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A structural model for scattering intensities with multiple fractal regions

E. M. ANITAS1,2,*

Affiliation

  1. Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russian Federation
  2. Horia Hulubei National Institute of Physics and Nuclear Engineering, RO-077125 Bucharest-Magurele, Romania

Abstract

We report here a new structural model based on deterministic fat fractals (fractals with positive Lebesgue measure) which describes experimental small-angle scattering (SAS) data characterized by a succesion of fractal regions with arbitrarily lengths. We calculate analytically the corresponding mono- and polydisperse structure factors. We study its properties in momentum space and show how one can extract the upper and lower edges of the fractals and the crossover position between fractal regions with different scattering exponents. The latter quantities are correlated to the variation of scaling factor with the iteration number, and can be used to estimate the sizes of fractal subunits. In order to illustrate the applicability of the obtained results to various nano- and microstructures, we study the scattering properties of the fattened version of two well-known regular 3𝐷 fractals: Cantor sets and Menger sponge..

Keywords

Small-angle scattering, Fractals, Structural properties.

Submitted at: May 7, 2015
Accepted at: June 24, 2015

Citation

E. M. ANITAS, A structural model for scattering intensities with multiple fractal regions, Journal of Optoelectronics and Advanced Materials Vol. 17, Iss. 7-8, pp. 1122-1127 (2015)