On the use of model diffraction profiles in the microstructure analysis of nanocrystalline metal oxides based on powder x-ray diffraction data

The study of the microstructure of nanocrystalline substances by the method of powder diffractometry based on the physical broadening of diffraction lines involves the use of diffraction data of standard polycrystalline samples, preferably, one nature with the test samples with the size of crystallites exceeding 100 nm. In the absence of such standards, researchers resort to the existing dependence of the width of diffraction peaks on the angle of diffraction for the standard sample or the construction of theoretical instrumental profiles due to the collimation parameters of x -rays used. In this paper a comparative study of the microstructure of nanocrystalline titanium oxide (anatase), tin oxide iron oxide (magnetite), synthesized in various ways, using several methods of analysis of powder diffractograms, was carried out. To evaluate the average crystallite sizes of the studied oxides, the Sherer equation with a graphical method of determining the width of instrumental profile and the influence of dublet radiation was chosen. Methods of profile analysis of diffraction spectra, such as a method of whole profile modeling of powder diffractograms (WPPM) and the chord method, were used to construct crystallite size distribution functions and determine the average size of crystallites of the oxides. Modeling of instrumental diffraction profiles of titanium, tin and iron oxides was performed using X -rays collimation parameters determinated using a polycrystalline silicon as standard and pseudo -Voigt function, which best describes the form of diffraction peak. The crystallite size distribution functions were constructed by means of WPPM and chords methods based on the instrumental profiles. It has been found that the values of average size of the crystallites, obtained by the methods of Sherer, WPPM and chords, differ within the one order of magnitude for each oxide. Thus, for titanium oxide this value is within 12-18 nm, for tin oxide within 7-10 nm, the iron oxide of iron within 9-12 nm. Analysis of size crystallite distribution functions and average sizes of the crystallites of the studied oxides showed the advisability of using different methods of studying microstructure to clarify the true type of the size crystallites distribution and establish its connection with the conditions and the synthesis method.