Low-energy lattice excitations in the decagonal Al–Ni–Fe and icosahedral Al–Cu–Fe quasicrystals and the (Al, Si)–Cu–Fe cubic phase

The specific heat of decagonal Al$_{71.3}$Ni$_{24.0}$Fe$_{4.7}$ and icosahedral Al$_{62}$Cu$_{25.5}$Fe$_{12.5}$ quasicrystals and the Al$_{55.0}$Si$_{7.0}$Cu$_{25.5}$Fe$_{12.5}$ cubic phase approximating the structure of the icosahedral alloy has been studied in the temperature range 4.2–40.0 K. All the three compounds exhibit low coefficients of the electronic heat capacity and pronounced deviations of the low-temperature lattice heat capacity from a cubic temperature law in the range 5–10 K. The results obtained by the thermodynamic method and inelastic neutron scattering have been compared and analyzed. It has been established that, at energies $\varepsilon<$ 14 meV, the spectral density of thermal vibrations in the icosahedral quasicrystal is substantially higher than those in the cubic approximant and in decagonal quasicrystal.