Mapping the 3D position of battery cathode particles in Bragg coherent diffractive imaging.

In Bragg coherent diffractive imaging, the precise location of the measured crystals in the interior of the sample is usually missing. Obtaining this information would help the study of the spatially dependent behavior of particles in the bulk of inhomogeneous samples, such as extra-thick battery cathodes. This work presents an approach to determine the 3D position of particles by precisely aligning them at the instrument axis of rotation. In the test experiment reported here, with a 60 µm-thick LiNi0.5Mn1.5O4 battery cathode, the particles were located with a precision of 20 µm in the out-of-plane direction, and the in-plane coordinates were determined with a precision of 1 µm.

Inhomogeneity of charge-density-wave order and quenched disorder in a high-Tc superconductor.

It has recently been established that the high-transition-temperature (high-Tc) superconducting state coexists with short-range charge-density-wave order and quenched disorder arising from dopants and strain. This complex, multiscale phase separation invites the development of theories of high-temperature superconductivity that include complexity. The nature of the spatial interplay between charge and dopant order that provides a basis for nanoscale phase separation remains a key open question, because experiments have yet to probe the unknown spatial distribution at both the nanoscale and mesoscale (between atomic and macroscopic scale). Here we report micro X-ray diffraction imaging of the spatial distribution of both short-range charge-density-wave 'puddles' (domains with only a few wavelengths) and quenched disorder in HgBa2CuO4 + y, the single-layer cuprate with the highest Tc, 95 kelvin (refs 26-28). We found that the charge-density-wave puddles, like the steam bubbles in boiling water, have a fat-tailed size distribution that is typical of self-organization near a critical point. However, the quenched disorder, which arises from oxygen interstitials, has a distribution that is contrary to the usually assumed random, uncorrelated distribution. The interstitial-oxygen-rich domains are spatially anticorrelated with the charge-density-wave domains, because higher doping does not favour the stripy charge-density-wave puddles, leading to a complex emergent geometry of the spatial landscape for superconductivity.

Structural studies of the bond-orientational order and hexatic-smectic transition in liquid crystals of various compositions.

We report on the X-ray studies of freely suspended hexatic films of three different liquid crystal compounds. By applying angular X-ray cross-correlation analysis (XCCA) to the measured diffraction patterns the parameters of the bond-orientational (BO) order in the hexatic phase were directly determined. The temperature evolution of the BO order parameters was analyzed on the basis of the multicritical scaling theory (MCST). Our results confirmed the validity of the MCST in the whole temperature range of the existence of the hexatic phase for all three compounds. The temperature dependence of the BO order parameters in the vicinity of the hexatic-smectic transition was fitted by a conventional power law with a critical exponent ß ≈ 0.1 of extremely small value. We found that the temperature dependence of higher order harmonics of the BO order scales as the powers of the first harmonic, with an exponent equal to the harmonic number. This indicates a nonlinear coupling of the BO order parameters of different order. We demonstrate that compounds of various compositions, possessing different phase sequences at low temperatures, display the same thermodynamic behavior in the hexatic phase and in the vicinity of the smectic-hexatic phase transition.

Revealing Three-Dimensional Structure of an Individual Colloidal Crystal Grain by Coherent X-Ray Diffractive Imaging.

We present results of a coherent x-ray diffractive imaging experiment performed on a single colloidal crystal grain. The full three-dimensional (3D) reciprocal space map measured by an azimuthal rotational scan contained several orders of Bragg reflections together with the coherent interference signal between them. Applying the iterative phase retrieval approach, the 3D structure of the crystal grain was reconstructed and positions of individual colloidal particles were resolved. As a result, an exact stacking sequence of hexagonal close-packed layers including planar and linear defects were identified.

Colloidal crystallite suspensions studied by high pressure small angle x-ray scattering.

We report on high pressure small angle x-ray scattering on suspensions of colloidal crystallites in water. The crystallites made out of charge-stabilized poly-acrylate particles exhibit a complex pressure dependence which is based on the specific pressure properties of the suspending medium water. The dominant effect is a compression of the crystallites caused by the compression of the water. In addition, we find indications that also the electrostatic properties of the system, i.e. the particle charge and the dissociation of ions, might play a role for the pressure dependence of the samples. The data further suggest that crystallites in a metastable state induced by shear-induced melting can relax to a similar structural state upon the application of pressure and dilution with water. X-ray cross correlation analysis of the two-dimensional scattering patterns indicates a pressure-dependent increase of the orientational order of the crystallites correlated with growth of these in the suspension. This study underlines the potential of pressure as a very relevant parameter to understand colloidal crystallite systems in aqueous suspension.

Tomography of a Cryo-immobilized Yeast Cell Using Ptychographic Coherent X-Ray Diffractive Imaging.

