Icosahedral order and disorder in tetrahedral semiconductors - Three-dimensional and six-dimensional views

Different approaches to tetrahedrally coordinated quasicrystals are discuss ed. It is shown that the BC8 phase, which is observed in silicon and german ium, has a hidden icosahedral symmetry of tetrahedral interatomic bonds. In this cubic crystal with the Ia (3) over bar space group, 75% of all bonds are directed almost exactly along fivefold icosahedral axes. This structure (16 atoms per unit cell) is the 1/0 approximant of a hypothetical icosahed ral quasicrystal with a body-centered six-dimensional lattice. The 1/1 appr oximant is also constructed (64 atoms per unit cell with Ia (3) over bar sp ace symmetry). A specific type of topological disorder, related with partia l phason flips, is shown to be possible in both the approximants. The struc ture of the approximants and the atomic flips are analyzed both in physical and in perpendicular space and their energies are studied ab initio within the density functional theory. The considered phason disorder provides a n ew insight into crystalline-to-amorphous transformations. (C) 2000 Elsevier Science B.V. All rights reserved.