversion using the nearest neighbor distance. We employ Gaussian process regression to achieve the inverse mapping and extract the characteristic parameters of polymers from the structure factor with low relative error.
Innovations in small-angle X-ray and neutron scattering (SAXS and SANS) at major X-ray and neutron facilities offer new characterization tools for researching materials phenomena relevant to advanced applications. For SAXS, the new generation of diffraction-limited storage rings, incorporating multi-bend achromat concepts, dramatically decrease electron beam emittance and significantly increase X-ray brilliance over previous third-generation sources. This results in intense X-ray incident beams that are more compact in the horizontal plane, allowing significantly improved spatial resolution, better time resolution, and a new era for coherent-beam SAXS methods such as X-ray photon correlation spectroscopy. Elsewhere, X-ray free-electron laser sources provide extremely bright, fully coherent, X-ray pulses of <100 fs and can support SAXS studies of material processes where entire SAXS data sets are collected in a single pulse train. Meanwhile, SANS at both steady-state reactor and pulsed spallation neutron sources has significantly evolved. Developments in neutron optics and multiple detector carriages now enable data collection in a few minutes for materials characterization over nanometre-to-micrometre scale ranges, opening up real-time studies of multi-scale materials phenomena. SANS at pulsed neutron sources is becoming more integrated with neutron diffraction methods for simultaneous structure characterization of complex materials. In this paper, selected developments are highlighted and some recent state-of-the-art studies discussed, relevant to hard matter applications in advanced manufacturing, energy and climate change.
Here, we use machine learning (ML) enhanced computational reverse engineering analysis of scattering experiments (CREASE) to interpret small-angle X-ray scattering (SAXS) data obtained from a system of nanoparticles without a priori knowledge of their exact shapes (e.g. spheres or ellipsoids), sizes (0.5–50 nm) and distributions. The SAXS measurements yielded three categories of scattering profiles exhibiting 'strong', 'weak' and 'no' features. Diminishing features (e.g. broadening or disappearing peaks) in scattering profiles have always been attributed to the presence of significant dispersity in the system. Such featureless SAXS data are not suitable for traditional analysis using analytical models. If one were to fit a relevant analytical model (e.g. the lmfit analytical model for polydisperse spheres) to these 'weak' and 'no' SAXS profiles from our nanoparticle systems, one would obtain non-unique interpretations of the data. Relying on electron microscopy to identify the distributions of nanoparticle shapes and sizes is also unfeasible, especially in high-throughput synthesis and characterization loops. In such situations, to identify the distributions of particle sizes and shapes that could be present in the sample, one must rely on methods like ML-CREASE to interpret the data quickly and output all relevant interpretations about the structure present in the system. The ML-CREASE optimization loop takes the experimental scattering profile as input and outputs multiple candidate solutions whose computed scattering profiles match the SAXS profile input. The ML-CREASE method outputs distributions of relevant structural features, such as the volume fraction of the nanoparticles in the system and the mean and standard deviation of the particle size and aspect ratio, assuming a type of distribution (e.g. normal, log-normal) for size and aspect ratio. We find that, for the SAXS profiles analyzed here, accounting for the shape dispersity along with size dispersity of the nanoparticles using ML-CREASE improved the match between the computed scattering profiles and input experimental profiles.
The structures of RNA:RNA complexes regulate many biological processes. Despite their importance, protein-free RNA:RNA complexes represent a tiny fraction of experimentally determined structures. Here, we describe a joint small-angle X-ray and neutron scattering (SAXS/SANS) approach to structurally interrogate conformational changes in a model RNA:RNA complex. Using SAXS, we measured the solution structures of the individual RNAs and of the overall RNA:RNA complex. With SANS, we demonstrate, as a proof of principle, that isotope labeling and contrast matching (CM) can be combined to probe the bound state structure of an RNA within a selectively deuterated RNA:RNA complex. Furthermore, we show that experimental scattering data can validate and improve predicted AlphaFold 3 RNA:RNA complex structures to reflect its solution structure. In conclusion, our work demonstrates that in silico modeling, SAXS, and CM-SANS can be used in concert to directly analyze conformational changes within RNAs when in complex, enhancing our understanding of RNA structure in functional assemblies.
The first in situ characterization of the pore morphology evolution during the cold sintering process (CSP) is presented using small-angle X-ray scattering methods. For practical reasons, measurements have been made on a model system, KH 2 PO 4 (KDP). The scattering signal revealed a striking behavior that could be modeled with nanoscale structural features associated with the dissolution and reprecipitation of KDP close to the grain/pore interface during CSP. The prospects for future more quantitative experiments under a range of temperature and pressure conditions, as well as for studies of more technologically important materials such as ZnO are considered.
