Skip to main content

Abstract

The main theoretical predictions on vibrational excitations of fractal networks are first summarized. The application of the fracton theory to glasses and other amorphous materials is then critically discussed. The early experimental evidence for fractons obtained on demonstrated fractal systems is also surveyed. Finally, the extensive observations performed recently on silica aerogels are reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H.P. McKean and I.M. Singer, J. Differential Geometry 1, 43 (1967).

    Google Scholar 

  2. M.L. Lapidus and J. Fleckinger-Pellé, C. R. Acad. Sci. Paris 306, Série I, 171 (1988).

    Google Scholar 

  3. S. Alexander and R. Orbach, J. Phys. (Paris) Lett. 43, L625 (1982).

    Article  Google Scholar 

  4. R. Rammal and G. Toulouse, J. Phys. (Paris) Lett. 44, L13 (1983).

    Article  Google Scholar 

  5. R. Orbach, in Scaling Phenomena in Disordered Systems, R. Pynn and A. Skjeltorp, Eds. (Plenum, New York, 1985) p. 335.

    Google Scholar 

  6. S. Alexander, Physica 140A, 397 (1986).

    CAS  Google Scholar 

  7. S. Alexander, presented at this workshop and to be published.

    Google Scholar 

  8. S. Alexander, O. Entin-Wohlman, and R. Orbach, Phys. Rev. B 34, 2726 (1986).

    Article  Google Scholar 

  9. A. Jagannathan, R. Orbach, and O. Entin-Wohlman, Phys. Rev. B (to be published).

    Google Scholar 

  10. A. Aharony, S. Alexander, O. Entin-Wohlman, and R. Orbach, Phys. Rev. Lett. 58, 132 (1987).

    Article  PubMed  CAS  Google Scholar 

  11. S. Alexander, J. Phys. (Paris), 45, 1939 (1984).

    Article  CAS  Google Scholar 

  12. Y. Gefen, A. Aharony, and S. Alexander, Phys. Rev. Lett. 50, 77 (1983).

    Article  Google Scholar 

  13. O. Entin-Wohlman, Y. Kantor, and R. Orbach, private communication.

    Google Scholar 

  14. I. Webman and G. Grest, Phys. Rev. B 31, 1689 (1985).

    Article  Google Scholar 

  15. J. Kieffer and C. A. Angell, J. Non-Cryst. Solids 106, 336 (1988).

    Article  CAS  Google Scholar 

  16. R. Vacher, T. Woignier, J. Pelous, and E. Courtens, Phys. Rev. B 37, 6500 (1988).

    Article  CAS  Google Scholar 

  17. E. Courtens and R. Vacher, Z. Phys. B 68, 355 (1987).

    Article  Google Scholar 

  18. Y. Tsujimi, E. Courtens, J. Pelous, and R. Vacher, Phys. Rev. Lett. 60, 2757 (1988).

    Article  PubMed  CAS  Google Scholar 

  19. P.F. Tua, S.J. Putterman, and R. Orbach, Phys. Lett. 98A, 357 (1983).

    Article  CAS  Google Scholar 

  20. S. Alexander, C. Laermans, R. Orbach, and H.M. Rosenberg, Phys. Rev. B 28, 4615 (1983).

    Article  CAS  Google Scholar 

  21. A. Aharony, S. Alexander, O. Entin-Wohlman, and R. Orbach, Phys. Rev. B 31, 2565 (1985).

    Article  Google Scholar 

  22. A. Aharony, O. Entin-Wohlman, and R. Orbach, in Time-dependent Effects in Disordered Materials, R. Pynn and T. Riste, Eds. (Plenum, New York, 1987) p. 233.

