Dynamical theory of diffraction: Difference between revisions

Revision as of 11:46, 7 June 2017

Latest revision as of 03:07, 18 May 2024

(4 intermediate revisions by 4 users not shown)

Line 1:

The '''dynamical theory of diffraction''' describes the interaction of [[wave]]s with a regular lattice. The wave fields traditionally described are [[X-rays]], [[neutron radiation|neutron]]s 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.

[[Image:LaueBraggGeometry.png|thumb|right|250px|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. ([http://liss.freeshell.org/kdl/DissLiss/ Ref.])]]

[[Image:RLaueBragg.png|thumb|right|250px|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]]. ([http://liss.freeshell.org/kdl/DissLiss/ Ref.])]]

The '''dynamical theory of diffraction''' describes the interaction of [[wave]]s with a regular [[Lattice model (physics)|lattice]]. The wave fields traditionally described are [[X-rays]], [[neutron radiation|neutron]]s or [[electrons]] and the regular lattice, are atomic [[crystal structuresstructure]]s or [[nanometer]]-scale scaled [[multi-layerslayer]]s 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]]. The sections below deal with dynamical diffraction of X-rays.

==Principle of theory==

[[Image:RLaueBragg.png|thumb|right|250px|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]]. ([http://liss.freeshell.org/kdl/DissLiss/ Ref.])]]

==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 [[Diffraction formalism|kinematic theory of diffraction]] which describes the approximate position of [[Bragg diffraction|Bragg]] or [[X-ray crystallography|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.

Line 42 ⟶ 44:

* 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.

* K.-D. Liss: "Strukturelle Charakterisierung und Optimierung der Beugungseigenschaften von Si(1-x)Ge(x) Gradientenkristallen, die aus der Gasphase gezogen wurden", Dissertation, Rheinisch Westfälische Technische Hochschule Aachen, (27 October 1994), [httphttps://nbn-resolving.deorg/urn/resolver.pl?urn=urn:nbn:de:hbz:82-opus-2227 urn:nbn:de:hbz:82-opus-2227]

{{DEFAULTSORT:Dynamical Theory Of Diffraction}}

{{Crystallography}}

[[Category:Neutron-related techniques]]

[[Category:Synchrotron-related techniques]]