Aperiodic crystal
In aperiodic crystals is crystalline solids that do not by the three-dimensional periodic array of unit cells can be described.
Aperiodic crystals were discovered relatively late and their existence was initially contested by important scientists (e.g. Linus Carl Pauling ). In 1931 it was found in the mineral calaverite (gold-silver-telluride) that René-Just Haüy's law of rational indices was not fulfilled. The first aperiodic crystal was found, but the explanation was still decades away. In the 1960s, using X-ray diffraction on -Na 2 CO 3 , it was found that reflections occurred in the diffraction pattern that could not be indexed with whole numbers (so-called satellite reflections ). It follows that this crystal cannot be described with a single unit cell.
The four-dimensional space in which all X-ray reflections can be indexed was used to describe -Na 2 CO 3 . There are also cases (icosahedral quasicrystals) in which up to six dimensions are necessary. If a complete description of the crystal in three-dimensional space is possible, then it is a periodic crystal . If more dimensions are required for a complete description, one speaks of an aperiodic crystal .
Aperiodic Crystals fall into three categories: