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Synchrotron X-Ray and Neutron Diffraction, Total Scattering, and Small-Angle Scattering Techniques for Rechargeable Battery Research

Synchrotron X-ray and neutron scientific facilities are the most advanced resources with a large variety of state of the art instrumentations and powerful tools for materials research. X-rays and neutrons interact with matter in different ways and offer complementary views of materials at various levels. In this article, we will focus on the techniques and applications of synchrotron X-ray and neutron diffraction, total scattering and small-angle scattering for rechargeable battery research. They all belong to the elastic scattering category and provide structure information at different length scales. Here, the diffraction method is generally used to determine the phase and precise atomistic information of crystalline materials, while the total scattering coupled with pair-distribution function analysis can probe local atomic structure of materials no matter they are well crystallized or in amorphous/liquid phases. The small-angle scattering techniques provide us with material size and shape information at nanometer scales. Advantages of synchrotron high-energy X-rays will also be presented, which is particularly suited for the pair-distribution-function studies. We will pay much attention to the technical perspectives and some experimental specifications for the best uses of these methods for battery materials research.

25 ENERGY STORAGE↗

Small-angle scattering of polychromatic X-rays: effects of bandwidth, spectral shape and high harmonics

Polychromatic X-ray sources can be useful for photon-starved small-angle X-ray scattering given their high spectral fluxes. Their bandwidths, however, are 10–100 times larger than those using monochromators. To explore the feasibility, ideal scattering curves of homogeneous spherical particles for polychromatic X-rays are calculated and analyzed using the Guinier approach, maximum entropy and regularization methods. Monodisperse and polydisperse systems are explored. The influence of bandwidth and asymmetric spectra shape are explored via Gaussian and half-Gaussian spectra. Synchrotron undulator spectra represented by two undulator sources of the Advanced Photon Source are examined as an example, as regards the influence of asymmetric harmonic shape, fundamental harmonic bandwidth and high harmonics. The effects of bandwidth, spectral shape and high harmonics on particle size determination are evaluated quantitatively.

Chen, Sen↗

Information theory optimization of signals from small-angle scattering measurements

Small-angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions is resolution limited, and through an inverse Fourier transform, the measured SAXS intensities directly relate to the physical space occupied by the particles via the P (r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible, provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment, suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P (r)-distribution. The hybrid score utilizes the Akaike information criteria and Durbin-Watson statistic that considers parameter-model complexity, i.e., degrees of freedom, and the randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best parameter model appropriately representing the observed scattering data.

Rambo, Robert P. [Science and Technology Facilitie↗

Small-angle scattering of particle assemblies

Small-angle scattering formulae for crystalline assemblies of arbitrary particles are derived from powder diffraction theory using the decoupling approximation. To do so, the pseudo-lattice factor is defined, and methods to overcome the limitations of the decoupling approximation are investigated. Further, approximated equations are suggested for the diffuse scattering from various defects of the first kind due to non-ideal particles, including size polydispersity, orientational disorder and positional fluctuation about their ideal positions. Calculated curves using the formalism developed herein are compared with numerical simulations computed without any approximation. For a finite-sized assembly, the scattering from the whole domain of the assembly must also be included, and this is derived using the correlation function approach.

assembly↗

On the estimation of statistical uncertainties on powder diffraction and small-angle scattering data from two-dimensional X-ray detectors

Optimal methods are explored for obtaining one-dimensional powder pattern intensities from two-dimensional planar detectors with good estimates of their standard deviations. Methods are described to estimate uncertainties when the same image is measured in multiple frames as well as from a single frame. The importance of considering the correlation of diffraction points during the integration and the resampling process of data analysis is shown. It is found that correlations between adjacent pixels in the image can lead to seriously overestimated uncertainties if such correlations are neglected in the integration process. Off-diagonal entries in the variance–covariance (VC) matrix are problematic as virtually all data processing and modeling programs cannot handle the full VC matrix. It is shown that the off-diagonal terms come mainly from the pixel-splitting algorithm used as the default integration algorithm in many popular two-dimensional integration programs, as well as from rebinning and resampling steps later in the processing. When the full VC matrix can be propagated during the data reduction, it is possible to get accurate refined parameters and their uncertainties at the cost of increasing computational complexity. However, as this is not normally possible, the best approximate methods for data processing in order to estimate uncertainties on refined parameters with the greatest accuracy from just the diagonal variance terms in the VC matrix is explored.

