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http://dx.doi.org/10.3795/KSME-B.2003.27.8.1165

Impact of Phonon Dispersion on Thermal Conductivity Model  

Chung, Jae-Dong (세종대학교 기계공학과)
Publication Information
Transactions of the Korean Society of Mechanical Engineers B / v.27, no.8, 2003 , pp. 1165-1173 More about this Journal
Abstract
The effects of (1) phonon dispersion on thermal conductivity model and (2) differentiation of group velocity and phase velocity are examined for germanium. The results show drastic change of thermal conductivity regardless of the same relaxation time model. Also the contribution of transverse acoustic (TA) phonon and longitudinal acoustic (LA) phonon on the thermal conductivity at high temperatures is reassessed by considering more rigorous dispersion model. Holland model, which is commonly used for modeling thermal conductivity, underestimates the scattering rate for TA phonon at high frequency. This leads the conclusion that TA is dominant heat transfer mode at high temperatures. But according to the rigorous consideration of phonon dispersion, the reduction of thermal conductivity is much larger than the estimation of Holland model, thus the TA at high frequency is expected to be no more dominant heat transfer mode. Another heat transfer mechanism may exist at high temperatures. Two possible explanations we the roles of (1) Umklapp scattering of LA phonon at high frequency and (2) optical phonon.
Keywords
Thermal Conductivity; Phonon; Dispersion Relation; Relaxation Time;
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1 Holland, M. G., 1963, 'Analysis of Lattice Thermal Conductivity,' Phys. Rev., Vol. 132, pp. 2461-2471   DOI
2 Hamilton, R. A. and Parrott, J. E., 1969, 'Variational Calculation of the Thermal Conductivity of Germanium,' Physical Review, Vol. 178, pp. 1284-1292   DOI
3 Omini, M. and Sparavigna, A., 1995, 'An Iterative Approach to the Phonon Boltzmann Equation in the Theory of Thermal Conductivity,' Physica B, Vol. 212, pp. 101-112   DOI   ScienceOn
4 McGaughey, A. J. H. and Kaviany, M., 'Thermal Conductivity Decomposition and Analysis Using Molecular Dynamics Simulations. Part II. Complex silica Structures,' submitted to International Journal of Heat and Mass Transfer   DOI   ScienceOn
5 Klemens, P. G., 1958, Solid State Physics, Academic Press Inc., New York
6 Bhandari, C. M. and Rowe, D., 1979, 'The Generalisation of the Callaway Thermal Conductivity Equation,' J. Phys. C: Solid State Phys., Vol. 12, pp. L883-L885   DOI   ScienceOn
7 Tiwari, M. D. and Agrawal, B. K., 1971, 'Analysis of the Lattice Thermal conductivity of Germanium,' Physical Review B, Vol. 4, pp. 3527-3532   DOI
8 Parrott, J. E., 1971, 'Generalization of the Callaway Thermal Conductivity Equation,' Phys. Status Solidi B, Vol. 48, pp. K159-K161   DOI
9 Sood, K. C. and Roy, M, 1993, 'Longitudinal Phonons and High-Temperature Heat Conduction in Germanium,' J. Phys:Condens. Matter, Vol. 5, pp. 301-312   DOI   ScienceOn
10 Ziman, J. M., 1960, Electrons and Phonons, Oxford University Press, London
11 Nilsson, G. and Nelin, G., 1971, 'Phonon Dispersion Relations in Ge at 80K,' Physical Review B, Vol. 3, pp. 364-369   DOI
12 Callaway, J., 1959, 'Model of Lattice Thermal Conductivity at Low Temperatures,' Phys. Rev., Vol. 113, pp. 1046-1051   DOI