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Here, it is investigated how optical properties of single scatterers in interacting multi‐particle systems influence measurable structure factors. Both particles with linear gradients of their scattering length density and core–shell structures evoke characteristic deviations between the weighted sum ⟨S(Q)⟩ of partial structure factors in a multi‐component system and experimentally accessible measurable structure factors SM(Q). While ⟨S(Q)⟩ contains only the structural information of self‐organizing systems, SM(Q) is additionally influenced by the optical properties of their constituents, resulting in features such as changing amplitudes, additional peaks in the low‐wavevector region or splitting of higher‐order maxima, which are not related to structural reasons. It is shown that these effects can be systematically categorized according to the qualitative behaviour of the form factor in the Guinier region, which enables assessing the suitability of experimentally obtained structure factors to genuinely represent the microstructure of complex systems free from any particular model assumption. Hence, a careful data analysis regarding size distribution and optical properties of single scatterers is mandatory to avoid a misinterpretation of measurable structure factors. [ABSTRACT FROM AUTHOR]

In molten metals, the atomic dynamics have been studied in the present study with the help of equations of motion in terms of the velocity autocorrelation function (VACF), power spectrum $ G(\omega) $ G (ω) , and mean square displacement $ {r^2}(t) $ r 2 (t). The pair correlation function $ g(r) $ g (r) is used to produce VACF for molten metals in the current study with the help of three different types of structure factor methods i.e. hard sphere Yukawa (HSY) method, optimised random phase approximation (ORPA) method and charged hard sphere (CHS) method. The presently obtained results for molten metals of different groups like Na (Z = 1), Mg (Z = 2), Al (Z = 3), Sn (Z = 4), and Sb (Z = 5) are compared with the molecular dynamic (MD) study and also with the other theoretical data available in the literature. For the present study, our own developed pseudopotential has been used for the calculations of the above-mentioned properties. The screening effect is also been observed over and beyond the bare ion potential with Hartree (H) and the effects of exchanges and correlation were computed using procedures given by Taylor (T) and Nagy (N). [ABSTRACT FROM AUTHOR]

The superstructure spots that appear in diffraction patterns of tilted perovskites are well documented and easily calculated using crystallographic software. Here, by considering a distortion mode as a perturbation of the prototype perovskite structure, it is shown how the structure‐factor equation yields Boolean conditions for the presence of superstructure reflections. This approach may have some advantages for the analysis of electron diffraction patterns of perovskites. [ABSTRACT FROM AUTHOR]

An innovative strategy is presented that incorporates deep auto‐encoder networks into a least‐squares fitting framework to address the potential inversion problem in small‐angle scattering. To evaluate the performance of the proposed approach, a detailed case study focusing on charged colloidal suspensions was carried out. The results clearly indicate that a deep learning solution offers a reliable and quantitative method for studying molecular interactions. The approach surpasses existing deterministic approaches with respect to both numerical accuracy and computational efficiency. Overall, this work demonstrates the potential of deep learning techniques in tackling complex problems in soft‐matter structures and beyond. [ABSTRACT FROM AUTHOR]

Abstract—The isothermal compressibilities (χT) of individual potassium halides and some binary mixtures, namely, KI–KX (X = F, Cl, Br), are calculated using classical molecular dynamics simulation. The modeling of molten potassium halides using the Born–Mayer–Huggins pair potential shows good agreement between the calculated values of isothermal compressibility and the experimental data. A systematic underestimation of the calculated values is found for individual melts, with the maximum difference between the calculated and experimental values being 24% for potassium chloride. For binary KI–KX (X = F, Cl, Br) mixtures, the experimental concentration dependences of χT during the transition from the bromide ion to the fluoride ion are characterized by an increasing deviation from additivity. Even for a KI–KBr binary mixture, the calculated concentration dependence is shown to have a pronounced nonlinear character. The maximum differences (about 34%) between the calculated and experimental values of χT are observed for a binary equimolar KI–KF mixture. [ABSTRACT FROM AUTHOR]

This article presents an upgrade of the D+ software [Ginsburg et al. (2019). J. Appl. Cryst.52, 219–242], expanding its hierarchical solution X‐ray scattering modeling capabilities for fiber diffraction and single crystallographic orientations. This upgrade was carried out using the reciprocal grid algorithm [Ginsburg et al. (2016). J. Chem. Inf. Model.56, 1518–1527], providing D+ its computational strength. Furthermore, the extensive modifications made to the Python API of D+ are described, broadening the X‐ray analysis performed with D+ to account for the effects of the instrument‐resolution function and polydispersity. In addition, structure‐factor and radial‐distribution‐function modules were added, taking into account the effects of thermal fluctuations and intermolecular interactions. Finally, numerical examples demonstrate the usage and potential of the added features. [ABSTRACT FROM AUTHOR]

Shape2SAS is a web application that allows researchers and students to build intuition about and understanding of small‐angle scattering. It is available at https://somo.chem.utk.edu/shape2sas. The user defines a model of arbitrary shape by combining geometrical subunits, and Shape2SAS then calculates and displays the scattering intensity and the pair distance distribution, as well as a visualization of the user‐defined shape. Simulated data with realistic noise are also generated. Here, it is demonstrated how Shape2SAS can calculate and display the different scattering patterns for various geometrical shapes, such as spheres and cylinders. It is also shown how the effect of structure factors can be visualized. Finally, it is indicated how multi‐contrast particles can readily be generated, and how the calculated scattering may be used to validate and visualize analytical models generated in analysis software for fitting small‐angle scattering data. [ABSTRACT FROM AUTHOR]

