Real‐space multiple‐scattering Hubbard model calculations for d‐ and f‐state materials

Calculations are presented of the electronic structure and X‐ray spectra of materials with correlated d‐ and f‐electron states based on the Hubbard model, a real‐space multiple‐scattering formalism and a rotationally invariant local density approximation. Values of the Hubbard parameter are calculated ab initio using the constrained random‐phase approximation. The combination of the real‐space Green's function with Hubbard model corrections provides an efficient approach to describe localized correlated electron states in these systems, and their effect on core‐level X‐ray spectra. Results are presented for the projected density of states and X‐ray absorption spectra for transition metal‐ and lanthanide‐oxides. Results are found to be in good agreement with experiment.     

SaxsMDView: a three‐dimensional graphics program for displaying force vectors

A new three‐dimensional graphics program, SaxsMDView, is described. The program performs a three‐dimensional graphical representation for protein molecules along with the force vector (or vector potential) applying to each atom. The displayed object can be rotated and translated in arbitrary directions by interactive mouse manipulation. While SaxsMDView was originally intended to visualize the result of SAXS_MD, a previously developed program based on the restrained molecular dynamics with small‐angle X‐ray scattering constraints, it can also be useful for graphical representation of other objects such as coarse‐grained molecular models reconstructed by ab initio modelling or solvent site‐dipole field vectors induced around the protein molecule. Some examples of the application of the program including the graphical analyses of the results with SAXS_MD are also presented.     

Performance of the micro‐PIC gaseous area detector in small‐angle X‐ray scattering experiments

The application of a two‐dimensional photon‐counting detector based on a micro‐pixel gas chamber (µ‐PIC) to high‐resolution small‐angle X‐ray scattering (SAXS), and its performance, are reported. The µ‐PIC is a micro‐pattern gaseous detector fabricated by printed circuit board technology. This article describes the performance of the µ‐PIC in SAXS experiments at SPring‐8. A dynamic range of >10⁵ was obtained for X‐ray scattering from a polystyrene sphere solution. A maximum counting rate of up to 5 MHz was observed with good linearity and without saturation. For a diffraction pattern of collagen, weak peaks were observed in the high‐angle region in one accumulation of photons.     

Simultaneous small‐ and wide‐angle scattering at high X‐ray energies

Combined small‐ and wide‐angle X‐ray scattering (SAXS/WAXS) is a powerful technique for the study of materials at length scales ranging from atomic/molecular sizes (a few angstroms) to the mesoscopic regime (～1 nm to ～1 µm). A set‐up to apply this technique at high X‐ray energies (E > 50 keV) has been developed. Hard X‐rays permit the execution of at least three classes of investigations that are significantly more difficult to perform at standard X‐ray energies (8–20 keV): (i) in situ strain analysis revealing anisotropic strain behaviour both at the atomic (WAXS) as well as at the mesoscopic (SAXS) length scales, (ii) acquisition of WAXS patterns to very large q (>20 Å^?1) thus allowing atomic pair distribution function analysis (SAXS/PDF) of micro‐ and nano‐structured materials, and (iii) utilization of complex sample environments involving thick X‐ray windows and/or samples that can be penetrated only by high‐energy X‐rays. Using the reported set‐up a time resolution of approximately two seconds was demonstrated. It is planned to further improve this time resolution in the near future.     

One‐dimensional small‐angle X‐ray scattering tomography of dip‐coated polyamide 6 monofilaments

A synchrotron study is presented in which the concept of one‐dimensional tomographic reconstruction of small‐angle X‐ray scattering patterns is applied to investigate polyamide 6 monofilaments, dip‐coated with alumina particles. The filaments are scanned with a focused synchrotron beam and the resulting scattering patterns are recorded with a PILATUS 2M detector. The reconstructed sequence of SAXS images reflects the local nanostructure variation along the filament radius. In particular, the influence of coating process parameters on the polyamide 6 is investigated.     

