chapter  11
32 Pages

Comparison Between Image Analyses Methods for the Determination of the Fractal Dimension of Fat Crystal Networks

ByTarek S. Awad, Alejandro G. Marangoni

Fractal structures are created by agglomeration, or clustering, of small particles to form a larger object in a random, iterative fashion under some constraint [1-4]. In a similar fashion, fat crystal networks are built from clusters of polycrystalline particles (crystallites) that aggregate in a diffusionally limited,

fractal fashion [5,6]. With time, clusters continue to increase in size and number to the point where clusters touch their nearest neighbors. Eventually, the network develops into an amorphous three-dimensional space-filling structure. Fat crystal networks are statistically self-similar, which means that the microstructure in a fat crystal network looks similar at different magnifications. All of these criteria indicate the fractal nature of fat crystal networks, which would thus have fractional dimensions.