Phason effects around a crack in Al–Pb–Mn quasicrystals: stochastic aspects of the phonon–phason coupling

We determine the distribution of phonon and phason displacements around the tip of a crack in Al–Pb–Mn quasicrystals. We find an increment of phason activity, due to crystal substructural changes, around the crack. A transfer of energy from the macroscopic level to the phason one and vice versa, as a consequence of phonon–phason coupling, influences the force driving the crack tip. Finally, we interpret the scattering of data about the phonon–phason coupling coefficient from a random point of view considering such a coupling as a stochastic field over the body.