The application of hybrid pixel detectors for in‐house SAXS instrumentation with a view to combined chromatographic operation

This study analyses the potential for laboratory‐based size‐exclusion chromatography (SEC) integrated small‐angle X‐ray scattering (SAXS) instrumentation to characterize protein complexes. Using a high‐brilliance home source in conjunction with a hybrid pixel X‐ray detector, the efficacy of SAXS data collection at pertinent protein concentrations and exposure times has been assessed. Scattering data from SOD1 and from the complex of SOD1 with its copper chaperone, using 10 min exposures, provided data quality in the range 0.03 < q < 0.25 Å^?1 that was sufficient to accurately assign radius of gyration, maximum dimension and molecular mass. These data demonstrate that a home source with integrated SEC–SAXS technology is feasible and would enable structural biologists studying systems containing transient protein complexes, or proteins prone to aggregation, to make advanced preparations in‐house for more effective use of limited synchrotron beam time.     

On the Supermolecular Structure of Fullerene C60 Solutions

Small angle X‐ray scattering (SAXS) and wide angle X‐ray scattering (WAXS) techniques were used for investigation of fullerene C₆₀ solutions in toluene and p‐xylene. On all SAXS curves, intensity decreases to some constant value of I_C with increase of scattering angle. The value of I_C depends on concentration non‐monotonically: it first slightly increases, then drops sharply to some minimal value, and then increases again. A qualitative explanation of such dependence is offered. It is supposed that the presence of fullerene C₆₀ in solution suppresses thermal fluctuations of density in the solvent. In combination with the X‐ray data the results obtained for solutions of fullerene C₆₀ by various others techniques (calorimetry, densimetry, etc.) are discussed. Possible models of a supermolecular structure of fullerene C₆₀ solutions in good solvents are considered.     

Investigation of short‐range structural order in Zr69.5Cu12Ni11Al7.5 and Zr41.5Ti41.5Ni17 glasses,using X‐ray absorption spectroscopy and ab initio molecular dynamics simulations

Short‐range order has been investigated in Zr_69.5Cu₁₂Ni₁₁Al_7.5 and Zr_41.5Ti_41.5Ni₁₇ metallic glasses using X‐ray absorption spectroscopy and ab initio molecular dynamics simulations. While both of these alloys are good glass formers, there is a difference in their glass‐forming abilities (Zr_41.5Ti_41.5Ni₁₇ > Zr_69.5Cu₁₂Ni₁₁Al_7.5). This difference is explained by inciting the relative importance of strong chemical order, icosahedral content, cluster symmetry and configuration diversity.     

Small‐angle solution scattering using the mixed‐mode pixel array detector

Solution small‐angle X‐ray scattering (SAXS) measurements were obtained using a 128 × 128 pixel X‐ray mixed‐mode pixel array detector (MMPAD) with an 860 µs readout time. The MMPAD offers advantages for SAXS experiments: a pixel full‐well of >2 × 10⁷ 10 keV X‐rays, a maximum flux rate of 10⁸ X‐rays pixel^?1 s^?1, and a sub‐pixel point‐spread function. Data from the MMPAD were quantitatively compared with data from a charge‐coupled device (CCD) fiber‐optically coupled to a phosphor screen. MMPAD solution SAXS data from lysozyme solutions were of equal or better quality than data captured by the CCD. The read‐noise (normalized by pixel area) of the MMPAD was less than that of the CCD by an average factor of 3.0. Short sample‐to‐detector distances were required owing to the small MMPAD area (19.2 mm × 19.2 mm), and were revealed to be advantageous with respect to detector read‐noise. As predicted by the Shannon sampling theory and confirmed by the acquisition of lysozyme solution SAXS curves, the MMPAD at short distances is capable of sufficiently sampling a solution SAXS curve for protein shape analysis. The readout speed of the MMPAD was demonstrated by continuously monitoring lysozyme sample evolution as radiation damage accumulated. These experiments prove that a small suitably configured MMPAD is appropriate for time‐resolved solution scattering measurements.     

