Anisotropy of acoustic-phonon properties of an icosahedral quasicrystal athigh temperature due to phonon-phason coupling

The equations of motions for the medium with an icosahedral qusicrystalline symmetry are generalized. It is shown that phonon-phason coupling in an ic osahedral quasicrystal leads to the dependence of the acoustic phonons; vel ocity and the attenuation coefficient on the propagation direction in a tem perature region close to the fusion point. The analytical expressions for t he dispersion of waves propagating along the symmetry axes are obtained. Th e anisotropy of acoustic properties of decagonal and dodecagonal quasicryst als due to phonon-phason interaction is shown to be impossible. The obtaine d results may be used for experimental acoustic determination of the elasti c constants of icosahedral quasicrystals.