Vibrational density of states in the archetypical icosahedral quasicrystal i-Al62Cu25.5Fe12.5:: Neutron time-of-flight results

We study the neutron-weighted vibrational density of states g(E) in the i-AlCuFe quasicrystal measured by time-of-flight inelastic neutron scattering (INS). The samples studied were i-Al62Cu25.5Fe12.5 with different isotopic substitutions. These results are compared to our previous Fe-57 inelastic nuclear-resonant absorption (INA) results for the iron-partial g(E) [R. A. Brand et at, Phys. Rev. B 59, R14 145 (1999)]. The neutron-weighted g(E) measured on samples with different isotopes (natural Cu and Cu-65; natural Fe and Fe-57) shows that the aluminum and copper-partial g(E) is strongly peaked at a significantly lower energy than that for iron. We show in addition that the low-energy square term in g(E) is the same for both INS and INA but a significant quartic term exists in the neutron-weighted g(E). The neutron-weighted and iron-partial g(E) are used to calculate lattice-dynamical properties such as the lattice specific heat C-latt(T). The C-latt(T) as calculated from the neutron-weighted g(E) agrees with the experimental C-latt in the low T range where an anomalous power law had previously been found [J. C. Lasjaunias et al., J. phys. I 7, 959 (1997)]. These results are discussed in terms of possible non-acoustic modes at low energy.