Abstract
The ranges of statistical description of the systems may be determined on the basis of inverse power law (Mandelbrot law). The slope of the straight line representing the power law in a double-logarithmic plot, determined as (−1/μ) (μ being a critical exponent), characterizes the distribution of elements in the microstructure. For μ>2, two parameters of distribution (the mean value and the variance) are finite, Gaussian or log-normal distribution describes the system. When 1<μ<2 only the mean value is finite. Therefore, for a description of such system, a statistical distribution with one parameter may be used. For μ<1, both the mean value and the variance are infinite. The objects of such microstructure are distributed according to the Lévy stable distribution. In this paper the inverse power law is used to describe the microstructure and the statistical distribution of discontinuous metal films on dielectric substrates for μ>2 (first case). The homogeneous films were obtained experimentally and using the computer simulations. The ranges of critical exponent μ, for which the Gaussian or log-normal distribution describes the microstructure, were determined. The statistics determined on the basis of microscopic examination is compared with that for the simulated microstructure.
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