Fracton Excitation in Silica Smoke-Particle Aggregates

  • D. Richter
  • T. Freltoft
  • J. K. Kjems
Part of the NATO ASI Series book series (volume 167)


The dynamic properties of random networks are not very well understood [1]. Alexander and Orbach [2] first pointed out that the thermal excitation spectra are strongly influenced by the fractal structure of such systems and they introduced a new dynamical exponent, ds, to describe the vibrational density of states, Z(ω) x ωds−1 for the fracton modes. In normal, homogeneous systems, ds corresponds to the Euclidian dimension. It was also shown [3] that an anomalous enhancement of the density of states, the so-called fracton edge, could be expected at the crossover between the homogeneous, long wavelength phonon regime and the fracton regime at shorter wavelengths. Neutron scattering experiments on epoxy resins [4,5] and vitrious silica [6] have been interpreted in these terms. In the analysis it is presumed that the fractal nature originates from the chemical bonding network rather than the mass distribution which is quite uniform on length scales that exceed the atomic distances. A recent Brillouin scattering experiment [7] has shown the long wavelength phonon excitations near the expected cross-over to the fracton regime in aerogel samples of different densities. In a neutron scattering experiment [8] on a dilute antiferromagnet the similar magnetic excitations were followed through the cross-over region.


Random Network Fractal Nature Aerogel Sample Euclidian Dimension Neutron Scattering Experiment 
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.
    Scaling Phenomena in Disordered Systems edited by R. Pynn and A. Skjeltorp ( Plenum Press, New York, 1985 ).Google Scholar
  2. 2.
    S. Alexander and R. Orbach, J. Phys. (Paris) Lett. 43, L-625 (1983).Google Scholar
  3. 3.
    A. Aharony, S. Alexander, O. Entin-Wohlman, and R. Orbach, Phys. Rev. 831, 2565 (1985).Google Scholar
  4. 4.
    H.M. Rosenberg, Phys. Rev. Lett. 54, 704 (1985).CrossRefGoogle Scholar
  5. 5.
    R. Orbach in ref. 1. pp. 335–359.Google Scholar
  6. 6.
    U. Buchenau, N. Nicker, and A.J. Dianoux, Phys. Rev. Lett. 53, 2316 (1984) and A.J. Dianoux, J.N. Page and H.M. Rosenberg, Phys. Rev. Lett. 58, 886 (1987).Google Scholar
  7. 7.
    Eric Courtens, Phys. Rev. Lett. 58, 128 (1987).CrossRefGoogle Scholar
  8. 8.
    Y.J. Uemura and R.J. Birgeneau, Phys. Rev. Lett. 57, 1947 (1986).ADSCrossRefGoogle Scholar
  9. 9.
    T. Freltoft, J.K. Kjems, and S.K. Sinha, Phys. Rev. B33, 269 (1986).ADSCrossRefGoogle Scholar
  10. 10.
    Cab-O-Sil (grade M5) is a trademark of Cabot Corporation; Alfasil was stock no. D 89376 ( Alfa Products 1981 Catalogue).Google Scholar
  11. 11.
    D. Richter and L. Passell, Phys. Rev. Lett. 44, 1593 (1980).ADSCrossRefGoogle Scholar
  12. 12.
    D. Richter and L. Passell, Phys. Rev. B26, 4078 (1982).ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • D. Richter
    • 1
  • T. Freltoft
    • 2
  • J. K. Kjems
    • 2
  1. 1.Institut Laue-LangevinGrenoble CedexFrance
  2. 2.Ris ψ National LaboratoryRoskildeDenmark

Personalised recommendations