Temperature dependence of the phonon density of states in decagonal Al–Ni–Co

We have analyzed the experimentally measured temperature dependence of the phonon density of states (DOS) in d-Al–Ni–Co [1] in the range 300–1100 K, assuming that the relationship between the DOS at different temperatures can be expressed in terms of frequency shifts of the phonon modes. The ω-dependent frequency shifts were determined using a Monte Carlo method. They exhibit a pronounced structure, with two prominent features: a broad maximum near 30 meV and a local minimum around 11 meV. For ω>11 meV, the frequency shifts change with the temperature such that the Grüneisen parameter, relating frequency shifts to the volume expansion, remains approximately constant, γ∼3.5. For the modes with γ<11 meV, the frequency shifts increase faster and γ is temperature dependent, varying from γ∼1.2 at 470 K to γ∼4.6 at T=1100 K. y, we estimate that the frequency shifts relating the phonon DOS at 300 K and at 1100 K contribute ∼0.42kB per atom extra vibrational entropy at the higher temperature.