Quantitative nanotomography of amorphous and polycrystalline samples using coherent X-ray diffraction

This article presents a combined approach where quantitative forward-scattering coherent diffraction imaging (CDI) is supported by crystal diffraction using 8.1 keV synchrotron X-ray radiation. The method allows the determination of the morphology, mass density and crystallinity of an isolated microscopic specimen. This approach is tested on three homogeneous samples made of different materials with different degrees of crystallinity. The mass density and morphology are revealed using three-dimensional coherent diffraction imaging with a resolution better than 36 nm. The crystallinity is extracted from the diffraction profiles measured simultaneously with coherent diffraction patterns. The presented approach extends CDI to structural characterization of samples when crystallinity aspects are of interest.

Experimental 3D coherent diffractive imaging from photon-sparse random projections

The routine atomic resolution structure determination of single particles is expected to have profound implications for probing structure-function relationships in systems ranging from energy-storage materials to biological molecules. Extremely bright ultrashort-pulse X-ray sources - X-ray free-electron lasers (XFELs) - provide X-rays that can be used to probe ensembles of nearly identical nanoscale particles. When combined with coherent diffractive imaging, these objects can be imaged; however, as the resolution of the images approaches the atomic scale, the measured data are increasingly difficult to obtain and, during an X-ray pulse, the number of photons incident on the 2D detector is much smaller than the number of pixels. This latter concern, the signal 'sparsity', materially impedes the application of the method. An experimental analog using a conventional X-ray source is demonstrated and yields signal levels comparable with those expected from single biomolecules illuminated by focused XFEL pulses. The analog experiment provides an invaluable cross check on the fidelity of the reconstructed data that is not available during XFEL experiments. Using these experimental data, it is established that a sparsity of order 1.3 × 10-3 photons per pixel per frame can be overcome, lending vital insight to the solution of the atomic resolution XFEL single-particle imaging problem by experimentally demonstrating 3D coherent diffractive imaging from photon-sparse random projections.

X-ray nanotomography of coccolithophores reveals that coccolith mass and segment number correlate with grid size

Coccolithophores of the Noëlaerhabdaceae family are covered by imbricated coccoliths, each composed of multiple calcite crystals radially distributed around the periphery of a grid. The factors that determine coccolith size remain obscure. Here, we used synchrotron-based three-dimensional Coherent X-ray Diffraction Imaging to study coccoliths of 7 species of Gephyrocapsa, Emiliania and Reticulofenestra with a resolution close to 30 nm. Segmentation of 45 coccoliths revealed remarkable size, mass and segment number variations, even within single coccospheres. In particular, we observed that coccolith mass correlates with grid perimeter which scales linearly with crystal number. Our results indirectly support the idea that coccolith mass is determined in the coccolith vesicle by the size of the organic base plate scale (OBPS) around which R-unit nucleation occurs every 110–120 nm. The curvation of coccoliths allows inference of a positive correlation between cell nucleus, OBPS and coccolith sizes.

Coccolithophores are one of the most abundant phytoplankton and calcifying organisms, well-known to produce intricate calcareous exoskeletons made of coccoliths. Here the authors show, by using X-ray nanotomography, the dependence of the grid size on the calcite nucleation site number and on the mass of coccoliths.

Silica nanoparticles as tracers of the gelation dynamics of a natural biopolymer physical gel

The gelation of methylcellulose in water has been studied by X-ray photon correlation spectroscopy, electrophoresis and rheological measurements by looking into the dynamics of silica nanoparticles as tracers in the polymer matrix. The temperature and scattering vector dependence of the structural relaxation time is investigated at the nanometric length scale during the formation of the strong gel state. We find a stress-dominated dynamics on approaching the gel state, characterized by a hyper-diffusive motion of the silica particles. These results support the idea of a unifying scenario for the dynamics of complex out of equilibrium soft materials.

Three-dimensional coherent diffractive imaging on non-periodic specimens at the ESRF beamline ID10

The progress of tomographic coherent diffractive imaging with hard X-rays at the ID10 beamline of the European Synchrotron Radiation Facility is presented. The performance of the instrument is demonstrated by imaging a cluster of Fe2P magnetic nanorods at 59 nm 3D resolution by phasing a diffraction volume measured at 8 keV photon energy. The result obtained shows progress in three-dimensional imaging of non-crystalline samples in air with hard X-rays.

