Developing and programming the algorithm of refinement of the crystal structure of materials with possible isomorphous substitution - Yaremiy, Ivan; Yaremiy, Sofiya; Fedoriv, Vasyl; Vlasii, Olesia; Luсas, Anna (Eastern-European Journal of Enterprise Technologies, 2018)
In general, the software for analyzing data using the X-ray diffraction method does not include the possibility for using stoichiometric principles between chemical elements and the relations between the occupation of crystallographic positions by atoms. In the article, the algorithm and its program realization for defining the distribution of atoms according to the crystallographic positions using stoichiometric principles in materials with isomorphous substitution are developed. A combination of using the developed algorithm and the FullProf program is proposed for taking into account different conditions that should be satisfied by the distribution of atoms according to the crystallographic positions. It is proposed to estimate the unambiguity of the initially defined distribution of atoms by finding local minima in certain physically substantiated limits of changes in the parameters of the structure. The complex method for minimization of a function of the deviation of the theoretically calculated diffractograms from the experimental ones is given to avoid falling of the objective function to a local minimum. Two ways for minimization of the difference between theoretically calculated and experimental diffractograms are proposed. By the first of them, with the help of the developed algorithm, the occupation of crystallographic positions can be established, and the minimization method built-in in FullProf calculates all other parameters. By the other way, the developed algorithm is used only and the rest of parameters approximately calculated by FullProf before are fixed. The efficiency of the developed algorithm is illustrated by finding the distribution of atoms in sublattices in ferrite-spinels. The developed algorithm can be used for any materials in which isomorphous substitution is possible, such as spinels, garnets, perovskites, and others