A new small‐angle X‐ray scattering set‐up on the crystallography beamline I711 at MAX‐lab

A small‐angle X‐ray scattering (SAXS) set‐up has recently been developed at beamline I711 at the MAX II storage ring in Lund (Sweden). An overview of the required modifications is presented here together with a number of application examples. The accessible q range in a SAXS experiment is 0.009–0.3 Å^?1 for the standard set‐up but depends on the sample‐to‐detector distance, detector offset, beamstop size and wavelength. The SAXS camera has been designed to have a low background and has three collinear slit sets for collimating the incident beam. The standard beam size is about 0.37 mm × 0.37 mm (full width at half‐maximum) at the sample position, with a flux of 4 × 10¹⁰ photons s^?1 and λ = 1.1 Å. The vacuum is of the order of 0.05 mbar in the unbroken beam path from the first slits until the exit window in front of the detector. A large sample chamber with a number of lead‐throughs allows different sample environments to be mounted. This station is used for measurements on weakly scattering proteins in solutions and also for colloids, polymers and other nanoscale structures. A special application supported by the beamline is the effort to establish a micro‐fluidic sample environment for structural analysis of samples that are only available in limited quantities. Overall, this work demonstrates how a cost‐effective SAXS station can be constructed on a multipurpose beamline.     

Thorough small‐angle X‐ray scattering analysis of the instability of liquid micro‐jets in air

Liquid jets are of interest, both for their industrial relevance and for scientific applications (more important, in particular for X‐rays, after the advent of free‐electron lasers that require liquid jets as sample carrier). Instability mechanisms have been described theoretically and by numerical simulation, but confirmed by few experimental techniques. In fact, these are mainly based on cameras, which is limited by the imaging resolution, and on light scattering, which is hindered by absorption, reflection, Mie scattering and multiple scattering due to complex air/liquid interfaces during jet break‐up. In this communication it is demonstrated that synchrotron small‐angle X‐ray scattering (SAXS) can give quantitative information on liquid jet dynamics at the nanoscale, by detecting time‐dependent morphology and break‐up length. Jets ejected from circular tubes of different diameters (100–450 µm) and speeds (0.7–21 m s^?1) have been explored to cover the Rayleigh and first wind‐induced regimes. Various solvents (water, ethanol, 2‐propanol) and their mixtures have been examined. The determination of the liquid jet behaviour becomes essential, as it provides background data in subsequent studies of chemical and biological reactions using SAXS or X‐ray diffraction based on synchrotron radiation and free‐electron lasers.     

A dedicated small‐angle X‐ray scattering beamline with a superconducting wiggler source at the NSRRC

At the National Synchrotron Radiation Research Center (NSRRC), which operates a 1.5 GeV storage ring, a dedicated small‐angle X‐ray scattering (SAXS) beamline has been installed with an in‐achromat superconducting wiggler insertion device of peak magnetic field 3.1 T. The vertical beam divergence from the X‐ray source is reduced significantly by a collimating mirror. Subsequently the beam is selectively monochromated by a double Si(111) crystal monochromator with high energy resolution (ΔE/E? 2 × 10^?4) in the energy range 5–23 keV, or by a double Mo/B₄C multilayer monochromator for 10–30 times higher flux (～10¹¹ photons s^?1) in the 6–15 keV range. These two monochromators are incorporated into one rotating cradle for fast exchange. The monochromated beam is focused by a toroidal mirror with 1:1 focusing for a small beam divergence and a beam size of ～0.9 mm × 0.3 mm (horizontal × vertical) at the focus point located 26.5 m from the radiation source. A plane mirror installed after the toroidal mirror is selectively used to deflect the beam downwards for grazing‐incidence SAXS (GISAXS) from liquid surfaces. Two online beam‐position monitors separated by 8 m provide an efficient feedback control for an overall beam‐position stability in the 10 µm range. The beam features measured, including the flux density, energy resolution, size and divergence, are consistent with those calculated using the ray‐tracing program SHADOW. With the deflectable beam of relatively high energy resolution and high flux, the new beamline meets the requirements for a wide range of SAXS applications, including anomalous SAXS for multiphase nanoparticles (e.g. semiconductor core‐shell quantum dots) and GISAXS from liquid surfaces.     

