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 -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, |F_h|², according to the geometrical, or kinematical theory. The structure factor is given by:

F_h = Σ_j f_j exp - 2 π i h . r_j

where f_j is the atomic scattering factor of atom j, h the reflection vector and r_j the position vector of atom j. There comes:

|F_h|² = F_h F_h* = F_h F_-h = |F_-h|²

if the atomic scattering factor, f_j, 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 ≠ 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