Multiple-energy x-ray holography: Atomic images of hematite (Fe2O3)

On incoherent diffractive imaging

Incoherent diffractive imaging (IDI) promises structural analysis with atomic resolution based on intensity interferometry of pulsed X-ray fluorescence emission. However, its experimental realization is still pending and a comprehensive theory of contrast formation has not been established to date. Explicit expressions are derived for the equal-pulse two-point intensity correlations, as the principal measured quantity of IDI, with full control of the prefactors, based on a simple model of stochastic fluorescence emission. The model considers the photon detection statistics, the finite temporal coherence of the individual emissions, as well as the geometry of the scattering volume. The implications are interpreted in view of the most relevant quantities, including the fluorescence lifetime, the excitation pulse, as well as the extent of the scattering volume and pixel size. Importantly, the spatiotemporal overlap between any two emissions in the sample can be identified as a crucial factor limiting the contrast and its dependency on the sample size can be derived. The paper gives rigorous estimates for the optimum sample size, the maximum photon yield and the expected signal-to-noise ratio under optimal conditions. Based on these estimates, the feasibility of IDI experiments for plausible experimental parameters is discussed. It is shown in particular that the mean number of photons per detector pixel which can be achieved with X-ray fluorescence is severely limited and as a consequence imposes restrictive constraints on possible applications.

Reconstruction of evolving nanostructures in ultrathin films with X-ray waveguide fluorescence holography

Controlled synthesis of nanostructure ultrathin films is critical for applications in nanoelectronics, photonics, and energy generation and storage. The paucity of structural probes that are sensitive to nanometer-thick films and also capable of in-operando conditions with high spatiotemporal resolutions limits the understanding of morphology and dynamics in ultrathin films. Similar to X-ray fluorescence holography for crystals, where holograms are formed through the interference between the reference and the object waves, we demonstrated that an ultrathin film, being an X-ray waveguide, can also generate fluorescence holograms as a result of the establishment of X-ray standing waves. Coupled with model-independent reconstruction algorithms based on rigorous dynamical scattering theories, the thin-film-based X-ray waveguide fluorescence holography becomes a unique in situ and time-resolved imaging probe capable of elucidating the real-time nanostructure kinetics with unprecedented resolutions. Combined with chemical sensitive spectroscopic analysis, the reconstruction can yield element-specific morphology of embedding nanostructures in ultrathin films.

The authors introduce X-ray waveguide fluorescence holography based on the waveguiding properties of thin films. Combined with model-independent reconstruction algorithms, they show that the method can be used for real-time nanostructure kinetic studies.

Fast inside-source X-ray fluorescent holography

Atomic resolution X-ray holography can be realized by using the atoms of the sample as inside sources or inside detectors. However, until now there were only very few experiments in which the atoms played the role of inside sources. The reason is twofold: (i) technically, inside-detector experiments are much easier and faster; (ii) by using atoms as inside detectors one can measure holograms at many energies on the same sample, which helps the reconstruction. This paper shows that, using new technical developments, inside-source holograms can be taken much faster than inside-detector holograms and, by applying a sophisticated evaluation method, high-quality reconstruction from a single-energy hologram can also be obtained.

Hydrothermal synthesis, characterization and enhanced photocatalytic activity and toxicity studies of a rhombohedral Fe2O3nanomaterial

The present investigation focuses on the synthesis of metal oxide nanoparticles (MONPs)viaa facile hydrothermal route.

Size and Shape Controlled Crystallization of Hemoglobin for Advanced Crystallography

While high-throughput screening for protein crystallization conditions have rapidly evolved in the last few decades, it is also becoming increasingly necessary for the control of crystal size and shape as increasing diversity of protein crystallographic experiments. For example, X-ray crystallography (XRC) combined with photoexcitation and/or spectrophotometry requires optically thin but well diffracting crystals. By contrast, large-volume crystals are needed for weak signal experiments, such as neutron crystallography (NC) or recently developed X-ray fluorescent holography (XFH). In this article, we present, using hemoglobin as an example protein, some techniques for obtaining the crystals of controlled size, shape, and adequate quality. Furthermore, we describe a few case studies of applications of the optimized hemoglobin crystals for implementing the above mentioned crystallographic experiments, providing some hints and tips for the further progress of advanced protein crystallography.

