# Friedel's law

(Difference between revisions)
 Revision as of 09:33, 24 March 2006 (view source)← Older edit Revision as of 09:53, 24 March 2006 (view source)Newer edit → Line 12: Line 12:
- |''Fh''|2 = ''Fh Fh*'' = ''Fh F-h'' + |''Fh''|2 = ''Fh Fh*'' = ''Fh F-h'' = |''F-h''|2
- if the atomic scattering factor, ''fj'', is real. + 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 == == 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.