scholarly journals What is an `ideally imperfect' crystal? Is kinematical theory appropriate?

2016 ◽  
Vol 72 (1) ◽  
pp. 50-54 ◽  
Author(s):  
Paul F. Fewster
Keyword(s):  
Dynamical Theory ◽  
Experimental Results ◽  
Biological Molecules ◽  
X Rays ◽  
Interatomic Distances ◽  
Atoms And Molecules ◽  
Imperfect Crystal ◽  
Diffraction Patterns ◽  
Inorganic Molecules ◽  
Kinematical Theory

Most materials are crystalline because atoms and molecules tend to form ordered arrangements, and since the interatomic distances are comparable with the wavelength of X-rays, their interaction creates diffraction patterns. The intensity in these patterns changes with crystal quality. Perfect crystals,e.g. semiconductors, fit well to dynamical theory, whereas crystals that reveal the stereochemistry of complex biological molecules, the structure of organic and inorganic molecules and powders are required to be fragmented (termed `ideally imperfect') to justify the use of the simpler kinematical theory. New experimental results of perfect and imperfect crystals are interpreted with a fundamental description of diffraction, which does not need fragmented crystals but just ubiquitous defects. The distribution of the intensity is modified and can influence the interpretation of the patterns.

Nanoscale determination of interatomic distance by ptychography-EXAFS method using advanced Kirkpatrick–Baez mirror focusing optics

2020 ◽  
Vol 27 (2) ◽  
pp. 455-461
Author(s):  
Makoto Hirose ◽  
Kei Shimomura ◽  
Takaya Higashino ◽  
Nozomu Ishiguro ◽  
Yukio Takahashi
Keyword(s):  
Wide Energy Range ◽  
X Rays ◽  
Bulk Materials ◽  
Interatomic Distances ◽  
X Ray ◽  
Combination Technique ◽  
Wide Energy ◽  
Diffraction Patterns ◽  
X Ray Absorption

This work demonstrates a combination technique of X-ray ptychography and the extended X-ray absorption fine structure (ptychography-EXAFS) method, which can determine the interatomic distances of bulk materials at the nanoscale. In the high-resolution ptychography-EXAFS method, it is necessary to use high-intense coherent X-rays with a uniform wavefront in a wide energy range, hence a ptychographic measurement system installed with advanced Kirkpatrick–Baez mirror focusing optics is developed and its performance is evaluated. Ptychographic diffraction patterns of micrometre-size MnO particles are collected by using this system at 139 energies between 6.504 keV and 7.114 keV including the Mn K absorption edge, and then the EXAFS of MnO is derived from the reconstructed images. By analyzing the EXAFS spectra obtained from a 48 nm × 48 nm region, the nanoscale bond lengths of the first and second coordination shells of MnO are determined. The present approach has great potential to elucidate the unclarified relationship among the morphology, electronic state and atomic arrangement of inhomogeneous bulk materials with high spatial resolution.

scholarly journals Time-resolved X-ray diffraction at NERL

2001 ◽  
Vol 19 (1) ◽  
pp. 125-131 ◽  
Author(s):  
KENICHI KINOSHITA ◽  
HIDEKI HARANO ◽  
KOJI YOSHII ◽  
TAKERU OHKUBO ◽  
ATSUSHI FUKASAWA ◽  
...  
Keyword(s):  
Research Laboratory ◽  
Experimental Results ◽  
X Rays ◽  
Nuclear Engineering ◽  
X Ray Diffraction ◽  
Time Resolved ◽  
X Ray ◽  
Engineering Research ◽  
Fs Laser ◽  
Diffraction Patterns

For ultrafast material analyses, we constructed the time-resolved X-ray diffraction system utilizing ultrashort X-rays from laser-produced plasma generated by the 12-TW–50-fs laser at the Nuclear Engineering Research Laboratory. Ultrafast transient changes in laser-irradiated GaAs crystals were observed as X-ray diffraction patterns. Experimental results were compared with numerical analyses.

Diffraction of 100 to 200 keV X-rays from an Si1−x Ge x gradient crystal: comparison with results from dynamical theory

1999 ◽  
Vol 55 (5) ◽  
pp. 855-863 ◽  
Author(s):  
Steffen Keitel ◽  
Cécile Malgrange ◽  
Thomas Niemöller ◽  
Jochen R. Schneider
Keyword(s):  
Critical Value ◽  
Dynamical Theory ◽  
X Rays ◽  
Full Width ◽  
Half Maximum ◽  
Strain Gradients ◽  
Normal Absorption ◽  
Diffraction Patterns ◽  
Laue Geometry ◽  
Good Agreement

In a large Czochralski-grown Si1−x Ge x (0.02 \leq x \leq 0.07) gradient crystal, diffraction patterns have been measured in symmetrical Laue geometry using synchrotron radiation in the energy range 100–200 keV. The experimental data are in very good agreement with the results from geometrical optics theory for distorted crystals, if the creation of new wavefields for strain gradients larger than a critical value is taken into account. In this sense, the crystal behaves like an ideal gradient crystal. If the normal absorption is disregarded, for reflection 111 and 100 keV energy, the full width at half-maximum values and the peak reflectivities of the diffraction patterns range from 14.6′′ and 97%, respectively, to 70.9′′ and 74%, respectively, for a variation in the Ge concentration from 3.5 to 5.3 at.%.

