Quasicrystal as a locally deformed crystal structure

Lattice models for a two-dimensional octagonal quasicrystal and a three-dimensional icosahedral quasicrystal with the icosahedral-dodecahedral local order are introduced. It is shown that an octagonal quasicrystal may be obtained as a result of the local deformation of an ideal square atomic lattice. Possible paths of structural transformations between various phases of an AlPd crystal are determined. It is shown that icosahedral quasicrystals of aluminum alloys with transition metals can be considered to be a result of the local distortions of an ideal fcc lattice of elemental aluminum induced by a transition metal impurity.