Yang, X.↗

Atomistic modelling of scattering data in the Collaborative Computational Project for Small Angle Scattering (CCP-SAS)

The capabilities of current computer simulations provide a unique opportunity to model small-angle scattering (SAS) data at the atomistic level, and to include other structural constraints ranging from molecular and atomistic energetics to crystallography, electron microscopy and NMR. This extends the capabilities of solution scattering and provides deeper insights into the physics and chemistry of the systems studied. Realizing this potential, however, requires integrating the experimental data with a new generation of modelling software. To achieve this, the CCP-SAS collaboration (http://www.ccpsas.org/) is developing open-source, high-throughput and user-friendly software for the atomistic and coarse-grained molecular modelling of scattering data. Robust state-of-the-art molecular simulation engines and molecular dynamics and Monte Carlo force fields provide constraints to the solution structure inferred from the small-angle scattering data, which incorporates the known physical chemistry of the system. The implementation of this software suite involves a tiered approach in which GenApp provides the deployment infrastructure for running applications on both standard and high-performance computing hardware, and SASSIE provides a workflow framework into which modules can be plugged to prepare structures, carry out simulations, calculate theoretical scattering data and compare results with experimental data. GenApp produces the accessible web-based front end termed SASSIE-web , and GenApp and SASSIE also make community SAS codes available. Applications are illustrated by case studies: (i) inter-domain flexibility in two- to six-domain proteins as exemplified by HIV-1 Gag, MASP and ubiquitin; (ii) the hinge conformation in human IgG2 and IgA1 antibodies; (iii) the complex formed between a hexameric protein Hfq and mRNA; and (iv) synthetic `bottlebrush' polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nanostructuring and Underscreening of Bisalt Electrolytes with Dual-Anion Effects: Insights from Small-Angle Scattering Prepeak Analysis

Using small-angle neutron scattering, we studied the nanostructure of a prototypical D(H)-bonded network electrolyte, alkaline sodium aluminate bisalt, at concentrations up to solute volume fraction of ~0.5. Analysis of the structure factor prepeak at 0.1 < Q < 1.0 Å-1 showed that its evolution is associated with nanoscopic species distribution in water-anion network., with differences in characteristic distance d between OD- and Al(OD)4- anions related to their distinct sizes and interactions. When the solute volume fraction approached 0.5, a common/maximum value of ~4.5 Å was found for the correlation length ? that characterizes the electrostatic force in concentrated electrolyte solution before precipitation occurred. This implies that the solutions’ morphology and behavior at high concentrations may be governed by geometric factors, rather than the chemistry of the specific anion. Furthermore, the scaling of ? with concentration yielded an exponent of 1.25(1), suggesting that ? is limited to a few Å. By combining the current observations of structural heterogeneity at the nanoscale, with dynamic heterogeneity at the microscopic scale from our previous quasi-elastic neutron scattering study, we have established a structural origin of local “caging” and restricted structural relaxation processes. These local solvent-solute interactions not only control dynamics heterogeneity in concentrated electrolytes but also are responsible for crystallization processes in industrial setting, such as aluminum production and radioactive waste treatment.

Wang, Hsiu-Wen↗

Efficient analysis of small-angle scattering curves for large biomolecular assemblies using Monte Carlo methods

