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 firstname.lastname@example.org
Revised: 20 September 2006
Published online: 8 December 2006
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.
PACS: 61.14.Dc – Theories of diffraction and scattering / 61.44.Br – Quasicrystals / 66.30.-h – Diffusion in solids
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006