## German Crystallographic Association ( DGK )## Study Group 16 (AK16): Aperiodic Crystals |
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## Aperiodic crystalsAperiodic crystals are crystals with an, in principle, perfect long-range order in the spatial arrangement of their atomic constituents. They are distinguished from the three-dimensional periodic crystals (the "normal" crystals in the classical sense) by just this fact, that their structures lack three-dimensional translational symmetry ( i.e. periodicity). Three different kinds of aperiodic crystals are considered. It has however to be stressed, that these represent only borderline cases, the limits between them are not clearly defined but depend on the beholder and the applied structural model.
The structure of an
The atomic parameter, i.e. fractional coordinates, occupancy and/or ADP, are given as the sum of the atomic parameter in the basic structure plus a deviation thereof (modulated structure = basic structure + modulation).
A The single lattices are not sublattices of a common (three-dimensional) one and it is not possible to express one lattice by the other one with rational numbers. These compounds do not possess one common basic lattice. As a consequence, one has for each subsystem one set of main reflections. Also the basic structures themselves are modulated due to the interaction between the subsystems. Nevertheless, the intergrowth is coherent, the composite crystals have to be considered as single thermodynamic phases.
The point symmetry of a In contrast with modulated and composite crystals and because of the lack of a periodic basic structure, quasicrystals do not exhibit a clear lattice of main reflections. A simple distinction between main and satellite reflections is not possible.
The structural study of aperiodic crystals as well as the quantitative analysis of bond
lengths, coordination spheres, and physical properties, requires methods which are
different from those for periodic crystals. As example one might mention, that the
symmetries of incommensurately modulated crystals and composite crystals can be described
by so-called (3+
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