Techniques for characterization of fractal clusters using X-ray microscopy

X-ray microscopy is well suited to study cluster formation of colloidal particles experimentally. Presenting different techniques for characterizing the structure of colloidal clusters we show how the fractal dimension of the clusters can be calculated from the X-ray micrographs, which may be considered as projections of these clusters. Dealing with simple projections we show that the fractal dimension is not preserved in the projection, but about $\Delta d=0.15$ smaller than the fractal dimension itself. This method can be applied to clusters with $d\leq 1.9$. Generally colloidal particles have a non zero transmission for X-rays leading different greyscales of the pixels in X-ray micrographs. These greyscales can be used to calculate the fractal dimension in the interval $1.8\leq d\leq2.2$ exceeding the principle limit $\rm d=2$ given for simple projections. Combining both methods the fractal dimension of colloidal clusters can be calculated in a broad range