Utilizing broadband X‐rays in a Bragg coherent X‐ray diffraction imaging experiment

A method is presented to simplify Bragg coherent X‐ray diffraction imaging studies of complex heterogeneous crystalline materials with a two‐stage screening/imaging process that utilizes polychromatic and monochromatic coherent X‐rays and is compatible with in situ sample environments. Coherent white‐beam diffraction is used to identify an individual crystal particle or grain that displays desired properties within a larger population. A three‐dimensional reciprocal‐space map suitable for diffraction imaging is then measured for the Bragg peak of interest using a monochromatic beam energy scan that requires no sample motion, thus simplifying in situ chamber design. This approach was demonstrated with Au nanoparticles and will enable, for example, individual grains in a polycrystalline material of specific orientation to be selected, then imaged in three dimensions while under load.     

X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

Development of variable‐magnification X‐ray Bragg optics

A novel X‐ray Bragg optics is proposed for variable‐magnification of an X‐ray beam. This X‐ray Bragg optics is composed of two magnifiers in a crossed arrangement, and the magnification factor, M, is controlled through the azimuth angle of each magnifier. The basic properties of the X‐ray optics such as the magnification factor, image transformation matrix and intrinsic acceptance angle are described based on the dynamical theory of X‐ray diffraction. The feasibility of the variable‐magnification X‐ray Bragg optics was verified at the vertical‐wiggler beamline BL‐14B of the Photon Factory. For X‐ray Bragg magnifiers, Si(220) crystals with an asymmetric angle of 14° were used. The magnification factor was calculated to be tunable between 0.1 and 10.0 at a wavelength of 0.112 nm. At various magnification factors (M≥ 1.0), X‐ray images of a nylon mesh were observed with an air‐cooled X‐ray CCD camera. Image deformation caused by the optics could be corrected by using a 2 × 2 transformation matrix and bilinear interpolation method. Not only absorption‐contrast but also edge‐contrast due to Fresnel diffraction was observed in the magnified images.     

IDATEN and G‐SITENNO: GUI‐assisted software for coherent X‐ray diffraction imaging experiments and data analyses at SACLA

Using our custom‐made diffraction apparatus KOTOBUKI‐1 and two multiport CCD detectors, cryogenic coherent X‐ray diffraction imaging experiments have been undertaken at the SPring‐8 Angstrom Compact free electron LAser (SACLA) facility. To efficiently perform experiments and data processing, two software suites with user‐friendly graphical user interfaces have been developed. The first is a program suite named IDATEN, which was developed to easily conduct four procedures during experiments: aligning KOTOBUKI‐1, loading a flash‐cooled sample into the cryogenic goniometer stage inside the vacuum chamber of KOTOBUKI‐1, adjusting the sample position with respect to the X‐ray beam using a pair of telescopes, and collecting diffraction data by raster scanning the sample with X‐ray pulses. Named G‐SITENNO, the other suite is an automated version of the original SITENNO suite, which was designed for processing diffraction data. These user‐friendly software suites are now indispensable for collecting a large number of diffraction patterns and for processing the diffraction patterns immediately after collecting data within a limited beam time.     

Application of a pnCCD in X‐ray diffraction: a three‐dimensional X‐ray detector

The first application of a pnCCD detector for X‐ray scattering experiments using white synchrotron radiation at BESSY II is presented. A Cd arachidate multilayer was investigated in reflection geometry within the energy range 7 keV < E < 35 keV. At fixed angle of incidence the two‐dimensional diffraction pattern containing several multilayer Bragg peaks and respective diffuse‐resonant Bragg sheets were observed. Since every pixel of the detector is able to determine the energy of every incoming photon with a resolution ΔE/E? 10^?2, a three‐dimensional dataset is finally obtained. In order to achieve this energy resolution the detector was operated in the so‐called single‐photon‐counting mode. A full dataset was evaluated taking into account all photons recorded within 10⁵ detector frames at a readout rate of 200 Hz. By representing the data in reciprocal‐space coordinates, it becomes obvious that this experiment with the pnCCD detector provides the same information as that obtained by combining a large number of monochromatic scattering experiments using conventional area detectors.     

