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Quasikristalle sind neuartige Phasen, die in schnell abgekuhlten Metall-Legierungen vorkommen. Ihre wichtigste Eigenschaft ist, dass Ihre Fourier-Transformierte aus scharfen Bragg-Peaks besteht, deren Positionen und Intensitaten eine Punktsymmetrie haben, die mit einer dreidimensionalen periodischen Struktur nicht vertraglich ist. Die Positionen der Bragg-Peaks eines Quasikristalls konnen jedoch alle als ganzzahlige Linearkombinationen von endlich vielen fundamentalen Wellenvektoren geschrieben werden; dies legt nahe, diese Strukturen als Schnitt durch eine hoherdimensionale, periodische Struktur aufzufassen. Quasicrystals are novel phases of rapidly quenched metal alloys. Their main feature is that their Fourier spectrum consists of sharp Bragg peaks whose positions and intensities are invariant under a point symmetry which is incompatible with a three dimensional periodic structure. However, all the peak positions can be written as integer linear combinations of finitely many basic wave vectors. This fact allows to view these structures as intersections of physical space with a higher-dimensional periodic structure.

Quasicrystal structures from the crystallographic viewpoint