Phonons in the icosahedral quasicrystal i-AlPdMn studied by coherent inelastic scattering of synchrotron radiation

The thermal and vibrational properties of quasicrystals have remained difficult to understand. It has been noted that specific heat measurements do not agree with the experimental sound velocity and vibrational density of states (DOS). To explain these discrepancies, non-acoustic localized states have been postulated but never directly observed. We have studied the phonon dispersion curves of the icosahedral i-AlPdMn using a new method: coherent inelastic scattering of synchrotron radiation at the ID28 beamline of ESRF on a single grain i-AlPdMn. We have studied both the longitudinal (LA) parallel to and the transverse acoustic (TA) modes perpendicular to the 2-fold axis up to a reduced scattering vector q = Q - G = 5 nmBoth TA and LA branches agree well in the q → 0 limit given by the sound velocity. Both branches deviate from linearity even at very low q: at ca. 2 (LA) to 3 (TA) nm, as has been found from inelastic neutron scattering. Some evidence was found for non-acous tic, probably dispersionless, modes around the LA and TA branches. One advantage of this new method is the necessity for only small single grain samples.