# Friedel's law

### From Online Dictionary of Crystallography

AndreAuthier (Talk | contribs) |
AndreAuthier (Talk | contribs) |
||

Line 12: | Line 12: | ||

<center> | <center> | ||

- | |''F<sub>h</sub>''|<sup>2</sup> = ''F<sub>h</sub> F<sub>h</sub>*'' = ''F<sub>h</sub> F<sub>-h</sub>'' | + | |''F<sub>h</sub>''|<sup>2</sup> = ''F<sub>h</sub> F<sub>h</sub>*'' = ''F<sub>h</sub> F<sub>-h</sub>'' = |''F<sub>-h</sub>''|<sup>2</sup> |

</center> | </center> | ||

- | if the atomic scattering factor, ''f<sub>j</sub>'', is real. | + | if the atomic scattering factor, ''f<sub>j</sub>'', 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 |

+ | |||

+ | <center> | ||

+ | ''F<sub>-h</sub> ≠ F<sub>h</sub>*''. | ||

+ | </center> | ||

+ | |||

+ | Friedel's law does not hold for absorbing crystals. | ||

+ | |||

== History == | == History == | ||

## Revision as of 09:53, 24 March 2006

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.