PHONONS IN MODELS FOR ICOSAHEDRAL QUASI-CRYSTALS - LOW-FREQUENCY BEHAVIOR AND INELASTIC-SCATTERING PROPERTIES

A detailed study of the low frequency behaviour of the phonon spectrum for 3-dimensional tiling models of icosahedral quasicrystals is prese nted, in commensurate approximations with up to 10 336 atoms per unit cell. The scaling behaviour of the lowest phonon branches shows that t he widths of the gaps relative to the bandwidths vanish in the low fre quency limit. The density of states at low frequencies is calculated b y Brillouin zone integration, using either local linear or local quadr atic interpolation of the branch surface. For perfect approximants it appears that there is a deviation from the normal omega2-behaviour alr eady at relatively low frequencies, in the form of pseudogaps. Also ra ndomized approximants are considered, and it turns out that the pseudo gaps in the density of states are flattened by randomization. When app roaching the quasiperiodic limit, the dispersion of the acoustic branc hes becomes more and more isotropic, and the two transversal sound vel ocities tend to the same value. The dynamical structure factor is dete rmined for several approximants, and it is shown that the linearity an d the isotropy of the dispersion are extended far beyond the range of the acoustic branches inside the Brillouin zone. A sharply peaked resp onse is observed at low frequencies, and broadening at higher frequenc ies. To obtain these results, an efficient algorithm based on Lanczos tridiagonalisation is used.