Third‐order nonlinear and linear time‐dependent dynamical diffraction of X‐rays in crystals

For the first time the third‐order nonlinear time‐dependent Takagi's equations of X‐rays in crystals are obtained and investigated. The third‐order nonlinear and linear time‐dependent dynamical diffraction of X‐rays spatially restricted in the diffraction plane pulses in crystals is investigated theoretically. A method of solving the linear and the third‐order nonlinear time‐dependent Takagi's equations is proposed. Based on this method, results of analytical and numerical calculations for both linear and nonlinear diffraction cases are presented and compared.     

Diffractive–refractive optics: X‐ray splitter

The possibility of splitting a thin (e.g. undulator) X‐ray beam based on diffraction–refraction effects is discussed. The beam is diffracted from a crystal whose diffracting surface has the shape of a roof with the ridge lying in the plane of diffraction. The crystal is cut asymmetrically. One half of the beam impinges on the left‐hand part of the roof and the other half impinges on the right‐hand side of the roof. Owing to refraction the left part of the beam is deviated to the left whereas the right part is deviated to the right. The device proposed consists of two channel‐cut crystals with roof‐like diffraction surfaces; the crystals are set in a dispersive position. The separation of the beams after splitting is calculated at a distance of 10 m from the crystals for various asymmetry and inclination angles. It is shown that such a splitting may be utilized for long beamlines. Advantages and disadvantages of this method are discussed.     

Multiple‐element spectrometer for non‐resonant inelastic X‐ray spectroscopy of electronic excitations

A multiple‐analyser‐crystal spectrometer for non‐resonant inelastic X‐ray scattering spectroscopy installed at beamline ID16 of the European Synchrotron Radiation Facility is presented. Nine analyser crystals with bending radii R = 1 m measure spectra for five different momentum transfer values simultaneously. Using a two‐dimensional detector, the spectra given by all analysers can be treated individually. The spectrometer is based on a Rowland circle design with fixed Bragg angles of about 88°. The energy resolution can be chosen between 30–2000 meV with typical incident‐photon energies of 6–13 keV. The spectrometer is optimized for studies of valence and core electron excitations resolving both energy and momentum transfer.     

Spatial structure of a focused X‐ray beam diffracted from crystals

The spatial structure of a beam focused by a planar refractive lens and Bragg diffracted from perfect silicon crystals was experimentally studied at the focal plane using a knife‐edge scan and a high‐resolution CCD camera. The use of refractive lenses allowed for a detailed comparison with theory. It was shown that diffraction leads to broadening of the focused beam owing to the extinction effect and, for a sufficiently thin crystal, to the appearance of a second peak owing to reflection from the back surface. It was found that the spatial structure of the diffracted beam depends on whether the crystal diffracts strongly (dynamically) or weakly (kinematically). The results help to understand the physical origin of the diffracted intensity recorded in a typical microbeam diffraction experiment.     

Theoretical consideration of an X‐ray Bragg‐reflection lens using the eikonal approximation

On the basis of the eikonal approximation, X‐ray Bragg‐case focusing by a perfect crystal with parabolic‐shaped entrance surface is considered theoretically. Expressions for focal distances, intensity gain and distribution around the focus spot as well as for the focus spot sizes are obtained. The condition of point focusing is presented. The experiment can be performed using X‐ray synchrotron radiation sources (particularly free‐electron lasers).     

Pressure study of monoclinic ReO2 up to 1.2 GPa using X‐ray absorption spectroscopy and X‐ray diffraction

The crystal and local atomic structure of monoclinic ReO₂ (α‐ReO₂) under hydrostatic pressure up to 1.2 GPa was investigated for the first time using both X‐ray absorption spectroscopy and high‐resolution synchrotron X‐ray powder diffraction and a home‐built B₄C anvil pressure cell developed for this purpose. Extended X‐ray absorption fine‐structure (EXAFS) data analysis at pressures from ambient up to 1.2 GPa indicates that there are two distinct Re—Re distances and a distorted ReO₆ octahedron in the α‐ReO₂ structure. X‐ray diffraction analysis at ambient pressure revealed an unambiguous solution for the crystal structure of the α‐phase, demonstrating a modulation of the Re—Re distances. The relatively small portion of the diffraction pattern accessed in the pressure‐dependent measurements does not allow for a detailed study of the crystal structure of α‐ReO₂ under pressure. Nonetheless, a shift and reduction in the (011) Bragg peak intensity between 0.4 and 1.2 GPa is observed, with correlation to a decrease in Re—Re distance modulation, as confirmed by EXAFS analysis in the same pressure range. This behavior reveals that α‐ReO₂ is a possible inner pressure gauge for future experiments up to 1.2 GPa.     

