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

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. <Emphasis Type="Bold">91, 225501 (2003); A. Létoublon et al. <Emphasis Type="Bold">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 <Emphasis Type="Bold">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/q<Superscript>2</Superscript>; and (4) has a time decay constant that is proportional to 1/Dq<Superscript>2</Superscript>. 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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006