Laue Geometry Research Articles

The theory of synchrotron radiation limited beams diffraction in single crystal in the Laue case

The features of the Bragg diffraction of coherent synchrotron radiation on the atomic lattice of a single crystal in the Laue geometry are studied theoretically, provided that the radiation beam is limited by a relatively large slit placed in front of the crystal. The method of numerical simulation is used and dependences of the intensity distribution are obtained for various thicknesses of the crystal. It is shown that the slit edges introduce inhomogeneous intensity distortions inside the Bormann triangles with an angle of 2θB, where θB is the Bragg angle. In the area where the triangles intersect, the intensity distribution is similar to that for diffraction by a slit in air at a certain (large) distance. An equation for the correspondence between the distance and the thickness of the crystal is obtained, which describes well the results of numerical calculations.

К теории рентгеновской Лауэ дифракции в термомиграционном кристаллическом канале с легирующей примесью

X-ray Laue diffraction in a silicon crystal with Si(Al) thermomigration channels has been theoretically considered. Based on the model of elastic fields of atomic displacements in the channel, expressions for the distribution of strains have been obtained to describe diffraction in the Laue geometry. A numerical calculation of the X-ray scattering intensity distribution near a reciprocal lattice point has been performed. The difference between diffraction in a perfect and strained crystal has been shown.

Calculation of the Rocking Curve of a Double-Crystal Neutron Spectrometer on Strongly Absorbing InSb Crystals in Laue–Laue Geometry

Calculation of the Rocking Curve of a Double-Crystal Neutron Spectrometer on Strongly Absorbing InSb Crystals in Laue–Laue Geometry

Crystal Analyzer Based Multispectral Microtomography Using CCD-Sensor.

To solve the problems of spectral tomography, an X-ray optical scheme was proposed, using a crystal analyzer in Laue geometry between the sample and the detector, which allowed for the selection of predetermined pairs of wavelengths from the incident polychromatic radiation to obtain projection images. On a laboratory X-ray microtomography setup, an experiment was carried out for the first time where a mixture of micro-granules of sodium chloride NaCl, silver behenate AgC22H43O2, and lithium niobate LiNbO3 was used as a test sample to identify their spatial arrangement. The elements were chosen based on the presence of absorption edges in two of the elements in the energy range of the polychromatic spectrum of the probing radiation. The method of projection distortion correction was used to preprocess the obtained projections. To interpret the obtained reconstruction results, the segmentation method based on the analysis of joint histograms was used. This allowed us to identify each of the three substances. To compare the results obtained, additional "reference" tomographic measurements were performed: one in polychromatic and two in monochromatic (MoKα-, MoKβ-lines) modes. It took three times less time for the tomographic experiment with the crystal analyzer, while the reconstruction accuracy was comparable to that of the "reference" tomography.

COMPUTER SIMULATION OF THE EFFECT OF COHERENT DYNAMICAL DIFFRACTION OF SYNCHROTRON RADIATION IN CRYSTALS OF ARBITRARY SHAPE AND STRUCTURE

A new scheme for the numerical solution of Takagi–Taupin equations, which makes it possible to simulate the effect of synchrotron radiation diffraction in crystals of arbitrary structure, is described in detail. The new scheme is convenient to perform calculations for crystals of arbitrary shape. The rectangular coordinate system and the algorithm for calculating derivatives at half of step have proven their efficiency and are used, but the recurrence equations of this algorithm have been modified towards simplification. The boundary conditions are in no way related to the crystal boundaries. A computer program is developed, and two examples are considered for the cases of diffraction in the Laue and Bragg geometries, for which the analyticl solutions are known. The calculation results are in complete agreement with these solutions.

Determination of the superlattice structure factor by X-ray diffraction using a temperature gradient.

The influence of a temperature gradient directed perpendicular to the crystal surface on the diffraction focusing of a spherical X-ray wave in a superlattice is studied for the Laue geometry. It is shown that different satellites can be focused on the exit surface of the crystal by a smooth change in the gradient value, which can become the basis for the experimental determination of the structure factor of the superlattice.