Polarization control of an X‐ray free‐electron laser with a diamond phase retarder

A diamond phase retarder was applied to control the polarization states of a hard X‐ray free‐electron laser (XFEL) in the photon energy range 5–20 keV. The horizontal polarization of the XFEL beam generated from the planar undulators of the SPring‐8 Angstrom Compact Free‐Electron Laser (SACLA) was converted into vertical or circular polarization of either helicity by adjusting the angular offset of the diamond crystal from the exact Bragg condition. Using a 1.5 mm‐thick crystal, a high degree of circular polarization, 97%, was obtained for 11.56 keV monochromatic X‐rays, whereas the degree of vertical polarization was 67%, both of which agreed with the estimations including the energy bandwidth of the Si 111 beamline monochromator.     

Spectrometer for hard X‐ray free‐electron laser based on diffraction focusing

X‐ray free‐electron lasers (XFELs) generate sequences of ultra‐short spatially coherent pulses of X‐ray radiation. A diffraction focusing spectrometer (DFS), which is able to measure the whole energy spectrum of the radiation of a single XFEL pulse with an energy resolution of ΔE/E? 2 × 10^?6, is proposed. This is much better than for most modern X‐ray spectrometers. Such resolution allows one to resolve the fine spectral structure of the XFEL pulse. The effect of diffraction focusing occurs in a single‐crystal plate due to dynamical scattering, and is similar to focusing in a Pendry lens made from a metamaterial with a negative refraction index. Such a spectrometer is easier to operate than those based on bent crystals. It is shown that the DFS can be used in a wide energy range from 5 keV to 20 keV.     

The competitive growth of cubic domains in Ti1–xAlxN films studied by diffraction anomalous near‐edge structure spectroscopy

Titanium and aluminium nitride films deposited by magnetron sputtering generally grow as columnar domains made of oriented nanocrystallites with cubic or hexagonal symmetry depending on Al content, which are embedded in more disordered grain boundaries. The substitution of Al atoms for Ti in the cubic lattice of the films improves their resistance to wear and oxidation, allowing their use as protective coatings. Ti K‐edge X‐ray absorption spectroscopy, which probes both crystallized and more disordered grain boundaries, and X‐ray diffraction anomalous fine structure, which is sensitive to short‐ and long‐range order within a given crystallized domain, are carried out on a set of Ti_1–xAl_xN films deposited by magnetron sputtering on Si substrates. Attention is paid to the shape of the pre‐edge region, which is sensitive to the symmetry of the site occupied by Ti atoms, either octahedral in face‐centred‐cubic Ti‐rich (TiN, Ti_0.54Al_0.46N) samples or tetrahedral in hexagonal‐close‐packed Al‐rich (Ti_0.32Al_0.68N) films. In order to obain information on the titanium environment in the well crystallized areas, subtraction of the smooth part of the energy‐dependent structure factor for the Bragg reflections is applied to the pre‐edge region of the diffraction anomalous data in order to restore their spectroscopic appearance. A flat pre‐edge is related to the typical octahedral environment of Ti atoms for cubic reflections. The difference observed between pre‐edge spectra associated with face‐centred‐cubic 200 and 111 Bragg reflections of Ti_0.54Al_0.46N is assigned to Ti enrichment of 111 large well ordered domains compared with the more disordered 200 ones. The sharp peak observed in the spectrum recorded from the hexagonal 002 peak of Ti_0.32Al_0.68N can be regarded as a standard for the pure tetrahedral Ti environment in hexagonal‐close‐packed nitride.     