Diffraction intensities from a crystallographic experiment include contributions from the entire unit cell of the crystal: the macromolecule, the solvent around it and eventually other compounds. These contributions cannot typically be well described by an atomic model alone, i.e. using point scatterers. Indeed, entities such as disordered (bulk) solvent, semi‐ordered solvent (e.g. lipid belts in membrane proteins, ligands, ion channels) and disordered polymer loops require other types of modeling than a collection of individual atoms. This results in the model structure factors containing multiple contributions. Most macromolecular applications assume two‐component structure factors: one component arising from the atomic model and the second one describing the bulk solvent. A more accurate and detailed modeling of the disordered regions of the crystal will naturally require more than two components in the structure factors, which presents algorithmic and computational challenges. Here an efficient solution of this problem is proposed. All algorithms described in this work have been implemented in the computational crystallography toolbox (CCTBX) and are also available within Phenix software. These algorithms are rather general and do not use any assumptions about molecule type or size nor about those of its components. [ABSTRACT FROM AUTHOR]

The partial structure factors (PSFs) of molten lithium fluoride at a temperature of 1200 K are calculated using the following three methods: ab initio and classical molecular dynamics and the charged hard sphere model in the mean-spherical approximation. Despite the common topology of the PSFs calculated by all three methods, the key feature of the computer simulation results is shown to be the absence of a shoulder on the right side of the first peak of the cation–cation structure factor. The observed difference is assumed to be associated with the softness of the repulsive branch of the Buckingham pair potential in the case of the classical model in the molecular dynamics calculation. The ab initio molecular dynamics calculations also confirm this conclusion. The results of calculating the density–density structure factor by computer simulation methods demonstrate the presence of two maxima at k ≈ 2.4 and ≈4.4 Å–1, respectively. The charged hard sphere model demonstrates the presence of one maximum at k ≈ 3.5 Å–1 and a small shoulder on the left, the position of which coincides with the first maximum obtained by computer simulation methods. The observed differences can be attributed to the fact that the cation–anion PSF curve calculated in terms of the charged hard sphere model has a higher amplitude in the vicinity of a wavevector of ≈3.5 Å–1. [ABSTRACT FROM AUTHOR]

Small‐angle scattering is an increasingly common method for characterizing particle ensembles in a wide variety of sample types and for diverse areas of application. SASfit has been one of the most comprehensive and flexible curve‐fitting programs for decades, with many specialized tools for various fields. Here, a selection of enhancements and additions to the SASfit program are presented that may be of great benefit to interested and advanced users alike: (a) further development of the technical basis of the program, such as new numerical algorithms currently in use, a continuous integration practice for automated building and packaging of the software, and upgrades on the plug‐in system for easier adoption by third‐party developers; (b) a selection of new form factors for anisotropic scattering patterns and updates to existing form factors to account for multiple scattering effects; (c) a new type of a very flexible distribution called metalog [Keelin (2016). Decis. Anal.13, 243–277], and regularization techniques such as the expectation‐maximization method [Dempster et al. (1977). J. R. Stat. Soc. Ser. B (Methodological), 39, 1–22; Richardson (1972) J. Opt. Soc. Am.62, 55; Lucy (1974). Astron. J.79, 745; Lucy (1994). Astron. Astrophys.289, 983–994], which is compared with fits of analytical size distributions via the non‐linear least‐squares method; and (d) new structure factors, especially for ordered nano‐ and meso‐scaled material systems, as well as the Ornstein–Zernike solver for numerical determination of particle interactions and the resulting structure factor when no analytical solution is available, with the aim of incorporating its effects into the small‐angle scattering intensity model used for fitting with SASfit. [ABSTRACT FROM AUTHOR]

The design of X-ray optics based on diffraction from crystals depends on the accurate calculation of the structure factors of their Bragg reflections over a wide range of temperatures. In general, the temperature dependence of the lattice parameters, the atomic positions and the atomic thermal vibrations is both anisotropic and nonlinear. Implemented here is a software package for precise and flexible calculation of structure factors for dynamical diffraction. α-Quartz is used as an example because it presents the challenges mentioned above and because it is being considered for use in high-resolution X-ray spectroscopy. The package is designed to be extended easily to other crystals by adding new material files, which are kept separate from the package's stable core. Python 3 was chosen as the language to allow the easy integration of this code into existing packages. The importance of a correct anisotropic treatment of the atomic thermal vibrations is demonstrated by comparison with an isotropic Debye model. Discrepancies between the two models can be as much as 5% for strong reflections and considerably larger (even to the level of 100%) for weak reflections. A script for finding Bragg reflections that backscatter X-rays of a given energy within a given temperature range is demonstrated. The package and example scripts are available on request. Also discussed, in detail, are the various conventions related to the proper description of chiral quartz. [ABSTRACT FROM AUTHOR]

