Friedel's law
Encyclopedia
Friedel's law, named after Georges Friedel
, is a property of Fourier transform
s of real functions.
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 (aka Opération de maclage) is equivalent to an inversion centre and the intensities from the individuals are equivalent under Friedel's law.
Georges Friedel
Georges Friedel was a French mineralogist and crystallographer.- Life :Georges was the son of the famous chemist Charles Friedel...
, is a property of Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
s of real functions.
Given a real function
, its Fourier transformFourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
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 antisymmetricAntisymmetric
The word antisymmetric refers to a change to an opposite quantity when another quantity is symmetrically changed. This concept is related to that of Symmetry and Asymmetry. The difference between these three concepts can be simply illustrated with Latin letters. The character "A" is symmetric about...
:
-
.
Friedel's law is used in X-ray diffraction, crystallography
Crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...
and scattering from real potential within the Born approximation
Born approximation
In scattering theory and, in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as the driving field at each point in the scatterer. Born approximation is named after Max Born, winner of the 1954 Nobel Prize for physics.It is...
. Note that a twin operation (aka Opération de maclage) is equivalent to an inversion centre and the intensities from the individuals are equivalent under Friedel's law.