Phonons in the icosahedral quasicrystali-AlPdMn studied by inelastic x-ray scattering

The phonon branches of a i-AlPdMn icosahedral quasicrystal are studied, using inelastic x-ray scattering (IXS) with meV energy resolution. Longitudinal and transverse phonon branches are recorded, starting from a (52,84) reflection along the twofold axis. In both cases we observe an acoustic mode whose speed of sound agrees very well with the sound velocity at small reduced wave vectors q, but becomes nondispersive near q~0.35 ^-1. A second mode, dispersionless over the whole spanned q range, can be clearly identified only in a purely longitudinal geometry. Our findings are in general agreement with previous inelastic neutron scattering (INS) results. However, at variance with the INS results, we observe a weaker increase of the longitudinal acoustic phonon line width with reduced momentum transfer. The present study presents a benchmark for future IXS work on quasicrystalline materials which will be of particular value for single crystals, only available in very small quantities or containing elements not suitable for INS due to their large incoherent cross section.