Approximate Estimation of Contributions to Pure X-Ray Diffraction Line Profiles from Crystallite Shapes, Sizes and Strains by Analysing Peak Widths

A polycrystalline material may be considered as a set of crystallites. Since the crystallites have rather regular shapes, the assumption about the same shape is not far from physical reality for most polycrystals, especially powders. Such a system may be characterised in a statistical manner by two functions, the crystallite size distribution and the crystalline lattice strain distribution (for some materials other lattice distortions inside the crystallites, like stacking faults or dislocations, are to be considered additionally). The crystalline microstructure can be determined by investigating an X-ray diffraction pattern, what should be based on comparing an experimental pattern with a simulated one, derived from an appropriate physical model. Pure X-ray diffraction line profiles, containing information about crystalline microstructure, can be extracted from experimental data. An important step in analysing them is the separation of contributions from crystallite shapes and sizes and from strains, enabling the proper determination of both distributions together with the estimation of prevalent crystallite shape. A model of polycrystalline material combined with a description of X-ray diffraction on it, making such an analysis possible, is presented in this article. An approximate formula for separating both effects is based on results of computer simulation of pure X-ray diffraction line profiles from different crystalline powders, done under simplifying assumptions that the crystallites are prismatic or spherical, the size distribution is logarithmic-normal and the second-order strain distribution is normal.