# Friedel's law

(Difference between revisions)
 Revision as of 09:53, 24 March 2006 (view source)← Older edit Revision as of 17:11, 24 March 2006 (view source)Newer edit → Line 3: Line 3: == Definition == == 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: + Friedel's law, or rule, states that the intensities of the ''h'', ''k'', ''l'' and ${\bar h}, {\bar k}, {\bar l}$ 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'' = Σ''j'' ''fj'' exp - 2 π i '''h . rj''' + F_h = \Sigma_j f_j {\rm exp - 2 \pi i} {\bold h} . {\bold r_j}
- where ''fj'' is the atomic scattering factor of atom ''j'', '''h''' the reflection vector and '''rj''' the position vector of atom ''j''. There comes: + where ''fj'' is the atomic scattering factor of atom ''j'', '''h''' the reflection vector and {\bold r_j} the position vector of atom ''j''. There comes:
- |''Fh''|2 = ''Fh Fh*'' = ''Fh F-h'' = |''F-h''|2 + |F_h|^2 = F_h F_h^* = F_h F_{\bar h} = |F_{\bar 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 + if the atomic scattering factor, ''fj'', is real. The intensities of the ''h'', ''k'', ''l'' and ${\bar h}, {\bar k}, {\bar l}$ reflections are therefore equal. If the crystal is absorbing, however, due to [[anomalous dispersion]], the atomic scattering factor is complex and
- ''F-h ≠ Fh*''. + F_{\bar h} \ne F_h^*

## Revision as of 17:11, 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 ${\bar h}, {\bar k}, {\bar l}$ 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:

$F_h = \Sigma_j f_j {\rm exp - 2 \pi i} {\bold h} . {\bold r_j}$

where fj is the atomic scattering factor of atom j, h the reflection vector and ${\bold r_j}$ the position vector of atom j. There comes:

$|F_h|^2 = F_h F_h^* = F_h F_{\bar h} = |F_{\bar h}|^2$

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

$F_{\bar h} \ne F_h^*$

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.