Quasicrystal

Quasicrystal

Quasicristal (Fr.)

Definition

There are two definitions of the notion of quasicrystal.

• 1) A quasicrystal is an aperiodic crystal that is not an incommensurate

modulated structure, nor an aperiodic composite crystal. Often, quasicrystals have crystallographically 'forbidden' symmetries. These are rotations of order different from 1, 2, 3, 4 and 6. In three dimensions a lattice periodic structure may only have rotation symmetry of an order equal to one of these numbers. However, presence of such a forbidden symmetry is not required for a quasicrystal. A system with crystallographically allowed rotation symmetry that is locally similar to one with forbidden symmetries is also a quasicrystal.

• 2) The term quasicrystal stems from the property of quasiperiodicity

observed for the first alloys found with forbidden symmetries. Therefore, the alternative definition is: a quasicrystal is an aperiodic crystal with diffraction peaks that may be indexed by n integral indices, where n is a finite number, larger than the dimension of the space (in general). This definition is similar to that of aperiodic crystal.

See also: Aperiodic crystal.