scholarly journals Theoretical study of the properties of X-ray diffraction moiré fringes. I

2015 ◽  
Vol 71 (4) ◽  
pp. 368-381 ◽  
Author(s):  
Jun-ichi Yoshimura
Keyword(s):  
Plane Wave ◽  
Theoretical Study ◽  
Diffraction Theory ◽  
Theoretical Description ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
X Ray ◽  
Moiré Fringes ◽  
Plane Wave Diffraction ◽  
Interference Phase

A detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory. Firstly, prior to discussing the main subject of the paper, a previous article [Yoshimura (1997).Acta Cryst.A53, 810–812] on the two-dimensionality of diffraction moiré patterns is restated on a thorough calculation of the moiré interference phase. Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect ofPendellösungintensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images. Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.

scholarly journals Theoretical study of the properties of X-ray diffraction moiré fringes. I. Corrigenda and addenda

2019 ◽  
Vol 75 (4) ◽  
pp. 652-654 ◽  
Author(s):  
Jun-ichi Yoshimura
Keyword(s):  
Theoretical Study ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
X Ray ◽  
Moiré Fringes

Seven corrections are made and several supplementary equations are added to the article by Yoshimura [Acta Cryst. (2015), A71, 368–381].

scholarly journals Theoretical study of the properties of X-ray diffraction moiré fringes. II. Illustration of angularly integrated moiré images

2019 ◽  
Vol 75 (4) ◽  
pp. 610-623
Author(s):  
Jun-ichi Yoshimura
Keyword(s):  
Incident Wave ◽  
Angular Width ◽  
X Ray Diffraction ◽  
Experimental Conditions ◽  
Acta Cryst ◽  
Low Contrast ◽  
X Ray ◽  
Moiré Fringes ◽  
Wide Range ◽  
Fringe Patterns

Using a theory of X-ray diffraction moiré fringes developed in a previous paper, labelled Part I [Yoshimura (2015). Acta Cryst. A71, 368–381], the X-ray moiré images of a silicon bicrystal having a weak curvature strain and an interspacing gap, assumed to be integrated for an incident-wave angular width, are simulation-computed over a wide range of crystal thicknesses and incident-wave angular width, likely under practical experimental conditions. Along with the simulated moiré images, the graphs of characteristic quantities on the moiré images are presented for a full understanding of them. The treated moiré images are all of rotation moiré. Mo Kα1 radiation and the 220 reflection were assumed in the simulation. The results of this simulation show that fringe patterns, which are significantly modified from simple straight fringes of rotation moiré, appear in some ranges of crystal thicknesses and incident-wave angular width, due to a combined effect of Pendellösung oscillation and an added phase difference from the interspacing gap, under the presence of a curvature strain. The moiré fringes which slope to the perpendicular direction to the diffraction vector in spite of the assumed condition of rotation moiré, and fringe patterns where low-contrast bands are produced with a sharp bend of fringes arising along the bands are examples of the modified fringe pattern. This simulation study provides a wide theoretical survey of the type of bicrystal moiré image produced under a particular condition.

scholarly journals Estimating the structure factors in X-ray diffraction

2018 ◽  
Vol 74 (5) ◽  
pp. 481-498 ◽  
Author(s):  
Paul F. Fewster
Keyword(s):  
Diffraction Theory ◽  
Bragg Angle ◽  
Enhancement Effect ◽  
Diffraction Effect ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
X Ray ◽  
Background Removal ◽  
Structure Factors ◽  
Path Lengths

This article takes the concepts of the `new diffraction theory' [Fewster (2014). Acta Cryst. A70, 257–282] and examines the implications for the interpretation of experimental results and the estimation of structure factors. Further experimental evidence is included to justify the conclusions in the theory, showing that the residual intensity at twice the Bragg angle is a diffraction effect and not associated with the crystal shape. This `enhancement' effect is independent of whether kinematical or dynamical theories are applied and can lead to a clearer understanding of how the dynamical effects are suppressed in imperfect crystals. By applying the idea that the higher-order peaks are due to path lengths of nλ, it is shown that `systematically absent' reflections in the conventional theory may not be absent. Because this new theory considers the intensity to be more distributed, it suggests that the entire structure factor can be difficult to capture by experiment. This article suggests some routes to achieve a good approximation of the structure factors for typical methods of data collection. Any measurement of intensity with background removal will exclude some of the distributed intensity, again leading to an underestimate of the structure factors, and therefore the missing intensity needs to be estimated.

scholarly journals Takagi–Taupin dynamical X-ray diffraction simulations of asymmetric X-ray diffraction from crystals: the effects of surface undulations

2020 ◽  
Vol 53 (3) ◽  
pp. 793-799 ◽  
Author(s):  
Albert Macrander
Keyword(s):  
Flat Surface ◽  
Diffraction Theory ◽  
X Ray Diffraction ◽  
Acta Cryst ◽  
Separate Paper ◽  
X Ray ◽  
Kinematic Theory ◽  
Round Cylinder ◽  
Primary Means ◽  
Good Agreement