Structure elucidation from small-angle scattering curves of large biomolecular assemblies is notoriously challenging. This is because the simulation of high-resolution features in the structure of large macromolecular assemblies, such as de novo protein assemblies, is computationally demanding when it needs to cover a broad range of length scales. Conventional methods, such as the numerical approximation to the Debye equation or the use of spherical harmonics, do not scale well as the size of the assembly increases, which limits their application to small structures (e.g. individual proteins). This work explores the effectiveness of a Monte Carlo method to simulate and fit scattering curves for large biomolecular assemblies spanning over ranges covering atomic and molecular detail (e.g. spacing and orientation of proteins in an assembly) as well as large-scale (hundreds of nanometres) features. Owing to its speed and scalability, it can be combined with a fitting algorithm to extract structural features from experimental small-angle scattering curves in biomolecular assemblies that are otherwise intractable for interpretation. This work first demonstrates the effectiveness of the tool using experimental small-angle X-ray scattering (SAXS) data from tile-like proteins that assemble into 1D tube-like macromolecular structures. Here, the diameter distribution of tubes is extracted from SAXS fits, and this is quantitatively compared with distributions from electron microscopy. SAXS data are also obtained from 2D sheet-like protein assemblies, and the proposed method is used to quantify structural features such as the separation distance between protein building blocks and the flexing of the sheet. An open-source implementation of the methodology is provided for use in a broad range of biological systems involving multi-scale scattering analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

2017 publication guidelines for structural modelling of small-angle scattering data from biomolecules in solution: an update

In 2012, preliminary guidelines were published addressing sample quality, data acquisition and reduction, presentation of scattering data and validation, and modelling for biomolecular small-angle scattering (SAS) experiments. Biomolecular SAS has since continued to grow and authors have increasingly adopted the preliminary guidelines. In parallel, integrative/hybrid determination of biomolecular structures is a rapidly growing field that is expanding the scope of structural biology. For SAS to contribute maximally to this field, it is essential to ensure open access to the information required for evaluation of the quality of SAS samples and data, as well as the validity of SAS-based structural models. To this end, the preliminary guidelines for data presentation in a publication are reviewed and updated, and the deposition of data and associated models in a public archive is recommended. These guidelines and recommendations have been prepared in consultation with the members of the International Union of Crystallography (IUCr) Small-Angle Scattering and Journals Commissions, the Worldwide Protein Data Bank (wwPDB) Small-Angle Scattering Validation Task Force and additional experts in the field.

Biochemistry & Molecular Biology↗

Small Angle Scattering Data Analysis Assisted by Machine Learning Methods

Small angle scattering (SAS) is a widely used technique for characterizing structures of wide ranges of materials. For such wide ranges of applications of SAS, there exist a large number of ways to model the scattering data. While such analysis models are often available from various suites of SAS data analysis software packages, selecting the right model to start with poses a big challenge for beginners to SAS data analysis. Here, we present machine learning (ML) methods that can assist users by suggesting scattering models for data analysis. A series of one-dimensional scattering curves have been generated by using different models to train the algorithms. The performance of the ML method is studied for various types of ML algorithms, resolution of the dataset, and the number of the dataset. The degree of similarities among selected scattering models is presented in terms of the confusion matrix. The scattering model suggestions with prediction scores provide a list of scattering models that are likely to succeed. Therefore, if implemented with extensive libraries of scattering models, this method can speed up the data analysis workflow by reducing search spaces for appropriate scattering models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reconstruction of three-dimensional anisotropic structure from small-angle scattering experiments

When subjected to flow, the structures of many soft-matter systems become anisotropic due to the symmetry breaking of the spatial arrangements of constituent particles at the microscopic level. At present, it is common practice to use various small-angle scattering techniques to explore flow-induced microstructural distortion. However, there has not been a thorough discussion in the literature on how a three-dimensional anisotropic structure can be faithfully reconstructed from two-dimensional small-angle scattering spectra. Here, in this work, we address this issue rigorously from a mathematical perspective by using real spherical harmonic expansion analysis. We first show that, except for cases in which mechanical perturbation is sufficiently small, the existing small-angle scattering techniques generally do not provide complete information on structural distortion. This limitation is caused by the linear dependence of certain real spherical harmonic basis vectors on the flow-vorticity and flow-velocity gradient planes in the Couette shear cell. To circumvent the constraint imposed by this geometry, an alternative approach is proposed in which a parallel sliding plate shear cell is used with a central rotary axis along the flow direction. Finally, from the calculation of rotation of the reference frame, we demonstrate the feasibility of this experimental implementation for a fully resolved three-dimensional anisotropic structure via a case study of sheared polymers.

