# Quasicrystal

### From Online Dictionary of Crystallography

Quasicristal (Fr.), Quasicristallo (It.), 準結晶 (Ja.),

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.