Small-angle scattering from the deterministic fractal systems1

Abstract

The intensity profile of small-angle neutron sc attering from three-dimensional triadic Cantor and Vicsek fractals is calculated when the fractal sets are monodisperse and their positions are uncorrelated. It is shown that the scattering intensities present minima and maxima superimposed on a power-law decay with the exponent coinciding with the fractal dimension of the scatterer. This is in accordance with the scattering from similar systems like Menger sponge or fractal jacks, which all exhibit the same behavior. For a finite iteration, the Porod power decay of the intensity is displayed at large values of momenta beyond the fractal region.