Large-area total-thickness imaging and Burgers vector analysis of dislocations in β -Ga2O3 using bright-field x-ray topography based on anomalous transmission

Using bright-field x-ray topography based on anomalous transmission (AT), we have demonstrated the first large-area total-thickness imaging of dislocations in β-Ga2O3 at the substrate scale. The dislocation images were acquired from the entire 10 mm × 15 mm × 680 μm (001)-oriented substrate prepared by edge-defined film-fed growth (EFG) by stitching together hundreds of topographic images, each recorded with the forward-diffracted beam in the Laue geometry for g = 020, 0–20, 022, and 400, under the conditions in which AT occurred. Dislocations distributed over the entire crystal volume were imaged as long as their Burgers vectors (b) were not orthogonal to the g-vectors. The results of the g·b analysis of the dislocation contrasts clearly revealed three major dislocation types that were numerically dominant in the EFG crystal: (i) b-axis screw-type dislocations with b∥ξ∥[010] (ξ is the unit vector of line direction), (ii) b-axis edge-type dislocations with b∥[001] and ξ∥[010], and (iii) curved mixed-type dislocations lying on the (001) planes with b∥[010]. Based on their b- and ξ-vectors, types (i) and (ii) were attributed to dislocations that propagated during EFG pulling up along the [010] direction, while type (iii) was attributed to dislocations generated through glide in the [010](001) slip system under stress. The extent to which AT can manifest itself is explained by using the effective absorption coefficient calculated for the above g-vectors based on dynamical x-ray diffraction theory.

Observation of dislocations in thick β-Ga2O3 single-crystal substrates using Borrmann effect synchrotron x-ray topography

We performed Borrmann effect x-ray topography (XRT) to observe dislocations and other structural defects in a thick β-Ga2O3 (001) substrate. The Borrmann effect was realized by working in a symmetrical Laue geometry (g = 020). Anomalous transmission occurred under the exact Bragg condition, producing a strong diffraction beam that allowed us to image defects across the entire thickness of the substrate. The analysis clearly revealed straight b-axis screw-type and curved dislocations and allowed assessing the corresponding behaviors. Other structural defects, including pipe-shaped voids and dislocation loops produced by mechanical damage, were also observed. Finally, we compared Borrmann effect transmission topography and conventional reflection topography and explained the appearance of some characteristic defects in the two modes. Our results show that Borrmann effect XRT is a powerful and effective technique to study the spatial distribution and structural properties of defects in highly absorbing β-Ga2O3.

X-ray focusing by bent crystals: focal positions as predicted by the crystal lens equation and the dynamical diffraction theory.

The location of the beam focus when monochromatic X-ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It has little utility for diffraction in Laue geometry. The focusing effect in the Laue symmetrical case is discussed using concepts of dynamical theory and an extension of the lens equation is proposed. The existence of polychromatic focusing is considered and the feasibility of matching the polychromatic and monochromatic focal positions is discussed.

Simultaneous two-color X-ray absorption spectroscopy using Laue crystals at an inverse-compton scattering X-ray facility.

X-ray absorption spectroscopy (XAS) is an element-selective technique that provides electronic and structural information of materials and reveals the essential mechanisms of the reactions involved. However, the technique is typically conducted at synchrotrons and usually only probes one element at a time. In this paper, a simultaneous two-color XAS setup at a laboratory-scale synchrotron facility is proposed based on inverse Compton scattering (ICS) at the Munich Compact Light Source (MuCLS), which is based on inverse Compton scattering (ICS). The setup utilizes two silicon crystals in a Laue geometry. A proof-of-principle experiment is presented where both silver (Ag) and palladium (Pd) K-edge X-ray absorption near-edge structure spectra were simultaneously measured. The simplicity of the setup facilitates its migration to other ICS facilities or maybe to other X-ray sources (e.g. a bending-magnet beamline). Such a setup has the potential to study reaction mechanisms and synergistic effects of chemical systems containing multiple elements of interest, such as a bimetallic catalyst system.

Lateral deformations of a crystal of potassium acid phthalate in an external electric field

The anisotropy of deformations in potassium acid phthalate crystals arising under the action of an external electric field up to 1 kV mm−1 applied along the [001] polar axis was studied using X-ray diffraction methods at room temperature. Electrical conductivity was measured and rocking curves for reflections 400, 070 and 004 were obtained by time-resolved X-ray diffractometry in Laue and Bragg geometries. Two saturation processes were observed from the time dependences of the electrical conductivity. A shift in the diffraction peaks and a change in their intensity were found, which indicated a deformation of the crystal structure. Rapid piezoelectric deformation and reversible relaxation-like deformation, kinetically similar to the electrical conductivity of a crystal, were revealed. The deformation depended on the polarity and strength of the applied field. The deformation was more noticeable in the [100] direction and was practically absent in the [001] direction of the applied field. X-ray diffraction analysis revealed a disordered arrangement of potassium atoms, i.e. additional positions and vacancies. The heights of potential barriers between the positions of K+ ions and the paths of their possible migration in the crystal structure of potassium acid phthalate were determined. The data obtained by time-resolved X-ray diffractometry and X-ray structure analysis, along with additional electrophysical measurements, allow the conclusion that the migration of charge carriers (potassium cations) leads to lateral deformation of the crystal structure of potassium phthalate in an external electric field.