Background: Hospital and ICU structural factors are key factors affecting the quality of care as well as ICU patient outcomes. However, the data from China are scarce. This study was designed to investigate how differences in patient outcomes are associated with differences in hospital and ICU structure variables in China throughout 2019. Methods: This was a multicenter observational study. Data from a total of 2820 hospitals were collected using the National Clinical Improvement System Data that reports ICU information in China. Data collection consisted of a) information on the hospital and ICU structural factors, including the hospital type, number of beds, staffing, among others, and b) ICU patient outcomes, including the mortality rate as well as the incidence of ventilator-associated pneumonia (VAP), catheter-related bloodstream infections (CRBSIs), and catheter-associated urinary tract infections (CAUTIs). Generalized linear mixed models were used to analyse the association between hospital and ICU structural factors and patient outcomes. Results: The median ICU patient mortality was 8.02% (3.78%, 14.35%), and the incidences of VAP, CRBSI, and CAUTI were 5.58 (1.55, 11.67) per 1000 ventilator days, 0.63 (0, 2.01) per 1000 catheter days, and 1.42 (0.37, 3.40) per 1000 catheter days, respectively. Mortality was significantly lower in public hospitals (β = − 0.018 (− 0.031, − 0.005), p = 0.006), hospitals with an ICU-to-hospital bed percentage of more than 2% (β = − 0.027 (− 0.034, -0.019), p < 0.001) and higher in hospitals with a bed-to-nurse ratio of more than 0.5:1 (β = 0.009 (0.001, 0.017), p = 0.027). The incidence of VAP was lower in public hospitals (β = − 0.036 (− 0.054, − 0.018), p < 0.001). The incidence of CRBSIs was lower in public hospitals (β = − 0.008 (− 0.014, − 0.002), p = 0.011) and higher in secondary hospitals (β = 0.005 (0.001, 0.009), p = 0.010), while the incidence of CAUTIs was higher in secondary hospitals (β = 0.010 (0.002, 0.018), p = 0.015). Conclusion: This study highlights the association between specific ICU structural factors and patient outcomes. Modifying structural factors is a potential opportunity that could improve patient outcomes in ICUs. [ABSTRACT FROM AUTHOR]

Background: Hospital and ICU structural factors are key factors affecting the quality of care as well as ICU patient outcomes. However, the data from China are scarce. This study was designed to investigate how differences in patient outcomes are associated with differences in hospital and ICU structure variables in China throughout 2019.Methods: This was a multicenter observational study. Data from a total of 2820 hospitals were collected using the National Clinical Improvement System Data that reports ICU information in China. Data collection consisted of a) information on the hospital and ICU structural factors, including the hospital type, number of beds, staffing, among others, and b) ICU patient outcomes, including the mortality rate as well as the incidence of ventilator-associated pneumonia (VAP), catheter-related bloodstream infections (CRBSIs), and catheter-associated urinary tract infections (CAUTIs). Generalized linear mixed models were used to analyse the association between hospital and ICU structural factors and patient outcomes.Results: The median ICU patient mortality was 8.02% (3.78%, 14.35%), and the incidences of VAP, CRBSI, and CAUTI were 5.58 (1.55, 11.67) per 1000 ventilator days, 0.63 (0, 2.01) per 1000 catheter days, and 1.42 (0.37, 3.40) per 1000 catheter days, respectively. Mortality was significantly lower in public hospitals (β =  - 0.018 (- 0.031, - 0.005), p = 0.006), hospitals with an ICU-to-hospital bed percentage of more than 2% (β =  - 0.027 (- 0.034, -0.019), p < 0.001) and higher in hospitals with a bed-to-nurse ratio of more than 0.5:1 (β = 0.009 (0.001, 0.017), p = 0.027). The incidence of VAP was lower in public hospitals (β =  - 0.036 (- 0.054, - 0.018), p < 0.001). The incidence of CRBSIs was lower in public hospitals (β =  - 0.008 (- 0.014, - 0.002), p = 0.011) and higher in secondary hospitals (β = 0.005 (0.001, 0.009), p = 0.010), while the incidence of CAUTIs was higher in secondary hospitals (β = 0.010 (0.002, 0.018), p = 0.015).Conclusion: This study highlights the association between specific ICU structural factors and patient outcomes. Modifying structural factors is a potential opportunity that could improve patient outcomes in ICUs. [ABSTRACT FROM AUTHOR]

Many experimental methods are available for the characterization of nanostructures, but most of them are limited by stringent experimental conditions. When it comes to analysing nanostructures in the bulk or in their natural environment – even as ordinary as water at room temperature – small‐angle scattering (SAS) of X‐rays or neutrons is often the only option. The rapid worldwide development of synchrotron and neutron facilities over recent decades has opened unprecedented possibilities for using SAS in situ and in a time‐resolved way. But, in spite of its huge potential in the field of nanomaterials in general, SAS is covered far less than other characterization methods in non‐specialized curricula. Presented here is a rigorous discussion of small‐angle scattering, at a technical level comparable to the classical undergraduate coverage of X‐ray diffraction by crystals and which contains diffraction as a particular case. [ABSTRACT FROM AUTHOR]

