Difference between revisions of "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>'' | + | |''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. | + | 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> ≠ 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.