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 H1 = (hkl)1 and H2 = (hkl)2, the corresponding Laue conditions are:
(s1-s0)/λ =r*H1; (s2-s0)/λ =r*H2
and, by subtracting the second equation from the first, one obtains:
(s1-s2)/λ =r*H1-r*H2 = r*H1-H2
The beam diffracted by the plane H1 in the direction s1 overlaps with a double-diffraction beam, first by the plane H2 in the direction s2 and then by the plane H1-H2 in the direction s1-s2.
If the Renninger effect is strong enough, the intensity of the beam with Laue indices H1 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). Z. Phys. 106, 141-176. Umweganregung, eine bisher unbeachtete Wechselwirkungserscheinung bei Raumgitterinterferenzen.