Investigation of phason statics and dynamics

Abstract

The experimental observation of phason fluctuations, both static and dynamic, is well established and has been interpreted within the framework of a hydrodynamic theory. Theoretically, it is still open in what temperature range a hydrodynamic description of phasons is applicable. It has been proposed in the literature that towards low temperatures the hydrodynamic regime is terminated because the form of the phason elastic energy changes from harmonic to non-analytical. Here we report two contributions to the field. Firstly, for a two-dimensional binary model quasicrystal at zero temperature we have investigated the relation between atomic two-body potentials and the phason elastic energy. It turns out that there are indeed certain potentials that can induce a non-analytical phason elastic energy, but these must have very peculiar features in their long-range part, rendering their existence highly unlikely. Secondly, one solution of the hydrodynamic equations is a phasonic excitation riding on a phonon. We have studied the atomistic counterpart via a nonlinear chain with double-well potentials, which resembles a dynamic Fibonacci sequence. We see correlated phason flips propagating with phonon excitations and the dynamic structure factor can separate phonon from phason dynamics.

Acknowledgements

We thank Dr Franz Gähler, Michael Engel and Steffen Sonntag for valuable discussions.