# Friedel's law

### From Online Dictionary of Crystallography

##### Revision as of 09:53, 24 March 2006 by AndreAuthier (talk | contribs)

Loi de Friedel (*Fr*). Friedelsche Gesetz (*Ge*). Ley de Friedel (*Sp*).

## Definition

Friedel's law, or rule, states that the intensities of the *h*, *k*, *l* and *-h*, *-k*, *-l* reflections are equal. The reason is that the diffracted intensity is proportional to the the square of the modulus of the structure factor, |*F _{h}*|

^{2}, according to the geometrical, or kinematical theory. The structure factor is given by:

*F _{h}* = Σ

_{j}

*f*exp - 2 π i

_{j}**h . r**

_{j}where *f _{j}* is the atomic scattering factor of atom

*j*,

**h**the reflection vector and

**r**the position vector of atom

_{j}*j*. There comes:

|*F _{h}*|

^{2}=

*F*=

_{h}F_{h}**F*= |

_{h}F_{-h}*F*|

_{-h}^{2}

if the atomic scattering factor, *f _{j}*, is real. The intensities of the

*h*,

*k*,

*l*and

*-h*,

*-k*,

*-l*reflections are therefore equal. If the crystal is absorbing, however, due to anomalous dispersion, the atomic scattering factor is complex and

*F _{-h} ≠ F_{h}**.

Friedel's law does not hold for absorbing crystals.

## History

Friedel's law was stated by G. Friedel (1865-1933) in 1913 (Friedel G., 1913, *Sur les symétries cristallines que peut révéler la diffraction des rayons X.*, *C.R. Acad. Sci. Paris*, **157**, 1533-1536.