International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 64   | 1 | 2 |

## Section 1.3.4.2.1.4. Friedel's law, anomalous scatterers

G. Bricognea

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#### 1.3.4.2.1.4. Friedel's law, anomalous scatterers

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If the wavelength λ of the incident X-rays is far from any absorption edge of the atoms in the crystal, there is a constant phase shift in the scattering, and the electron density may be considered to be real-valued. ThenThus ifthenThis is Friedel's law (Friedel, 1913). The set of Fourier coefficients is said to have Hermitian symmetry.

If λ is close to some absorption edge(s), the proximity to resonance induces an extra phase shift, whose effect may be represented by letting take on complex values. Letand correspondingly, by termwise Fourier transformation

Since and are both real, and are both Hermitian symmetric, hencewhileThus , so that Friedel's law is violated. The components and , which do obey Friedel's law, may be expressed as:

### References

Friedel, G. (1913). Sur les symétries cristallines que peut révéler la diffraction des rayons Röntgen. C. R. Acad. Sci. Paris, 157, 1533–1536.