Anisotropy of the phonon-phason dynamics and the pinning effect in icosahedral AlPdMn quasicrystals

A minimal model of the phonon-phason dynamics in icosahedral quasicrystals with inclusion of the pinning effect is suggested. Resonant attenuation of low-frequency acoustic waves in the temperature range corresponding to thermal activation of phasons is considered. In the long-wave length limit, the velocity of acoustic phonons is isotropic; however, the phonon-phason coupling causes anisotropy of the velocity and of the attenuation of acoustic waves with small wave vectors. These effects manifest themselves most strongly at an acoustic wave frequency close to the inverse relaxation time of phasons with the same wave vector. The pinning effect can cause a significant decrease in the anisotropy of the velocity and of attenuation of acoustic waves.