# On the effective Debye temperatures of the C60 fullerite

Research paper by V. P. Mikhal’chenko

Indexed on: 08 Jul '10Published on: 08 Jul '10Published in: Physics of the Solid State

#### Abstract

The effective Debye temperatures Θeff determined for solids by different physical methods have been analyzed and compared. Attention has been focused on the original parameter of the Debye theory of heat capacity, i.e., the translational calorimetric Debye temperature Θct(0), and the X-ray Debye temperature Θx in the framework of the Debye-Waller theory for the C60 fullerite. It has been established that the true Debye law T3 is satisfied for the C60 fullerite over a very narrow range of temperatures: 0.4 K ≤ T ≤ 1.8 K. For this reason, the experimental Debye temperatures Θct(0) obtained for the C60 fullerite by different authors in the range T > 4.2 K are characterized by a large scatter (by a factor of ∼5). It has been revealed that the value Θct(0) = 77.12 K calculated in this paper with the use of the six-term Betts formula from the harmonic elastic constants $$\tilde C_{ijkl}$$ of the C60 single crystal in the limit T = 0 K is closest to the true Debye temperature. It has been demonstrated using the method of equivalent moments that the real spectral frequency distribution of translational lattice vibrations g(ω) for the C60 fullerite deviates from a parabolic distribution. The effective Debye temperatures Θeff involved in applied problems of thermodynamics of crystals and elastic scattering of different radiations from lattice vibrations have been determined. The quantitative measure of anharmonicity of translational and librational lattice vibrations of the C60 fullerite has been determined. This has made it possible to empirically evaluate the lattice thermal conductivity κ of the C60 fullerite at T ≈ 300 K: κ(300) = 0.80 W (m/K), which is in good agreement with the experimental thermal conductivity κexp = 0.78 W (m/K) at T ≈ 250 K.