Propagating and localized phonons in amorphous and quasicrystalline alloys

Abstract

The state-of-the art of computational studies of dynamical properties of quasicrystalline and amorphous alloys is reviewed. It is shown that the properties of propagating collective excitations in both quasicrystals and glasses are dominated by ‘quasi’- or ‘pseudo-Brillouin zone’ effects, with the most intense Bragg reflections of the quasicrystal or the main peak in the static structure factor of the glass playing a role of analogous to the Γ-points in the reciprocal lattice of a crystal. It is shown that localized modes exist in both glasses and quasicrystals. However, by contrast with glasses where localization appears only at the edges of the vibrational spectrum, in quasicrystals localized modes exist also at intermediate frequencies and interesting correlations with the topological properties of the quasilattice can be established.