The structural investigation of noncrystalline, soft biological matter using x-rays is of rapidly increasing interest. Large-scale x-ray sources, such as synchrotrons and x-ray free electron lasers, are becoming ever brighter and make the study of such weakly scattering materials more feasible. Variants of coherent diffractive imaging (CDI) are particularly attractive, as the absence of an objective lens between sample and detector ensures that no x-ray photons scattered by a sample are lost in a limited-efficiency imaging system. Furthermore, the reconstructed complex image contains quantitative density information, most directly accessible through its phase, which is proportional to the projected electron density of the sample. If applied in three dimensions, CDI can thus recover the sample's electron density distribution. As the extension to three dimensions is accompanied by a considerable dose applied to the sample, cryogenic cooling is necessary to optimize the structural preservation of a unique sample in the beam. This, however, imposes considerable technical challenges on the experimental realization. Here, we show a route toward the solution of these challenges using ptychographic CDI (PCDI), a scanning variant of coherent imaging. We present an experimental demonstration of the combination of three-dimensional structure determination through PCDI with a cryogenically cooled biological sample--a budding yeast cell (Saccharomyces cerevisiae)--using hard (7.9 keV) synchrotron x-rays. This proof-of-principle demonstration in particular illustrates the potential of PCDI for highly sensitive, quantitative three-dimensional density determination of cryogenically cooled, hydrated, and unstained biological matter and paves the way to future studies of unique, nonreproducible biological cells at higher resolution.

Suspensions of polymer-grafted nanoparticles with added polymers-Structure and effective pair-interactions.

We present the results of combined experimental and theoretical (molecular dynamics simulations and integral equation theory) studies of the structure and effective interactions of suspensions of polymer grafted nanoparticles (PGNPs) in the presence of linear polymers. Due to the absence of systematic experimental and theoretical studies of PGNPs, it is widely believed that the structure and effective interactions in such binary mixtures would be very similar to those of an analogous soft colloidal material-star polymers. In our study, polystyrene-grafted gold nanoparticles with functionality f = 70 were mixed with linear polystyrene (PS) of two different molecular weights for obtaining two PGNP:PS size ratios, ξ = 0.14 and 2.76 (where, ξ = Mg/Mm, Mg and Mm being the molecular weights of grafting and matrix polymers, respectively). The experimental structure factor of PGNPs could be modeled with an effective potential (Model-X), which has been found to be widely applicable for star polymers. Similarly, the structure factor of the blends with ξ = 0.14 could be modeled reasonably well, while the structure of blends with ξ = 2.76 could not be captured, especially for high density of added polymers. A model (Model-Y) for effective interactions between PGNPs in a melt of matrix polymers also failed to provide good agreement with the experimental data for samples with ξ = 2.76 and high density of added polymers. We tentatively attribute this anomaly in modeling the structure factor of blends with ξ = 2.76 to the questionable assumption of Model-X in describing the added polymers as star polymers with functionality 2, which gets manifested in both polymer-polymer and polymer-PGNP interactions especially at higher fractions of added polymers. The failure of Model-Y may be due to the neglect of possible many-body interactions among PGNPs mediated by matrix polymers when the fraction of added polymers is high. These observations point to the need for a new framework to understand not only the structural behavior of PGNPs but also possibly their dynamics and thermo-mechanical properties as well.

Direct measurement of antiferromagnetic domain fluctuations.

Measurements of magnetic noise emanating from ferromagnets owing to domain motion were first carried out nearly 100 years ago, and have underpinned much science and technology. Antiferromagnets, which carry no net external magnetic dipole moment, yet have a periodic arrangement of the electron spins extending over macroscopic distances, should also display magnetic noise. However, this must be sampled at spatial wavelengths of the order of several interatomic spacings, rather than the macroscopic scales characteristic of ferromagnets. Here we present a direct measurement of the fluctuations in the nanometre-scale superstructure of spin- and charge-density waves associated with antiferromagnetism in elemental chromium. The technique used is X-ray photon correlation spectroscopy, where coherent X-ray diffraction produces a speckle pattern that serves as a 'fingerprint' of a particular magnetic domain configuration. The temporal evolution of the patterns corresponds to domain walls advancing and retreating over micrometre distances. This work demonstrates a useful measurement tool for antiferromagnetic domain wall engineering, but also reveals a fundamental finding about spin dynamics in the simplest antiferromagnet: although the domain wall motion is thermally activated at temperatures above 100 K, it is not so at lower temperatures, and indeed has a rate that saturates at a finite value-consistent with quantum fluctuations-on cooling below 40 K.

Sub-10 nm beam confinement by X-ray waveguides: design, fabrication and characterization of optical properties.

