Bragg Geometry Research Articles

DuMond analysis of bending in single crystals by Laue diffraction using σ–π polarization geometry

A DuMond analysis of X-ray diffraction patterns has been carried out in the case of a combined σ–π polarization configuration, obtained using a setup with a double-crystal monochromator in reflection (Bragg) geometry and an analyser in transmission (Laue) geometry. The derived analytical expressions allow the characterization of the bending of the analyser and the quantitative estimation of the curvature radius and its sign from the width of the crystal rocking curves. The theoretical analysis is applied to the case of a thin, accidentally bent, Si crystal.

Beam conditioning by diffractive–refractive crystal monochromators in Bragg and Laue geometries

Beam conditioning by diffractive–refractive crystal monochromators in Bragg and Laue geometries

Diffraction of X-ray free-electron laser femtosecond pulses on single crystals in the Bragg and Laue geometry

A solution of the problem of dynamical diffraction for X-ray pulses with arbitrary dimensions in the Bragg and Laue cases in a crystal of any thickness and asymmetry coefficient of reflection is presented. Analysis of pulse form and duration transformation in the process of diffraction and propagation in a vacuum is conducted. It is shown that only the symmetrical Bragg case can be used to avoid smearing of reflected pulses.

Orbital domain dynamics in a doped manganite

We explore a number of novel effects near the orbital-order phase transition in a half-doped manganite, Pr0.5Ca0.5MnO3. To probe the unusual short-range orbital order in this system, we have performed coherent soft x-ray resonant scattering measurements in a Bragg geometry to measure dynamics. Near the transition temperature, we observe a small fluctuating component in the scattered signal that is correlated with three effects: a rapidly decreasing total signal and orbital domain size, as well as an abrupt onset of a broad background intensity that we attribute to the thermal production of correlated polarons. Our speckle results suggest that the transition is characterized by a competition between a pinned orbital domain topology that remains static and mobile domain boundaries that exhibit slow, temporal fluctuations.

Bulk strains in Si induced by thickness mode ultrasonic waves and analysed with x-ray Bragg diffraction

In-depth thickness mode ultrasonic deformations were monitored by hard (22 keV) x-ray diffraction in Bragg geometry on a Si (1 1 1) crystal. The ultrasonic thickness mode standing wave was applied with a PZT transducer coupled to the Si crystal. Measurements were taken on the time-integrated mode and also at different phases of the ultrasonic excitation in stroboscopic mode. In-depth (2 mm) x-ray stroboscopic measurements on Si showed dynamical strains that were enough to set the crystal out of the diffraction condition. This opens new possibilities for applications such as a stroboscopic gradient x-ray monochromator made out of Si at back-diffraction geometry and stress–strain curve determination of crystals.

A note on Bragg-casePendellösungand dispersion surface

It is usual to state, since Ewald [Ann. Phys. (1917), 54, 519-597], that Bragg-case Pendellösung involves two wavefields belonging to the same branch of the dispersion surface. However, in the Bragg geometry or when crystals are highly absorbing, the dispersion surface can no longer be approximated by the dispersion surface valid for a non-absorbing infinite medium. When considering the real part of the dispersion surface, it is found that the interfering wavefields producing Pendellösung in the Bragg geometry belong in fact to different branches. This paradox is explained by noting that the actual dispersion surface in the semi-infinite medium where the wavefields are generated by the incident wave differs from the dispersion surface in an infinite medium.

An active-optic x-ray fluorescence analyzer with high energy resolution, large solid angle coverage, and a large tuning range

A crystal-optic x-ray fluorescence energy analyzer has been designed and tested, which combines the features of electron-volt energy resolution, large solid angle coverage, and tunability over several kilo-electron-volts. The design is based upon the principle of active optics, with ten actuators available to optimally adjust the shape of a silicon crystal used in the Bragg geometry. In most applications the shape is that of a logarithmic spiral for high energy resolution with a spatially nonresolving detector, but a wide range of other shapes is also possible for applications such as imaging or single-shot spectroscopy in a spectral range of the operator's choosing.

