Mathematical model of horizontal divergence contribution to the integrated intensity of single crystal diffraction in XRD analysis of materials

Abstract

This paper examine a number of factors involved in the phenomena occurring into the interaction of X-rays and crystals. The mathematical modeling are the scientific way of proposal and implementation of analysis techniques based on previously models tested in laboratory. Normally, in diffraction experiments, a beam of incident X-ray radiation is simultaneously affecting both vertical divergence and horizontal divergence. To obtain more precise results after achieving structural analysis by X-ray diffraction on nanostructured materials is necessary to develop physical-mathematical model of Lorentz factor.It is well known that in difractometry, horizontal divergence effects are “filtered” by the detector slit width and goniometric assembly geometry (Bragg–Brentano). These are explained by: (i) Soller slits (slits for the slot height d is much smaller than the slot length l, d≪l) does not limit the horizontal divergence of the incident beam, but limit on the vertical one and (ii) the horizontal openings of diffracted radiation measuring device (detector) are about 0.25mm for a distance of about 35cm from the crystal detector. As a result, the horizontal divergence strongly influences the integrated intensity at high angles, when cos θ take low values.Considering the importance of horizontal divergence on the integrated intensity diffraction, the aim of this paper is to obtain a physical–mathematical model that quantify through a mathematical formula, the horizontal divergence contribution to the integrated intensity of a single crystal diffraction.