Icosahedral order and disorder in semiconductors

Hidden icosahedral symmetry of tetrahedral interatomic bonds is found in the BC8-Ia (3) over bar phase of silicon and germanium (75% of all bonds are directed almost exactly along fivefold icosahedral axes). It is shown that this phase may be considered as a crystalline approximant of a hypothetical icosahedral quasicrystal with a body-centred six-dimensional lattice and that all the atomic positions in BC8 crystals may be obtained as projections from that six-dimensional lattice. The diffraction pattern of the BC8 phase has hierarchical organisation typical of both approximants and quasicrystals. A specific type of topological disorder, related with phason flips, is suggested. The experimentally observed BC8-R8 phase transition can be considered as resulting from coherent phason flips of this type. Dual relationships with approximants of conventional quasicrystals are used to construct a higher order approximant without dangling bonds. A new scenario for crystalline-to-amorphous transformation is discussed.