Fractal analysis of powder X-ray diffraction patterns

X-ray diffraction (XRD) patterns with broad background are commonly found in the characterization of materials with a certain degree of amorphicity, so the sharp intensity peaks associated with material phases are not well defined. This work used rescaled range (denoted by R/S) analysis, a method intended for fractal analysis of noisy signals, to characterize XRD patterns with broad background. It is found that XRD patterns with broad background are not random at all, but contain information on regularities expressed as autocorrelations of the intensity signal. Sol–gel alumina fired at different temperatures was used as an example to illustrate the applicability of the method. It is shown that fractal R/S analysis is able to locate angular regions that can be associated to ideal International Centre for Diffraction Data Powder Diffraction File (ICDD PDF) lines of diverse alumina phases.