Fractal correlation analysis of x-ray diffraction patterns with broad background

X-ray diffraction (XRD) patterns with broad background are commonly found in powders where crystallization is incomplete or mixed with amorphous material. This is the case of alumina used for, for example, heterogeneous catalysis purposes where a certain degree of amorphicity is desired for obtaining prescribed material texture (e.g., porosity and area). This work uses detrended fluctuation analysis (DFA), a method intended for fractal analysis of noisy signals, to characterize an XRD pattern with broad background. The idea is that an XRD with broad background is not fully random, but contains information on regularity patterns expressed as correlations of the intensity signal. Sol-gel alumina fired at 500 C and mixed aluminum/zirconium oxides fired at three different temperatures were used as examples for illustrating the applicability of the method. It is shown that the fractal DFA is able to locate angular regions associated ideal Powder Diffraction File-ICDD lines of diverse alumina phases. The results are discussed in terms of the corresponding Raman spectrometry analysis for contrasting the possible phases contained in the material. A crystallinity index is introduced in terms of a distance to randomness, so the regularity of a given phase can be quantified when the material is not fully crystalline.