Formulation of dynamical theory of X-ray diffraction for perfect crystals in the Laue case using the Riemann surface

2016 ◽  
Vol 72 (3) ◽  
pp. 338-348 ◽  
Author(s):  
Takashi Saka
Keyword(s):  
Riemann Surface ◽  
Complex Analysis ◽  
Dynamical Theory ◽  
Bragg Condition ◽  
X Ray Diffraction ◽  
X Ray ◽  
The Real ◽  
Dispersion Surface ◽  
Complex Planes ◽  
Characteristic Features

The dynamical theory for perfect crystals in the Laue case was reformulated using the Riemann surface, as used in complex analysis. In the two-beam approximation, each branch 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 specifying the degree of departure from the exact Bragg condition and the reflection strength. By representing these parameters on complex planes, these characteristics can be graphically depicted on the Riemann surface. In the conventional case, the absorption is small and the real part of the reflection strength is large, so the formulation is the same as the traditional analysis. However, when the real part of the reflection strength is small or zero, the two branches of the dispersion surface cross, and the dispersion relationship becomes similar to that of the Bragg case. This is because the geometrical relationships among the parameters are similar in both cases. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters. Furthermore, the present method analytically revealed many characteristic features of the dispersion surface and will be quite instructive for further numerical calculations of rocking curves.

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.

Properties of X-ray resonant scattering in the Bragg case revealed on the Riemann surface

2016 ◽  
Vol 72 (4) ◽  
pp. 472-479 ◽  
Author(s):  
Takashi Saka
Keyword(s):  
Riemann Surface ◽  
Numerical Analysis ◽  
Strength Characteristic ◽  
Resonant Scattering ◽  
Dynamical Theory ◽  
Acta Cryst ◽  
Rocking Curve ◽  
X Ray ◽  
Dispersion Surface ◽  
Characteristic Features

Continuing the work described in the previous paper [Saka (2016).Acta Cryst.A72, 338–348], the dynamical theory for perfect crystals in the Bragg case is reformulated using the Riemann surface. In particular, diffraction under resonant scattering conditions is investigated. The characteristic features of the dispersion surface and the rocking curve are analytically revealed using four parameters, which are the real and imaginary parts of two quantities specifying the degree of departure from the exact Bragg conditions and the reflection strength. Characteristic properties that have been deduced through numerical analysis are derived analytically using these four parameters. Visualization of the geometric relationships between the four parameters on the Riemann surface is useful for understanding many properties such as symmetry and sharpness of the rocking curve under special conditions. Therefore, employing the Riemann surface is instructive for numerical analysis and useful for understanding dynamical diffraction in the Bragg case.

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.

Multiple reflection optimization package for X-ray diffraction

CrystEngComm ◽  
2021 ◽  
Author(s):  
S. Magalhães ◽  
J. S. Cabaço ◽  
J. P. Araújo ◽  
E. Alves
Keyword(s):  
Dynamical Theory ◽  
Multiple Reflection ◽  
X Ray Diffraction ◽  
X Ray

New software for the simulation and fitting of 2θ–ω scans of symmetric and asymmetric reflections based on the dynamical theory of X-ray diffraction is presented.

Synthesis, Characterization and Thermal Behavior of  HYP2O7·3H2O Electrical Properties of  HYP2O7

2021 ◽  
Author(s):  
Rahma Rahzelli Zrelli ◽  
Fathia Chehimi-Moumen ◽  
Dalila Ben Hassen-Chehimi ◽  
Malika Trabelsi-Ayadi
Keyword(s):  
Infrared Spectroscopy ◽  
Electrical Properties ◽  
Complex Analysis ◽  
Optical Band Gap ◽  
Water Molecules ◽  
X Ray Diffraction ◽  
Soft Chemistry ◽  
Medium Temperature ◽  
X Ray ◽  
Three Stages

Abstract The synthesis of the diphosphate HYP2O7·3H2O was made via soft chemistry route from evaporation of aqueous solution at room temperature. The obtained compound, was characterized by means of X-ray diffraction (XRD) and infrared spectroscopy (IR). The results showed a high purity phase. IR spectrum of this diphosphate revealed usual signals related to P2O7 diphosphate group and water molecules. The thermal decomposition of the synthesized product by DTA / TG proceeded through four stages leading to the formation of the Y2P4O13 as a final product. On the other hand, its decomposition by CRTA took place in three stages leading to the formation of the anhydrous diphosphate HYP2O7 as a final product. X-ray powder diffraction and infrared spectroscopy were used to identify these materials. Furthermore the electrical properties of the HYP2O7 were investigated through impedance complex analysis. Modest conductivity has been observed in this material at relatively medium temperature range. Activation energy of 0.67 and 1.44 eV, was deduced from the corresponding Arrhenius plot.The optical band gap of the title compound is calculated and found to be 2.71 eV.

An algorithm for calculating diffraction profiles of 2θ scans for multiple diffraction from crystals and thin films

2014 ◽  
Vol 70 (6) ◽  
pp. 572-582
Author(s):  
Hsin-Yi Chen ◽  
Mau-Sen Chiu ◽  
Chia-Hung Chu ◽  
Shih-Lin Chang
Keyword(s):  
Initial Phase ◽  
Atomic Layer ◽  
Dynamical Theory ◽  
Far Field ◽  
X Rays ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
X Ray ◽  
Beam Surface ◽  
Surface Diffraction

An algorithm is developed based on the dynamical theory of X-ray diffraction for calculating the profiles of the diffracted beam,i.e.the diagrams of the intensity distributionversus2θ when a crystal is fixed at an angle of its maximum diffracted intensity. Similar to Fraunhofer (far-field) diffraction for a single-slit case, in the proposed algorithm the diffracted beam from one atomic layer excited by X-rays is described by the composition of (N+ 1) coherent point oscillators in the crystal. The amplitude and the initial phase of the electric field for each oscillator can be calculated based on the dynamical theory with given boundary conditions. This algorithm not only gives diffraction profiles but also provides the contribution of the excitation of modes when extremely asymmetric diffraction is involved in the diffraction process. Examples such as extremely asymmetric two-beam surface diffraction and three-beam surface diffraction are presented and discussed in detail.

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