Eur. Phys. J. B 54, 37-65 (2006)
https://doi.org/10.1140/epjb/e2006-00429-9

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

Laboratoire des Solides Irradiés, École Polytechnique, CEA-DSM/CNRS, 91128 Palaiseau Cedex, France

Corresponding author: ^a gerrit.coddens@polytechnique.fr

Received: 26 April 2006
Revised: 20 September 2006
Published online: 8 December 2006

Abstract

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals [S. Francoual et al. Phys. Rev. Lett. 91, 225501 (2003); A. Létoublon et al. 54, 753 (2001)]. We will show that the data reported call for a more detailed development of the elasticity theory of Jarić and Nelsson [M.V. Jarić and D.R. Nelsson, Phys. Rev. B 37, 4458 (1988)] 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/q²; and (4) has a time decay constant that is proportional to 1/Dq². 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.