36 MATERIALS SCIENCE↗

Relaxation dynamics of deformed polymer nanocomposites as revealed by small-angle scattering and rheology

Here, the relaxation dynamics of polystyrene (PS)/silica nanocomposites after a large step deformation are studied by a combination of small-angle scattering techniques and rheology. Small-angle X-ray scattering measurements and rheology show clear signatures of nanoparticle aggregation that enhances the mechanical properties of the polymer nanocomposites (PNCs) in the linear viscoelastic regime and during the initial phase of stress relaxation along with accelerated relaxation dynamics. Small-angle neutron scattering experiments under the zero-average-contrast condition reveal, however, smaller structural anisotropy in the PNCs than that in the neat polymer matrix, as well as accelerated anisotropy relaxation. In addition, the degrees of anisotropy reduction and relaxation dynamics acceleration increase with increasing nanoparticle loading. These results are in sharp contrast to the prevailing viewpoint of enhanced molecular deformation as the main mechanism for the mechanical enhancement in PNCs. Furthermore, the observed acceleration of stress relaxation and reduction in structural anisotropy point to two types of nonlinear effects in the relaxation dynamics of PNCs at large deformation.

36 MATERIALS SCIENCE↗

Direct comparison of Fe-Cr unmixing characterization by atom probe tomography and small angle scattering

The fine microstructure obtained by unmixing of a solid solution either by classical precipitation or spinodal decomposition is often characterized either by small angle scattering or atom probe tomography. This article shows that a common data analysis framework can be used to analyze data obtained from these two techniques. An example of the application of this common analysis is given for characterization of the unmixing of the Fe-Cr matrix of a 15-5 PH stainless steel during long-term ageing at 350 °C and 400 °C. A direct comparison of the Cr composition fluctuations amplitudes and characteristic lengths obtained with both techniques is made showing a quantitative agreement for the fluctuation amplitudes. The origin of the discrepancy remaining for the characteristic lengths is discussed. - Highlights: •Common analysis framework for atom probe tomography and small angle scattering •Comparison of same microstructural characteristics obtained using both techniques •Good correlation of Cr composition fluctuations amplitudes from both techniques •Good correlation of Cr composition fluctuations amplitudes with classic V parameter.

36 MATERIALS SCIENCE↗

Desmearing small-angle scattering data by central moment expansions

This article proposes a robust method for desmearing 1D small-angle scattering (SAS) intensity profiles. Using the central-moment-expansion technique, smearing in SAS intensity profiles is achieved in a model-free manner, eliminating the need for presumptive input during the desmearing. This innovative approach enables data analysis of SAS data without the resolution being convoluted with the structural model, thereby facilitating faster implementation and performance of fitting functions directly from the scattering models.

42 ENGINEERING↗

Biological Small Angle Scattering: Techniques, Strategies and Tips

This book provides a clear, comprehensible and up-to-date description of how Small Angle Scattering (SAS) can help structural biology researchers. SAS is an efficient technique that offers structural information on how biological macromolecules behave in solution. SAS provides distinct and complementary data for integrative structural biology approaches in combination with other widely used probes, such as X-ray crystallography, Nuclear magnetic resonance, Mass spectrometry and Cryo-electron Microscopy. The development of brilliant synchrotron small-angle X-ray scattering (SAXS) beam lines has increased the number of researchers interested in solution scattering. SAS is especially useful for studying conformational changes in proteins, highly flexible proteins, and intrinsically disordered proteins. Small-angle neutron scattering (SANS) with neutron contrast variation is ideally suited for studying multi-component assemblies as well as membrane proteins that are stabilized in surfactant micelles or vesicles. SAS is also used for studying dynamic processes of protein fibrillation in amyloid diseases, and pharmaceutical drug delivery. The combination with size-exclusion chromatography further increases the range of SAS applications.The book is written by leading experts in solution SAS methodologies. The principles and theoretical background of various SAS techniques are included, along with practical aspects that range from sample preparation to data presentation for publication. Topics covered include techniques for improving data quality and analysis, as well as different scientific applications of SAS. With abundant illustrations and practical tips, we hope the clear explanations of the principles and the reviews on the latest progresses will serve as a guide through all aspects of biological solution SAS.The scope of this book is particularly relevant for structural biology researchers who are new to SAS. Advanced users of the technique will find it helpful for exploring the diversity of solution SAS methods and applications.

Chaudhuri, Barnali↗