X-ray diffraction in superabsorbing crystals: absorption intrinsic width

2019 ◽  
Vol 75 (5) ◽  
pp. 772-776
Author(s):  
A. N. C. Lima ◽  
M. A. R. Miranda ◽  
J. M. Sasaki
Keyword(s):  
Diffraction Theory ◽  
Dynamical Theory ◽  
X Rays ◽  
X Ray Diffraction ◽  
Linear Absorption ◽  
New Techniques ◽  
Diffraction Profile ◽  
X Ray ◽  
Kinematical Theory ◽  
Special Case

The several mathematical formulations of X-ray diffraction theory facilitate its understanding and use as a materials characterization technique, since one can opt for the simplest formulation that adequately describes the case being studied. As synchrotrons advance, new techniques are developed and there is a need for simple formulations to describe them. One of these techniques is soft resonant X-ray diffraction, in which the X-rays suffer large attenuation due to absorption. In this work, an expression is derived for the X-ray diffraction profiles of reflections where the linear absorption is far greater than primary extinction; in other words, the crystal is superabsorbing. The case is considered of a parallel plate crystal, for which the diffraction profile of the superabsorbing crystal is computed as a function of crystal size normal to the diffraction planes. For thin crystals or those with negligible absorption, the diffraction profile of a superabsorbing crystal coincides with the result of the kinematical theory. For thick crystals, the absorption intrinsic profile is obtained, described by a Lorentzian function and characterized by the absorption intrinsic width. This absorption intrinsic width is proportional to the linear absorption coefficient and its expression is similar to that for the Darwin width, while the absorption intrinsic profile is a special case of the Laue dynamical theory, and it is similar to the Ornstein–Zernike Lorentzian. The formulation of X-ray diffraction of superabsorbing crystals is simple and provides new perspectives for the soft resonant X-ray diffraction technique.

scholarly journals Hard X-ray Fourier transform holography from an array of oriented referenced objects

2011 ◽  
Vol 18 (4) ◽  
pp. 564-568 ◽  
Author(s):  
Hiroyuki Iwamoto ◽  
Naoto Yagi
Keyword(s):  
Fourier Transform ◽  
Cross Section ◽  
Test Pattern ◽  
Biological Molecules ◽  
Imaging Plate ◽  
Object Size ◽  
X Rays ◽  
X Ray ◽  
Ccd Detector ◽  
Diffraction Patterns

Hard X-ray Fourier transform holography (HXFTH) is a promising method for imaging nanoscale objects, including biological molecules, with a spatial resolution of a nanometer or better. However, it suffers from low scattering intensities being available for imaging owing to smaller object size and the low scattering cross section inherent in hard X-rays. One technique to overcome the problem would be to use an array of oriented objects, each with its own reference. Here the feasibility of this approach was experimentally tested by recording diffraction patterns from nanofabricated test patterns arranged in a 5 × 5 matrix. At an X-ray energy of 8 keV (λ = 1.55 Å), the image of the original test pattern was clearly restored with 60 s exposure on an imaging plate; the image was still recognizable with a 500 ms exposure on a CCD detector at the BL40XU beamline at SPring-8. The results demonstrate that the use of an array of referenced oriented objects for HXFTH is workable, and that it can be considered as a practical candidate for imaging biological molecules, identical particles of which are available but diffract even more weakly than artificially fabricated test patterns.

Spacings and Intensities of Weak-Beam Dark Field Thickness Fringes

1981 ◽  
Vol 39 ◽  
pp. 222-223
Author(s):  
M. Avalos-Borja ◽  
K. Heinemann
Keyword(s):  
Selection Criterion ◽  
Dark Field ◽  
Dynamical Theory ◽  
Bragg Condition ◽  
Weak Beam ◽  
Kinematical Theory ◽  
Equal Thickness

Weak-beam dark field (WBDF) TEM produces narrowly spaced equal-thickness fringes in wedge-shaped crystals. Using non-systematic diffraction conditions, we have shown elsewhere that simple 2-beam kinematical theory (KT) calculations yield average fringe spacings that are for most practical purposes as satisfactorily accurate as the average spacings obtained from optimized multibeam dynamical theory (DT) calculations, As Fig. 1 shows, this result holds for deviations from the Bragg condition as low as 2x10-1 nm-1, and the differences between the results from the two calculational methods become increasingly insignificant for larger excitation errors. (Unless otherwise noted, all results reported here are for gold crystals, using the 200 beam at 100 KV; the DT calculations were made for 74 beams, using the selection criterion D as discussed in ref. [3]).