Accessible reciprocal-space region for non-coplanar Bragg and Laue geometries

Accurate shapes of the accessible reciprocal-space region for non-coplanar Bragg and Laue geometries are given. Vector formulae for finding these regions and for experimental geometry calculations for obtaining diffraction from any accessible (using a given wavelength) reciprocal node are presented. A method for converting these formulae to scalar equations is proposed. Solutions are given and illustrated as three-dimensional figures in reciprocal space.

Studies of III-Nitride Superlattice Structures Implanted with Lanthanide Ions

AbstractCathodoluminescence (CL) of rare earth (RE) ions implanted AlN/GaN superlattice (SL) structures grown by chemical vapor deposition (CVD) technique on GaN/(0001) sapphire substrate was measured at 10 K and 300 K. Implantation of terbium and thulium in SLs was done at 150 keV with a dose of up to 1×1015 cm-2 at 300 K. Samples were given post implantation isochronal thermal treatment at 900 °C in nitrogen ambient. The interface quality between the SL layers before and after implantation as well as after thermal annealing treatment has been investigated by X-ray diffraction (XRD). The characteristic satellite peaks of the SLs were measured for the (0002) reflection in the symmetric Bragg geometry for the reference, RE-implanted, and annealed SLs. Furthermore, the luminescence intensity of a RE3+ ion doped AlN/GaN SL was compared with the one from RE-implanted GaN epilayers. Despite the structural damage of the AlN/GaN structures, an enhancement of the characteristic emission intensities from RE3+ ions in the SLs was observed compared to emission from RE ions in epilayers.

Crystallization of amorphous zirconium thin film using ion implantation by a plasma focus of 1 kJ

In this work preliminary results of amorphous zirconium crystallization using ion beam pulses are presented. Energetic argon- and oxygen-ion beams generated by a plasma focus device were used to promote crystallization on amorphous ZrO 2–2.5 mol% Y 2O 3 film deposited by chemical solution deposition onto silica glass substrate. The films were burnt at 370 ° C for 1 h in normal atmosphere previous to plasma irradiation. The irradiation was performed by means of successive pulses of ion beams. The evolution of the surface morphology and crystallization was followed by AFM and X-rays diffraction in a grazing incidence asymmetric Bragg geometry (GIAB), respectively. Argon-irradiated films showed highly nucleated cubic zirconia after 10 pulses. On the other hand, oxygen-irradiated films showed a delayed and less extensive cubic nucleation, but a more ordered structure and well-defined grains.

Diffraction reflection of x-ray radiation with a two-dimensionally bounded wavefront from perfect crystals

The problem of dynamical diffraction of x-ray radiation with a two-dimensionally bounded wavefront is solved in the Bragg and Laue geometries in a crystal with an arbitrary thickness and an arbitrary reflection asymmetry parameter. An analysis of the wavefront deformation during the diffraction and subsequent propagation is carried out. It is shown that the most favorable conditions for the reflected beam to retain its shape are accomplished in a crystal whose thickness is less than the extinction depth.

Crystalline texture and magnetic anisotropy of Co-P films prepared by chemical deposition

Chemically deposited Co-P films with a P concentration of 2.5% have been studied by X-ray diffraction (Bragg geometry), electron microscopy, and magnetometry. The films have been found to represent a fine-grained medium in which the orientation of crystallites depends on the film thickness. At a thickness less than 70 nm, the films have a certain crystalline texture with a preferred orientation of the hexagonal axis c of the crystallites perpendicular to the film plane. With increasing film thickness, the character of the texture changes; the c axes of crystallites lie now predominantly in the film plane. At thicknesses exceeding 500 nm, the texture becomes stronger; the c axes are now distributed in the film plane equiprobably. These results can be used when producing magnetic media for longitudinal and transverse magnetic recording.

