Abstract:
Modulations in the crystal lead to additional diffraction spots which cannot be indexed by three integer indices and therefore the basic property of the crystal, the 3-dimensional periodicity, is lost. On the other hand the additional (satellite) spots are regularly distributed in the reciprocal space. They can be indexed by adding a few additional (modulation) vectors. This fact makes possible to generalize the classical definition of crystal in a straightforward way. The generalized crystal has periodicity in a 3+d dimensional superspace. The main ideas of the superspace theory will be presented on simple simulated examples.
All crystallographic methods used for solution and interpretation have been generalized for modulated and composite crystals by applying of the superspace theory. This enabled to develop computing programs, such as Jana2000, which can handle different types of modulation in the crystal. Several examples of soled modulated crystals will be presented to demonstrate meaning of the superspace theory.
The modulation in the crystal originates very often from a simple discontinuous perturbation. The crenel-like and saw-tooth like functions introduced to our system of programs some years ago can be used to describe them efficiently. The basic ideas and some real examples will be present as well.