PROPAGATING AND LOCALIZED PHONONS IN AMORPHOUS AND QUASI-CRYSTALLINE ALLOYS

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 quasicry stals 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 Gamma-points in the reciprocal lattice of a crystal. It is shown that localized modes exist in both glasses and qu asicrystals. However, by contrast with glasses where localization appe ars only at the edges of the vibrational spectrum, in quasicrystals lo calized modes exist also at intermediate frequencies and interesting c orrelations with the topological properties of the quasilattice can be established.