Integrated intensities in Laue-Bragg cases for non-absorbing crystals in X-ray dynamical diffraction

2009 ◽  
Vol 206 (8) ◽  
pp. 1870-1874
Author(s):  
Takashi Saka
Keyword(s):  
Dynamical Diffraction ◽  
X Ray ◽  
Integrated Intensities

scholarly journals Imperfect Crystals and Dynamical X-ray Diffraction in the Complex Reflectance Plane

1991 ◽  
Vol 44 (6) ◽  
pp. 693 ◽  
Author(s):  
TJ Davis
Keyword(s):  
Stochastic Model ◽  
Parameter Space ◽  
Langevin Equation ◽  
Planck Equation ◽  
Theoretical Framework ◽  
Crystal Defects ◽  
X Rays ◽  
X Ray Diffraction ◽  
Dynamical Diffraction ◽  
X Ray

A theoretical framework is developed to describe the dynamical diffraction of X-rays in perfect and imperfect crystals. The propagation of the X-ray beam inside the crystal is described by the evolution of a set of trajectories in the complex reflectance plane. The trajectory path is determined from a form of the Takagi-Taupin equations and leads naturally to simple forms for the crystal reflectivity for perfect crystals. A stochastic model for the effects of crystal defects is developed in terms of the Langevin equation which leads to a description of diffraction from imperfect crystals as the evolution of densities in a parameter space, described by a Fokker-Planck equation.

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals

2018 ◽  
Vol 74 (5) ◽  
pp. 586-594 ◽  
Author(s):  
Takashi Saka
Keyword(s):  
Riemann Surface ◽  
Analytical Method ◽  
Bragg Condition ◽  
Approximation Characteristic ◽  
Dynamical Diffraction ◽  
X Ray ◽  
The Real ◽  
Dispersion Surface ◽  
Beam Approximation ◽  
Characteristic Features

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals is analysed using a Riemann surface. In the conventional two-beam approximation, each branch or wing of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities that specify the degree of departure from the exact Bragg condition and the reflection strength. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters with no approximation. Characteristic features of the dispersion surface are also revealed by geometrical considerations with respect to the Riemann surface.

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.

New developments including X-ray standing waves in the dynamical Bragg diffraction program of X-ray Server

2021 ◽  
Vol 54 (5) ◽  
pp. 1530-1534
Author(s):  
Sergey Stepanov
Keyword(s):  
Standing Waves ◽  
Grazing Incidence ◽  
Bragg Diffraction ◽  
Use Cases ◽  
X Ray Diffraction ◽  
New Developments ◽  
Dynamical Diffraction ◽  
X Ray

X-ray Server (https://x-server.gmca.aps.anl.gov) is a collection of programs for online modelling of X-ray diffraction and scattering. The dynamical diffraction program is the second most popular Server program, contributing 34% of total Server usage. It models dynamical X-ray diffraction from strained crystals and multilayers for any Bragg-case geometry including grazing incidence and exit. This paper reports on a revision of equations used by the program, which yields ten times faster calculations in most use cases, on implementing calculations of X-ray standing waves and on adding new options for modelling diffraction from monolayers.

scholarly journals X-Ray Dynamical Diffraction in Powder Samples with Time-Dependent Particle Size Distributions - ADDENDUM

MRS Advances ◽  
2020 ◽  
Vol 5 (29-30) ◽  
pp. 1623-1623
Author(s):  
Adriana Valério ◽  
Sérgio L. Morelhão ◽  
Alex J. Freitas Cabral ◽  
Márcio M. Soares ◽  
Cláudio M. R. Remédios
Keyword(s):  
Particle Size ◽  
Time Dependent ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Powder Samples
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