The dynamical theory of X-ray Bragg diffraction from a crystal with a uniform strain gradient. The Green–Riemann functions

1978 ◽  
Vol 34 (4) ◽  
pp. 610-621 ◽  
Author(s):  
F. N. Chukhovskii ◽  
K. T. Gabrielyan ◽  
P. V. Petrashen'
Author(s):  
V. B. Molodkin ◽  
S. I. Olikhovskii ◽  
S. V. Dmitriev ◽  
V. V. Lizunov

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.


2020 ◽  
Vol 76 (1) ◽  
pp. 45-54
Author(s):  
V. B. Molodkin ◽  
S. I. Olikhovskii ◽  
S. V. Dmitriev ◽  
A. I. Nizkova ◽  
V. V. Lizunov

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.


2002 ◽  
Vol 35 (6) ◽  
pp. 713-719
Author(s):  
T. Tchen

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.


2019 ◽  
Vol 75 (6) ◽  
pp. 842-850
Author(s):  
Tomoe Fukamachi ◽  
Sukswat Jongsukswat ◽  
Dongying Ju ◽  
Riichirou Negishi ◽  
Keiichi Hirano ◽  
...  

Under the anomalous transmission condition in the Bragg mode, X-ray interference fringes were observed between two beams with different hyperbolic trajectories in a very weakly bent plane-parallel perfect crystal with negative strain gradient. The origin of the fringes was analysed based on the dynamical theory of diffraction for a distorted crystal. In the reflected beam from the entrance surface, the interference fringes were observed between once- and twice-reflected beams from the back surface. In the transmitted beam from the back surface, the interference fringes were observed between the direct beam and once-reflected beam from the entrance surface. In the emitted beam from the lateral surface, the interference fringes were observed between the beams after different numbers of reflections in the crystal. The multiply reflected beams were formed by a combined result of long propagation length along the beam direction with large divergence of the refracted beams when the strain gradient was negative. The period of these interference fringes was sensitive to very weak strain, of the order of 10−7.


1994 ◽  
Vol 04 (C9) ◽  
pp. C9-191-C9-194
Author(s):  
I. A. Vartanyantz ◽  
M. V. Kovalchuk ◽  
I. N. Ustimenko

2008 ◽  
Vol 41 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Václav Holý ◽  
Paul F. Fewster

A new method is presented for a calculation of the reciprocal-space distribution of X-ray diffracted intensity along a crystal truncation rod. In contrast to usual kinematical or dynamical approaches, the method is correct both in the reciprocal-lattice points and between them. In the method, the crystal is divided into a sequence of very thin slabs parallel to the surface; in contrast to the well known Darwin dynamical theory, the electron density in the slabs is constant along the surface normal. The diffracted intensity is calculated by a matrix formalism based on the Fresnel reflection and transmission coefficients. The method is applicable for any polarization of the primary beam and also in a non-coplanar scattering geometry.


2006 ◽  
Vol 18 (49) ◽  
pp. 11195-11202 ◽  
Author(s):  
A M Mulders ◽  
U Staub ◽  
V Scagnoli ◽  
S W Lovesey ◽  
E Balcar ◽  
...  
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