The phonon density of states in the archetypical icosahedral quasicrystal Al62Cu25.5Fe12.5

We study the vibrational density of states (VDOS) in the i-AlCuFe quasicrystal measured by different methods: (i) 57Fe inelastic nuclear-resonant absorption (INA) of X-rays (ii) and time-of-flight inelastic neutron scattering (INS). The samples studied were i-Al62Cu25.5Fe12.5 with different isotopic substitutions. INA measures the Fe-partial VDOS while INS the neutron-weighted ‘generalised’ GVDOS. We find the unexpected result that the iron-partial VDOS has a single sharp maximum. The neutron-weighted GVDOS for different isotopes (natural Cu and 65Cu; natural Fe and 57Fe shows that the copper-partial VDOS is strongly peaked as well but at significantly lower energy. These results are discussed in light of the icosahedral quasicrystal model of Katz and Gratias, as well as specific heat results which indicate a discrepancy between the speed of sound, the specific heat and the low energy limit of the VDOS.