Structures of Ti₂(Ni, V) in crystalline and quasicrystalline phases

Abstract

A new criterion for the classification of quasicrystalline structures is proposed. A quasicrystal with composition close to a Frank-Kasper phase, which consists exclusively of tetrahedra, should belong to the i((Al, Zn)₄₉Mg₃₂) class whereas one with composition close to that of the crystal, which consists of both tetrahedra and octahedra, should belong to the i(A1MnSi) class. The Ti₂(Ni, V) building block consists of four icosahedra and a truncated tetrahedron. Replacing the eight carbon atoms of a diamond unit cell with this building block produces the Ti₂(Ni, V) crystal. Placing a distorted Ti₂(Ni, V) building block on a threefold axis of an icosahedrally symmetric point group and operating on it by this point group gives a double Mackay icosahedron. It can be concluded that the Ti₂(Ni, V) and α-AlMnSi quasicrystals are isomorphic structures since Ti₂(Ni, V) and α-A1MnSi crystals consist of both tetrahedra and octahedra.