A numerical wave-optical approach for the simulation of analyzer-based x-ray imaging

An advanced wave-optical approach for simulating a monochromator-analyzer set-up in Bragg geometry with high accuracy is presented. The polychromaticity of the incident wave on the monochromator is accounted for by using a distribution of incoherent point sources along the surface of the crystal. The resulting diffracted amplitude is modified by the sample and can be well represented by a scalar representation of the optical field where the limitations of the usual 'weak object' approximation are removed. The subsequent diffraction mechanism on the analyzer is described by the convolution of the incoming wave with the Green-Riemann function of the analyzer. The free space propagation up to the detector position is well reproduced by a classical Fresnel-Kirchhoff integral. The preliminary results of this innovative approach show an excellent agreement with experimental data.

First observation of parametric X-rays produced by moderate relativistic protons and carbon nuclei in Si crystals

Spectral maxima of parametric X-ray radiation from moderately relativistic protons and carbon nuclei interacting with (001) silicon crystals have been observed for the first time. The PXR emitted due to the interaction of nuclei with silicon crystals in the Bragg geometry were detected by the semiconductor spectrometer. The positions of the radiation maxima in the spectra depend on the crystal angle and correspond to the theoretical values. The PXR yield per particle observed from carbon nuclei is considerably higher than from protons. This agrees with the theory statement about the Z2-dependence of the yield. The spectra contain the considerable contribution from side PXR reflections. The measurements have been performed at the Nuclotron (LHE JINR) extracted beams of 5GeV protons and 2.2GeV/u carbon nuclei. It was the first observation of PXR from heavy particles–relativistic nuclei. Moreover, the PXR was observed from particles with the lowest relativistic factor (γ=3.36) among all used before.

X-ray phase contrast imaging at MAMI

Experiments have been performed to explore the potential of the low emittance 855MeV electron beam of the Mainz Microtron MAMI for imaging with coherent X-rays. Transition radiation from a micro-focused electron beam traversing a foil stack served as X-ray source with good transverse coherence. Refraction contrast radiographs of low absorbing materials, in particular polymer strings with diameters between 30 and 450μm, were taken with a polychromatic transition radiation X-ray source with a spectral distribution in the energy range between 8 and about 40keV. The electron beam spot size had standard deviation σh = (8.6±0.1)μm in the horizontal and σv = (7.5±0.1)μm in the vertical direction. X-ray films were used as detectors. The source-to-detector distance amounted to 11.4m. The objects were placed in a distance of up to 6m from the X-ray film. Holograms of strings were taken with a beam spot size σv = (0.50±0.05)μm in vertical direction, and a monochromatic X-ray beam of 6keV energy. A good longitudinal coherence has been obtained by the (111) reflection of a flat silicon single crystal in Bragg geometry. It has been demonstrated that a direct exposure CCD chip with a pixel size of 13×13μm^2 provides a highly efficient on-line detector. Contrast images can easily be generated with a complete elimination of all parasitic background. The on-line capability allows a minimization of the beam spot size by observing the smallest visible interference fringe spacings or the number of visible fringes. It has been demonstrated that X-ray films are also very useful detectors. The main advantage in comparison with the direct exposure CCD chip is the resolution. For the Structurix D3 (Agfa) X-ray film the standard deviation of the resolution was measured to be σf = (1.2±0.4)μm, which is about a factor of 6 better than for the direct exposure CCD chip. With the small effective X-ray spot size in vertical direction of σv = (1.2±0.3)μm and a geometrical magnification of up to 7.4 high-quality holograms of tiny transparent strings were taken in which the holographic information is contained in up to 18 interference fringes.

Coherent bremsstrahlung and parametric X-ray radiation from nonrelativistic electrons in a crystal

X-ray radiation generated by nonrelativistic electrons interacting with a crystal target exhibits several distinctive features in comparison to the relativistic case. The difference is related to the interference of the parametric X-ray radiation and coherent bremsstrahlung, which takes place for the nonrelativistic electrons. The characteristics of this radiation have been studied in the Bragg and Laue geometries in an electron microscope using a beam of electrons with energies in the 50–100 keV range. The necessary requirements on the target parameters, the measuring instrumentation, and the experimental geometry are established. Variation of the X-ray radiation frequency depending on the angle of electron beam incidence on the target in the region of non-relativistic electron energies has been observed for the first time. The X-ray radiation frequency has been also studied as a function of the primary electron beam energy. Tunable soft X-ray radiation with quantum energy in the range below 1 keV is obtained. The radiation quantum yield per electron within a unit solid angle amounts to ∼10−8.