Towards quantitative simulations of inelastic electron diffraction patterns and images

1992 ◽  
Vol 50 (2) ◽  
pp. 1170-1171
Author(s):  
Z. L. Wang
Keyword(s):  
Phonon Scattering ◽  
Incident Beam ◽  
Dynamical Theory ◽  
Inelastic Electron ◽  
Additional Advantage ◽  
Coupled Equations ◽  
Atomic Vibrations ◽  
Diffraction Patterns ◽  
Primary Advantage ◽  
The One

A new dynamical theory has been developed based on Yoshioka's coupled equations for describing inelastic electron scattering in thin crystals. Compared to existing theories, the primary advantage of this theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of different excited states has been evaluated before any numerical calculation. An additional advantage is that the phase correlations of atomic vibrations are considered, so that full lattice dynamics can be combined in the phonon scattering calculation. The new theory has been proven to be equivalent to the inelastic multislice theory, and has been applied to calculate energy-filtered diffraction patterns and images formed by phonon, single electron and valence scattered electrons.A calculated diffraction pattern of elastic and phonon scattered electrons for a parallel incident beam case is in agreement with the one observed (Fig. 1), showing thermal diffuse scattering (TDS) streaks and Kikuchi pattern.

Structural studies of small amorphous volumes by electron diffraction

1990 ◽  
Vol 48 (4) ◽  
pp. 122-123
Author(s):  
Pierre Moine
Keyword(s):  
Electron Diffraction ◽  
Born Approximation ◽  
Structural Information ◽  
Fundamental Relation ◽  
X Rays ◽  
Structural Studies ◽  
Diffraction Experiment ◽  
Transmission Electron ◽  
Amorphous Structures ◽  
Diffraction Patterns

Qualitatively, amorphous structures can be easily revealed and differentiated from crystalline phases by their Transmission Electron Microscopy (TEM) images and their diffraction patterns (fig.1 and 2) but, for quantitative structural information, electron diffraction pattern intensity analyses are necessary. The parameters describing the structure of an amorphous specimen have been introduced in the context of scattering experiments which have been, so far, the most used techniques to obtain structural information in the form of statistical averages. When only small amorphous volumes (< 1/μm in size or thickness) are available, the much higher scattering of electrons (compared to neutrons or x rays) makes, despite its drawbacks, electron diffraction extremely valuable and often the only feasible technique.In a diffraction experiment, the intensity IN (Q) of a radiation, elastically scattered by N atoms of a sample, is measured and related to the atomic structure, using the fundamental relation (Born approximation) : IN(Q) = |FT[U(r)]|.

K shell X-ray intensity ratios, K-Li, K-L, and K-M vacancy transfer probabilities of Ba and Tl following internal conversion process

2014 ◽  
Vol 92 (11) ◽  
pp. 1489-1493 ◽  
Author(s):  
P.V. Sreevidya ◽  
S.B. Gudennavar ◽  
Daisy Joseph ◽  
S.G. Bubbly
Keyword(s):  
Beta Decay ◽  
Internal Conversion ◽  
Experimental Results ◽  
Conversion Process ◽  
X Rays ◽  
X Ray ◽  
Multichannel Analyser ◽  
Intensity Ratios

K shell X-rays of barium and thallium following internal conversion decay in Cs137 and Hg203, respectively, were detected using a Si(Li) X-ray detector coupled to PC-based 8k multichannel analyser employing the method suggested earlier by our group. The K shell X-ray intensity ratios and vacancy transfer probabilities for thallium and barium were calculated. The obtained results are compared with theoretical, semiempirical, and others’ experimental results obtained via photoionization as well as decay processes. The effects of beta decay and internal conversion on X-ray emission probabilities are discussed.

Morphological and synchrotron X-ray microdiffraction studies of large columnar CVD diamond crystallites

1999 ◽  
Vol 32 (5) ◽  
pp. 924-933 ◽  
Author(s):  
A. R. Lang ◽  
A. P. W. Makepeace ◽  
J. E. Butler
Keyword(s):  
Vapour Deposition ◽  
Chemical Vapour ◽  
Coarse Grained ◽  
X Rays ◽  
Small Cross Section ◽  
X Ray ◽  
Chemical Vapour Deposition Diamond ◽  
Core Column ◽  
Diffraction Patterns ◽  
Goniometric Measurements

Optical microscopic and goniometric measurements were combined with microradiography, diffraction-pattern analysis and topography to study a 2 mm thick [001]-texture CVD (chemical vapour deposition) diamond film that had developed a coarse-grained structure composed of separate columnar crystallites. Individual columns were capped by large (001) facets, with widths up to 0.5 mm, and which were smooth but not flat, whereas the column sides were morphologically irregular. The refractive deviation of X-rays transmitted through the crystallites was exploited for delineating facet edges, thereby facilitating the controlled positioning of small-cross-section X-ray beams used for recording diffraction patterns from selected volumes in two representative crystallites. Their structure consisted of a [001]-axial core column surrounded by columns in twin orientation with respect to the core. The diamond volume directly below the (001) facets was free from low-angle boundaries, and no dislocation outcrops on the facets were detected. Significant elastic deformation of this volume was only present close to the facet periphery, where misorientations reached a few milliradians. Lattice imperfection was high in the twins, with ∼1° misorientations.

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