Fracton Excitation in Silica Smoke-Particle Aggregates
The dynamic properties of random networks are not very well understood . Alexander and Orbach  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  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  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  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  on a dilute antiferromagnet the similar magnetic excitations were followed through the cross-over region.
KeywordsRandom Network Fractal Nature Aerogel Sample Euclidian Dimension Neutron Scattering Experiment
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