Fracton Interpretation of Thermal Conductivity of Amorphous Materials

  • O. Entin-Wohlman
  • R. Orbach
Part of the NATO ASI Series book series (volume 167)


It is shown that the fracton model for the vibrational spectrum of amorphous systems predicts a linear temperature dependence of the thermal conductivity at high temperatures. The mechanism proposed is phonon-assisted hopping of localized fractons and the linear dependence arises from the occupation number of the phonons participating in the process.


Thermal Conductivity Occupation Number Localization Length Anharmonic Oscillator Plateau Temperature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    For a review, see Amorphous Solids: Low Temperature Properties, ed. by W.A. Phillips ( Springer, Berlin 1981 ).Google Scholar
  2. 2.
    R.C. Zeller and R.O. Pohl, Phys. Rev. B4, 2029 (1971).ADSGoogle Scholar
  3. 3.
    J.J. De Yoreo, R.O. Pohl and G. Burns, Phys. Rev. B32, 5780 (1985).Google Scholar
  4. 4.
    P.W. Anderson, B.I. Halperin and C.M. Varma, Phil. Mag. 25, 1 (1972)ADSMATHCrossRefGoogle Scholar
  5. W.A. Phillips, J. Low Temp. Phys. 7, 351 (1972).ADSCrossRefGoogle Scholar
  6. 5.
    V.G. Karpov and D.A. Parshin, Sov. Phys. JETP 61, 1308 (1985) Zh. Eksp. Teor. Fiz. 88, 2212 (1985).Google Scholar
  7. 6.
    S. Hunklinger and W. Arnold, Physical Acoustics, ed. by W.P. Mason and R.N. Thurston, 12, 155 (1976)Google Scholar
  8. J.T. Krauss and C.R. Kurkjian, J. Am. Ceram. Soc. 51, 226 (1968)CrossRefGoogle Scholar
  9. C.K. Jones, P.G. Klemens and J.A. Rayne, Phys. Lett. 8, 31 (1964).ADSCrossRefGoogle Scholar
  10. 7.
    M. Randeria and J.P. Sethna, preprint (1987).Google Scholar
  11. 8.
    E. Akkermans and R. Maynard, Phys. Rev. B32, 7850 (1985).ADSGoogle Scholar
  12. 9.
    S. John, H. Sompolinsky and M.J, Stephen, Phys. Rev. B27, 5592 (1983).ADSGoogle Scholar
  13. 10.
    S. Alexander, O. Entin-Wohlman and R. Orbach, in “Phonon Scattering in Condensed Matter ”, eds. A.C. Anderson and J.P. Wolfe ( Springer, Berlin, 1986 ) p. 15.Google Scholar
  14. 11.
    S. Alexander, C. Laermans, R. Orbach and H.M. Rosenberg, Phys. Rev. B28, 4615 (1983).ADSGoogle Scholar
  15. 12.
    R. Orbach and H.M. Rosenberg, LT-17 Proceedings, ed. by U. Eckern, A. Schmid, W. Weber and H. Wühl ( Elsevier Science Publishers B.V., Amsterdam, 1984 ), p. 375.Google Scholar
  16. 13.
    S. Kelham and H.M. Rosenberg, J. Phys. C14, 1737 (1981); A.J. Dianoux, J.N. Page and H.M. Rosenberg, Phys. Rev. Lett. 58, 886 (1987).Google Scholar
  17. 14.
    M.R. Zaitlin and A.C. Anderson, Phys. Rev. B12, 4475 (1975).ADSGoogle Scholar
  18. 15.
    A.F. Ioffe and A.R. Regel, Prog. Semicond. 4, 237 (1960); N.F. Mott, Phil. Mag. 19, 835 (1969).Google Scholar
  19. 16.
    J.E. Graebner, B. Golding and L.C. Allen, Phys. Rev. B34, 5696 (1986).ADSGoogle Scholar
  20. 17.
    S. Alexander, Physica 140A, 397 (1986).CrossRefGoogle Scholar
  21. 18.
    S. Alexander and R. Orbach, J. de Physique Lett. 43, L625 (1982).CrossRefGoogle Scholar
  22. A.K. Raychaudhuri, Ph.D. Thesis, Cornell University (1980), unpublished; J.E. de Oliveira and H.M. Rosenberg, private communication (1986).Google Scholar
  23. 20.
    S. Alexander, O. Entin-Wohlman and R. Orbach, Phys. Rev. B34, 2726 (1986).ADSGoogle Scholar
  24. 21.
    S. Alexander, Ann. Isr. Phys. Soc. 5, 149 (1983).Google Scholar
  25. 22.
    See Fig. 2 of Ref. 20.Google Scholar
  26. 23.
    D.G. Cahill and R.O. Pohl, Phys. Rev. B35, 4067 (1987).ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • O. Entin-Wohlman
    • 1
  • R. Orbach
    • 2
  1. 1.Lab. de Physique des SolidesOrsayFrance
  2. 2.Dept. of PhysicsUniversity of CaliforniaLos AngelesUSA

Personalised recommendations