Sound-mode broadening in quasicrystals: A simple phenomenological model

We propose a simple phenomenological model to analyze vibrational characteristics of quasicrystals (QCs). The interpretation of the obtained recently data is based on the existence of almost dispersionless optical modes most probably related to the specific clusters which constitute the characteristic building blocks of any QC structure. We generalize to QCs the well-known Akhiezer mechanism (responsible for the absorption of sound even in an ideal crystal), which in our case is related to a ``long wave'' disturbance of the quasicrystalline optical modes by the propagating sound modes. At higher wave vectors strong hybridization of acoustic and optical modes takes place, and it leads to a more steep broadening dependence on wave vectors, and besides the excitation can no longer be described as a single acoustic mode with a well defined wave vector. We show that the observed sound-mode attenuation behavior can be consistently described by these scenarios without invoking additional mechanisms.