Structural Analysis of Deterministic Mass Fractals Using Small- Angle Scattering and Lacunarity Techniques

Abstract

The structural characterization of deterministic mass fractals at nano-and microscales is presented in this chapter using two complementary techniques in both reciprocal and real spaces. In the former case, fractal and geometrical features are obtained from the smallangle scattering (SAS) (neutrons, X-rays, light) spectrum in the reciprocal space. The lacunarity technique is considered to extract structural properties and differentiate textures of fractals in real space. We present and discuss various types of mass fractals, such as thin and fat fractals, as well as fractals generated with the Chaos game representation (CGR). We show how the main structural properties of the fractals, such as the fractal dimension, the iteration number, the scaling factor, the overall size of the fractal, and the size of the basic units of the fractal, can be extracted by using SAS and lacunarity techniques.