Tetrahedral structures with icosahedral order and their relation to quasicrystals

The possible existence of quasicrystals in tetrahedral phases is considered . It is shown that one of the well-known crystalline silicon phases (the BC 8 phase or silicon III) is characterized by the icosahedral local order wit h three-quarters of the interatomic bonds being directed along the fivefold axes of an icosahedron. This crystal is considered as an approximant of an icosahedral quasicrystal. Higher order approximants and other tetrahedral structures related to quasicrystals are also constructed. It is shown that in these structures, the formation of the intrinsic phason disorder with th e preservation of the energetically favorable coordination number four is p ossible. The ab initio quantum-mechanical calculations for carbon and silic on show that, although all the considered phases are metastable, their ener gies only slightly differ from the energies of the corresponding stable pha ses. (C) 2001 MAIK "Nauka/Interperiodica".