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Structure and dynamics of fractal aerogels

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Zeitschrift für Physik B Condensed Matter

Abstract

Silica aerogels form mutually self-similar fractal structures for a broad range of densities and preparation conditions. This allows to scale dynamical results obtained on longitudinal acoustic waves up to the onset of the phonon to fracton crossover. An “effective” value of the fracton dimension\(\bar \bar d = 1.3 \pm 0.1\) is found, and various possible interpretations of that value are discussed.

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References

  1. Spinoza, B.: Opera Posthuma, Letter to H. Oldenburg, Voorburg, Nov. 20, 1665, freely translated from the Latin edition of Carl Gebhardt. Heidelberg: Winters 1924

    Google Scholar 

  2. Thomas, H.: In: Structural transitions and soft modes. Samuelsen, E.J., Andersen, E., Feder, J. (eds.). Oslo: Universitetforlaget 1971

    Google Scholar 

  3. Thomas, H.: In: Anharmonic lattices, structural transitions and melting. Riste, T. (ed.). Leiden: Noordhoff 1974

    Google Scholar 

  4. Mandelbrot, B.: The fractal geometry of nature. San Fransisco: Freeman 1982

    Google Scholar 

  5. See, e.g.: Time dependent effects in disordered materials. Pynn, R., Riste, T. (eds.). New York: Plenum Press (to be published)

  6. Alexander, S., Laermans, C., Orbach, R., Rosenberg, H.M.: Phys. Rev. B28, 4615 (1983)

    Google Scholar 

  7. Pohl, R.O.: In: Amorphous solids, low temperature properties. Phillips, W.A. (ed.). Berlin, Heidelberg, New York: Springer 1981

    Google Scholar 

  8. Krumhansl, J.A.: Phys. Rev. Lett.56, 2696 (1986)

    Google Scholar 

  9. Alexander, S.: In: Statphys 16. Stanley, H.E. (ed.). Amsterdam: North-Holland 1986

    Google Scholar 

  10. Stauffer, D.: In: On growth and form. Stanley, H.E., Ostrowsky, N. (eds.). Dordrecht: Nijhoff 1986

    Google Scholar 

  11. For several reviews, see, e.g.: Scaling phenomena in disordered systems. Pynn, R., Skjeltorp, A. (eds.). New York: Plenum Press 1985

    Google Scholar 

  12. de Gennes, P.G.: J. Phys. Lett.37, L1 (1976)

    Google Scholar 

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

    Google Scholar 

  14. Alexander, S., Orbach, R.: J. Phys. Lett.43, L625 (1982)

    Google Scholar 

  15. Rammal, R., Toulouse, G.: J. Phys. Lett.44, L13 (1983)

    Google Scholar 

  16. Kantor, Y., Webmann, I.: Phys. Rev. Lett.52, 1891 (1984)

    Google Scholar 

  17. Webman, I., Grest, G.S.: Phys. Rev. B31, 1689 (1985)

    Google Scholar 

  18. Feng, Shechao: Phys. Rev. B32, 5793 (1985)

    Google Scholar 

  19. Alexander, S.: Private communication

  20. Alexander, S.: J. Phys.45, 1939 (1984)

    Google Scholar 

  21. Benguigui, L.: Phys. Rev. Lett.53, 2028 (1984)

    Google Scholar 

  22. Allen, L.C., Golding, B., Haemmerle, W.H.: (to be published)

  23. Adam, M., Delsanti, M., Durand, D., Hild, G., Munch, J.P.: Pure and Appl. Chem.53, 1489 (1981); Gauthier-Manuel, B., Guyon, E.: J. Phys. Lett.41, L503 (1980); Tokita, M., Niki, R., Hikichi, K.: J. Phys. Soc. Jpn.53, 480 (1984)

    Google Scholar 

  24. Deptuck, D., Harrison, J.P., Zawadzki, P.: Phys. Rev. Lett.54, 913 (1985)

    Google Scholar 

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

    Google Scholar 

  26. Kapitulnik, A., Aharony, A., Deutscher, G., Stauffer, D.: J. Phys. A16, L269 (1983)

    Google Scholar 

  27. Iler, R.K.: The chemistry of silica. New York: Wiley 1979

    Google Scholar 

  28. Prassas, M., Phalippou, J., Zarzycki, J.: J. Mater. Sci.19, 1656 (1984)

    Google Scholar 

  29. Witten, T.A., Sander, J.M.: Phys. Rev. Lett.47, 1400 (1981)

    Google Scholar 

  30. Schaefer, D.W., Keefer, K.D.: Phys. Rev. Lett.56, 2199 (1986)

    Google Scholar 

  31. Vacher, R., Woignier, T., Pelous, J., Courtens, E.: (to be published)

  32. Kolb, M., Jullien, R., Botet, R. In: Scaling phenomena in disordered systems. Pynn R., Skjeltorp, A. (eds.). New York: Plenum Press 1985

    Google Scholar 

  33. Woignier, T., Phalippou, J.: Riv. d Staz. Sper. Vetro5, 47 (1984)

    Google Scholar 

  34. Sinha, S.K., Freltoft, T., Kjems, J.: In: Kinetics of aggregation and gelation. Family F., Landau, D.P. (eds.). Amsterdam: Elsevier 1984

    Google Scholar 

  35. Teixeira, J.: In: On growth and form. Stanley, H.E., Ostrowski, N. (eds.) Dordrecht: Nijhoff 1986

    Google Scholar 

  36. Guinier, A.: Théorie et technique de la radiocristallographie. Paris: Dunod 1956

    Google Scholar 

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

    Google Scholar 

  38. Sandercock, J.: In: Topics in Applied Physics. Vol. 51: Light scattering in solids III. Cardona, M., Güntherodt, G. (eds.). p. 176. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

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

    Google Scholar 

  40. Pelous, J., Woignier, T.: (unpublished)

  41. Entin-Wohlman, O., Alexander, S., Orbach, R., Yu, K.-Wah.: Phys. Rev. B29, 4588 (1984); Orbach, R.: In: Scaling phenomena in disordered systems. Pynn, R., Skjeltorp, A. (eds.). New York: Plenum Press 1985

    Google Scholar 

  42. Woignier, T., Phalippou, J., Sempere, R., Pelous, J.: (to be published)

  43. Feng, S.: Private communication

  44. Feng, S., Sen, P.N., Halperin, B.I., Lobb, C.J.: Phys. Rev. B30, 5386 (1984)

    Google Scholar 

  45. Calemczuk, R., de Goër, A.M., Salce, B., Maynard, R., Zarembovitch, A.: Europhys. Lett. (to be published); Calemczuk, R., de Goër, A.M., Salce, B., Maynard, R.: In: Phonon scattering in condensed matter. Anderson, A.C., Wolfe, J.P. (eds.). Berlin, Heidelberg, New York: Springer 1986

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Authors and Affiliations

  1. IBM Research Division, Zurich Research Laboratory, Säumerstrasse 4, CH-8803, Rüschlikon, Switzerland

    E. Courtens

  2. Laboratoire de Science des Matériaux Vitreux, Université des Sciences et Techniques du Languedoc, F-34060, Montpellier, France

    R. Vacher

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  1. E. Courtens
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  2. R. Vacher
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Dedicated to Professor Harry Thomas on the occasion of his 60th birthday

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Courtens, E., Vacher, R. Structure and dynamics of fractal aerogels. Z. Physik B - Condensed Matter 68, 355–361 (1987). https://doi.org/10.1007/BF01304252

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  • DOI: https://doi.org/10.1007/BF01304252

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