Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. I. Semi-dynamical model

2020 ◽  
Vol 76 (1) ◽  
pp. 45-54
Author(s):  
V. B. Molodkin ◽  
S. I. Olikhovskii ◽  
S. V. Dmitriev ◽  
A. I. Nizkova ◽  
V. V. Lizunov
Keyword(s):  
Silicon Crystal ◽  
Azimuthal Angle ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
X Ray Diffraction ◽  
X Ray ◽  
X Ray Scattering ◽  
Diffraction Geometry ◽  
Coulomb Type ◽  
Analytical Expressions

The analytical expressions for the coherent and diffuse components of the integrated reflection coefficient are considered in the case of asymmetric Bragg diffraction geometry for a single crystal of arbitrary thickness, which contains randomly distributed Coulomb-type defects. The possibility to choose the combinations of diffraction conditions optimal for characterizing defects of several types by accounting for dynamical effects in the integrated coherent and diffuse scattering intensities, i.e. primary extinction and anomalous absorption, has been analysed based on the statistical dynamical theory of X-ray diffraction by imperfect crystals. The measured integrated reflectivity dependencies of the imperfect silicon crystal on azimuthal angle were fitted to determine the diffraction parameters characterizing defects in the sample using the proposed formulas in semi-dynamical and semi-kinematical approaches.

Dynamical effects in the integrated X-ray scattering intensity from imperfect crystals in Bragg diffraction geometry. II. Dynamical theory

2021 ◽  
Vol 77 (5) ◽  
Author(s):  
V. B. Molodkin ◽  
S. I. Olikhovskii ◽  
S. V. Dmitriev ◽  
V. V. Lizunov
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
Three Dimensions ◽  
X Ray ◽  
X Ray Scattering ◽  
Diffraction Geometry ◽  
Lattice Space ◽  
Integrated Intensities ◽  
Ray Scattering

The analytical expressions for coherent and diffuse components of the integrated reflection coefficient are considered in the case of Bragg diffraction geometry for single crystals containing randomly distributed microdefects. These expressions are analyzed numerically for the cases when the instrumental integration of the diffracted X-ray intensity is performed on one, two or three dimensions in the reciprocal-lattice space. The influence of dynamical effects, i.e. primary extinction and anomalously weak and strong absorption, on the integrated intensities of X-ray scattering is investigated in relation to the crystal structure imperfections.

Investigation of the phase shift in X-ray forward diffraction using an X-ray interferometer

1998 ◽  
Vol 5 (3) ◽  
pp. 967-968 ◽  
Author(s):  
Keiichi Hirano ◽  
Atsushi Momose
Keyword(s):  
Phase Shift ◽  
Silicon Crystal ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Bragg Geometry

The phase shift of forward-diffracted X-rays by a perfect crystal is discussed on the basis of the dynamical theory of X-ray diffraction. By means of a triple Laue-case X-ray interferometer, the phase shift of forward-diffracted X-rays by a silicon crystal in the Bragg geometry was investigated.

scholarly journals Experimentally obtained and computer-simulated X-ray non-coplanar 18-beam pinhole topographs for a silicon crystal

2019 ◽  
Vol 75 (3) ◽  
pp. 483-488 ◽  
Author(s):  
Kouhei Okitsu ◽  
Yasuhiko Imai ◽  
Yoshitaka Yoda
Keyword(s):  
Silicon Crystal ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Good Agreement

Non-coplanar 18-beam X-ray pinhole topographs for a silicon crystal were computer simulated by fast Fourier transforming the X-ray rocking amplitudes that were obtained by solving the n-beam (n = 18) Ewald–Laue dynamical theory (E-L&FFT method). They were in good agreement with the experimentally obtained images captured using synchrotron X-rays. From this result and further consideration based on it, it has been clarified that the X-ray diffraction intensities when n X-ray waves are simultaneously strong in the crystal can be computed for any n by using the E-L&FFT method.

Characterizing nanoparticles with a laboratory diffractometer: from small-angle to total X-ray scattering

2014 ◽  
Vol 29 (S1) ◽  
pp. S47-S53 ◽  
Author(s):  
Marco Sommariva ◽  
Milen Gateshki ◽  
Jan-André Gertenbach ◽  
Joerg Bolze ◽  
Uwe König ◽  
...  
Keyword(s):  
Small Angle ◽  
Structural Features ◽  
Bragg Diffraction ◽  
X Ray Diffraction ◽  
X Ray ◽  
X Ray Scattering ◽  
Transmission Electron ◽  
Pdf Analysis ◽  
Comprehensive Picture ◽  
Ray Scattering

X-ray diffraction and scattering on a single multipurpose X-ray platform have been used to probe the structure, composition, and thermal behavior of TiO2 nanoparticles ranging in size from 1 to 10 nm. Ambient and non-ambient Bragg diffraction, small-angle X-ray scattering (SAXS), as well as total scattering and pair-distribution function (PDF) analysis are combined to obtain a comprehensive picture of the samples. At these ultrasmall particle-size dimensions, SAXS and PDF prove powerful in distinguishing the salient features of the materials, in particular the size distribution of the primary particles (SAXS) and the identification of the TiO2 polymorphs (PDF). Structural features determined by X-ray scattering techniques are corroborated by high-resolution transmission electron microscopy. The elemental make-up of the materials has been measured using X-ray fluorescence spectrometry and energy-dispersive X-ray analysis.

scholarly journals Femtosecond X-ray diffraction from an aerosolized beam of protein nanocrystals

2018 ◽  
Vol 51 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Salah Awel ◽  
Richard A. Kirian ◽  
Max O. Wiedorn ◽  
Kenneth R. Beyerlein ◽  
Nils Roth ◽  
...  
Keyword(s):  
High Repetition Rate ◽  
Bragg Diffraction ◽  
Liquid Jet ◽  
X Ray Diffraction ◽  
Single Particles ◽  
Jet Injection ◽  
X Ray ◽  
High Repetition ◽  
High Particle ◽  
X Ray Scattering

