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Following many years of evolutionary development, first at the National Synchrotron Light Source, Brookhaven National Laboratory, and then at the Advanced Photon Source (APS), Argonne National Laboratory, the APS ultra-small-angle X-ray scattering (USAXS) facility has been transformed by several new developments. These comprise a conversion to higher-order crystal optics and higher X-ray energies as the standard operating mode, rapid fly scan measurements also as a standard operational mode, automated contiguous pinhole small-angle X-ray scattering (SAXS) measurements at intermediate scattering vectors, and associated rapid wide-angle X-ray scattering (WAXS) measurements for X-ray diffraction without disturbing the sample geometry. With each mode using the USAXS incident beam optics upstream of the sample, USAXS/SAXS/WAXS measurements can now be made within 5 min, allowing in situ and operando measurement capabilities with great flexibility under a wide range of sample conditions. These developments are described, together with examples of their application to investigate materials phenomena of technological importance. Developments of two novel USAXS applications, USAXS-based X-ray photon correlation spectroscopy and USAXS imaging, are also briefly reviewed.

A UHV non-magnetic kappa geometry diffractometer has been designed for the resonant soft X-ray scattering (RSXS) branch of the Intermediate Energy X-ray (IEX) beamline at the Advanced Photon Source (APS), Argonne National Laboratory. The kappa geometry allows for a large q-range and space for a sample environment (electric or magnetic fields). To avoid distorting the sample environment field, non-magnetic SmarAct, GmbH stages are used for the ϕ-axis, X, Y, and Z linear stages. The κ and θ axes are controlled by high-precision UHV compatible Physik Instrumente (PI) GmbH & Co. rotation stages. The design goal was to achieve a 50 µm sphere of confusion. To achieve this, iterative designs were developed using FEA and commercial stages were chosen that had minimal wobble, eccentricity, and flatness errors.

Electrochemical interfaces are key to the direct conversion of fuels to electrical energy and lend energy converters like solid oxide fuel cells (SOFC) their functionality. Over extended operation at high temperatures, the microstructure of the underlying component materials in the cathodes, anodes and electrolytes evolve to an extent that these interfaces become affected and ultimately impaired, giving rise to performance degradation. We present anomalous ultra-small-angle X-ray scattering (anomalous USAXS) measurements to quantify the component phase interfacial surface areas as a function of position within the electrodes and electrolyte of a SOFC assembly. Using USAXS at a 3rd generation X-ray synchrotron facility, the primary microstructural parameters obtained are the mean feature size, size distribution and surface area, determined over a contiguous length scale from nanometers to micrometers in a single measurement at a given position. Here, a spatial resolution of

The 25-year history and development of an ultra-small-angle X-ray scattering (USAXS) instrument dedicated to serving materials research is presented and discussed. The instrument’s successful track record is attributed to three factors. The first, and surely the most important, is that all development has been driven by scientific research directions and opportunities. Second, the USAXS instrument is a core capability rather than an add-on facility, with measurement capability from micrometers to nanometers, which is precisely the size range where microstructures determine physical properties. The third is that the instrument’s range of capabilities has continually expanded, now including 2D collimation, imaging, and dynamics. And finally, USAXS has enjoyed the benefit of a management structure that has consistently appreciated the unique experimental measurement capabilities that USAXS delivers.

Absolute calibration of small-angle scattering (SAS) intensity data (measured in terms of the differential scattering cross section per unit sample volume per unit solid angle) is essential for many important aspects of quantitative SAS analysis, such as obtaining the number density, volume fraction, and specific surface area of the scatterers. It also enables scattering data from different instruments (light, X-ray, or neutron scattering) to be combined, and it can even be useful to detect the existence of artifacts in the experimental data. Different primary or secondary calibration methods are available. In the latter case, absolute intensity calibration requires a stable artifact with the necessary scattering profile. Glassy carbon has sometimes been selected as this intensity calibration standard. Here we review the spatial homogeneity and temporal stability of one type of commercially available glassy carbon that is being used as an intensity calibration standard at a number of SAS facilities. We demonstrate that glassy carbon is sufficiently homogeneous and stable during routine use to be relied upon as a suitable standard for absolute intensity calibration of SAS data.