    Chapter  Google Scholar 

  23. B.W. Southern and A.R. Douchant, Phys. Rev. Lett. 55, 966 (1985).

    Article  PubMed  CAS  Google Scholar 

  24. K. Yakubo and T. Nakayama, Phys. Rev. B 36, 8933 (1987).

    Article  Google Scholar 

  25. T. Nakayama, K. Yakubo, and R. Orbach, Phys. Rev. B (to be published).

    Google Scholar 

  26. R.C. Zeller and R.O. Pohl, Phys. Rev. B 4, 2029 (1971).

    Article  Google Scholar 

  27. See, e.g., Amorphous Solids: Low-Temperature Properties, W.A. Phillips, Ed. (Springer, Berlin, 1981).

    Google Scholar 

  28. P.W. Anderson, B.I. Halperin, and C.M. Varma, Philos. Mag. 25, 1 (1972)

    Article  CAS  Google Scholar 

  29. W.A. Phillips, J. Low Temp. Phys. 7, 351 (1972).

    Article  CAS  Google Scholar 

  30. As discussed above, such a hump is not an intrinsic feature of the fracton model. It is also not a specific feature of glasses, since good single crystals often show such a hump, e.g. W.N. Lawless, Phys. Rev. B 14, 134 (1976). In fact, humps of comparable size are found in fused silica and in crystalline quartz.26

    Article  CAS  Google Scholar 

  31. H.M. Rosenberg, Phys. Rev. Lett. 54, 704 (1985).

    Article  PubMed  CAS  Google Scholar 

  32. A.J. Dianoux, J.N. Page, and H.M. Rosenberg, Phys. Rev. Lett. 58, 886 (1987).

    Article  PubMed  CAS  Google Scholar 

  33. A. Boukenter, E. Duval, and H.M. Rosenberg, J. Phys. C 21, L541 (1988).

    Article  CAS  Google Scholar 

  34. M. Arai and J.E. Jörgensen, Phys. Lett. A 133, 70 (1988).

    Article  CAS  Google Scholar 

  35. J.E. de Oliveira, J.N. Page, and H.M. Rosenberg, Phys. Rev. Lett. 62, 780 (1989).

    Article  PubMed  Google Scholar 

  36. A. Avogadro, S. Aldrovandi, and F. Borsa, Phys. Rev. B 33, 5637 (1986).

    Article  CAS  Google Scholar 

  37. A. Fontana, F. Rocca, and M.P. Fontana, Phys. Rev. Lett. 58, 503 (1987).

    Article  PubMed  CAS  Google Scholar 

  38. J.E. Graebner, B. Golding, and L.C. Allen, Phys. Rev. B 34, 5696 (1986)

    Article  CAS  Google Scholar 

  39. J.E. Graebner and B. Golding, Phys. Rev. B 34, 5788 (1986).

    Article  CAS  Google Scholar 

  40. E. Duval, G. Mariotto, M. Montagna, O. Pilia, G. Viliani, and M. Barland, Europhys. Lett. 3, 333 (1987).

    Article  CAS  Google Scholar 

  41. A. Boukenter, B. Champagnon, E. Duval, J. Dumas, J.F. Quinson, and J. Serughetti, Phys. Rev. Lett. 57, 2391 (1986).

    Article  PubMed  CAS  Google Scholar 

  42. G. Mariotto, M. Montagna, G. Viliani, R. Campostrini, and G. Carturan, J. Phys. C 21, L797 (1988).

    Article  CAS  Google Scholar 

  43. A. Boukenter, B. Champagnon, E. Duval, J.L. Rousset, J. Dumas, and J. Serughetti, J. Phys. C 21, L1097 (1988)

    Article  CAS  Google Scholar 

  44. J.L. Rousset, E. Duval, A. Boukenter, B. Champagnon, A. Monteil, J. Serughetti, and J. Dumas, J. Non-Cryst. Solids 107, 27 (1988).

