Quasicrystals

Abstract

Quasicrystals are solid materials exhibiting diffraction patterns with apparently sharp spots containing symmetry axes such as fivefold or eightfold axes, which are incompatible with the three‐dimensional periodicity associated with crystal lattices. Many such materials are aluminum alloys that exhibit diffraction patterns with fivefold symmetry axes; such materials are called icosahedral quasicrystals. The location of atoms in quasicrystals requires the use of six‐dimensional crystallography. However, a polyhedral shell structure using a number of polyhedra of icosahedral symmetry provides a three‐dimensional model for the structure of many icosahedral quasicrystals.