The design and operation of a versatile ultra-small-angle X-ray scattering (USAXS) instrument at the Advanced Photon Source (APS) at Argonne National Laboratory are presented. The instrument is optimized for the high brilliance and low emittance of an APS undulator source. It has angular and energy resolutions of the order of 10−4, accurate and repeatable X-ray energy tunability over its operational energy range from 8 to 18 keV, and a dynamic intensity range of 108to 109, depending on the configuration. It further offers quantitative primary calibration of X-ray scattering cross sections, a scattering vector range from 0.0001 to 1 Å−1, and stability and reliability over extended running periods. Its operational configurations include one-dimensional collimated (slit-smeared) USAXS, two-dimensional collimated USAXS and USAXS imaging. A robust data reduction and data analysis package, which was developed in parallel with the instrument, is available and supported at the APS.

Irena, a tool suite for analysis of both X-ray and neutron small-angle scattering (SAS) data within the commercialIgor Proapplication, brings together a comprehensive suite of tools useful for investigations in materials science, physics, chemistry, polymer science and other fields. In addition to Guinier and Porod fits, the suite combines a variety of advanced SAS data evaluation tools for the modeling of size distribution in the dilute limit using maximum entropy and other methods, dilute limit small-angle scattering from multiple non-interacting populations of scatterers, the pair-distance distribution function, a unified fit, the Debye–Bueche model, the reflectivity (X-ray and neutron) using Parratt's formalism, and small-angle diffraction. There are also a number of support tools, such as a data import/export tool supporting a broad sampling of common data formats, a data modification tool, a presentation-quality graphics tool optimized for small-angle scattering data, and a neutron and X-ray scattering contrast calculator. These tools are brought together into one suite with consistent interfaces and functionality. The suite allows robust automated note recording and saving of parameters during export.

Results are presented for anin situsynchrotron-based ultra-small-angle X-ray scattering (USAXS) study of the solution-mediated formation and growth of nanocrystalline ceria (n-CeO2) using a new remote-controlled, isothermal, circulating fluid flow cell. The fluid flow mitigates or reduces X-ray beam-induced damage, air bubbles or particulate flocculation within the bulk solution, but prevents any coarse particulates that do form from settling out from suspension. Combined with the large-scale range accessible in USAXS studies, the flow cell has enabled measurement,in situand in real time, of structural characteristics from 10 Å to a few micrometres in size as a function of the changing physical and chemical conditions. By applying a multi-component model, the nanoparticle formation and growth component has been identified. Control and online monitoring of flow rate, temperature and pH suspension conditions have permitted real-time studies of the formation and growth of the individual n-CeO2particles from homogeneous dilute solution over several hours. Aspects of the nanoparticle nucleation and growth are revealed that have not been observed directly in measurements on this system.

A new colloidal stabilization mechanism, known as nanoparticle "haloing" (Tohver, V.; Smay, J. E.; Braem, A.; Braun, P. V.; Lewis, J. A. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, (16), 8950-8954), has been predicted theoretically and inferred experimentally in microsphere-nanoparticle mixtures that possess high charge and size asymmetry. The term "halo" implies the existence of a nonzero separation distance between the highly charged nanoparticles and the negligibly charged microspheres that they surround. By means of ultrasmall-angle X-ray scattering, we have quantified the microsphere-nanoparticle separation distance as well as the number of nanoparticles and their lateral separation distance within the self-organized halos that form in these binary mixtures.