Ferroelectric lead-free BaTi1−xZrxO3 ceramic powder samples with various compositions (x = 0, 0.04, 0.06) have been synthesized by conventional high-temperature solid-state reaction method at 1450 °C for 10 h. Influences of Zr doping on the inter-atomic bonding and charge density distributions inside the lattice structure of BaTiO3 were analyzed through powder X-ray diffraction (XRD) and maximum entropy method. Lattice parameter and cell volume values are found to be increasing with the incorporation of Zr content. Calculated average grain sizes are found to be in the range of 23–28 nm. Maximum entropy mapping of electron density analysis reveals the reduction in ionic nature along Ba–O bond and the enhancement of covalent nature along Ti–O bond. Energy band gap values were determined from ultraviolet–visible (UV–Vis) spectra. Surface morphology and microstructures of the samples were analyzed from scanning electron microscopy (SEM) micrographs. Particles with irregular sizes were observed in all the prepared ceramics. Stoichiometry of the samples was further confirmed by energy-dispersive X-ray spectroscopy (EDAX). [ABSTRACT FROM AUTHOR]

A local structure analysis method based on convergent‐beam electron diffraction (CBED) has been used for refining isotropic atomic displacement parameters and five low‐order structure factors with sin gθ/λ ≤ 0.28 Å−1 of potassium tantalate (KTaO3). Comparison between structure factors determined from CBED patterns taken at the zone‐axis (ZA) and Bragg‐excited conditions is made in order to discuss their precision and sensitivities. Bragg‐excited CBED patterns showed higher precision in the refinement of structure factors than ZA patterns. Consistency between higher precision and sensitivity of the Bragg‐excited CBED patterns has been found only for structure factors of the outer zeroth‐order Laue‐zone reflections with larger reciprocal‐lattice vectors. Correlation coefficients among the refined structure factors in the refinement of Bragg‐excited patterns are smaller than those of the ZA ones. Such smaller correlation coefficients lead to higher precision in the refinement of structure factors. [ABSTRACT FROM AUTHOR]

Lens‐less imaging of crystals with coherent X‐ray diffraction offers some unique possibilities for strain‐field characterization. It relies on numerically retrieving the phase of the scattering amplitude from a crystal illuminated with coherent X‐rays. In practice, the algorithms encode this amplitude as a discrete Fourier transform of an effective or Bragg electron density. This short article suggests a detailed route from the classical expression of the (continuous) scattering amplitude to this discrete function. The case of a heterogeneous incident field is specifically detailed. Six assumptions are listed and quantitatively discussed when no such analysis was found in the literature. Details are provided for two of them: the fact that the structure factor varies in the vicinity of the probed reciprocal lattice vector, and the polarization factor, which is heterogeneous along the measured diffraction patterns. With progress in X‐ray sources, data acquisition and analysis, it is believed that some approximations will prove inappropriate in the near future. [ABSTRACT FROM AUTHOR]

Scattering methods are widely used in many research areas to analyze and resolve material structures. Given its importance, a large number of textbooks are devoted to this topic. However, technical details in experiments and disconnection between explanations from different perspectives often confuse and frustrate beginner students and researchers. To create an effective learning path, the core concepts of scattering and structure factor are reviewed in this article in a self‐contained way. Classical examples of scattering photography and intensity scanning are calculated. Sample CPU and GPU codes are provided to facilitate the understanding and application of these methods. [ABSTRACT FROM AUTHOR]

The two‐dimensional wide‐angle X‐ray diffraction technique was applied to a Cm‐doped borosilicate glass in a beryllium container. The experiment involved a high‐energy X‐ray beam and an image plate. It is shown that it is possible to extract the structure factor of the radioactive glass successfully from diffraction patterns and compare it with that of the pristine one. Striking differences appear under the first diffraction peak, revealing new sub‐structures for the radioactive glass. It is suggested that they could be related to structural changes in the medium‐range order, in particular the size distribution of rings or chains under the influence of mixed interactions between the glass network, α‐particles and recoil nuclei. [ABSTRACT FROM AUTHOR]

Measuring the structure factor, S(q), of a dispersion of particles by small‐angle X‐ray scattering provides a unique method to investigate the spatial arrangement of colloidal particles. However, it is impossible to find the exact location of the particles from S(q) because some information is inherently lacking in the measured signal. The two standard ways to analyse an experimental S(q) are then to compare it either with structure factors computed from simulated systems or with analytical ones calculated from approximated systems. However, such approaches may prove inadequate for dispersions of variously polydisperse particles. While Vrij, Bloom and Stell established a mean‐field approach that could yield fairly accurate approximations for experimental S(q), this solution has remained underused because of its mathematical complexity. In the present work, the complete Percus–Yevick solution for general polydisperse hard‐sphere systems is derived in a concise form that is straightforward to use. The form of the solution has been simplified enough to provide experimentalists with ready solutions of several commonly encountered particle‐radius distributions in real systems (Schulz, truncated normal and inverse Gaussian). The approach is also illustrated with a case study of the exponential radius distribution. Finally, the application of the proposed solution to the power‐law radius distribution is discussed in detail by comparing the calculations with experimentally measured S(q) for an Apollonian packing of spherical droplets recently reported in high‐internal‐phase‐ratio emulsions. [ABSTRACT FROM AUTHOR]

X-ray diffraction experiments contain much more information than the information usually exploited for structure determination. In quantum crystallography, quantum mechanical wavefunctions are used to extract that information about bonding and properties from the measured X-ray structure factors. Here we show how quantum mechanically derived structure factors and atomic form factors are constructed to allow the improved description of the diffraction experiment. Subsequently, we discuss the basics and the applications of the advanced structure refinement method Hirshfeld atom refinement and of the X-ray constrained wavefunction fitting technique. [ABSTRACT FROM AUTHOR]

