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