The propagation of hard X-ray synchrotron beams in waveguides with guiding layer diameters in the 9-35 nm thickness range has been studied. The planar waveguide structures consist of an optimized two-component cladding. The presented fabrication method is suitable for short and leak-proof waveguide slices with lengths (along the optical axis) in the sub-500 µm range, adapted for optimized transmission at photon energies of 11.5-18 keV. A detailed comparison between finite-difference simulations of waveguide optics and the experimental results is presented, concerning transmission, divergence of the waveguide exit beam, as well as the angular acceptance. In a second step, two crossed waveguides have been used to create a quasi-point source for propagation-based X-ray imaging at the new nano-focus endstation of the P10 coherence beamline at Petra III. By inverting the measured Fraunhofer diffraction pattern by an iterative error-reduction algorithm, a two-dimensional focus of 10 nm × 10 nm is obtained. Finally, holographic imaging of a lithographic test structure based on this optical system is demonstrated.

Microfocusing transfocator for 1D and 2D compound refractive lenses.

An x-ray transfocator design for the combined use of 1D and 2D compound refractive lenses is described. The device includes stacks of beryllium parabolic lenses with different radii of curvature and provides microfocused x-ray beams in the 4-20 keV photon energy range. The transfocator has been implemented at the P10 Coherence Beamline of the PETRA III synchrotron at DESY, Hamburg. Results of transfocator performance and applications for coherent x-ray scattering experiments are presented.

Three-dimensional structure of a single colloidal crystal grain studied by coherent x-ray diffraction.

A coherent x-ray diffraction experiment was performed on an isolated colloidal crystal grain at the coherence beamline P10 at PETRA III. Using azimuthal rotation scans the three-dimensional (3D) scattered intensity from the sample in the far-field was measured. It includes several Bragg peaks as well as the coherent interference around these peaks. The analysis of the scattered intensity reveals the presence of plane defects in a single grain of the colloidal sample. We confirm these findings by model simulations. In these simulations we also analyze the experimental conditions required to phase the 3D diffraction pattern from a single colloidal grain. This approach has the potential to produce a high resolution image of the sample revealing its inner structure, with possible structural defects.

Single shot spatial and temporal coherence properties of the SLAC Linac Coherent Light Source in the hard x-ray regime.

We measured the transverse and longitudinal coherence properties of the Linac Coherent Light Source (LCLS) at SLAC in the hard x-ray regime at 9 keV photon energy on a single shot basis. Speckle patterns recorded in the forward direction from colloidal nanoparticles yielded the transverse coherence properties of the focused LCLS beam. Speckle patterns from a gold nanopowder recorded with atomic resolution allowed us to measure the shot-to-shot variations of the spectral properties of the x-ray beam. The focused beam is in the transverse direction fully coherent with a mode number close to 1. The average number of longitudinal modes behind the Si(111) monochromator is about 14.5 and the average coherence time τ(c)=(2.0±1.0) fc. The data suggest a mean x-ray pulse duration of (29±14) fs behind the monochromator for (100±14) fc electron pulses.

Gelation Dynamics upon Pressure-Induced Liquid-Liquid Phase Separation in a Water-Lysozyme Solution.

Employing X-ray photon correlation spectroscopy, we measure the kinetics and dynamics of a pressure-induced liquid-liquid phase separation (LLPS) in a water-lysozyme solution. Scattering invariants and kinetic information provide evidence that the system reaches the phase boundary upon pressure-induced LLPS with no sign of arrest. The coarsening slows down with increasing quench depths. The g2 functions display a two-step decay with a gradually increasing nonergodicity parameter typical for gelation. We observe fast superdiffusive (γ ≥ 3/2) and slow subdiffusive (γ < 0.6) motion associated with fast viscoelastic fluctuations of the network and a slow viscous coarsening process, respectively. The dynamics age linearly with time τ ∝ tw, and we observe the onset of viscoelastic relaxation for deeper quenches. Our results suggest that the protein solution gels upon reaching the phase boundary.

X-ray near-field speckle: implementation and critical analysis.

The newly introduced coherence-based technique of X-ray near-field speckle (XNFS) has been implemented at 8-ID-I at the Advanced Photon Source. In the near-field regime of high-brilliance synchrotron X-rays scattered from a sample of interest, it turns out that, when the scattered radiation and the main beam both impinge upon an X-ray area detector, the measured intensity shows low-contrast speckles, resulting from interference between the incident and scattered beams. A micrometer-resolution XNFS detector with a high numerical aperture microscope objective has been built and its capability for studying static structures and dynamics at longer length scales than traditional far-field X-ray scattering techniques is demonstrated. Specifically, the dynamics of dilute silica and polystyrene colloidal samples are characterized. This study reveals certain limitations of the XNFS technique, especially in the characterization of static structures, which is discussed.