A general treatment of X-ray imaging contrast for ultra-small-angle X-ray scattering (USAXS) imaging is presented; this approach makes use of phase propagation and dynamical diffraction theory to account quantitatively for the intensity distribution at the detector plane. Simulated results from a model system of micrometre-sized spherical SiO2particles embedded in a polypropylene matrix show good agreement with experimental measurements. Simulations by means of a separate geometrical ray-tracing method also account for the features in the USAXS images and offer a complementary view of small-angle X-ray scattering as a contrast mechanism. The ray-tracing analysis indicates that refraction, in the form of Porod scattering, and, to a much lesser extent, X-ray reflection account for the USAXS imaging contrast.

Small-angle X-ray scattering (SAXS) measurements have been performed to study helium-bubble formation in borosilicate glass. Helium was introduced by He+implantation over an energy range of 1 to 2 MeV to give a uniform distribution over ∼1 µm depth. The implanted dose was varied from 9 × 1013to 2.8 × 1016 ions cm−2, corresponding to a local concentration range of 40 to 11200 atomic parts per million (a.p.p.m.) averaged over the implantation depth. The SAXS response was fit with the Percus–Yevick hard-sphere interaction potential to account for interparticle interference. The fits yield helium-bubble radii and helium-bubble volume fractions that vary from 5 to 15 Å and from 10−3to 10−1, respectively, as the dose increased from 9 × 1013to 2.8 × 1016 cm−2. The SAXS data are also consistent with maximum helium solubility with respect to bubble formation between 40 and 200 a.p.p.m. in the borosilicate glass matrix.

Monolithic silica aerogels with radial symmetry were synthesized by supercritical drying, doped to 2% and 10% with cobalt, and reduced with hydrogen. All samples were investigated with ultra-small-angle X-ray scattering. The non-doped aerogels have three populations of scatterers with radii of gyration of about 10, 40 and 60–70 Å. The doped aerogels show an additional structure with a radius of gyration ranging from 1050 to 3000 Å. This structure causes intensity oscillations, thus revealing a relatively narrow size distribution. Scattering curves of the 10%-doped aerogels fitted well to a Lifshitz–Slyozov–Wagner particle size distribution, thus revealing that Ostwald ripening might have occurred during aerogel preparation. The same range also shows differences depending on whether the samples were reduced, or in their as-prepared condition. Scattering curves obtained from the cylinder-axis region were different from the scattering curves obtained from the sample boundary, indicating a process-dependent skin effect.

This paper reports recent tests performed on the Bonse–Hart-type ultra-small-angle X-ray scattering (USAXS) instrument at the Advanced Photon Source with higher-order reflection optics – Si(440) instead of Si(220) – and with X-ray energies greater than 20 keV. The results obtained demonstrate the feasibility of high-energy operation with narrower crystal reflectivity curves, which provides access to a scatteringqrange from ∼2 × 10−5to 1.8 Å−1and up to 12 decades in the associated sample-dependent scattering intensity range. The corresponding size range of the scattering features spans about five decades – from less than 10 Å to ∼15 µm. These tests have indicated that mechanical upgrades are required to ensure the alignment capability and operational stability of this instrument for general user operations because of the tighter angular-resolution constraints of the higher-order crystal optics.

Intensity distribution of x-ray scattering by thermal phonons in Si was recorded using synchrotron undulator radiation. A high-energy beam sent through a Si(111) wafer in a transmission Laue geometry yielded a threefold symmetric pattern for the scattering cross section with rich details governed by phonon dispersion, population, and polarization.

Analysis of small-angle scattering data to obtain a particle-size distribution is dependent upon the shape function used to model the scattering. From a maximum-entropy analysis of small-angle scattering data, the effect of shape-function selection on the obtained size distribution is demonstrated using three different shape functions to describe the same scattering data from each of two alloys. The alloys have been revealed by electron microscopy to contain a distribution of randomly oriented and mainly noninteracting irregular ellipsoidal precipitates. A comparison is made between the different forms of the shape function. The effect of an incident-wavelength distribution is also shown. The importance of testing appropriate shape functions and validating these against other microstructural studies is discussed.