X‐ray dynamical diffraction Fraunhofer holography

An X‐ray dynamical diffraction Fraunhofer holographic scheme is proposed. Theoretically it is shown that the reconstruction of the object image by visible light is possible. The spatial and temporal coherence requirements of the incident X‐ray beam are considered. As an example, the hologram recording as well as the reconstruction by visible light of an absolutely absorbing wire are discussed.     

Full‐field X‐ray reflection microscopy of epitaxial thin‐films

Novel X‐ray imaging of structural domains in a ferroelectric epitaxial thin film using diffraction contrast is presented. The full‐field hard X‐ray microscope uses the surface scattering signal, in a reflectivity or diffraction experiment, to spatially resolve the local structure with 70 nm lateral spatial resolution and sub‐nanometer height sensitivity. Sub‐second X‐ray exposures can be used to acquire a 14 µm × 14 µm image with an effective pixel size of 20 nm on the sample. The optical configuration and various engineering considerations that are necessary to achieve optimal imaging resolution and contrast in this type of microscopy are discussed.     

Focusing femtosecond X‐ray free‐electron laser pulses by refractive lenses

The possibility of using a parabolic refractive lens with initial X‐ray free‐electron laser (XFEL) pulses, i.e. without a monochromator, is analysed. It is assumed that the measurement time is longer than 0.3 fs, which is the time duration of a coherent pulse (spike). In this case one has to calculate the propagation of a monochromatic wave and then perform an integration of the intensity over the radiation spectrum. Here a general algorithm for calculating the propagation of time‐dependent radiation in free space and through various objects is presented. Analytical formulae are derived describing the properties of the monochromatic beam focused by a system of one and two lenses. Computer simulations show that the European XFEL pulses can be focused with maximal efficiency, i.e. as for a monochromatic wave. This occurs even for nanofocusing lenses.     

An alternative scheme of angular‐dispersion analyzers for high‐resolution medium‐energy inelastic X‐ray scattering

The development of medium‐energy inelastic X‐ray scattering optics with meV and sub‐meV resolution has attracted considerable efforts in recent years. Meanwhile, there are also concerns or debates about the fundamental and feasibility of the involved schemes. Here the central optical component, the back‐reflection angular‐dispersion monochromator or analyzer, is analyzed. The results show that the multiple‐beam diffraction effect together with transmission‐induced absorption can noticeably reduce the diffraction efficiency, although it may not be a fatal threat. In order to improve the efficiency, a simple four‐bounce analyzer is proposed that completely avoids these two adverse effects. The new scheme is illustrated to be a feasible alternative approach for developing meV‐ to sub‐meV‐resolution inelastic X‐ray scattering spectroscopy.     

XDS: a flexible beamline for X‐ray diffraction and spectroscopy at the Brazilian synchrotron

The majority of the beamlines at the Brazilian Synchrotron Light Source Laboratory (LNLS) use radiation produced in the storage‐ring bending magnets and are therefore currently limited in the flux that can be used in the harder part of the X‐ray spectrum (above ～10 keV). A 4 T superconducting multipolar wiggler (SCW) was recently installed at LNLS in order to improve the photon flux above 10 keV and fulfill the demands set by the materials science community. A new multi‐purpose beamline was then installed at the LNLS using the SCW as a photon source. The XDS is a flexible beamline operating in the energy range between 5 and 30 keV, designed to perform experiments using absorption, diffraction and scattering techniques. Most of the work performed at the XDS beamline concentrates on X‐ray absorption spectroscopy at energies above 18 keV and high‐resolution diffraction experiments. More recently, new setups and photon‐hungry experiments such as total X‐ray scattering, X‐ray diffraction under high pressures, resonant X‐ray emission spectroscopy, among others, have started to become routine at XDS. Here, the XDS beamline characteristics, performance and a few new experimental possibilities are described.     

Coherent X‐ray scattering beamline at port 9C of Pohang Light Source II

The coherent X‐ray scattering beamline at the 9C port of the upgraded Pohang Light Source (PLS‐II) at Pohang Accelerator Laboratory in Korea is introduced. This beamline provides X‐rays of 5–20 keV, and targets coherent X‐ray experiments such as coherent diffraction imaging and X‐ray photon correlation spectroscopy. The main parameters of the beamline are summarized, and some preliminary experimental results are described.