PHONON-SPECTRUM OF THE ONE-DIMENSIONAL 2-COMPONENT QUASI-PERIODIC CRYSTAL

The properties of an one-dimensional quasicrystal consisting of two types of atoms with masses m and M, and with nearest neighbour elastic interaction constants k and K, are studied. The velocity of long-wavelength phonons and the dependence of the maximum oscillation frequency on lattice parameters are derived analytically. The classification procedure of quasicrystal spectra is performed in the limit of large difference of masses and elastic constants. Five different limiting kinds of the spectra are shown to occur.