Friedel's law

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 [math]{\bar h}, {\bar k}, {\bar l}[/math] reflections are equal. The reason is that the diffracted intensity is proportional to the the square of the modulus of the structure factor, |F_h|², according to the geometrical, or kinematical theory. The structure factor is given by:

[math]F_h = \Sigma_j f_j {\rm exp - 2 \pi i} {\bold h} . {\bold r_j}[/math]

where f_j is the atomic scattering factor of atom j, h the reflection vector and [math]{\bold r_j}[/math] the position vector of atom j. There comes:

[math]|F_h|^2 = F_h F_h^* = F_h F_{\bar h} = |F_{\bar h}|^2 [/math]

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

[math]F_{\bar h} \ne F_h^*[/math]

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