Determination of Real Crystal Structure Characteristics from X-Ray Diffraction Line Profiles *

Abstract

A method for determination of two important characteristics of polycrystals or crystalline powder, crystallite size distribution and crystalline lattice strain distribution, from X-ray diffraction line profiles (standard and experimental) is proposed. The method, developed in the frame of the kinematical theory of X-ray diffraction, is based on three linear integral equations of the first kind describing X-ray diffraction on a set of deformed crystallites of the same (assumed) shape. A method for solving these integral equations, based on Tikhonov's regularisation method with the choice of the regularisation parameter according to the modified generalised discrepancy principle, is also proposed (this is also a method for separation of the influences of crystallite sizes and strains on the line profile). The application of the method to materials consisting of cubic or column-like crystallite of a cubic lattice is presented. A criterion for the proper choice of the crystallite shape is suggested. Having both distributions, one can easily calculate the averaged crystal structure characteristics: mean crystallite size, mean square crystallite size, mean absolute lattice strain and mean square lattice strain. Results of computation of all these characteristics for magnesium oxide powder are demonstrated as an example of the usefulness of the method.