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The Mg–Nd alloy system is of particular interest in the development of high-strength, lightweight structural alloys due to the formation of strengthening metastable Mg–Nd β-series precipitates during heat treatment. The strengthening is primarily provided by a combination of the β''' and β 1 precipitation. It is therefore important to understand how the precipitation behavior can be enhanced by other common alloying elements. In this work, the effects of 0.2 wt pct Zn and Ca on β-series precipitation were studied. Small-angle/ultra-small-angle X-ray scattering (SAXS/USAXS) techniques in combination with scanning transmission electron microscopy (STEM) were used to study the evolution of precipitation microstructure. Here, it is found that the Zn additions refine the precipitates, leading to an increase in hardness with aging at 200 °C. On the other hand, the Ca additions result in an acceleration in the formation of larger β 1 precipitates and chains which provides less strengthening. The β 1 chains are surrounded by precipitate-free zones (PFZs) that further contribute to the decreases in hardness observed in the over-aged condition. This paper demonstrated that SAXS/USAXS provides a powerful tool for an in situ study of the early stages of precipitation in the Mg–Nd-based alloys.
Macroscopic phase equilibria between solutions define the functionality of many biological and industrial processes, yet they are challenging to predict due to the inherent complexity of liquids containing large molecules. This work introduces an approach for the purely predictive calculation of such phase equilibria in temperature-composition space from molecular dynamics (MD) simulations at one temperature in the single-phase region. We use an approach developed previously to obtain the entropic and enthalpic contributions to the free energy of mixing from the atomic-scale information given by MD simulations via Kirkwood–Buff theory. This allows us to accurately estimate the free energy of mixing as a function of temperature, and thus obtain liquid–liquid phase equilibria, including liquid–liquid critical points, associated binodal and spinodal lines, and composition fluctuations across a region of temperature and composition. Results for binary malonamide–alkane systems are validated by comparison to a direct experimental probe of the fluctuations: the small angle X-ray scattering intensity near zero wavenumber. The MDKB → Phase method demonstrated here provides a significant improvement in predicting liquid–liquid equilibria and free energy as a function of temperature for our systems of interest compared to conventional thermodynamic models. The accurate performance of this purely predictive approach lies in its preservation of atomistic details when determining thermodynamic properties. Furthermore, its inherent extensibility to multi-component systems will likely make the MDKB → Phase approach a valuable general tool for connecting molecular interactions to macroscopic phase equilibria and for the computational screening of materials for targeted thermodynamic behavior.
Accurate lifetime predictions are critical for repurposing existing pipelines for hydrogen transmission as well as for developing novel steels which are minimally susceptible to lifetime degradation by hydrogen. Ultimately, lifetime prediction models assess the amount of damage a material undergoes during a typical service cycle and the cumulative damage a material can withstand prior to failure. However, not all damage processes are equal, and neither is the manner in which mechanical loading translates to damage the same when materials are in inert environments compared to in hydrogen environments. For example, in the three leading proposed mechanisms of hydrogen embrittlement (Hydrogen-Enhanced Decohesion (HEDE), the Hydrogen-Enhanced Localized Plasticity (HELP), and the Nano-Void Coalescence (NVC)), hydrogen is proposed to enhance the manifestation of grain separation, dislocation generation/movement, and void coalescence, respectively. A full understanding of the damage modes requires a measurement capable of probing all three mechanisms at once. Here we present simultaneous High Energy X-ray Diffraction (HEXRD) and Small-Angle X-ray Scattering (SAXS) during fatiguing of steel in hydrogen. HEXRD measurements probe strain and dislocation density; SAXS measurements probe nano-pore generation and coalescence. We will discuss the differences in damage modes between steels fatigued in air and in hydrogen and the role these difference play in lifetime predictions.
The disruptive effect of organic solvents on microbial membranes represents a significant challenge to the economical production of green fuels and value-added chemicals from lignocellulosic feedstocks. One route to overcoming this challenge is to engineer microbes with membranes capable of resisting organic solvent stresses. In this regard, it is useful to understand the mechanisms by which organic solvents disrupt typical biomembranes. In this study, molecular dynamics (MD) simulation, complemented by small-angle X-ray and neutron scattering (SANS/SAXS), provide a molecular-scale view of the disruption of a microbial model membrane by 1-butanol and tetrahydrofuran (THF), two common water–organic cosolvent mixtures of importance in biofuel production. Solvent interactions at the interface between the head-group and fatty acid tail regions lead to more dramatic membrane changes than interactions solely at the head-groups or tails. Although both organic solvents are found to partition into the membrane, the depth of solvent penetration into the membrane is quite different. Specifically, 1-butanol localizes near the interface between the lipid heads and tails at low concentrations, but partitions into both the head and tail regions at high concentrations. In contrast, THF, overall, partitions less than 1-butanol and prefers the lipid tail regions. Importantly, the presence of 1-butanol near the head/tail interface introduces drastic membrane changes not seen with THF. The organic solvent interactions with the lipids lead to membrane thinning and fluidization, but more so for 1-butanol than for THF. These results suggest that an aim for the future engineering of robust membranes could be to design lipid head groups that reduce the accumulation of organic solvents at the head–tail interface and that rational designs need also be cognizant of the different solvent-specific mechanisms responsible for membrane disruption.
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