Small-angle scattering is widely used for measuring materials microstructure in the 1–100 nm size range. Ultrasmall-angle x-ray scattering (USAXS), typically achieved through crystal collimation, extends this size range to include features over 1 μm in size. This article reports on USAXS on the UNICAT beam line 33-ID at the Advanced Photon Source. The instrument makes use of a six-reflection crystal pair as a collimator and another six-reflection crystal pair as an analyzer. First principle absolute calibration and a broad scattering vector range make this a very effective instrument, limited only by the fact that the measurement of anisotropic microstructures is excluded due to slit smearing from the crystal collimation. This limitation has recently been removed by adding a horizontally reflecting crystal before and another after the sample. This creates a USAXS instrument with collimation in two orthogonal directions. We call this configuration effective pinhole USAXS. Now, anisotropic materials are probed using 9–17 keV photons in the same physically-relevant (from 50 nm to over 1 μm) microstructural size range as that available for materials which scatter isotropically.

The size distribution and volume fraction of Cr23C6 precipitates in 9Cr-1MoVNb steel have been isolated from the distributions of all other precipitates by the technique of anomalous small-angle X-ray scattering. Three X-ray wavelengths near the Cr K absorption edge were used to vary the scattering contrast of Cr23C6 while that of the other precipitates was left unchanged. Size distributions calculated from each scattering curve using a maximum entropy method were combined by a scattering contrast gradient analysis to isolate the volume-fraction size distribution of the chromium carbides. Behavior of these carbides was studied as a function of isothermal aging temperature. Mean diameter is smallest and Cr23C6 number density is highest after aging at 811 K. Above 811 K, the mean diameter of the chromium carbides increases with increasing aging temperature.

The design and operation of a new small-angle X-ray scattering instrument, optimized for high throughput at a synchrotron source, high angular and wavelength resolution, large sample cross-sectional area, accurate energy tuning, excellent signal-to-noise ratio and harmonic rejection are presented. The principles of design and implementation are given, as are the details of primary calibration of absolute intensity and experimental desmearing. The instrument has been tested for application to anomalous-scattering measurements near the chromium K edge. Preliminary results on samples of a heat-treated steel are presented as a demonstration of the capability of this experiment to separate the microstructure evolution as a function of temperature of a chromium-rich precipitate from the thermal behavior of other precipitates in the steel.

Phonons are the fundamental quanta of lattice vibration in a solid. They play a critical role in phenomena such as superconductivity and many types of phase transitions, and are the basis for the acoustic, thermal, elastic, and infrared properties of solids [1]. A fundamental description of phonons is the dispersion relation, which is determined traditionally through neutron scattering [2 ‐4] or, more recently, through inelastic x-ray scattering [5]. However, these methods can be technically demanding, and alternative, complementary methods have been long sought. This study demonstrates a new approach based on x-ray intensity patterns produced by scattering from thermally populated phonons using silicon as a test case. Intensity patterns with a wide dynamic range were recorded in a matter of seconds at the third-generation synchrotron, the Advanced Photon Source. A least-squares analysis in terms of lattice dynamics yields dispersions for all six phonon branches in excellent agreement with neutron scattering results. The fast data acquisition rate, simplicity of the

Small-angle X-ray and small-angle neutron scattering measurements were carried out on a series of porous silica precursor (unsintered) bodies with different starting chemistries. The samples were prepared from mixtures containing 10 to 30 wt% colloidal silica sol and 90 to 70 wt% potassium silicate. Particle-size distributions were derived from the data using a maximum-entropy technique. Scattering data from the porous silica samples are especially suitable for such an analysis because the colloidal particles and clusters and aggregates of these particles are verified in detail to be spherical, and the scattering instrument use for this study covered the entire range of sizes in this material and was very well calibrated. It was found that the lower the amount of colloidal silica, the broader the size distribution of the silica aggregates.

We observe large-scale structures in hydrogels of poly(l-lactide)-poly(ethylene oxide)-poly(l-lactide) (PLLA-PEO-PLLA) ranging in size from a few hundred nanometers to several micrometers. These structures are apparent through both ultra-small angle scattering (USAS) techniques and confocal microscopy. The hydrogels showed power law scattering in the USAS regime, which is indicative of scattering from fractal structures. The fractal dimension of the scattering from hydrogels revealed that the gels have large size aggregates with a mass fractal structure over the nanometer-to-micrometer length scales. The aggregates also seem to become more "dense" with an increase in the molecular weight of crystalline PLLA domains. Visualization through confocal microscopy confirms that the gels have a microstructure of interspersed micrometer-sized polymer inhomogeneities with water channels running between them. The presence of micrometer-sized water channels in the hydrogels has very important implications for biomedical applications.

To determine the suitability of commonly used windows for small-angle X-ray scattering, a range of materials, including Kapton, (aluminized) Mylar, beryllium, high-purity aluminium foil, mica and silicon nitride have been studied. At small wavevector transfers, Q, in the range 2 x 10(-3) to 0.2 nm(-1), the scattering from Kapton, mica and beryllium is reasonably well described by power laws in Q with exponents of -3.25, -3.6 and -3.9, respectively. There are large variations in the scattering from mica, but a freshly cleaved natural mica window was by far the weakest scatterer. For applications where radiation in the infrared or visible range should be blocked, aluminized Mylar is the most suitable material. Both Mylar and Kapton can be used to make very simple demountable superfluid-tight windows using indium O-ring seals.

This paper describes the further development of a scene simulation model to include the phenomenology of scattering. Scattering gives rise to increased absorption within media and forward and backscatter leads to a modification of the subject illumination. The amount of scattering from objects is linked to the relation between the radiation wavelength and the composition of the objects. When the object surface roughness and the particulate composition is of the order of the radiation wavelength, scattering dominates. However, for longer wavelengths, reflections tend to be more specular in character and the wave propagating within the medium retains the spatial coherence. Imaging of people and man made objects in the low frequency band of the millimetre wave region appears to be associated with this longer wavelength regime. However, in moving up in frequency to the sub-millimetre wave band, the fibrous composition of clothing and hair is likely to change this imaging phenomenology. This paper investigates how scattering phenomena can be included in polarimetric scene simulation. Simulated images are shown for passive and active imaging to demonstrate the scattering phenomenology.

We have measured the small angle x‐ray scattering from Kapton and Mylar films used as cryostat windows. Both Mylar and Kapton can be used to make very simple, demountable, superfluid tight windows using indium o‐ring seals. Aluminized Mylar offers the advantage of effectively blocking infrared radiation while simultaneously reducing helium diffusion rates at room temperature by a factor of 25.

The UNICAT collaboration at the APS has constructed an insertion device beamline facility to support fundamental research in advanced materials and condensed matter physics. The primary research techniques used by UNICAT members include structural crystallography, diffuse x-ray scattering, magnetic x-ray scattering, ultra-small-angle x-ray scattering, micro-beam scattering, inelastic x-ray scattering and spectroscopy, surface and interface scattering, coherent x-ray diffraction, and time-resolved techniques. To support these advanced x-ray techniques for a diverse scientific community, we chose a liquid-nitrogen cooled Si (111) double crystal monochromator, and a pair of coated, striped mirrors. Important parameters considered in the design of the beamline are x-ray flux, energy range and bandwidth, source demagnification, and harmonic contamination. The APS type A undulator is used to produce high-brilliance X-rays between 4 and 40 KeV. We achieve sagittal focusing by dynamically bending the monochromator second crystal, and meridional focusing by cylindrically bending one of the flat mirrors. The resulting x-ray beam delivered to the experimental stations can be focused, unfocused, or collimated. The overall design of this beamline layout and the major beamline components are described, and its performance is discussed with respect to impact on the scientific programs proposed for the facility.

