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.
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