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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
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