Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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Impact of Phonon Dispersion on Thermal Conductivity Model

포논 분산이 열전달 모델에 미치는 영향

  • Published : 2003.08.01
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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.

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References

  1. Ziman, J. M., 1960, Electrons and Phonons, Oxford University Press, London
  2. Callaway, J., 1959, 'Model of Lattice Thermal Conductivity at Low Temperatures,' Phys. Rev., Vol. 113, pp. 1046-1051 https://doi.org/10.1103/PhysRev.113.1046
  3. Holland, M. G., 1963, 'Analysis of Lattice Thermal Conductivity,' Phys. Rev., Vol. 132, pp. 2461-2471 https://doi.org/10.1103/PhysRev.132.2461
  4. Hamilton, R. A. and Parrott, J. E., 1969, 'Variational Calculation of the Thermal Conductivity of Germanium,' Physical Review, Vol. 178, pp. 1284-1292 https://doi.org/10.1103/PhysRev.178.1284
  5. 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 https://doi.org/10.1016/0921-4526(95)00016-3
  6. Klemens, P. G., 1958, Solid State Physics, Academic Press Inc., New York
  7. Parrott, J. E., 1971, 'Generalization of the Callaway Thermal Conductivity Equation,' Phys. Status Solidi B, Vol. 48, pp. K159-K161 https://doi.org/10.1002/pssb.2220480266
  8. 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 https://doi.org/10.1088/0022-3719/12/23/002
  9. Tiwari, M. D. and Agrawal, B. K., 1971, 'Analysis of the Lattice Thermal conductivity of Germanium,' Physical Review B, Vol. 4, pp. 3527-3532 https://doi.org/10.1103/PhysRevB.4.3527
  10. 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 https://doi.org/10.1088/0953-8984/5/3/006
  11. Nilsson, G. and Nelin, G., 1971, 'Phonon Dispersion Relations in Ge at 80K,' Physical Review B, Vol. 3, pp. 364-369 https://doi.org/10.1103/PhysRevB.3.364
  12. 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 https://doi.org/10.1016/j.ijheatmasstransfer.2003.11.009