X‐ray microtomographic visualization of Escherichia coli by metalloprotein overexpression

This paper reports X‐ray microtomographic visualization of the microorganism Escherichia coli overexpressing a metalloprotein ferritin. The three‐dimensional distribution of linear absorption coefficients determined using a synchrotron radiation microtomograph with a simple projection geometry revealed that the X‐ray absorption was homogeneously distributed, suggesting that every E. coli cell was labeled with the ferritin. The ferritin‐expressing E. coli exhibited linear absorption coefficients comparable with those of phosphotungstic acid stained cells. The submicrometer structure of the ferritin‐expressing E. coli cells was visualized by Zernike phase contrast using an imaging microtomograph equipped with a Fresnel zone plate. The obtained images revealed curved columnar or bunching oval structures corresponding to the E. coli cells. These results indicate that the metalloprotein overexpression facilitates X‐ray visualization of three‐dimensional cellular structures of biological objects.     

Quality evaluation of quick‐frozen biological specimens by simultaneous microbeam SAXS/WAXS recordings

The quality of small‐angle X‐ray scattering (SAXS) patterns from quick‐frozen hydrated biological specimens was correlated with the extent of ice crystal formation by simultaneously recording wide‐angle X‐ray scattering (WAXS) of ice, at a micrometer‐order spatial resolution by using X‐ray microbeams. Flight muscle fibers from a giant waterbug, Lethocerus, known to generate well defined small‐angle reflection spots originating from the hexagonal lattices of myofilaments, were quick‐frozen in the presence or absence of various cryoprotectants. Freezing without a cryoprotectant resulted in massive ice‐crystal formation at almost all depths of the specimen, and the occurrence of reflection spots was limited to the region close to the specimen surface. Inclusion of 20% dimethyl sulfoxide or methylpentanediol ensured ideal vitreous ice formation and good diffraction qualities for up to 100 µm from the specimen surface. Glycerol and sucrose were found to be inferior at a 20% concentration, but left the reflection spots observable at depths of up to 100 µm. Thus, the microbeam SAXS/WAXS recording offers a high‐spatial‐resolution means of evaluating the extent of structure preservation of quick‐frozen biological specimens. The technique presented here may also provide useful information in cryoelectron microscopy.     

A large‐solid‐angle X‐ray Raman scattering spectrometer at ID20 of the European Synchrotron Radiation Facility

An end‐station for X‐ray Raman scattering spectroscopy at beamline ID20 of the European Synchrotron Radiation Facility is described. This end‐station is dedicated to the study of shallow core electronic excitations using non‐resonant inelastic X‐ray scattering. The spectrometer has 72 spherically bent analyzer crystals arranged in six modular groups of 12 analyzer crystals each for a combined maximum flexibility and large solid angle of detection. Each of the six analyzer modules houses one pixelated area detector allowing for X‐ray Raman scattering based imaging and efficient separation of the desired signal from the sample and spurious scattering from the often used complicated sample environments. This new end‐station provides an unprecedented instrument for X‐ray Raman scattering, which is a spectroscopic tool of great interest for the study of low‐energy X‐ray absorption spectra in materials under in situ conditions, such as in operando batteries and fuel cells, in situ catalytic reactions, and extreme pressure and temperature conditions.     

A novel multi‐detection technique for three‐dimensional reciprocal‐space mapping in grazing‐incidence X‐ray diffraction

A new scattering technique in grazing‐incidence X‐ray diffraction geometry is described which enables three‐dimensional mapping of reciprocal space by a single rocking scan of the sample. This is achieved by using a two‐dimensional detector. The new set‐up is discussed in terms of angular resolution and dynamic range of scattered intensity. As an example the diffuse scattering from a strained multilayer of self‐assembled (In,Ga)As quantum dots grown on GaAs substrate is presented.     