Upsampling speckle patterns for coherent X-ray diffraction imaging

Coherent X-ray diffraction imaging is a lensless imaging technique where an iterative phase-retrieval algorithm is applied to the speckle pattern, the far-field diffraction pattern produced by an isolated object. To ensure convergence to a unique solution, the diffraction pattern must be oversampled by a factor of two or more. Since the resolution in real space depends on the maximum wave vector where the intensity is detected,i.e.on the detector field of view, there is a practical limitation on oversampling in reciprocal space and resolution in real space that is ultimately determined by the number of pixels. This work shows that it is possible to reduce the effective pixel size and maintain the detector field of view by applying a linear combination method to shifted diffraction patterns. The feasibility of the method is demonstrated by reconstructing the images of test objects from diffraction patterns oversampled in each dimension by factors of 1.3 and 1.8 only. The described approach can be applied to any diffraction or imaging technique where the resolution is compromised by a large pixel size.

Photon correlation spectroscopy with high-energy coherent x rays

We performed x-ray photon correlation spectroscopy on a model suspension of colloidal particles using x rays of three different energies, namely, 8 keV, 13.5 keV, and 19 keV. The observed reduction in the degree of coherence with increasing x-ray energy, as measured by the contrast of the correlation functions, is consistent with theoretical estimates. We show that it is well possible and under certain circumstances even advantageous to perform experiments with coherent x rays at these higher energies. We argue that the reduced absorption may not only allow for thicker samples but also for longer acquisition times because of the reduced radiation damage, thus outweighing in many cases the effect of the reduced coherent flux. The use of higher energy x rays for photon correlation spectroscopy can therefore lead to a substantial increase in the signal-to-noise ratio and constitutes a promising option for future experiments on samples of polymeric or biological origin.

Microfocusing of hard X-rays with cylindrically bent crystal monochromators

High-energy X-ray focusing with bent-crystal monochromators is known to be hampered by so-called depth or crystal-thickness aberrations. A theoretical model of focus broadening based on the geometrical theory of X-ray diffraction in slightly deformed crystals is presented and compared with experimental data. First, it is shown that depth broadening can be avoided in the Laue geometry by an appropriate choice of asymmetry angle. Based on this finding, a monochromator for high-pressure diffraction experiments has been designed and a source-size-limited focal spot below 10 microns is observed. As a consequence of the box-shaped rocking curve of bent Laue crystals, the focus is free of long-ranging tails. Diffraction patterns of standard powder samples were recorded on imaging plates and a theoretical description of the energy-dispersion-related peak broadening is given. Finally, diffraction patterns of N2 at 180 kbar demonstrate the excellent data quality achievable with this monochromator.

Laue orientation imaging

Advantage was taken of the highly focused X-ray beam (10-30 microm) and the broad white spectrum of synchrotron X-rays at the ESRF for automatic recording of Laue patterns from polycrystals and extraction of orientation information. The procedure used is similar to that applied for electron-backscattering patterns in the scanning electron microscope and provides data for local orientation mapping used in texture analysis. Laue patterns are obtained from a thin slice of material in transmission and recorded with a CCD detector. The Laue geometry is converted into a gnomonic projection in which co-zonal reflections lie on straight lines. On applying the Hough transform these lines are merged into a single point, which is recognized by the computer and assigned zone indices [uvw] by comparison with a table of interzonal angles. From the angular positions of several [uvw] the crystal orientation is calculated. The method is illustrated for the orthorhombic magnesium silicate olivine.

New features of dislocation images in third-generation synchrotron radiation topographs

Some aspects of the dislocation contrast observed at third-generation synchrotron radiation set-ups are presented. They can be explained by taking into account angular deviation effects on the beam propagation, which are visible because of the ;almost plane-wave' character of these sources. In particular, we show how the evolution of the direct image width of a dislocation as a function of the sample-to-film distance can allow a complete determination of the Burgers vector, i.e. in sign and modulus. In addition, experimental results obtained in monochromatic beam topography are compared with simulated images calculated assuming plane-wave illumination and are demonstrated to show a satisfactory agreement. The utility of the weak-beam technique in enhancing the spatial resolution is demonstrated and a criterion for the selection of experimental conditions depending upon the required spatial resolution, signal-to-noise ratio and exposure time is presented.