    Article  CAS  Google Scholar 

  45. T. Keyes and T. Ohtsuki, Phys. Rev. Lett. 59, 603 (1987).

    Article  PubMed  CAS  Google Scholar 

  46. A. Boukenter, B. Champagnon, E. Duval, and J. Serughetti, Phys. Rev. Lett. 59, 604 (1987).

    Article  PubMed  CAS  Google Scholar 

  47. D. Deptuck, J.P. Harrison, and P. Zawadski, Phys. Rev. Lett. 54, 913 (1985).

    Article  PubMed  CAS  Google Scholar 

  48. J.H. Page and R.D. McCulloch, Phys. Rev. Lett. 57, 1324 (1986).

    Article  PubMed  CAS  Google Scholar 

  49. O. Entin-Wohlman, S. Alexander, R. Orbach, and K.-W. Yu, Phys. Rev. B 29, 4588 (1984).

    Article  Google Scholar 

  50. Y.J. Uemura and R.J. Birgeneau, Phys. Rev. Lett. 57, 1947 (1986) and Phys. Rev. B 36, 7024 (1987).

    Article  PubMed  CAS  Google Scholar 

  51. R. Orbach and K.-W. Yu, J. Appl. Phys. 61, 3689 (1987).

    Article  Google Scholar 

  52. M.B. Salamon and Y. Yeshurun, Phys. Rev. B 36, 5643 (1987).

    Article  Google Scholar 

  53. These phenomena have recently been reviewed in Random Fluctuations and Pattern Growth: Experiments and Models H.E. Stanley and N. Ostrowsky, Eds. (Kluwer Academic Publishers, Dordrecht, 1988).

    Google Scholar 

  54. J.H. Page, W.J.L. Buyers, G. Dolling, P. Gerlach, and J.P. Harrison, Phys. Rev. B (15 March 1989).

    Google Scholar 

  55. T. Freltoft, J. Kjems, and S.K. Sinha, Phys. Rev. B 33, 269 (1986).

    Article  CAS  Google Scholar 

  56. T. Freltoft, J. Kjems, and D. Richter, Phys. Rev. Lett. 59, 1212 (1987).

    Article  PubMed  CAS  Google Scholar 

  57. See, e.g., the Proceedings of the two Int’l Conferences on Aerogels: (a) Aerogels, J. Fricke, Ed., (Springer, Berlin, 1985); and

    Google Scholar 

  58. R. Vacher, J. Phalippou, J. Pelous, and T. Woignier, Rev. Phys. Appl. 24, C4 (1989).

    Google Scholar 

  59. D.W. Schaefer and K.D. Keefer, Phys. Rev. Lett. 56, 2199 (1986).

    Article  PubMed  CAS  Google Scholar 

  60. B. Nouailhas, F. Michard, R. Gohier, and A. Zarembowitch, in 11th I.C.A. (Paris, 1983) p. 179.

    Google Scholar 

  61. E. Courtens and R. Vacher, in Random Fluctuations and Pattern Growth: Experiments and Models H.E. Stanley and N. Ostrowsky, Eds. (Kluwer Academic Publishers, Dordrecht, 1988) p. 21.

    Google Scholar 

  62. E. Courtens and R. Vacher, Phil. Trans. Roy. Soc. (London), Series A (to be published).

    Google Scholar 

  63. R. Vacher, T. Woignier, J. Phalippou, J. Pelous, and E. Courtens, J. Non-Cryst. Solids 106, 161 (1988). p. 145.

    Google Scholar 

  64. E. Courtens, J. Pelous, J. Phalippou, R. Vacher, and T. Woignier, Phys. Rev. Lett. 58, 128 (1987).

    Article  PubMed  CAS  Google Scholar 

  65. E. Courtens, R. Vacher, J. Pelous, and T. Woignier, Europhys. Lett. 6, 245 (1988).

    Article  CAS  Google Scholar 

  66. R. Calemczuk, A.M. de Goër, B. Salce, R. Maynard, and A. Zarembowitch, Europhys. Lett. 3, 1205 (1987).

    Article  CAS  Google Scholar 

  67. R. Vacher, T. Woignier, J. Pelous, G. Coddens, and E. Courtens, Europhys. Lett. 8, 161 (1989).

    Article  CAS  Google Scholar 

  68. G. Reichenauer, J. Fricke, and U. Buchenau, Europhys. Lett. 8, 415 (1989).

    Article  CAS  Google Scholar 

  69. R. Vacher, E. Courtens, G. Coddens, J. Pelous, and T. Woignier, Phys. Rev. B (1st April 1989).

    Google Scholar 

  70. P. Meakin, in On Growth and Form, H.E. Stanley and N. Ostrowsky, Eds. (Nijhoff, Dordrecht, 1986) p. 111.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer Science+Business Media New York

About this chapter

Cite this chapter

Courtens, E., Vacher, R., Pelous, J. (1989). Observations of Fractons. In: Pietronero, L. (eds) Fractals’ Physical Origin and Properties. Ettore Majorana International Science Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3499-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-3499-4_17

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-3501-4

  • Online ISBN: 978-1-4899-3499-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics