Friedel's law

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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.

See also

Absolute structure