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The dynamical theory of diffraction describes the interaction of wave fields with a regular lattice. The wave fields traditionally described are X-rays, neutrons or electrons and the regular lattice atomic crystal structures or nanometer scaled multi-layers or self arranged systems. In a wider sense, similar treatment is related to the interaction of light with optical band-gap materials or related wave problems in acoustics. In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz...
Neutron radiation consists of free neutrons. ...
Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ...
 Laue and Bragg geometries, top and bottom, as distinguished by the Dynamical theory of diffraction with the Bragg diffracted beam leaving the back or front surface of the crystal, respectively. (Ref.)
 Reflectivities for Laue and Bragg geometries, top and bottom, respectively, as evaluated by the Dynamical theory of diffraction for the absorption-less case. The flat top of the peak in Bragg geometry is the so-called Darwin Plateau. (Ref.) Image File history File links Size of this preview: 381 × 600 pixel Image in higher resolution (469 × 738 pixel, file size: 170 KB, MIME type: image/png) Laue and Bragg geometries, top and bottom, as distinguished by the Dynamical theory of diffraction with the Bragg diffracted beam leaving the back...
Image File history File links Size of this preview: 381 × 600 pixel Image in higher resolution (469 × 738 pixel, file size: 170 KB, MIME type: image/png) Laue and Bragg geometries, top and bottom, as distinguished by the Dynamical theory of diffraction with the Bragg diffracted beam leaving the back...
Image File history File links Size of this preview: 333 × 598 pixel Image in higher resolution (467 × 839 pixel, file size: 193 KB, MIME type: image/png) Reflectivities for Laue and Bragg geometries, top and bottom, respectively, as evaluated by the Dynamical theory of diffraction for the absorption-less case. ...
Image File history File links Size of this preview: 333 × 598 pixel Image in higher resolution (467 × 839 pixel, file size: 193 KB, MIME type: image/png) Reflectivities for Laue and Bragg geometries, top and bottom, respectively, as evaluated by the Dynamical theory of diffraction for the absorption-less case. ...
Principle of theory The dynamical theory of diffraction considers the wave field in the periodic potential of the crystal and takes into account all multiple scattering effects. Unlike the kinematic theory of diffraction which describes the approximate position of Bragg or Laue diffraction peaks in reciprocal space, dynamical theory corrects for refraction, shape and width of the peaks, extinction and interference effects. Graphical representations are described in dispersion surfaces around reciprocal lattice points which fulfill the boundary conditions at the crystal interface. // To determine the pattern produced by diffraction we must determine the phase and amplitude of each of the Huygens wavelets at each point in space. ...
The Bragg formulation of X-ray diffraction (also referred to as Bragg diffraction) was first proposed by William Lawrence Bragg and William Henry Bragg in 1913 in response to their discovery that crystalline solids produced surprising patterns of reflected X-rays (in contrast to that of, say, a liquid). ...
X-ray crystallography, also known as single-crystal X-ray diffraction, is the oldest and most common crystallographic method for determining the structure of molecules. ...
In crystallography, the reciprocal lattice of a Bravais lattice is the set of all vectors K such that for all lattice point position vectors R. The reciprocal lattice is itself a Bravais lattice, and the reciprocal of the reciprocal lattice is the original lattice. ...
Outcomes - The crystal potential by itself leads to refraction and specular reflection of the waves at the interface to the crystal and delivers the refractive index off the Bragg reflection. It also corrects for refraction at the Bragg condition and combined Bragg and specular reflection in grazing incidence geometries.
- A Bragg reflection is the splitting of the dispersion surface at the border of the Brillouin zone in reciprocal space. There is a gap between the dispersion surfaces in which no travelling waves are allowed. For a non-absorbing crystal, the reflection curve shows a range of total reflection, the so-called Darwin plateau. Regarding the quantum mechanical energy of the system, this leads to the band gap structure which is commonly well known for electrons.
- Upon Laue diffraction, intensity is shuffled from the forward diffracted beam into the Bragg diffracted beam until extinction. The diffracted beam itself fulfills the Bragg condition and shuffles intensity back into the primary direction. This round-trip period is called the Pendellösung period.
- The extinction length is related to the Pendellösung period. Even if a crystal is infinitely thick, only the crystal volume within the extinction length contributes considerably to the diffraction in Bragg geometry.
- In Laue geometry, beam paths lie within the Borrmann triangle. Kato fringes are the intensity patterns due to Pendellösung effects at the exit surface of the crystal.
- Anomaleous absorption effects take place due to a standing wave patterns of two wave fields. Absorption is stronger if the standing wave has its anti-nodes on the lattice planes, i.e. where the absorbing atoms are, and weaker, if the anti-nodes are shifted between the planes. The standing wave shifts from one condition to the other on each side of the Darwin plateau which gives the latter an asymmetric shape.
The straw seems to be broken, due to refraction of light as it emerges into the air. ...
Diagram of specular reflection Specular reflection is the perfect, mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected onto a single outgoing direction. ...
The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ...
In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space. ...
This article or section does not adequately cite its references or sources. ...
A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ...
Applications X-ray crystallography is a technique in crystallography in which the pattern produced by the diffraction of x-rays through the closely spaced lattice of atoms in a crystal is recorded and then analyzed to reveal the nature of that lattice. ...
Neutron diffraction is a crystallography technique that uses neutrons to determine the atomic structure of a material. ...
This article is in need of attention from an expert on the subject. ...
Transmission electron microscopy (TEM) is an imaging technique whereby a beam of electrons is focused onto a specimen causing an enlarged version to appear on a fluorescent screen or layer of photographic film (see electron microscope), or can be detected by a CCD camera. ...
Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. ...
Grazing incidence X-ray and neutron diffraction (abbreviation GIXD or GID) uses small incident angles for the incoming X-ray or neutron beam, so that diffraction can be made surface sensitive. ...
X-ray Standing Waves The method of x-ray standing waves (XSW) is a well-established technique for the determination of adsorbate or dopant atom positions in perfect crystals. ...
In physics, a neutron interferometer is an interferometer capable of diffracting neutrons, allowing the wave-like nature of neutrons, and other related phenomena, to be explored. ...
Diffraction topography (short: topography) is an X-ray imaging technique based on Bragg diffraction. ...
A crystal monochromator is a device in neutron and X-ray optics to select a defined wavelength of the radiation for further purpose on a dedicated instrument or beamline. ...
In solid state physics, the electronic band structure (or simply band structure) of a solid describes ranges of energy that an electron is forbidden or allowed to have. ...
Literature
- Boris W. Batterman, Henderson Cole: Dynamical Diffraction of X Rays by Perfect Crystals. Reviews of Modern Physics, Vol. 36, No. 3, 681-717, July 1964. (PDF 7.7 MB)
- H. Rauch, D. Petrascheck, “Grundlagen für ein Laue-Neutroneninterferometer Teil 1: Dynamische Beugung”. , AIAU 74405b, Atominstitut der Österreichischen Universitäten, (1976)
- H. Rauch, D. Petrascheck, “Dynamical neutron diffraction and its application” in “Neutron Diffraction”, H. Dachs, Editor. (1978), Springer-Verlag: Berlin Heidelberg New York. p. 303.
- Authier, André: Dynamical theory of X-ray diffraction. IUCr monographs on crystallography, no. 11. Oxford University Press (1st edition 2001/ 2nd edition 2003). ISBN 0-19-852892-2.
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