Modern methods of quantum crystallography are techniques firmly rooted in quantum chemistry and, as in many quantum chemical strategies, electron densities are expressed as two‐centre expansions that involve basis functions centred on atomic nuclei. Therefore, the computation of the necessary structure factors requires the evaluation of Fourier transform integrals of basis function products. Since these functions are usually Cartesian Gaussians, in this communication it is shown that the Fourier integrals can be efficiently calculated by exploiting an extension of the Obara–Saika recurrence formulas, which are successfully used by quantum chemists in the computation of molecular integrals. Implementation and future perspectives of the technique are also discussed. [ABSTRACT FROM AUTHOR]

An acoustically levitated droplet has been used to collect synchrotron SAXS data on human serum albumin protein solutions up to a protein concentration of 400 mg ml−1. A careful selection of experiments allows for fast data collection of a large amount of data, spanning a protein concentration/solvent concentration space with limited sample consumption (down to 3 µL per experiment) and few measurements. The data analysis shows data of high quality that are reproducible and comparable with data from standard flow‐through capillary‐based experiments. Furthermore, using this methodology, it is possible to achieve concentrations that would not be accessible by conventional cells. The protein concentration and ionic strength parameter space diagram may be covered easily and the amount of protein sample is significantly reduced (by a factor of 100 in this work). Used in routine measurements, the benefits in terms of protein cost and time spent are very significant. [ABSTRACT FROM AUTHOR]

Noble metal nanoparticles exhibit unique physical, chemical, biomedical, catalytic and optical properties. Understanding these properties and further development of production methods entail detailed knowledge of the structure at the atomic scale. Gold nanoparticles with multimodal size distribution were synthesized on porous silica and their atomic scale structure was studied by X‐ray diffraction. The obtained experimental data are compared with molecular dynamics simulations. Spherical models of the Au nanoparticles, defined by ensembles of the Cartesian coordinates of constituent atoms, were generated and their geometry was optimized by applying the LAMMPS software. The comparison was performed in both reciprocal and real space. A good agreement is achieved for the models with disorder that can be related to surface relaxation effects and vacancy defects. The approach adopted here may have wider applications for further structural studies of other nanomaterials, offering direct verification of simulation results by experiment. [ABSTRACT FROM AUTHOR]

In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay. [ABSTRACT FROM AUTHOR]

A comprehensive Mathematica package for crystallographic computations, MaXrd, has been developed. It comprises space‐group representations based on International Tables for Crystallography, Vol. A, together with scattering factors from XOP and cross sections from xraylib. Featured functionalities include calculation of structure factors, linear absorption coefficients and crystallographic transformations. The crystal data used by MaXrd are normally generated from external.cif files. The package comes with a dynamic documentation seamlessly integrated with the Mathematica system, including code, examples, details and options. From the onset, minimal Mathematica experience is required to make use of the package. It may be a helpful supplement in research and teaching where crystallography and X‐ray diffraction are essential. Although Mathematica is a proprietary software, all the code of this package is open source. It may easily be extended to cover user‐specific applications. A package for Mathematica has been developed, containing the most important point‐ and space‐group information together with tables for various photon–atom interactions. It includes basic functions for handling crystallographic data as well as procedures for calculating various quantities in relation to crystallography and X‐ray diffraction. [ABSTRACT FROM AUTHOR]

Hard disks are one of the simplest interacting many-body model system in two dimensions (2D). Here, we present a comprehensive set of measurements of the static structure factors for quasi-2D monodisperse fluids and two different binary colloidal hard sphere mixtures: a small size ratio (SSR) system with a negligibly small negative non-additivity and a large size ratio system with a significantly larger non-additivity. We compare the experimental results for the monodisperse and SSR systems to those calculated using density functional theory (DFT) for additive mixtures. Furthermore, we determine the zero-wavevector limits of the static structure factors for the monodisperse and binary hard sphere fluids directly from an analysis of number and concentration fluctuations. For the monodisperse case, this leads to the isothermal compressibility, which agrees very well with DFT, and is consistent with the scaled particle theory equation of state for hard disks. For the binary fluids, the partial static structure factors are used to calculate the Bhatia-Thornton structure factors, and we find qualitative agreement with DFT for the SSR mixture. Finally, the zero-wavevector limits of the Bhatia-Thornton structure factors are determined and directly related to the thermodynamic factor, the dilatation factor and the isothermal compressibility. [ABSTRACT FROM AUTHOR]

This article takes the concepts of the `new diffraction theory' [Fewster (2014). Acta Cryst. A70, 257–282] and examines the implications for the interpretation of experimental results and the estimation of structure factors. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This `enhancement' effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. By applying the idea that the higher‐order peaks are due to path lengths of nλ, it is shown that `systematically absent' reflections in the conventional theory may not be absent. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated. [ABSTRACT FROM AUTHOR]