Observation of parametric X-ray radiation for the asymmetric Laue geometry

Angular distributions of parametric X-ray radiation from 255-MeV electrons in a thin Si crystal have been investigated for asymmetric Laue geometries using an imaging plate as a two-dimensional position-sensitive X-ray detector. The peak intensities of parametric X-ray radiation observed for (111) and (1¯1¯ 1) reflections, normalized by taking into account the effective target thickness and the transmission fraction of X-rays in the crystal, coincided within several percent. A large intensity difference depending on the asymmetry parameter, which is predicted by a dynamical theory dealing with the asymmetric Laue geometry, was not observed under the present experimental conditions. This indicates that the dependence of angular distributions of parametric X-ray radiation on the asymmetry parameter is negligibly weak, i.e., that it can be well explained by the well-established kinematical theory and dynamical theory as well as those for symmetric Laue and Bragg geometries.

Femtosecond laser pulse splitting effect in second harmonic generation under Laue diffraction in one-dimensional photonic crystals

The ability to manipulate the frequency of light is a cornerstone of a wide range of applications in photonics expanding spectral ranges of the light sources. To boost the second harmonic generation efficiency, intense efforts toward exploiting artificial microstructures for frequency doubling were carried out. The sought-after approach of utilizing photonic crystals is inspired by their unusual light dispersion. In such structures, the dynamics of the field of femtosecond laser pulses is of paramount importance for frequency conversion. In this work, we investigate the phase-matched second harmonic generation under the effect of diffraction-induced femtosecond laser pulse splitting in one-dimensional photonic crystals at the Bragg diffraction in the Laue geometry. We demonstrate that the interaction of the two pulses at the fundamental frequency that appears in photonic crystals through the dynamical light diffraction leads to a nonmonotonic dependence of the frequency up-conversion efficiency with respect to the laser pulse duration, thus allowing to increase the second harmonic power by tuning the pulse duration.

Chirped pulse propagation in a quasi-PT-symmetric medium with a broadband exceptional-point condition.

The boundary problem of dynamical Bragg diffraction of a chirped optical pulse in a dispersive quasi-PT-symmetric photonic crystal (PhC) in the Laue geometry ("on transmission") is solved by the analytical spectral method. It is shown that, in a quasi-PT-symmetric medium, in which an inhomogeneous spectral line width is much larger than the spectrum of investigated field, the exceptional-point (EP) condition is realized in a wide continuous frequency range, i.e., so-called broadband exceptional-point (BEP) condition takes place. If the Bragg condition is satisfied in a much narrower spectral range than the pulse spectrum, it leads to dramatic changes in the propagation dynamics and parameters of broadband chirped pulses in a quasi-PT-symmetric PhC. Indeed, for a positive Bragg angle of incidence in the case of diffraction in the Laue geometry, the entire spectrum of a broadband chirped pulse fulfills the BEP condition. The diffractionally reflected wave is absent in the BEP regardless of whether the Bragg condition is satisfied, and the pulse propagates as in a homogeneous conservative medium, i.e., without diffraction, gain and loss - unidirectional invisibility. When the sign of the angle of incidence changes, a unidirectional enhancement of the chirped diffracted pulse is observed in that part of it whose frequency simultaneously satisfies both the BEP condition and the Bragg condition. The rest part of the pulse, for which the Bragg condition is not satisfied, propagates as in the case of a positive angle of incidence - there is no diffracted wave. With a smooth change in the angle of incidence of the chirped pulse, a change in frequency that satisfies the Bragg condition occurs and, as a consequence, a smooth change appears in the frequency of the amplified output pulse, as well as in its duration and transverse size. It is also shown that the dispersion of the group velocity of the pulse is suppressed in the frequency range of the BEP condition. Therefore, all its frequency components propagate at a speed close to the speed of light in a conservative homogeneous medium.

Tomographic reconstruction using tilted Laue analyser-based X-ray phase-contrast imaging.

