Materials Science and Engineering 294–296 (2000) 658–661 Temperature dependence of the phonon density of states in decagonal Al–Ni–Co H. Elhor, M. Mihalkoviˇ c, J.-B. Suck * Materials Research and Liquids, Institute of Physics, TU Chemnitz, D-09107 Chemnitz, Germany Received 30 August 1999; accepted 3 November 1999 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 300–1100 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. Finally, we estimate that the frequency shifts relating the phonon DOS at 300 K and at 1100 K contribute ∼0.42k B per atom extra vibrational entropy at the higher temperature. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Phonons; Quasicrystals; d-Al–Ni–Co; Grüneisen parameter 1. Introduction A natural reason for studying the atomic dynamics of quasicrsytals at high temperatures is the observation that typically the quasicrystals do better in the competition with the related crystalline phases at the high temperatures. So far, no attempt has been made to assess the high-temperature dynamical properties of quasicrystals theoretically: the di- rect molecular dynamics approach is hampered by the lack of realistic interactions, realistic models, or simply compu- tation time requirements. Nevertheless, for the two promi- nent quasicrystal phases i-Al–Pd–Mn and d-Al–Ni–Co, the neutron-weighted phonon density of states (DOS) (called generalized vibrational DOS — GVDOS heretofore) has been measured up to 1100 K [1,2]. The main drawback in the analysis of these data are the unknown partial DOS of the constituent elements; optimally these should enter the iterative multi-phonon subtraction procedure [3]. In this paper, we analyze the temperature dependence of the phonon DOS in d-Al–Ni–Co using the experimental data in [1], and volume expansion data after Dugain [4]. We introduce a Monte Carlo technique for the reconstruction of the frequency shifts, and justify its validity, calculating * Correspoding author. Tel.: +49-371-5318033; fax: +49-371-5318049. E-mail address: suck@physik.tu.chemnitz.de (J.-B. Suck). the frequency shifts also directly from a trial model at two different volumes. Then we estimate the partial VDOS of the Al and TM (i.e. transition metal; representing a random mixture of Ni and Co) at room temperature, fitting a spring model to the experimental data, and apply the same MC technique to the VDOS reconstructed from the experimen- tal GVDOS and the fitted partial VDOS. Although realistic pair potentials for Al–Co system are available, and we used them in the detailed room temperature study of the atomic dynamics in the same system (see [6], Paper I heretofore), the spring model we refined here allows us to fit the experi- mental GVDOS more accurately, and provides a comparison with the partial VDOS derived from the pair potentials (in both cases, we used the same model of the atomic structure, described in Paper I). Finally, we discuss the reconstructed temperature dependence of the frequency shifts, calculate the Grüneisen parameter, and estimate the extra vibrational entropy S vib due to the observed frequency shifts between the phonon DOS at 300 and 1100 K. 2. Monte Carlo approach to the reconstruction of the frequency shifts In the following, we sketch an approach for calculat- ing frequency shifts ω(ω) from the phonon DOS at two 0921-5093/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII:S0921-5093(00)01135-7