Axial divergence in a conventional X-ray powder diffractometer. I. Theoretical foundations

A general model for the axial divergence aberration function has been devel oped for a conventional X-ray powder diffractometer equipped with either in cident-beam and/or diffracted-beam Seller slits. In this model, the axial d ivergence function is generated from the geometrical dimensions of the diff ractometer system, which include the axial lengths of the X-ray source, sam ple and receiving slit as well as the angular apertures of the incident-bea m and diffracted-beam Seller slits. The paper describes how the diffractome ter design and the extent of the axial divergence influence the shape of th e axial divergence aberration function. The model is developed in three sta ges starting with analytical profile shapes for a single-ray incident X-ray beam. The single-ray results are then generalized to represent a line X-ra y source and a specimen with axial length. In the third stage, the effects of the Seller slits in the beam path are incorporated by considering them a s angular selective filters in the incident and diffracted beams. A general discussion is presented on the axial divergence aberration function with 2 theta for a range of standard instrument configurations. This work forms t he basis of an accurate fundamental parameters approach to profile analysis and Rietveld refinement.