Fractal Region Research Articles

Transmittance and reflectance i n s i t u measurements of semicontinuous gold films during deposition

We have continuously measured in situ reflectance and transmittance of percolating gold films over the entire range of surface coverage P, in the IR regime (1.7 and 2.2 μm). The samples present similar optical and electrical behavior, when compared on a normalized thickness scale. In the fractal region, close to the percolation threshold, the optical properties show a linear dependence on the surface coverage parameter, in agreement with a renormalization argument previously suggested. A strong absorption (about 40%), whose origin is not well understood, is found in the fractal region. The interpretations previously proposed by other authors are not applicable. We conclude that geometrical effects must dominate the optical properties over a large range of surface coverage.

A light scattering study of turbulence

By scattering light from a turbulent fluid seeded with small particles, one obtains information about turbulent velocity fluctuations over varying spatial scales, R. The measured intensity autocorrelation function,g(t), is related to the probability density P(V(R)) of finding velocity fluctuations of magnitude V(R) associated with eddies of size R. The measurements described here strongly suggest that the energy-containing eddies occupy a fractal region whose dimension (or spectrum of dimensions) increases with the Reynolds number Re when Re exceeds some threshold value.

Effects of ion implantation on the annealing behaviour of amorphous germanium and gold bilayers

The annealing behaviour of amorphous germanium and gold bilayers before and after ion implantation has been investigated by transmission electron microscopy and X-ray energy-dispersive spectroscopy. In the implanted sample, the crystallization of amorphous germanium films on gold is activated by ion mixing, resulting in fractal-like regions with an average size of about 5μ. Energy-dispersive measurements reveal that the formation of fractal regions is accompanied by significant interdiffusion of gold and germanium. The decrease in the crystallization temperature is attributed to the increasing instability after ion mixing of germanium and gold at the interface.

Fractal structure appeared in ion-implanted a-Ge/Ag bilayer films after annealing

The agglomeration in ion-implanted a-Ge/Ag bilayer films has been investigated by use of transmission electron microscopy (TEM). There are two kinds of fractal structures, one of which is soot-like with fractal dimension (FD) of 1.515, the other is snow-flake-like with FD of 1.797. The result is compared with that of the unimplanted film, and the mechanism of the occurrence of fractal regions is also discussed.

Fractal analysis of pores

The fractal interpretation of porosimeter measurements leads to simple expressions which allow one to evaluate both cumulative pore volumes and surface areas over a range of three orders of magnitude. The pore system often consists of differently fractal regions which are superimposed on each other. Investigated were activated charcoals, lignite coke, ashes, gas purification agents and zeolites. In all cases, the fractal analysis showed fractal dimensions D between 2 and 3.

Fractal boundaries for exit in Hamiltonian dynamics.

Fractal boundaries can occur for certain situations involving chaotic Hamiltonian systems. In particular, situations are considered in which an orbit can exit from the system in one of several different ways, and the question is asked which of these ways applies for a given initial condition. As an illustration, specific examples are considered for which there are two possible ways in which a particle can exit from the system. We examine the space of initial conditions to see which of the two exit possibilities applies for each initial condition. It is found that the regions of initial-condition state space corresponding to the two exit modes are separated by a boundary that has both fractal and smooth (nonfractal) regions, for one example, and by a fractal boundary for the other example. Furthermore, it is found for the example where the boundary has fractal and smooth regions that these regions are intertwined on arbitrarily fine scale. The existence of fractal boundaries is conjectured to be a typical property of chaotic Hamiltonian dynamics with multiple exit modes. Two situations in space physics where our results may be relevant are discussed.

APPEARENCE OF FRACTAL REGION IN ANNEALED a-Ge/Au BILAYER THIN FILMS

Fractal regions in a-Ge/Au bilayer thin films after annealing at different temperatures were investigated by TEM, and fractal dimensions were calculated. For 100℃ annealing, un-cleating positions are fewer, large tenuous scale-invariant regions formed with fractal dimension of 1.785±0.01, for 200℃ annealing, uncleating positions increased rapidly, besides thic- ker fractal region with fractal dimension of 1.818±0.008, many isolated island-like regions formed. After 300℃ annealing, only two kind of island-like regions formed with very different size. The relationship between crystallization of a-Ge film, condensation of Au film and mechanism of appearence of fractal region was discussed based on structural and quantitative analyses.

Light scattering by fractons in polymers

In amorphous polymers (PMMA and PS) the low-frequency mode in Raman spectra is found to be dependent on frequency according to a power law. The exponent depends on the thermal history of the sample. The results obtained are explained in terms of a fracton description of localized vibrations. The spectral dimension of the vibrational excitations and the size of the fractal region in the investigated polymers are found to be 1.40 and 40 Å, respectively.