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

Abstract

We have analyzed the experimentally measured temperature dependence of the phonon density of states (DOS) in d-Al–Ni–Co [1] in the range 300–1100K, 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 30meV and a local minimum around 11meV. For ω>11meV, 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<11meV, the frequency shifts increase faster and γ is temperature dependent, varying from γ∼1.2 at 470K to γ∼4.6 at T=1100K.Finally, we estimate that the frequency shifts relating the phonon DOS at 300K and at 1100K contribute ∼0.42kB per atom extra vibrational entropy at the higher temperature.