Friedel's law

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|''F<sub>h</sub>''|<sup>2</sup> = ''F<sub>h</sub> F<sub>h</sub>*'' = ''F<sub>h</sub> F<sub>-h</sub>''
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|''F<sub>h</sub>''|<sup>2</sup> = ''F<sub>h</sub> F<sub>h</sub>*'' = ''F<sub>h</sub> F<sub>-h</sub>'' = |''F<sub>-h</sub>''|<sup>2</sup>
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if the atomic scattering factor, ''f<sub>j</sub>'', is real.
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if the atomic scattering factor, ''f<sub>j</sub>'', is real. The intensities of the ''h'', ''k'', ''l'' and ''-h'', ''-k'', ''-l'' reflections are therefore equal. If the crystal is absorbing, however, due to [[anomalous dispersion]], the atomic scattering factor is complex and
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''F<sub>-h</sub> &ne; F<sub>h</sub>*''.
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Friedel's law does not hold for absorbing crystals.
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== History ==
== History ==

Revision as of 09:53, 24 March 2006

Loi de Friedel (Fr). Friedelsche Gesetz (Ge). Ley de Friedel (Sp).

Definition

Friedel's law, or rule, states that the intensities of the h, k, l and -h, -k, -l reflections are equal. The reason is that the diffracted intensity is proportional to the the square of the modulus of the structure factor, |Fh|2, according to the geometrical, or kinematical theory. The structure factor is given by:

Fh = Σj fj exp - 2 π i h . rj

where fj is the atomic scattering factor of atom j, h the reflection vector and rj the position vector of atom j. There comes:

|Fh|2 = Fh Fh* = Fh F-h = |F-h|2

if the atomic scattering factor, fj, is real. The intensities of the h, k, l and -h, -k, -l reflections are therefore equal. If the crystal is absorbing, however, due to anomalous dispersion, the atomic scattering factor is complex and

F-h ≠ Fh*.

Friedel's law does not hold for absorbing crystals.

History

Friedel's law was stated by G. Friedel (1865-1933) in 1913 (Friedel G., 1913, Sur les symétries cristallines que peut révéler la diffraction des rayons X., C.R. Acad. Sci. Paris, 157, 1533-1536.

See also

Absolute structure