# Difference between revisions of "Kinematical theory"

### From Online Dictionary of Crystallography

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BrianMcMahon (talk | contribs) (Edits to align with printed edition) |
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− | <font color="blue">Théorie cinématique</font> (''Fr'') | + | <font color="blue">Théorie cinématique</font> (''Fr''). <Font color="red">Kinematische theorie</Font> (''Ge''). <Font color="green">Teoría cinemática</Font> (''Sp''). <Font color="black">Teoria cinematica</Font> (''It''). <Font color="brown">Кинематические теория</Font> (''Ru''). <Font color="purple">運動学的回折理論</Font> (''Ja''). |

== Definition == | == Definition == | ||

− | In the '''kinematical''' or '''geometrical''' theory, the amplitudes diffracted by a three-dimensional periodic assembly of atoms (Laue) or by a stack of planes (Darwin) is derived by adding the amplitudes of the waves diffracted by each atom or by each plane, simply taking into account the optical path differences between them, but neglecting the interaction of the propagating waves and matter. This approximation is not compatible with the law of conservation of energy and is only valid for very small or highly imperfect crystals. | + | In the '''kinematical''' or '''geometrical''' theory, the amplitudes diffracted by a three-dimensional periodic assembly of atoms (Laue) or by a stack of planes (Darwin) is derived by adding the amplitudes of the waves diffracted by each atom or by each plane, simply taking into account the optical path differences between them, but neglecting the interaction of the propagating waves and matter. This approximation is not compatible with the law of conservation of energy and is only valid for very small or highly imperfect crystals. This interaction is taken into account by the [[Dynamical theory|dynamical theory]]. |

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+ | In the kinematical theory, the integrated intensities of the Bragg reflections are proportional to the square of the modulus of the structure factor, <math>|F_{hkl}|^2</math>. In the dynamical theory, they are proportional to the modulus of the structure factor, <math>|F_{hkl}|</math>. | ||

[[Category:X-rays]] | [[Category:X-rays]] |

## Revision as of 14:32, 15 May 2017

Théorie cinématique (*Fr*). Kinematische theorie (*Ge*). Teoría cinemática (*Sp*). Teoria cinematica (*It*). Кинематические теория (*Ru*). 運動学的回折理論 (*Ja*).

## Definition

In the **kinematical** or **geometrical** theory, the amplitudes diffracted by a three-dimensional periodic assembly of atoms (Laue) or by a stack of planes (Darwin) is derived by adding the amplitudes of the waves diffracted by each atom or by each plane, simply taking into account the optical path differences between them, but neglecting the interaction of the propagating waves and matter. This approximation is not compatible with the law of conservation of energy and is only valid for very small or highly imperfect crystals. This interaction is taken into account by the dynamical theory.

In the kinematical theory, the integrated intensities of the Bragg reflections are proportional to the square of the modulus of the structure factor, [math]|F_{hkl}|^2[/math]. In the dynamical theory, they are proportional to the modulus of the structure factor, [math]|F_{hkl}|[/math].