TECHNICAL PAPERS: Micro/Nanoscale Heat Transfer

Role of Phonon Dispersion in Lattice Thermal Conductivity Modeling

[+] Author and Article Information
J. D. Chung

Department of Mechanical Engineering, Sejong University, Seoul, 143-147, Korea

A. J. H. McGaughey, M. Kaviany

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125e-mail: kaviany@umich.edu

J. Heat Transfer 126(3), 376-380 (Jun 16, 2004) (5 pages) doi:10.1115/1.1723469 History: Received June 13, 2003; Revised January 09, 2004; Online June 16, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Debye, P., 1914, Vortrage uber die kinetische Theorie der Materie und der Elektrizitat, Teubner, Berlin.
Peierls, R., 1997, “On the Kinetic Theory of Thermal Conduction,” Selected Scientific Papers of Sir Rudolf Peierls With Commentary, Dalitz, R. H. and Peierls, R., eds., World Scientific, Singapore, pp. 15–48.
Callaway,  J., 1959, “Model for Lattice Thermal Conductivity at Low Temperatures,” Phys. Rev., 113, pp. 1046–1051.
Holland,  M. G., 1963, “Analysis of Lattice Thermal Conductivity,” Phys. Rev., 132, pp. 2461–2471.
Tiwari,  M. D., and Agrawal,  B. K., 1971, “Analysis of the Lattice Thermal Conductivity of Germanium,” Phys. Rev. B, 4, pp. 3527–3532.
Sood,  K. C., and Roy,  M. K., 1993, “Longitudinal Phonons and High-Temperature Heat Conduction in Germanium,” J. Phys.: Condens. Matter, 5, pp. 301–312.
Asen-Palmer,  M., Bartkowski,  K., Gmelin,  E., Cardona,  M., Zhernov,  A. P., Inyushkin,  A. V., Taldenkov,  A., Ozhogin,  V. I., Itoh,  K. M., and Haller,  E. E., 1997, “Thermal Conductivity of Germanium Crystals With Different Isotopic Compositions,” Phys. Rev. B, 56, pp. 9431–9447.
Nilsson,  G., and Nelin,  G., 1971, “Phonon Dispersion Relations in Ge at 80 K,” Phys. Rev. B, 3, pp. 364–369.
Dove, M. T., 1993, Introduction to Lattice Dynamics, Cambridge, Cambridge.
Kittel, C., 1996, Introduction to Solid State Physics, Wiley, New York.
Geballe,  T. H., and Hull,  G. W., 1958, “Isotopic and Other Types of Thermal Resistance in Germanium,” Phys. Rev., 110, pp. 773–775.
Klemens,  P. G., 1958, “Thermal Conductivity and Lattice Vibrational Modes,” Solid State Phys., 7, pp. 1–98.
Slack,  G. A., 1957, “Effect of Isotopes on Low-Temperature Thermal Conductivity,” Phys. Rev., 105, pp. 829–831.
Ziman, J. M., 2001, Electrons and Phonons, Oxford, Oxford.
McGaughey,  A. J. H., and Kaviany,  M., 2004, “Quantitative Validation of the Boltzmann Transport Equation Thermal Conductivity Model Under the Single Mode Relaxation Time Approximation,” Phys. Rev. B, 69, 094303, pp. 1–12.
Hamilton,  R. A., and Parrott,  J. E., 1969, “Variational Calculation of the Thermal Conductivity of Germanium,” Phys. Rev., 178, pp. 1284–1292.
Mazumder,  S., and Majumdar,  A., 2001, “Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization,” ASME J. Heat Transfer, 123, pp. 749–759.
Ju,  Y. S., and Goodson,  K. E., 1999, “Phonon Scattering in Silicon Films With Thickness of Order 100 nm,” Appl. Phys. Lett., 74, pp. 3005–3007.
Slack,  G. A., and Glassbrenner,  C., 1960, “Thermal Conductivity of Germanium From 3 K to 1020 K,” Phys. Rev., 120, pp. 782–789.
McGaughey,  A. J. H., and Kaviany,  M., 2004, “Thermal Conductivity Decomposition and Analysis Using Molecular Dynamics Simulations. Part II. Complex Silica Structures,” Int. J. Heat Mass Transfer, 47, pp. 1799–1816.


Grahic Jump Location
Germanium phonon dispersion in the [100] direction. Experimental data 8 and five models used in this study for (a) LA phonons and (b) TA phonons.
Grahic Jump Location
vg/vp2 for the five dispersion models plotted as a function of normalized wave number for (a) LA phonons and (b) TA phonons.
Grahic Jump Location
Effect of refining the treatment of the dispersion on the prediction of the thermal conductivity of germanium. (a) Based on the original Holland fitting parameters, and (b) predictions refit to the experimental data.
Grahic Jump Location
(a) Three phonon relaxation times for refit data from Fig. 3(b) at T=80 K. (b) Cumulative frequency dependence of the thermal conductivity for refit data from Fig. 3(b) at T=80 K. The thermal conductivity is plotted as a percentage of the total value for each case. The curves show three distinct regions. The transition between the first and second regions takes place at ω1, where the form of the TA relaxation time changes. The transition between the second and third regions occurs at ωmT, after which there is no contribution from TA phonons [see Eq. (1)].
Grahic Jump Location
Contributions of LA and TA phonon branches to the thermal conductivity based on (a) Holland dispersion model, and (b) BZBC dispersion model.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In