Partially coherent nano-focused x-ray radiation characterized by Talbot interferometry.

We have studied the spatial coherence properties of a nano-focused x-ray beam by grating (Talbot) interferometry in projection geometry. The beam is focused by a fixed curvature mirror system optimized for high flux density under conditions of partial coherence. The spatial coherence of the divergent exit wave emitted from the mirror focus is measured by Talbot interferometry The results are compared to numerical calculations of coherence propagation. In view of imaging applications, the magnified in-line image of a test pattern formed under conditions of partial coherence is analyzed quantitatively. Finally, additional coherence filtering by use of x-ray waveguides is demonstrated. By insertion of x-ray waveguides, the beam diameter can be reduced from typical values of 200 nm to values below 15 nm. In proportion to the reduction in the focal spot size, the numerical aperture (NA) of the projection imaging system is increased, as well as the coherence length, as quantified by grating interferometry.

Kinoform optics applied to X-ray photon correlation spectroscopy.

Moderate-demagnification higher-order silicon kinoform focusing lenses have been fabricated to facilitate small-angle X-ray photon correlation spectroscopy (XPCS) experiments. The geometric properties of such lenses, their focusing performance and their applicability for XPCS measurements are described. It is concluded that one-dimensional vertical X-ray focusing via silicon kinoform lenses significantly increases the usable coherent flux from third-generation storage-ring light sources for small-angle XPCS experiments.

A bi-prism interferometer for hard X-ray photons.

Micro-fabricated bi-prisms have been used to create an interference pattern from an incident hard X-ray beam, and the intensity of the pattern probed with fluorescence from a 30 nm-thick metal film. Maximum fringe visibility exceeded 0.9 owing to the nano-sized probe and the choice of single-crystal prism material. A full near-field analysis is necessary to describe the fringe field intensities, and the transverse coherence lengths were extracted at APS beamline 8-ID-I. It is also shown that the maximum number of fringes is dependent only on the complex refractive index of the prism material.

Microscopic pathways for stress relaxation in repulsive colloidal glasses.

Residual stresses are well-known companions of all glassy materials. They affect and, in many cases, even strongly modify important material properties like the mechanical response and the optical transparency. The mechanisms through which stresses affect such properties are, in many cases, still under study, and their full understanding can pave the way to a full exploitation of stress as a primary control parameter. It is, for example, known that stresses promote particle mobility at small length scales, e.g., in colloidal glasses, gels, and metallic glasses, but this connection still remains essentially qualitative. Exploiting a preparation protocol that leads to colloidal glasses with an exceptionally directional built-in stress field, we characterize the stress-induced dynamics and show that it can be visualized as a collection of "flickering," mobile regions with linear sizes of the order of ≈20 particle diameters (≈2 µm here) that move cooperatively, displaying an overall stationary but locally ballistic dynamics.

Surface X-ray speckles: coherent surface diffraction from Au(001).

We present coherent speckled x-ray diffraction patterns obtained from a monolayer of surface atoms. We measured both the specular anti-Bragg reflection and the off-specular hexagonal reconstruction peak for the Au(001) surface reconstruction. We observed fluctuations of the speckle patterns even when the integrated intensity appears static. By autocorrelating the speckle patterns, we were able to identify two qualitatively different surface dynamic behaviors of the hex reconstruction depending on the sample temperature.

Morphological transitions in polymer monolayers under compression.

We present a systematic investigation of morphological transitions in poly vinylacetate Langmuir monolayers. On compression, the polymer monolayer is converted to a continuous membrane with a thickness of approximately 2-3 nm. Above a certain surface concentration the monolayer, on water, undergoes a morphological transition-buckling, leading to formation of striped patterns of period of lambda(b) approximately 160 nm, as determined from in situ grazing incidence small angle x-ray scattering measurements. The obtained value is much smaller than what has been typically observed for Langmuir monolayers on water or thin films on soft substrates. Using existing theories for buckling of fluidlike films on fluid substrates, we obtain very low values of bending rigidity and Young's modulus of the polymer monolayer compared to that observed earlier for lipid or polymeric monolayers. Since buckling in these monolayers occurs only above a certain surface concentration, we have looked at the possibility that the buckling in these films occurs due to changes in their mechanical properties under compression. Using the model of Huang and Suo of buckling of solidlike films on viscoelastic substrates, we find values of the mechanical properties, which are much closer to the bulk values but still significantly lower. Although the reduction could be along the lines of what has been observed earlier for ultrathin polymer film or surface layers of polymers, the possibility of micromechanical effects also determining the buckling in such polymer monolayers cannot be ruled out. We have provided possible explanation of the buckling of the poly vinylacetate monolayers in terms of the change in isothermal compression modulus with surface concentration.