Vitrification and structural differences between metal glass, quasicrystal, and Frank-Kasper phases

The concept of icosahedral short-range order is extended to metallic glass, quasicrystal, and Frank-Kasper phases. The cluster model, together with the theory of local structural fluctuations, explains the static elasticity of glass, which distinguishes glass from liquid. An elastic peak of the dynamic structural factor indicates the possibility of transverse mode propagation in glass. As opposed to dislocation and disclinations in crystals, those in glass are artificially introduced defects, which serve as easily perceptible structural models. Thermodynamic relaxation theory may only be used for limited groups of vitrifying compounds; the same applies to representation of vitrification as the second-order phase transition. The structure of real quasicrystals may not be adequately represented by Penrose tiling, even after it decoration. This is associated with packing defects, inclusions of other phases, and chemical inhomogeneities. Quasicrystals hav specific defects in an icosahedrally coordinated network of bonds, which distinguish them from Frank-Kasper phases. Criteria for isolating physically realizable Penrose tiling from all possible mosaics of this type are suggested. Structural distortion that transfer the diffraction rings of quasicrystalline samples into ellipses are explicable even in a linear approximation for the stress field created by a phason. The term ''long-range order'' seems to be wrong even for ordinary crystals. For quasicrystals, the notion of ''rotational'' order is more pertinent.