It has been recently established that the accuracy of structural parameters from X‐ray refinement of crystal structures can be improved by using a bank of aspherical pseudoatoms instead of the classical spherical model of atomic form factors. This comes, however, at the cost of increased complexity of the underlying calculations. In order to facilitate the adoption of this more advanced electron density model by the broader community of crystallographers, a new software implementation called DiSCaMB, `densities in structural chemistry and molecular biology', has been developed. It addresses the challenge of providing for high performance on modern computing architectures. With parallelization options for both multi‐core processors and graphics processing units (using CUDA), the library features calculation of X‐ray scattering factors and their derivatives with respect to structural parameters, gives access to intermediate steps of the scattering factor calculations (thus allowing for experimentation with modifications of the underlying electron density model), and provides tools for basic structural crystallographic operations. Permissively (MIT) licensed, DiSCaMB is an open‐source C++ library that can be embedded in both academic and commercial tools for X‐ray structure refinement. [ABSTRACT FROM AUTHOR]

The effect of structural factors, including the type of diisocyanates and glycols, degree of crosslinking, hard-segment content, crystallinity and hydrophilic group content, on optical properties of waterborne polyurethane (WPU) was investigated. Based on the relationship between structure and properties, a series of self-matting WPUs with excellent transmittance were synthesized. Results demonstrated that refractive index of constituent groups was an important factor to influence the optical properties of coatings. For multiphase polyurethane, aromatic ring, ester bond, NHCOO and urea groups with high refractive index could decrease the matting effect and transmittance. Higher hard-segment content resulting in an increase of the number of NHCOO or urea bonds also decreased the matting effect and transmittance. The aggregation structure of WPU was another factor to influence the optical properties of coatings. Crystalline soft and hard segment domains could decrease the transmittance and matting effect, whilst non-crystalline segments, pendent groups and crosslinking destroyed the regularity or crystallinity of macromolecules, behaving as an auxiliary function to improve the transmittance. The particle size of WPU was of great importance for the matting effect. Smaller particle size (<5.0 µm) would endow the coating with a smoother surface and higher reflected light ratio, and thus the expected matting effect was hard to be achieved. A larger particle size could improve the matting effect but impart to the coating a coarse surface and hand-feel. When the 2,2-bis(hydroxymethyl)propionic acid content was 1.6 wt%, spherical particles with a size distribution of 7-8 µm were aggregated on the coating surface, giving the coating an excellent matting effect and hand-feel. © 2017 Society of Chemical Industry [ABSTRACT FROM AUTHOR]

The decoupling approximation, proposed by Kotlarchyk & Chen [ J. Chem. Phys. (1983), 79, 2461-2469], is a first-order correction to the experimentally determined apparent structure factor that is necessary because of concentration effects in polydisperse and/or nonspherical systems. While the approximation is considered accurate for spheres with low polydispersity (<10%), the corresponding limitations for nonspherical particles are unknown. The validity of this approximation is studied for monodisperse dispersions of hard ellipsoids of revolution with aspect ratios ranging from 0.333 to 3 and a guide for its accuracy is provided. [ABSTRACT FROM AUTHOR]

Crystalline silicon is an ideal compound to test the current state of experimental structure factors and corresponding electron densities. High-quality structure factors have been measured on crystalline silicon with synchrotron powder X-ray diffraction. They are in excellent agreement with benchmark Pendellösung data having comparable accuracy and precision, but acquired in far less time and to a much higher resolution (sin θ/λ < 1.7 Å−1). The extended data range permits an experimental modelling of not only the valence electron density but also the core deformation in silicon, establishing an increase of the core density upon bond formation in crystalline silicon. Furthermore, a physically sound procedure for evaluating the standard deviation of powder-derived structure factors has been applied. Sampling statistics inherently account for contributions from photon counts as well as the limited number of diffracting particles, where especially the latter are particularly difficult to handle. [ABSTRACT FROM AUTHOR]

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Accurate determination of a liquid structure, especially at high temperatures, remains challenging, as reflected in the scatter between different measurements. The experimental challenge is compounded by the process of the numerical transformation from the structure factor to the radial distribution function. The resulting uncertainty is often greater than that required to resolve issues associated with changes in the short-range order of the liquid, such as the existence of liquid-liquid phase transitions or correlations between thermophysical properties and structure. In the present contribution it is demonstrated for liquid bismuth as a model system that the structure factor can be obtained to high accuracy, by comparing several independent measurements in different setups. A simple method is proposed for improving the accuracy of the radial distribution functions, based on the extension of the finite range of momentum transfer, q, in the measured data by analytical asymptotic expressions. A unified mathematical formalism for the asymptotic dependence of the structure factor is developed and the asymptotic form of the Percus-Yevick hard-sphere solution is obtained as a special limiting case. The multiple expressions in the literature are shown to reflect uncertainty in the nature of the repulsive interatomic interaction at short separation distances. Applying this asymptotic method, it is shown that it enables access to details of the fine structure of the liquid and its temperature dependence. [ABSTRACT FROM AUTHOR]

It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve compatible with the parameterization of the considered space. In particular, attention is drawn to the fact that one and only one finite and free module of the Lie algebra of the group of translations can generate both modulated and non-modulated lattices, the modulated character being given only by the parameterization of the space in which the lattice is generated. Moreover, it is shown that the diffraction pattern of a structure is directly linked to the action of that free and finite module. In the Fourier transform of a whole structure, the Fourier transform of the electron density of one unit cell ( i.e. the structure factor) appears concretely, whether the structure is modulated or not. Thus, there exists a neat separation: the geometrical aspect on the one hand and the action of the group on the other, without requiring additional dimensions. [ABSTRACT FROM AUTHOR]