Analyser-based phase-contrast imaging (ABPCI) is a highly sensitive phase-contrast imaging method that produces high-contrast images of weakly absorbing materials. However, it is only sensitive to phase gradient components lying in the diffraction plane of the analyser crystal [i.e. in one dimension (1-D)]. In order to accurately account for and measure phase effects produced by the wavefield-sample interaction, ABPCI and other 1-D phase-sensitive methods must achieve 2-D phase gradient sensitivity. An inclined geometry method was applied to a Laue geometry setup for X-ray ABPCI through rotation of the detector and object about the optical axis. This allowed this traditionally 1-D phase-sensitive phase-contrast method to possess 2-D phase gradient sensitivity. Tomographic datasets were acquired over 360° of a multi-material phantom with the detector and sample tilted by 8°. The real and imaginary parts of the refractive index were reconstructed for the phantom.

Spin waves in meander shaped YIG film: Toward 3D magnonics

We report on the experimental observation of a spin wave (SW) propagation in a magnetic film lying on a developed surface—a three-dimensional (3D) magnonic structure. The 3D magnonic structure was fabricated by deposition of a 180 nm thick yttrium iron garnet film on the patterned substrate with a one-dimensional array of 1.5 μm deep grooves with the period of 20 μm using ion beam sputtering. We experimentally explored SW propagation in such a periodic structure for Bragg and Laue geometries. Transmission characteristics showed that for the Bragg geometry, the examined structure works more like a system of coupled resonators that are formed by the flat segments of the 3D structure, whereas for the Laue geometry, the features related to a formation of width SW modes and to the discrete diffraction of the SW were observed.

Dual-energy crystal-analyzer scheme for spectral tomography.

In the present work, a method for adjusting a crystal analyzer to separate two characteristic lines from the spectrum of a conventional X-ray tube for simultaneous registration of tomographic projections is proposed. The experimental implementation of this method using radiation of a molybdenum anode (Kα1, Kβ lines) and a silicon Si(111) crystal analyzer in Laue geometry is presented. Projection images at different wavelengths are separated in space and can be recorded independently for further processing. Potential uses of this scheme are briefly discussed.

Broadband quasi-PT-symmetry sustained by inhomogeneous broadening of the spectral line

It is shown that inhomogeneous broadening of the spectral line of active impurities may sustain simultaneously parity ($\mathcal{P}$) and time ($\mathcal{T})$ symmetries of a medium, in a finite range of field frequencies, which is forbidden by the causality principle in media without broadening. If a spectral width of a propagating pulse is less than the inhomogeneous broadening, the medium for such a pulse becomes quasi-$\mathcal{PT}$-symmetric. The effect of the broadband quasi-$\mathcal{PT}$-symmetry in a finite frequency domain, is illustrated by examples of unidirectional diffraction of pulses in Bragg and Laue geometries, propagating in photonic crystals.

Development of a Synthesis Technique and Characterization of High-Quality Iron Borate FeBO3 Single Crystals for Applications in Synchrotron Technologies of a New Generation

A flux growth technique for synthesizing FeBO3 single crystals of high structural perfection was developed. The high structural quality of the synthesized FeBO3 crystals was confirmed by means of double-crystal X-ray diffraction analysis both in Laue and Bragg geometries. The diffraction rocking curves taken locally and integrally over the surface are in excellent agreement with the calculated curves. Some macrodefects were revealed by X-ray topography in the crystal volume. However, the local defects do not prevent the use of defect-free regions of the crystal for synchrotron Mossbauer experiments.

X-ray reflectivity of chemically vapor-deposited diamond single crystals in the Laue geometry.

The absolute X-ray reflectivity of chemically vapor-deposited (CVD) single-crystal diamond plates was measured in the Laue geometry in the double-crystal non-dispersive setting with an asymmetric Si beam-conditioner crystal. The measurements were supplemented by rocking-curve topography. The measured reflectivity curves are examined in the framework of the Darwin-Hamilton approach using a set of two independent parameters: the characteristic thickness of mosaic blocks and their average angular misorientation. Owing to strong extinction effects, the width of the reflectivity curves does not directly represent the average misorientation of the blocks. Two different sets of parameters were found for the 111 asymmetric reflection in the two different scattering configurations (beam compression and beam expansion). Analysis of the rocking-curve topographs shows that this discrepancy can be attributed to inhomogeneity of the diamond crystal microstructure.