High-resolution Bragg diffraction from aerosolized single granulovirus nanocrystals using an X-ray free-electron laser is demonstrated. The outer dimensions of the in-vacuum aerosol injector components are identical to conventional liquid-microjet nozzles used in serial diffraction experiments, which allows the injector to be utilized with standard mountings. As compared with liquid-jet injection, the X-ray scattering background is reduced by several orders of magnitude by the use of helium carrier gas rather than liquid. Such reduction is required for diffraction measurements of small macromolecular nanocrystals and single particles. High particle speeds are achieved, making the approach suitable for use at upcoming high-repetition-rate facilities.

Theory of moiré fringes on X-ray diffraction topographs of bicrystals

1999 ◽  
Vol 55 (3) ◽  
pp. 413-422 ◽  
Author(s):  
Michael Ohler ◽  
Jürgen Härtwig
Keyword(s):  
Optical Properties ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
X Ray Diffraction ◽  
X Ray ◽  
Moiré Fringes ◽  
Diffraction Geometry

The theory of moiré fringes on X-ray diffraction topographs of bicrystals is derived from the dynamical theory of X-ray diffraction for the reflection (Bragg) and the transmission (Laue) case. The influence on the moiré fringes of the diffraction geometry, of the geometry of the sample, of its optical properties and of the topographic method is investigated. The perfect-crystal theory is also expanded to weakly deformed bicrystals.

scholarly journals Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory

2018 ◽  
Vol 51 (1) ◽  
pp. 68-75 ◽  
Author(s):  
Hao Feng ◽  
Rana Ashkar ◽  
Nina Steinke ◽  
Robert Dalgliesh ◽  
Nickolay V. Lavrik ◽  
...  
Keyword(s):  
Spin Echo ◽  
Dynamical Theory ◽  
X Rays ◽  
Phase Approximation ◽  
X Ray Diffraction ◽  
Colloidal Structure ◽  
X Ray ◽  
X Ray Scattering ◽  
Weak Phase ◽  
Colloidal Fluids

A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography. It is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. While the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.

Exotic X-ray back-diffraction: a path toward a soft inelastic X-ray scattering spectrometer

2014 ◽  
Vol 47 (5) ◽  
pp. 1658-1665 ◽  
Author(s):  
Marcelo Goncalves Hönnicke ◽  
Raymond Conley ◽  
Cesar Cusatis ◽  
Edson Massayuki Kakuno ◽  
Juan Zhou ◽  
...  
Keyword(s):  
Dynamical Theory ◽  
Extreme Condition ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Magnetic Imaging ◽  
X Ray Scattering ◽  
Low Energies ◽  
Different Temperatures ◽  
Ray Scattering

In this work, soft X-ray back-diffraction (XBD; X-ray diffraction at angles near and exactly equal to 90°) is explored. The experiment was conducted at the SXS beamline at Laboratorio Nacional de Luz Sincrotron, Brazil, at ∼3.2 keV. A high-resolution Si(220) multi-bounce back-diffraction monochromator was designed and constructed for this experiment. An ultra-thin Si(220) crystal (5 µm thick) was used as the sample. This ultra-thin crystal was characterized by profilometry, rocking-curve measurements and X-ray topography prior to the XBD measurements. It is shown that the measured forward-diffracted beam (o-beam) profiles, taken at different temperatures, are in close agreement with profiles predicted by the extended dynamical theory of X-ray diffraction, with the absence of multiple-beam diffraction (MBD). This is an important result for future studies on the basic properties of back-diffracted X-ray beams at energies slightly above the exact XBD condition (extreme condition where XBD is almost extinguished). Also, the results presented here indicate that stressed crystals behave like ideal strain-free crystals when used for low-energy XBD. This is mainly due to the large widths of XBD profiles, which lead to a low strain sensitivity in the detection of defects. This result opens up new possibilities for mounting spherical analyzers without degrading the energy resolution, at least for low energies. This is a path that may be used to construct a soft inelastic X-ray scattering spectrometer where different applications such as element-specific magnetic imaging tools could be explored.

Generation and Proof of Elliptically Polarized X-Rays

1982 ◽  
Vol 37 (6) ◽  
pp. 524-527
Author(s):  
O. Brümmer ◽  
Ch. Eisenschmidt ◽  
H. R. Höche
Keyword(s):  
Phase Relation ◽  
Silicon Crystal ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
Wave Fields ◽  
X Ray ◽  
Polarized Waves ◽  
Angle Of Reflection ◽  
Elliptically Polarized

Abstract Using an arrangement being analogous to optics of visible light the phase relation of the mutually perpendicularly polarized wave fields are examined in the Laue case of X-ray diffraction. Bragg reflections at an angle of reflection of about 45° are used as polarizer and analyzer. The different phase relations result from different thicknesses of a wedge-shaped silicon crystal, which is placed between the polarizer and the analyzer and adjusted for the symmetric 220-CuKαl-Laue case. The determined polarization states produced by coherent excitation of both σ-polarized and π-polarized waves in the silicon crystal coincide very well with calculations of the dynamical theory of X-ray diffraction.

X-ray diffraction properties of curved crystal diffractors

1992 ◽  
Vol 50 (2) ◽  
pp. 1734-1735
Author(s):  
W. Z. Chang ◽  
D. B. Wittry
Keyword(s):  
Diffraction Theory ◽  
X Rays ◽  
Diffraction Image ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Bent Crystal ◽  
Diffraction Geometry ◽  
Crystal Parameter ◽  
Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

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