The structure factor and the effect of deviation from spherical symmetry are studied for elongated particles with axial ratios between 0.1 and 10. This is done using Monte Carlo simulation of the excluded-volume distance distribution function for ellipsoids of revolution, for cylinders and for cylinders with hemispherical end caps. The method suggested is general and is applicable to particles of any shape. The results of the calculations are compared with the Percus-Yevick formula [Percus & Yevick (1958), Phys. Rev. 110, 1-13] for hard spheres. The comparisons indicate that the Percus-Yevick formula should only be used for axial ratios close to 1. For larger deviations from spherical symmetry it is often better to use the excluded-volume distance distribution function for the particle, in combination with the single-particle distance distribution function, for the calculation of the structure factor. [ABSTRACT FROM AUTHOR]

The electron intensity of a beam from an amorphous surface layer on a crystal transmission electron microscopy (TEM) specimen has been found to have sufficient coherence to produce fringes in interferograms, created by interfering two electron diffracted beams from the crystal, using a method of electron interference referred to as diffracted beam interferometry. This interference method involves amplitude splitting of the electron beam by means of a crystal with a thin amorphous layer on its surface. The amorphous intensity is transferred along with the crystal's Bragg diffracted beams and is then self-interfered when the crystal's Bragg diffracted beams are interfered by an electron biprism. The interference fringes in the interferograms exist in low to high electron scattering angles. The spatial frequency of the amorphous intensity fringes depends on the Bragg angle of the crystal's interfered diffracted beams. It is shown that the absolute phase of the amorphous intensity is possibly obtained using a Cs-corrected TEM and two interfering diffracted beams having equal but opposite phases. This method of interference is a good step towards measuring the phase of amorphous materials that is useful in determining their complex atomic structures. [ABSTRACT FROM AUTHOR]

Inverting scattering experiments to obtain effective interparticle interactions is generally a poorly conditioned problem. L. Reatto [Phil. Mag. A 58, 37 (1986)] showed that for atomic liquids close to the triple point, inversions are hard because the structure closely resembles that of an equivalent hard-sphere fluid. Here I demonstrate that at low concentrations and for particles with short-ranged attractive potentials, S(k) also exhibits a very weak dependence on potential shape. Instead, different potentials all generate an S(k) that closely resembles that of the Baxter model with a similar second-virial coefficient. By contrast, in this energetic fluid regime, the inversion of an attractive interaction from real-space correlations such as the radial distribution function g(r) is well conditioned. Nevertheless, one may extract further information from S(k) by measuring isosbestic points, values of k where the scattering intensity I(k) or the structure factor S(k) is invariant to changes in interaction-potential well depth. These points suggest a new extended corresponding states principle for particles in solution based on the packing fraction, the second osmotic virial coefficient, and a new measure of effective potential range. [ABSTRACT FROM AUTHOR]

Ionic liquids are subjects of intense current interest within the physical chemistry community. A great deal of progress has been made in just the past five years toward identifying the factors that cause these salts to have low melting points and other useful properties. Supramolecular structure and organization have emerged as important and complicated topics that may be key to understanding how chemical reactions and other processes are affected by ionic liquids. New questions are posed, and an active debate is ongoing regarding the nature of nanoscale ordering in ionic liquids. The topic of reactivity in ionic liquids is still relatively unexplored; however, the results that have been obtained indicate that distributed kinetics and dynamical heterogeneity may sometimes, but not always, be influencing factors. [ABSTRACT FROM AUTHOR]

Ionic liquids are subjects of intense current interest within the physical chemistry community. A great deal of progress has been made in just the past five years toward identifying the factors that cause these salts to have low melting points and other useful properties. Supramolecular structure and organization have emerged as important and complicated topics that may be key to understanding how chemical reactions and other processes are affected by ionic liquids. New questions are posed, and an active debate is ongoing regarding the nature of nanoscale ordering in ionic liquids. The topic of reactivity in ionic liquids is still relatively unexplored; however, the results that have been obtained indicate that distributed kinetics and dynamical heterogeneity may sometimes, but not always, be influencing factors. [ABSTRACT FROM AUTHOR]

We compared two models of aggregation which represent the sol gel transition of base-catalyzed colloidal gels. The two models are a Langevin dynamics approach of this transition and the DLCA model (diffusion limited cluster-cluster aggregation). For large numbers of particles, we compared the fractal dimension of the gelling network via the structure factor of the bulk. We observed that the Langevin dynamics approach did give more realistic fractal dimension than the DLCA model. This is due to the fact that Langevin dynamics evolves as a function of a physical time. [ABSTRACT FROM AUTHOR]

Accurate structure factors of silicon and diamond have been experimentally determined from powder diffraction data measured at the third-generation synchrotron-radiation source SPring-8, BL02B2. The accuracy of the obtained structure factors has been evaluated by comparing with structure factors in the literature measured by the Pendellösung method and with some from theoretical calculations. The results indicate that the structure factors from powder data are accurate enough to discuss the experimental charge-density distributions of these materials. The number of structure factors of silicon determined in the present study is 104, which is three times more than that of previous Pendellösung data. The experimental charge densities have been obtained by the maximum-entropy method from the present structure factors. The charge densities at bond mid-points for silicon and diamond show good agreement with different kinds of theoretical calculations. The present study proved that the powder diffraction at SPring-8 is a promising method for determination of experimental charge density for a wider range of materials. [ABSTRACT FROM AUTHOR]

