Phonons and Phasons in Icosahedral Quasicrystals

The discovery of quasicrystals not only has changed our view on long-range order, but was a breakthrough for solid state physics and chemistry, since the Bloch theorem can no longer be applied. We review some of the results obtained for icosahedral quasicrystals for lattice dynamics and phonons, as well as for phason modes, which are diffusive excitations characteristic of the quasicrystalline state.