# Renninger effect

### From Online Dictionary of Crystallography

Effet Renninger (*Fr*). Effetto Renninger (*It*). Efecto Renninger (*Sp').*

The multiple diffraction affecting the appearance of a diffraction pattern is known under the name of **Renninger effect**. In reciprocal space it is interpreted as resulting from the simultaneous presence of two reciprocal lattice nodes on the surface of the Ewald sphere. If the Miller indices of the corresponding families of lattice planes are **H**1 = (*hkl*)_{1} and **H**2 = (*hkl*)_{2}, the corresponding Laue conditions are:

(**s**_{1}-**s**_{0})/λ =**r***_{H1}; (**s**_{2}-**s**_{0})/λ =**r***_{H2}

and, by subtracting the second equation from the first, one obtains:

(**s**_{1}-**s**_{2})/λ =**r***_{H1}-**r***_{H2} = **r***_{H1-H2}

The beam diffracted by the plane **H**1 in the direction **s**_{1} overlaps with a double-diffraction beam, first by the plane **H**2 in the direction **s**_{2} and then by the plane **H**1-**H**2 in the direction **s**_{1}-**s**_{2}.

If the Renninger effect is strong enough, the intensity of the beam with Laue indices **H**1 can be significantly different from its theoretical kinematical value. The Renninger effect may also result in apparent violation of the reflection conditions, when the doubly-diffracted beam strikes a position in the diffraction pattern corresponding to a beam with zero intensity due to systematic absences.

## References

Renninger, M. (1937). Umweganregung, eine bisher unbeachtete Wechselwirkungserscheinung bei Raumgitterinterferenzen. *Z. Phys*. **106**, 141-176.