A crystal-chemical model of atomic interactions. 5. Quasicrystal structures

Experimental data of quasicrystal structures are considered from the point of view of a crystal-chemical model of atomic interactions (CCMAI) developed earlier. It is demonstrated that a quasicrystal consists of adjoining clusters. Each cluster has an icosahedron as the nucleus of the cluster and a few coordination shells. All clusters are truncated except for the central one. The distribution of icosahedral nuclei of clusters is stochastic so that there is orientational order of the icosahedral nuclei without translational symmetry. As a result the atoms are distributed in accordance with a slightly distorted three-dimensional Penrose tiling. This approach explains the very close resemblance of the crystal and quasicrystal structures of substances under consideration and shows the process of quasicrystal formation. The existence of the quasicrystals predicted earlier [Aslanov (1989). Acta Cryst. A45, 671-678] with the atomic subsystem having translation symmetry is discusseed on the basis of the experimental facts.