International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B. ch. 4.6, p. 499
Section 4.6.3.3.1.2. Diffraction symmetry
aLaboratory of Crystallography, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerland |
The possible Laue symmetry group of the Fourier module is any one of the direct product . corresponds to one of the ten crystallographic 2D point groups, in the general case of a quasiperiodic stacking of periodic layers. Consequently, the nine Laue groups , , mmm, 4/m, 4/mmm, , , and are possible. These are all 3D crystallographic Laue groups except for the two cubic ones.
The (unweighted) Fourier module shows only 2D lattice symmetry. In the third dimension, the submodule remains invariant under the scaling symmetry operation with . The scaling symmetry operators form an infinite group of reciprocal-basis transformations in superspace, and act on the reciprocal basis in superspace.