Multiple-wavelength neutron holography with pulsed neutrons

Local structures around impurities in solids provide important information for understanding the mechanisms of material functions, because most of them are controlled by dopants. For this purpose, the x-ray absorption fine structure method, which provides radial distribution functions around specific elements, is most widely used. However, a similar method using neutron techniques has not yet been developed. If one can establish a method of local structural analysis with neutrons, then a new frontier of materials science can be explored owing to the specific nature of neutron scattering-that is, its high sensitivity to light elements and magnetic moments. Multiple-wavelength neutron holography using the time-of-flight technique with pulsed neutrons has great potential to realize this. We demonstrated multiple-wavelength neutron holography using a Eu-doped CaF₂ single crystal and obtained a clear three-dimensional atomic image around trivalent Eu substituted for divalent Ca, revealing an interesting feature of the local structure that allows it to maintain charge neutrality. The new holography technique is expected to provide new information on local structures using the neutron technique.

Development of an X-ray fluorescence holographic measurement system for protein crystals

Experimental procedure and setup for obtaining X-ray fluorescence hologram of crystalline metalloprotein samples are described. Human hemoglobin, an α2β2 tetrameric metalloprotein containing the Fe(II) heme active-site in each chain, was chosen for this study because of its wealth of crystallographic data. A cold gas flow system was introduced to reduce X-ray radiation damage of protein crystals that are usually fragile and susceptible to damage. A χ-stage was installed to rotate the sample while avoiding intersection between the X-ray beam and the sample loop or holder, which is needed for supporting fragile protein crystals. Huge hemoglobin crystals (with a maximum size of 8 × 6 × 3 mm(3)) were prepared and used to keep the footprint of the incident X-ray beam smaller than the sample size during the entire course of the measurement with the incident angle of 0°-70°. Under these experimental and data acquisition conditions, we achieved the first observation of the X-ray fluorescence hologram pattern from the protein crystals with minimal radiation damage, opening up a new and potential method for investigating the stereochemistry of the metal active-sites in biomacromolecules.

Direct Atom Imaging by Chemical-Sensitive Holography

In order to understand the physical and chemical properties of advanced materials, functional molecular adsorbates, and protein structures, a detailed knowledge of the atomic arrangement is essential. Up to now, if subsurface structures are under investigation, only indirect methods revealed reliable results of the atoms' spatial arrangement. An alternative and direct method is three-dimensional imaging by means of holography. Holography was in fact proposed for electron waves, because of the electrons' short wavelength at easily accessible energies. Further, electron waves are ideal structure probes on an atomic length scale, because electrons have a high scattering probability even for light elements. However, holographic reconstructions of electron diffraction patterns have in the past contained severe image artifacts and were limited to at most a few tens of atoms. Here, we present a general reconstruction algorithm that leads to high-quality atomic images showing thousands of atoms. Additionally, we show that different elements can be identified by electron holography for the example of FeS2.

X-ray holography with an atomic scatterer

X-ray holography scheme with reference scatterer consisting of heavy atom as reference center and its link to an object consisting of several light atoms and using controlled variation of the alignment is represented. The scheme can reproduce an object in three dimensions with atomic resolution. The distorting factors of reconstruction are considered.

