Dynamical Theory of X-Ray Diffraction for Restricted Beams: III. Analysis of Experimental Data for a Porous Crystal

2018 ◽  
Vol 127 (2) ◽  
pp. 236-243 ◽  
Author(s):  
V. I. Punegov ◽  
A. A. Lomov
1966 ◽  
Vol 10 ◽  
pp. 67-79
Author(s):  
P. Penning

AbstractComplete dynamical solutions for three coupled plane-wave components in crystal structures with inversion symmetry have been found. After reviewing briefly the dynamical solutions for wave fields with two coupled plane-wave components, the results for the three-beam case are discussed in qualitative terms. Attention is paid to singular points and lines on the ω-surface, and to the attenuation of the mode-intensity because of absorption. The most surprising result is that in the case one of the reflections is forbidden (Umweganregung) the absorption is reduced in comparison with the adjoining two-beam cases. Experimental data are in reasonable agreement with the theory. Quantitative data are presented for a few three-beam cases of simultaneous diffraction of Cu Kα. radiation in germanium.


Materials ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2518
Author(s):  
Dorota Kołodyńska ◽  
Yongming Ju ◽  
Małgorzata Franus ◽  
Wojciech Franus

The possibility of application of chitosan-modified zeolite as sorbent for Cu(II), Zn(II), Mn(II), and Fe(III) ions and their mixtures in the presence of N-(1,2-dicarboxyethyl)-D,L-aspartic acid, IDHA) under different experimental conditions were investigated. Chitosan-modified zeolite belongs to the group of biodegradable complexing agents used in fertilizer production. NaP1CS as a carrier forms a barrier to the spontaneous release of the fertilizer into soil. The obtained materials were characterized by Fourier transform infrared spectroscopy (FTIR); surface area determination (ASAP); scanning electron microscopy (SEM-EDS); X-ray fluorescence (XRF); X-ray diffraction (XRD); and carbon, hydrogen, and nitrogen (CHN), as well as thermogravimetric (TGA) methods. The concentrations of Cu(II), Zn(II), Mn(II), and Fe(III) complexes with IDHA varied from 5–20 mg/dm3 for Cu(II), 10–40 mg/dm3 for Fe(III), 20–80 mg/dm3 for Mn(II), and 10–40 mg/dm3 for Zn(II), respectively; pH value (3–6), time (1–120 min), and temperature (293–333 K) on the sorption efficiency were tested. The Langmuir, Freundlich, Dubinin–Radushkevich, and Temkin adsorption models were applied to describe experimental data. The pH 5 proved to be appropriate for adsorption. The pseudo-second order and Langmuir models were consistent with the experimental data. The thermodynamic parameters indicate that adsorption is spontaneous and endothermic. The highest desorption percentage was achieved using the HCl solution, therefore, proving that method can be used to design slow-release fertilizers.


1998 ◽  
Vol 5 (3) ◽  
pp. 967-968 ◽  
Author(s):  
Keiichi Hirano ◽  
Atsushi Momose

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.


CrystEngComm ◽  
2021 ◽  
Author(s):  
S. Magalhães ◽  
J. S. Cabaço ◽  
J. P. Araújo ◽  
E. Alves

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.


2014 ◽  
Vol 70 (6) ◽  
pp. 572-582
Author(s):  
Hsin-Yi Chen ◽  
Mau-Sen Chiu ◽  
Chia-Hung Chu ◽  
Shih-Lin Chang

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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