The sensitivity of atomic scattering factors to valence charge distributions has been compared quantitatively for X-ray and electron diffraction. It is found that below a critical scattering vector, s (| s| = sinθ/λ), ranging typically from 0.2 to 0.6 Å−1 depending on the atomic number, electron diffraction is more sensitive to valence charge densities than X-ray diffraction. Thus, electron diffraction provides crucial electronic structure information via the low-order structure factors, which are relatively insensitive to thermal vibrations, but sensitive to the charge distribution that characterizes the chemical bonding properties of the materials. On the other hand, the high-order structure factors, which are mainly influenced by atomic position and core charge, in many cases can be replaced by structure factors of a procrystal (superposition of neutral atoms), or by calculated structure factors from modern density functional theory (DFT), without losing significant accuracy. This is demonstrated by detailed analyses of an MgB2 superconductor. The work reveals the importance of accurate determination of a very few low-order structure factors in valence electron density studies, and suggests the merit of the combined use of electron diffraction and DFT calculations for solids, especially those with large unit cells and nanocrystalline grains, unsuitable for X-ray studies. [ABSTRACT FROM AUTHOR]

XISF is a MATLAB program developed to separate intermolecular structure factors from total X-ray scattering structure factors for molecular liquids and amorphous solids. The program is built on a trust-region-reflective optimization routine with the r.m.s. deviations of atoms physically constrained. XISF has been optimized for performance and can separate intermolecular structure factors of complex molecules. [ABSTRACT FROM AUTHOR]

The effect of the internal thermal structure of building walls and roofs on their frequency responses, of period of 24 h, is examined. The notion of the thermal structure factors of a wall is introduced. Correlation between the fre quency dependent and structure dependent thermal characteristics is analyzed for the representative sets of building walls and roofs from ASHRAE Handbook 1989: Fundamentals. Most evident is the correlation between the decrement factor and the structure dependent time constant, between the admittance response amplitude and the appropriate thermal mass factor, and between the time lag and its estimated value, and also thickness of a wall. [ABSTRACT FROM PUBLISHER]

Structure factors and site-site distribution functions for models of liquid carbon disulphide (CS) and acetonitrile (CHCN) are obtained by using the site-site Ornstein-Zernike (SSOZ) integral equation with the Percus-Yevick (PY) and the hypernetted chain (HNC) closures. The calculated structure factors are found to be in good agreement with the neutron and X-ray diffraction data as well as with the simulation data. The site charges have a significant effect on the distribution functions but not on the structure factors of both the systems. There is very good qualitative agreement between the calculated distribution functions and the results from computer simulations. Distinctive shoulders found in the simulation results for the first peaks of the C-N and CH-CH distribution functions are enhanced in the calculations using the integral equations. [ABSTRACT FROM AUTHOR]

A novel phase determination approach comparing FWHMs with intensities of rocking curves from the top and bottom surfaces of a polar crystal is proposed. The approach is applied to GaAs ±333 reflections in Bragg mode and the phases are determined with good accuracy. This approach is potentially very useful for determining the phase of a polar crystal, including that for a nearly perfect crystal. [ABSTRACT FROM AUTHOR]

The total scattering structure factors of pure liquid n‐pentanol, pentanal, and five of their mixtures, as determined by high energy synchrotron X‐ray diffraction experiments, are presented. For the interpretation of measured data, molecular dynamics computer simulations are performed, utilizing "all‐atom" type force fields. The diffraction signals in general resemble each other over most of the monitored scattering variable, Q, range above 1 Å−1, but the absolute values of the intensities of the small‐angle scattering maximum ("pre‐peak," "first sharp diffraction peak"), around 0.6 Å−1, change in an unexpected fashion, non‐linearly with the composition. Molecular dynamics simulations are not able to reproduce this low‐Q behavior; on the other hand, they do reproduce the experimental diffraction data above 1 Å−1 rather accurately. Partial radial distribution functions are calculated based on the atomic coordinates in the simulated configurations. Inspection of the various OO and OH partial radial distribution functions clearly shows that both the alcoholic and the aldehydic oxygens form hydrogen bonds with the hydrogen atoms of the alcoholic OH‐group. Total scattering structure factors of liquid n‐pentanol, pentanal, and five of their mixtures, as determined by high energy synchrotron X‐ray diffraction experiments, are presented. For interpreting the measured data, molecular dynamics computer simulations are conducted. It is clearly shown that both the alcoholic and the aldehydic oxygen atoms form hydrogen bonds with the hydrogen atoms of the alcoholic OH‐group. [ABSTRACT FROM AUTHOR]

A preliminary result of reverse Monte Carlo (RMC) analysis of small-angle X-ray scattering data for expanded fluid Hg with the help of wide-angle X-ray diffraction data in the same thermodynamic state is presented. In RMC analysis, three-dimensional configurations of 100000 Hg atoms were modeled to see the large density fluctuation associated with liquid–vapor critical phenomena. It was found that interpolation of measured structure factors is necessary for RMC analysis. [ABSTRACT FROM AUTHOR]