Experimental phase determination of the structure factor from Kossel line profile

Kossel lines are formed when radiation from point x-ray sources inside a single crystal are diffracted by the crystal itself. In principle, Kossel line patterns contain full information on the crystalline structure: phase and magnitude of the structure factors. The phase is coded into the profile of the lines. Although this was known for a long time, experimental realization has not been presented. In this work we demonstrate experimentally that phases can be directly determined from the profile of the Kossel lines. These measurements are interesting not only theoretically, but they would facilitate structure solution of samples within extreme conditions, such as high pressure, high and low temperatures, high magnetic fields and extremely short times. The parallel measurement of many diffraction lines on a stationary sample will allow a more efficient use of the new generation of x-ray sources the X-ray free electron lasers (XFELs).

Matrix effects in white-beam X-ray fluorescence holography

Recently, it has been shown that atomic structure determination with X-ray fluorescence holography (XFH) can be hindered by matrix effects,i.e.beam attenuation and indirect excitation. The analysis was limited to the monochromatic regime. In this work, the description of matrix effects is extended to the polychromatic case. It is shown that matrix effects affect the element sensitivity of white-beam XFH by introducing distortions in the holographic signal which may lead to spurious maxima in the reconstructed image. For high energies of the X-ray beam it is found that the effect of beam attenuation is very weak and indirect excitation mainly contributes to the distortions. A correction for matrix effects is proposed in the high-energy range, which allows one to remove the distortions and retrieve pure element-sensitive information. Numerical model calculations are performed to visualize the reduction of element sensitivity and its implications on local structure imaging.

Diffuse multiple scattering

A new form of diffraction lines similar to Rutherford, Kikuchi and Kossel lines has been identified. They can be used to eliminate the need for sample/source matching in Lonsdale’s triple convergent line method in lattice-parameter determination.

A new form of diffraction lines has been identified, similar to Rutherford, Kikuchi and Kossel lines. This paper highlights some of the properties of these lines and shows how they can be used to eliminate the need for sample/source matching in Lonsdale’s triple convergent line method in lattice-parameter determination.

X-ray fluorescence holography

X-ray fluorescence holography (XFH) is a method of atomic resolution holography which utilizes fluorescing atoms as a wave source or a monitor of the interference field within a crystal sample. It provides three-dimensional atomic images around a specified element and has a range of up to a few nm in real space. Because of this feature, XFH is expected to be used for medium-range local structural analysis, which cannot be performed by x-ray diffraction or x-ray absorption fine structure analysis. In this article, we explain the theory of XFH including solutions to the twin-image problem, an advanced measuring system, and data processing for the reconstruction of atomic images. Then, we briefly introduce our recent applications of this technique to the analysis of local lattice distortions in mixed crystals and nanometer-size clusters appearing in the low-temperature phase of a shape-memory alloy.

Fluorescence detection of white-beam X-ray absorption anisotropy: towards element-sensitive projections of local atomic structure

Projections of the atomic structure around Nb atoms in a LiNbO(3) single crystal were obtained from a white-beam X-ray absorption anisotropy (XAA) pattern detected using Nb K fluorescence. This kind of anisotropy results from the interference of X-rays inside a sample and, owing to the short coherence length of a white beam, is visible only at small angles around interatomic directions. Consequently, the main features of the recorded XAA corresponded to distorted real-space projections of dense-packed atomic planes and atomic rows. A quantitative analysis of XAA was carried out using a wavelet transform and allowed well resolved projections of Nb atoms to be obtained up to distances of 10 Å. The signal of nearest O atoms was detected indirectly by a comparison with model calculations. The measurement of white-beam XAA using characteristic radiation indicates the possibility of obtaining element-sensitive projections of the local atomic structure in more complex samples.

3D atomic imaging by internal-detector electron holography

A method of internal-detector electron holography is the time-reversed version of photoelectron holography. Using an energy-dispersive x-ray detector, an electron gun, and a computer-controllable sample stage, we measured a multiple-energy hologram of the atomic arrangement around the Ti atom in SrTiO3 by recording the characteristic Ti Kα x-ray spectra for different electron beam angles and wavelengths. A real-space image was obtained by using a fitting-based reconstruction algorithm. 3D atomic images of the elements Sr, Ti, and O in SrTiO3 were clearly visualized. The present work reveals that internal-detector electron holography has great potential for reproducing 3D atomic arrangements, even for light elements.

