Friedel's law, named after Georges Friedel, is a property of Fourier transforms of real functions.[1]
Given a real function f ( x ) {\displaystyle f(x)} , its Fourier transform
has the following properties.
where F ∗ ∗ --> {\displaystyle F^{*}} is the complex conjugate of F {\displaystyle F} .
Centrosymmetric points ( k , − − --> k ) {\displaystyle (k,-k)} are called Friedel's pairs.
The squared amplitude ( | F | 2 {\displaystyle |F|^{2}} ) is centrosymmetric:
The phase ϕ ϕ --> {\displaystyle \phi } of F {\displaystyle F} 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]
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