NONLINEAR OPTICS WITH HARD X-RAYS: HARMONIC GENERATION AND RAMAN SCATTERING IN PERFECT CRYSTALS

Based on dynamical diffraction theory, we study nonlinear processes in the hard X-ray region. First, we consider the process of frequency doubling in perfect crystals in the general case where the process of Bragg rescattering of the generated harmonic field should be taken into account. The optimum conversion conditions for the Bragg and Laue interaction geometry are determined and the efficiency is calculated. Secondly, we consider the modulation of X-ray diffraction by a wave of coherent optical phonons produced by an intense laser pulse. We show that in the optimum regime the modulation period of the X-ray beam may be even shorter than the period of the excited optical phonons, as a result of higher order Raman scattering. Generation of extremely short X-ray pulses using this technique is discussed. Our results suggest that synchronous interaction schemes analogous to the schemes long known in nonlinear optics can significantly increase the efficiency of nonlinear processes in the hard X-ray region.

Application of X-ray absorption near-edge structure (XANES) using bent crystal analyzer to speciation of trace Os in iron meteorites

X-ray absorption near-edge structure (XANES) spectroscopy at the Os L III-edge was measured for the speciation of trace Os in two iron meteorites, Negrillos and Bennett County, which contain 65.7 and 58.3 mg/kg of Os, respectively, while major elements, Fe + Ni, are more than 95 wt.%. During Os XANES measurement, intense Fe–K and Ni–K fluorescence and scattered X-rays existed as background noise, which were more than four orders higher than Os Lα fluorescence. To reject the unwanted X-rays, a log spiral bent crystal analyzer in Bragg geometry for X-ray fluorescence detection combined with a single-element pure Ge detector and slits was used. The system enabled us to obtain the Os L III-edge XANES spectra of the two iron meteorites with greater quality compared with those recorded in a conventional fluorescence mode by a 19-element Ge detector without analyzer crystals. In addition, a commercially available crystal analyzer (BCLA, Oxford danfysik) in Laue geometry was also tested, and it also gave similar high-quality XANES spectra. The Bragg geometry reduced the noise due to background X-rays more effectively than the Laue system, while the Laue geometry was efficient to collect target fluorescence X-ray, suggesting that a better spectrum in terms of statistics could be obtained using a Laue analyzer coupled with a multi-element Ge detector with a large acceptance area for fluorescence detection. The reliable spectral shape of XANES measured enabled us to simulate XANES spectra of Os in iron meteorites in a highly quantitative manner. A system using log spiral crystal analyzer coupled with a Ge detector is a powerful tool for the speciation of trace elements in natural minerals and rocks.

Polarizance of a synthetic mica crystal polarizer and the degree of linear polarization of an undulator beamline at 880eV evaluated by the rotating-analyzer method

The polarization performance of a reflection-type polarizer made with a synthetic mica (fluorophlogopite) single crystal (002) in symmetric Bragg geometry was evaluated at the photon energy of 880eV by means of the rotating-analyzer method. An experiment was performed at the undulator beamline at the SPring-8. The reflectance in the s-polarization configuration was 2.6% at an incidence angle of around 45°. As the result of the analysis based on the rotating-analyzer method, the polarizance of the polarizer and the degree of linear polarization of the incident light at 880eV were found to be 0.997±0.002 and 0.993±0.004, respectively.

An optimized two crystal arrangement for X-ray optics

Modification of the Schwarzschild optics for applications in hard X-ray imaging is discussed. The conditions necessary to achieve a high spatial resolution with two toroidally bent crystals in the Bragg geometry are formulated, and the focusing properties of the system are numerically simulated using the ray tracing method. It is predicted that such a system could provide a spatial resolution considerably higher than the resolution of the presently available X-ray optics.