On the problem of the relation between phason elasticity and phason dynamics in quasicrystals

TL;DR

This paper critically examines claims of observed phason dynamics in quasicrystals, arguing that existing elasticity theory and simple diffusion models sufficiently explain the data without invoking phason waves, which are physically problematic.

Contribution

It clarifies the relationship between phason elasticity and dynamics, showing that simple diffusion models can account for observed phenomena without the need for phason wave concepts.

Findings

Data can be explained by a diffusion model with a single diffusing tile.

Signal intensity scales with Bragg peak intensity.

Signal falls off as 1/q-squared and decay time is proportional to 1/(D q-squared).

Abstract

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals. We will show that the data reported call for a more detailed development of the elasticity theory of Jaric and Nelsson in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a "satellite position'' at a distance q from each Bragg peak, that (2) has an intensity that scales with the intensity of the corresponding Bragg peak, (3) falls off as 1/q-squared and (4) has a time decay constant that is proportional to 1/(D q-squared). It is thus superfluous to call for a picture of "phason waves'' in order to explain such data, especially as such "waves'' violate many physical principles.