VIBRATIONAL PROPERTIES OF AN OCTAGONAL QUASI-CRYSTAL

The vibrational densities of states for an octagonal quasiperiodic lattice are calculated. Crossovers from phonon excitations to fracton-like excitations are found in the low-frequency parts of the spectra (this part is referred to as the continuous spectrum); meanwhile, localized vibrational modes are observed in the high-frequency parts (this part is referred to as the characteristic spectrum). The spectral features are governed by alpha and beta, the central and non-central force constants of the Born model. For the low-frequency continuous spectrum, when alpha/beta equals unity (isotropic model) and when alpha/beta is not very large, a power law is satisfied in the fracton-like excitation frequency regime but, when alpha/beta approaches infinity, the spectrum deviates from the original power law. For the high-frequency characteristic spectrum, in an isotropic situation, i.e. in the case when alpha/beta = 1, the localized mode is isolated and a gap separates it from other modes but, when there is no longer isotropy, the gap disappears.