Hard X ray holographic diffraction imaging

We determine the absolute electron density of a lithographically grown nanostructure with 25 nm resolution by combining hard x-ray Fourier transform holography with iterative phase retrieval methods. While holography immediately reveals an unambiguous image of the object, we deploy in addition iterative phase retrieval algorithms for pushing the resolution close to the diffraction limit. The use of hard (8 keV) x rays eliminates practically all constraints on sample environment and enables a destruction-free investigation of relatively thick or buried samples, making holographic diffraction imaging a very attractive tool for materials science. We note that the technique is ideally suited for subpicosecond imaging that will become possible with the emerging hard x-ray free-electron lasers.

X-ray tomographic imaging of crystal structure at the atomic level

A direct nondiffractive tomographic algorithm is proposed for the determination of the crystal structure from real-space projections obtained by illuminating the sample with white x rays. This approach was applied to the pattern of the directional fine structure in absorption of white x rays recorded for a GaP crystal and allowed for a determination of the electron density distribution within the unit cell.

Brilliant opportunities across the spectrum

Third generation synchrotron light sources provide stable, tuneable light of energy up to the hard X-ray region. The gain of a trillion in brightness as compared to a conventional laboratory X-ray source transforms the opportunities for establishing structure-function relationships. The light may be quasi-continuous or pulsed, have controllable polarisation and have coherence lengths larger than the sample size. The high brightness provides a basis for adding time and spatial resolution to X-ray scattering and spectroscopy. It may also be used to identify very specific information about the magnetic properties of atoms within materials, element specific vibrations, and local structural descriptions identified with chemical speciation. More demanding scattering and diffraction problems can be solved such as weakly scattering materials, large unit cells and structural entities. The high collimation of the source also provides enhanced spectroscopic and diffraction resolution that gives more insight into molecular, extended and supramolecular structures. The length scales can be bridged from the atomic up to that of visible light microscopy and buried features within materials can be observed with the appropriate energy. With an increased emphasis on ease of use, such capabilities are open to exploitation for chemical challenges.

Site-selective holographic imaging of iron arrangements in magnetite

Complex gamma-ray holograms were recorded by tuning to the nuclear absorption lines of 57Fe in magnetite corresponding to different hyperfine fields. The numerical reconstruction of the holograms to real space provided three-dimensional images of local iron arrangements in octahedral and tetrahedral sublattices of magnetite. This direct site-selective imaging of atomic structure was performed using a tabletop experimental setup.

Fourier-expansion solution of atom distributions in a crystal using X-ray standing waves

Term-by-term Fourier-expansion series, each made up of components having element-specific phases and amplitudes acquired with x-ray standing wave measurements on successive orders of Bragg reflections, are used to reconstruct impurity atom distributions in muscovite mica with respect to the (001) lattice without a priori assumptions on their structures.

Surface atomic arrangement visualization via reference-atom-specific holography

We demonstrate the direct reconstruction of 3D atomic images from measured low-energy electron diffraction (LEED) intensity spectra. A multiple-incident angle and multiple-energy integral are first applied to the spectra to obtain a map of interatomic vectors. From this map, a nonbulk interatomic vector is chosen that points to a desired reference atom. A second integral transformation, using the chosen interatomic vector as a filter, is applied to the LEED spectra to produce images of individual atoms in the vicinity of the selected reference atom. This two-step method overcomes the problem of multiple, nonequivalent reference atoms and is applicable to elemental or compound materials.

X-ray absorption holography

The transmission of monochromatic x rays through a CoO single crystal was measured for different orientations of the sample. The small variations in the linear absorption coefficient were considered as a hologram and the real-space image of the local atomic environment was successfully reconstructed. The holographic signal constituted about 1% of the detected intensity. Besides other benefits, the use of the absorption holography can increase the signal-to-background ratio by more than 1 order compared with the fluorescence holography.

