Structural scattering of phonons in quasicrystals

The concept of phonon scattering known as the umklapp process is generalized to quasicrystals. It is shown that such processes in quasicrystals lead to a power-law temperature dependence of the mean free path of delocalized quasilattice excitations, contrary to the exponential temperature dependence of the phonon mean free path characteristic of periodically structured crystals at intermediate temperatures. This result provides a plausible explanation for the plateau-type feature in the quasilattice thermal conductivity ${\lambda }_{\mathrm{ph}}\mathrm{}\left(T\right)\mathrm{}$ of Al-Mn-Pd quasicrystals.