Friedel pair

Paire de Friedel (Fr). Coppia di Friedel (It). フリーデル対 (Ja).

Definition

The couple of reflections h, k, l and [math]{\bar h}, {\bar k}, {\bar l}[/math] is called a Friedel pair, or Bijvoet pair. Their intensities are equal either if the crystal structure is centrosymmetric or if there is no resonant scattering, but differ otherwise. Friedel's law then does not hold. For crystals with a non-centrosymmetric structure and significant resonant scattering, equivalent reflections generated by the symmetry operations of the point group of the crystal have intensities different from those of equivalent reflections generated by the introduction of an additional inversion centre in normal scattering. Friedel, or Bijvoet pairs are used in the resolution of the phase problem for the solution of crystal structures and in the determination of absolute structure.

History

The use of Friedel's pairs for helping in phase determinations was suggested by Bijvoet J. M., Peerdeman A. F. & van Bommel A. J. (1951), Determination of the absolute configuration of optically active compounds by means of X-rays. Nature (London), 168, 271–272.

See also

Friedel's law
Section 2.4.3 of International Tables of Crystallography, Volume B
Section 4.2.6 of International Tables of Crystallography, Volume C