A photodiode X-ray detector was built to measure small-angle X-ray scattering (SAXS) at a synchrotron-radiation source in conjunction with a double-crystal diffractometer SAXS camera at photon energies between 5 and 11 keV. The photodiode detector response in this energy range is linear at photon counting rates up to 1012 photons s−1 and thus it was not necessary to attenuate the monochromatic X-ray beam with calibrated foils. SAXS data taken with a scintillation counter and the photodiode detector are compared, demonstrating marked improvement in counting statistics, rate of data acquisition and signal-to-noise ratio.

Ultra-small-angle x-ray scattering provides quantitative and statistically significant information on the size distribution of electron density inhomogeneities with dimensions between ≈100 Å and ≈5 μm. All sizes are sampled simultaneously with a single experiment, removing the possibility of observational bias. In a material such as commercial silicon nitride, where the inhomogeneities are due to populations of intergranular secondary phases and voids of similar dimensions, the scattering contains contributions from each individual population. A single USAXS scan cannot separate overlapping populations of scatterers due to the different contrasts of the microstructural components. Anomalous USAXS (A-USAXS) is an elementspecific contrast variation method to vary the scattering contribution from one of the populations while holding that of the other populations fixed. To follow the size evolution under tensile creep of both the cavities and the Yb disilicate secondary phases, A-USAXS data was measured near the Yb LIII absorption edge. Creep cavity and disilicate size distributions were each determined as a function of deformation.

Anomalous small-angle x-ray scattering (ASAXS) experiments were performed at energies near the Mn-K and Fe-K absorption edges on an Fe-0.9 Cu wt.%-1.0 Mn wt.% alloy subjected to either annealing at 450°C, 24 hrs or irradiation with 10 MeV electrons to 0.5 mdpa at 300°C. A Guinier analysis of the net scattered intensity revealed scatterers with radii of 16.5.16.8 Å and 16.4.17.3 Å for the irradiated and annealed foils, respectively. The variation in net scattered intensity with photon energy in the annealed sample was consistent with scattering contrast variations expected for Cu-rich, Cu-Mn precipitates. Minimal variation in net intensity (scattering contrast) with energy determined that Cu-Mn precipitates were not detected in the irradiated sample.

The formation of Al nanocrystals from an amorphous Al92Sm8 alloy involves kinetic phenomena with very different characteristic length and timescales, including initial nucleation and later growth and coarsening. Insight into these processes can be derived from the evolution of the sizes of nanocrystals as a function of time. Synchrotron small angle x-ray scattering (SAXS) experiments provide information about the evolution of the nanocrystal size distribution, particularly at times after nucleation has reached saturation. Accurately interpreting the distribution of intensity measured using SAXS requires a nanoparticle model consisting of nanocrystalline core of pure Al surrounded by a shell enriched in Sm. With this approach, statistical parameters derived from SAXS are independent of detailed assumptions regarding the distribution of Sm around the nanocrystals and allow the maximum radius of nanocrystals within the distribution to be determined unambiguously. Sizes determined independently using transmis...

Diesel soot powder generated under idle and load engine conditions was pressed into pellets at pressures ranging up to approximately 8.5 GPa. Soot powder was also immersed in acetone in order to obtain soot aggregates without agglomeration. Small-angle x-ray scattering was carried out on the powder, the pellets, and on the acetone-immersed soot. Powder and pellets show characteristic aggregate structure at small scattering vectors. Scattering curves of the pellets show a shift of the aggregate size-related scattering feature towards larger scattering vectors for increasing pressure. For the highest pressures, this aggregate structure vanished, while the suspected primary particle scattering became visible as the asymptote of the aggregate scattering structure. Soot was immersed and ultrasonicated in acetone to prevent agglomeration of aggregates, which naturally occurs in powders. This can be considered as the simulation of asymptotic behavior for vanishing pressure. Aggregate size of powder was about 290...