Friedel's law
Appearance
Friedel's law, named after Georges Friedel, is a property of Fourier transforms of real functions.[1]
Given a real function , its Fourier transform
has the following properties.
where is the complex conjugate of .
Centrosymmetric points are called Friedel's pairs.
The squared amplitude () is centrosymmetric:
The phase of is antisymmetric:
- .
Friedel's law is used in X-ray diffraction, crystallography and scattering from real potential within the Born approximation. Note that a twin operation (a.k.a. Opération de maclage) is equivalent to an inversion centre and the intensities from the individuals are equivalent under Friedel's law.[2][3][4]
References
[edit]- ^ Friedel G (1913). "Sur les symétries cristallines que peut révéler la diffraction des rayons Röntgen". Comptes Rendus. 157: 1533–1536.
- ^ Nespolo M, Giovanni Ferraris G (2004). "Applied geminography - symmetry analysis of twinned crystals and definition of twinning by reticular polyholohedry" (PDF). Acta Crystallogr A. 60 (1): 89–95. Bibcode:2004AcCrA..60...89N. doi:10.1107/S0108767303025625. PMID 14691332.
- ^ Friedel G (1904). "Étude sur les groupements cristallins". Extract from Bullettin de la Société de l'Industrie Minérale, Quatrième série, Tomes III et IV. Saint-Étienne: Societè de l'Imprimerie Thèolier J. Thomas et C.
- ^ Friedel G. (1923). Bull. Soc. Fr. Minéral. 46:79-95.