Dynamical X-ray diffraction simulations from crystals with surface undulations are reported. The Takagi–Taupin equations are applied and used to derive results in good agreement with experimental data reported in a separate paper [Macrander, Pereira, Huang, Kasman, Qian, Wojcik & Assoufid (2020). J. Appl. Cryst. 53, 789–792]. The development of Uragami [J. Phys. Soc. Jpn, (1969), 27, 147–154] is followed. Although previous work by Olekhnovich & Olekhnovich [Acta. Cryst. (1980), A36, 22–27] treated a crystal in the shape of a round cylinder, there do not seem to be any reports of previous dynamical X-ray diffraction treatments specifically for surface undulations. The significance of the present work is that it bridges the diffraction treatment of more classical dynamical diffraction theory, which assumes a flat surface, and the simple kinematic diffraction theory. The kinematic theory has, to date, been the primary means of simulating X-ray diffraction from surfaces.

X-ray diffraction properties of curved crystal diffractors

1992 ◽  
Vol 50 (2) ◽  
pp. 1734-1735
Author(s):  
W. Z. Chang ◽  
D. B. Wittry
Keyword(s):  
Diffraction Theory ◽  
X Rays ◽  
Diffraction Image ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Bent Crystal ◽  
Diffraction Geometry ◽  
Crystal Parameter ◽  
Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

Highlights in the history of X-ray topography1

1995 ◽  
Vol 210 (6) ◽  
Author(s):  
A. R. Lang
Keyword(s):  
Magnetic Domain ◽  
Diffraction Theory ◽  
Dislocation Loops ◽  
X Ray Diffraction ◽  
X Ray ◽  
Domain Structures ◽  
Structure Factors ◽  
History Of ◽  
Dislocation Sources ◽  
Non Destructive

AbstractX-ray topography provides a non-destructive method of mapping point-by-point variations in orientation and reflecting power within crystals. The discovery, made by several workers independently, that in nearly perfect crystals it was possible to detect individual dislocations by X-ray diffraction contrast started an epoch of rapid exploitation of X-ray topography as a new, general method for assessing crystal perfection. Another discovery, that of X-ray Pendellösung, led to important theoretical developments in X-ray diffraction theory and to a new and precise method for measuring structure factors on an absolute scale. Other highlights picked out for mention are studies of Frank-Read dislocation sources, the discovery of long dislocation helices and lines of coaxial dislocation loops in aluminium, of internal magnetic domain structures in Fe-3 wt.% Si, and of stacking faults in silicon and natural diamonds.

An experimental assessment of X-ray diffraction theory in high purity aluminium crystals

1982 ◽  
Vol 55 (2) ◽  
pp. 219-229
Author(s):  
J.J. Urcola ◽  
J. Faustmann ◽  
M. Fuentes
Keyword(s):  
High Purity ◽  
Diffraction Theory ◽  
X Ray Diffraction ◽  
Experimental Assessment ◽  
X Ray ◽  
Purity Aluminium ◽  
High Purity Aluminium

scholarly journals Topology of the Electron Density and of Its Laplacian from Periodic LCAO Calculations on f-Electron Materials: The Case of Cesium Uranyl Chloride

Molecules ◽  
2021 ◽  
Vol 26 (14) ◽  
pp. 4227
Author(s):  
Alessandro Cossard ◽  
Silvia Casassa ◽  
Carlo Gatti ◽  
Jacques K. Desmarais ◽  
Alessandro Erba
Keyword(s):  
Electron Density ◽  
Chemical Bonding ◽  
Topological Analysis ◽  
Theoretical Description ◽  
Basis Functions ◽  
Quantum Mechanical ◽  
X Ray Diffraction ◽  
X Ray ◽  
Atomic Orbitals ◽  
Uranyl Chloride

The chemistry of f-electrons in lanthanide and actinide materials is yet to be fully rationalized. Quantum-mechanical simulations can provide useful complementary insight to that obtained from experiments. The quantum theory of atoms in molecules and crystals (QTAIMAC), through thorough topological analysis of the electron density (often complemented by that of its Laplacian) constitutes a general and robust theoretical framework to analyze chemical bonding features from a computed wave function. Here, we present the extension of the Topond module (previously limited to work in terms of s-, p- and d-type basis functions only) of the Crystal program to f- and g-type basis functions within the linear combination of atomic orbitals (LCAO) approach. This allows for an effective QTAIMAC analysis of chemical bonding of lanthanide and actinide materials. The new implemented algorithms are applied to the analysis of the spatial distribution of the electron density and its Laplacian of the cesium uranyl chloride, Cs2UO2Cl4, crystal. Discrepancies between the present theoretical description of chemical bonding and that obtained from a previously reconstructed electron density by experimental X-ray diffraction are illustrated and discussed.

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