Observation of Kossel and Kikuchi lines in thermal neutron incoherent scattering

In this Letter we report the observation of K lines (representing collectively, Kossel and Kikuchi lines) produced by monochromatic thermal neutrons interacting with a KDP (potassium dihydrogen phosphate) single crystal. Since K lines contain phase information, these observations establish the experimental basis for direct crystallographic phasing of atomic structures containing incoherent scatterers, such as hydrogen, via thermal neutron "inside source" holography.

Differential photoelectron holography: a new approach for three-dimensional atomic imaging

We propose differential holography as a method to overcome the long-standing forward-scattering problem in photoelectron holography and related techniques for the three-dimensional imaging of atoms. Atomic images reconstructed from experimental and theoretical Cu 3p holograms from Cu(001) demonstrate that this method suppresses strong forward-scattering effects so as to yield more accurate three-dimensional images of side- and backscattering atoms.

Atomic structure holography using thermal neutrons

The idea of atomic-resolution holography has its roots in the X-ray work of Bragg and in Gabor's electron interference microscope. Gabor's lensless microscope was not realized in his time, but over the past twelve years there has been a steady increase in the number of reports on atomic-resolution holography. All of this work involves the use of electrons or hard X-rays to produce the hologram. Neutrons are often unique among scattering probes in their interaction with materials: for example, the relative visibility of hydrogen and its isotopes is a great advantage in the study of polymers and biologically relevant materials. Recent work proposed that atomic-resolution holography could be achieved with thermal neutrons. Here we use monochromatic thermal neutrons, adopting the inside-source concept of Szöke, to image planes of oxygen atoms located above and below a single hydrogen atom in the oxide mineral simpsonite.

Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction

Inverse problems arise frequently in physics: The magnitude of the Fourier transform of some function is measurable, but not its phase. The "phase problem" in crystallography arises because the number of discrete measurements (Bragg peak intensities) is only half the number of unknowns (electron density points in space). Sayre first proposed that oversampling of diffraction data should allow a solution, and this has recently been demonstrated. Here we report the successful phasing of an oversampled hard x-ray diffraction pattern measured from a single nanocrystal of gold.

Real-space imaging of atomic structure with white x rays

The first real-space x-ray image of an atomic structure was obtained by illuminating a crystal with white synchrotron radiation. The internal photocurrent signal served as a probe of the x-ray interference field strength at the atomic sites and was accordingly measured as a function of illumination direction to record the two-dimensional image. This novel method of real-space imaging makes use of the fact that the interference field intensity is energy independent with respect to contributions from those scattering atoms which are brought via sample rotation into the forward scattering condition. In contrast, contributions from other atoms oscillate with energy and vanish for broadband illumination.

Complex gamma-ray hologram: solution to twin images problem in atomic resolution imaging

A new technique for high fidelity three-dimensional imaging of atomic structure with gamma-ray holography is demonstrated. A complex hologram was constructed from holograms recorded for different values of the nuclear scattering amplitude on both sides of the (57)Fe Mössbauer resonance. The holographic reconstruction was applied to this complex hologram resulting in a twin-image-free image of the bcc Fe local structure. The proposed procedure allows the removal of the twin images for all real space, making gamma-ray holography an unambiguous tool for atomic and magnetic structure imaging.

Direct 3D imaging of Al70.4Pd21Mn8.6 quasicrystal local atomic structure by X-ray holography

Inverse x-ray fluorescence holography was used to explore the local atomic order of a nearly perfect quasicrystal with composition Al70. 4Pd21Mn8.6. We have demonstrated the possibility of direct 3D imaging of the atomic decoration in a quasicrystal. We have obtained the average 3D environment of selected coordination shells around the Mn atoms. These results open the way to obtaining further and more complete information about the various coordination shells in complex materials by measuring multiple energy x-ray holograms at different sites.