Theory of two-dimensional focusing of a spherical X-ray wave by Bragg diffraction by two bent crystals

2002 ◽  
Vol 35 (6) ◽  
pp. 713-719
Author(s):  
T. Tchen
Keyword(s):  
Film Thickness ◽  
Spherical Aberration ◽  
Dynamical Theory ◽  
Bragg Diffraction ◽  
Two Dimensional ◽  
Double Crystal ◽  
X Ray ◽  
Point To Point ◽  
Bent Crystals

The dynamical theory of the diffractional Bragg focusing in a system of cylindrically bent crystals is developed. Two-dimensional focusing `point-to-point' is shown to be possible under certain conditions. The influence of geometrical aberrations (astigmatism, spherical aberration) on the focusing is discussed. The influence of X-ray source sizes and temperature on the focusing is treated theoretically. A double-crystal focusing spectrometer is analysed. Focusing of X radiation by crystals with thin epitaxic films is investigated theoretically. Sensitivity of this focusing to the film thickness (∼1 µm) is demonstrated.

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.

scholarly journals X-ray microscopy of laser-produced plasmas with the use of bent crystals

1991 ◽  
Vol 9 (1) ◽  
pp. 135-148 ◽  
Author(s):  
E. Förster ◽  
K. Gäbel ◽  
I. Uschmann
Keyword(s):  
Dynamical Theory ◽  
High Luminosity ◽  
Spectral Window ◽  
X Ray ◽  
Lyman Alpha ◽  
Laser Facility ◽  
Spectral Ranges ◽  
Bent Crystals ◽  
Intercombination Line

X-ray spectroscopical and microscopical methods are used for the determination of the spectral and spatial distribution of X-ray intensity of laser-produced plasmas. The use of Bragg reflections of two-dimensionally bent crystals enables the X-ray microscopical imaging in narrow spectral ranges (Δλ/λ = 10−4 to 10−2) with wavelengths 0.1 nm < λ > 2.6 nm. It is possible to adapt, in the X-ray microscope, the distances, magnification, position, and width of the spectral window to the special conditions of the laser facility. Manufacturing and testing of the two-dimensionally bent crystals requires a great deal of effort. It was demonstrated that a spatial resolution of about 5 μm was achieved, and that the experimentally determined reflectivity was found to be in close agreement with the dynamical theory of X-ray interferences. Due to high luminosity of the X-ray microscope, in experiments with laser-produced plasmas it was necessary to attenuate the radiation with aperture-limiting diaphragms or filters down to 0.01–1% of the original intensity in the case of a magnification of about one. Emission of the resonance line W 1–2, the intercombination line of helium-like ions, and Lyman alpha line were imaged simultaneously with a three-channel microscope. Such images form the foundation for establishing the Ne(r), Tz(r) maps.

scholarly journals Applications of dynamical theory of X-ray diffraction by perfect crystals to reciprocal space mapping

2017 ◽  
Vol 50 (5) ◽  
pp. 1256-1266 ◽  
Author(s):  
Vasily I. Punegov ◽  
Konstantin M. Pavlov ◽  
Andrey V. Karpov ◽  
Nikolai N. Faleev
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Two Dimensional ◽  
Instrumental Function ◽  
X Ray Diffraction ◽  
Reciprocal Space Mapping ◽  
Lattice Vector ◽  
Reflected Waves ◽  
X Ray ◽  
Special Case

The classical dynamical theory of X-ray diffraction is expanded to the special case of transversely restricted wavefronts of the incident and reflected waves. This approach allows one to simulate the two-dimensional coherently scattered intensity distribution centred around a particular reciprocal lattice vector in the so-called triple-crystal diffraction scheme. The effect of the diffractometer's instrumental function on X-ray diffraction data was studied.

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.

scholarly journals Femtosecond X-ray diffraction from two-dimensional protein crystals

IUCrJ ◽  
2014 ◽  
Vol 1 (2) ◽  
pp. 95-100 ◽  
Author(s):  
Matthias Frank ◽  
David B. Carlson ◽  
Mark S. Hunter ◽  
Garth J. Williams ◽  
Marc Messerschmidt ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Bragg Diffraction ◽  
Protein Crystal ◽  
Protein Crystals ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Linac Coherent Light Source ◽  
Diffraction Patterns ◽  
Better Than

X-ray diffraction patterns from two-dimensional (2-D) protein crystals obtained using femtosecond X-ray pulses from an X-ray free-electron laser (XFEL) are presented. To date, it has not been possible to acquire transmission X-ray diffraction patterns from individual 2-D protein crystals due to radiation damage. However, the intense and ultrafast pulses generated by an XFEL permit a new method of collecting diffraction data before the sample is destroyed. Utilizing a diffract-before-destroy approach at the Linac Coherent Light Source, Bragg diffraction was acquired to better than 8.5 Å resolution for two different 2-D protein crystal samples each less than 10 nm thick and maintained at room temperature. These proof-of-principle results show promise for structural analysis of both soluble and membrane proteins arranged as 2-D crystals without requiring cryogenic conditions or the formation of three-dimensional crystals.

Simulation of X-ray diffraction in a cylindrical crystal

2020 ◽  
Vol 53 (5) ◽  
pp. 1203-1211
Author(s):  
Vasily I. Punegov ◽  
Sergey I. Kolosov
Keyword(s):  
Numerical Simulation ◽  
Recurrence Relations ◽  
Bragg Diffraction ◽  
Small Radius ◽  
Large Radius ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Reflection And Transmission ◽  
X Ray ◽  
Cylindrical Crystal

Using the two-dimensional recurrence relations of X-ray dynamical diffraction, a numerical simulation of reflection and transmission intensity in a cylindrical crystal has been performed. It is shown that for crystals with a small radius Bragg diffraction is realized. For crystals of large radius, Bragg–Laue diffraction occurs, which is characterized by Bragg diffraction on the upper part of the crystal, as well as the presence of Pendellösung oscillations inside the cylindrical crystal. The reciprocal space maps of dynamical and kinematical diffraction have been calculated.

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