Characterization of an in‐vacuum PILATUS 1M detector

A dedicated in‐vacuum X‐ray detector based on the hybrid pixel PILATUS 1M detector has been installed at the four‐crystal monochromator beamline of the PTB at the electron storage ring BESSY II in Berlin, Germany. Owing to its windowless operation, the detector can be used in the entire photon energy range of the beamline from 10 keV down to 1.75 keV for small‐angle X‐ray scattering (SAXS) experiments and anomalous SAXS at absorption edges of light elements. The radiometric and geometric properties of the detector such as quantum efficiency, pixel pitch and module alignment have been determined with low uncertainties. The first grazing‐incidence SAXS results demonstrate the superior resolution in momentum transfer achievable at low photon energies.     

Colloidal Crystals of NaYF4 Upconversion Nanocrystals Studied by Small‐Angle X‐Ray Scattering (SAXS)

Spherical NaYF₄ upconversion nanocrystals with mean radii of about 5 and 11 nm are observed to form colloidal crystals, i.e., 3D assemblies of the particles with long‐range order. The colloidal crystals of the larger particles form directly in solution when dispersions of the particles in toluene are stored at room temperature for several weeks. Crystallization of the smaller particles takes place when their dispersions in hexane are slowly dried at elevated temperatures. The formation and the structure of the colloidal crystals are studied by small‐angle X‐ray scattering (SAXS). SAXS measurements show that the smaller as well as the larger particles assemble into a face‐centered cubic lattice with unit cell dimensions of a = 18.7 nm and a = 35.5 nm, respectively. The SAXS data also show that the particles in the colloidal crystals still bear a layer of oleic acid on their surfaces. The thickness of this layer is 1.5–1.8 nm, as determined by comparing the unit cell dimensions of the colloidal crystals with the mean particle sizes. The latter could be very precisely determined from the distinct oscillations observed in the SAXS data of dilute colloidal dispersions of the nanocrystals.     

Enhancement of measurement accuracy of X‐ray PIV in comparison with the micro‐PIV technique

The X‐ray PIV (particle image velocimetry) technique has been used as a non‐invasive measurement modality to investigate the haemodynamic features of blood flow. However, the extraction of two‐dimensional velocity field data from the three‐dimensional volumetric information contained in X‐ray images is technically unclear. In this study, a new two‐dimensional velocity field extraction technique is proposed to overcome technological limitations. To resolve the problem of finding a correction coefficient, the velocity field information obtained by X‐ray PIV and micro‐PIV techniques for disturbed flow in a concentric stenosis with 50% severity was quantitatively compared. Micro‐PIV experiments were conducted for single‐plane and summation images, which provide similar positional information of particles as X‐ray images. The correction coefficient was obtained by establishing the relationship between velocity data obtained from summation images (V_S) and centre‐plane images (V_C). The velocity differences between V_S and V_C along the vertical and horizontal directions were quantitatively analysed as a function of the geometric angle of the test model for applying the present two‐dimensional velocity field extraction technique to a conduit of arbitrary geometry. Finally, the two‐dimensional velocity field information at arbitrary positions could be successfully extracted from X‐ray images by using the correction coefficient and several velocity parameters derived from V_S.     

X‐ray‐Raman‐scattering‐based EXAFS beyond the dipole limit

X‐ray Raman scattering (XRS) provides a bulk‐sensitive method of measuring the extended X‐ray absorption fine structure (EXAFS) of soft X‐ray absorption edges. Accurate measurements and data analysis procedures for the determination of XRS‐EXAFS of polycrystalline diamond are described. The contributions of various angular‐momentum components beyond the dipole limit to the atomic background and the EXAFS oscillations are incorporated using self‐consistent real‐space multiple‐scattering calculations. The properly extracted XRS‐EXAFS oscillations are in good agreement with calculations and earlier soft X‐ray EXAFS results. It is shown, however, that under certain conditions multiple‐scattering contributions to XRS‐EXAFS deviate from those in standard EXAFS, leading to noticeable changes in the real‐space signal at higher momentum transfers owing to non‐dipole contributions. These results pave the way for the accurate application of XRS‐EXAFS to previously inaccessible light‐element systems.