Axial Divergence in a Conventional X-ray Powder Diffractometer. I. Theoretical Foundations

A general model for the axial divergence aberration function has been developed for a conventional X-ray powder diffractometer equipped with either incidentbeam and/or diffracted-beam Soller slits. In this model, the axial divergence function is generated from the geometrical dimensions of the diffractometer system, which include the axial lengths of the X-ray source, sample and receiving slit as well as the angular apertures of the incident-beam and diffracted-beam Soller slits. The paper describes how the diffractometer design and the extent of the axial divergence in ̄uence the shape of the axial divergence aberration function. The model is developed in three stages starting with analytical pro®le shapes for a single-ray incident X-ray beam. The singleray results are then generalized to represent a line X-ray source and a specimen with axial length. In the third stage, the effects of the Soller slits in the beam path are incorporated by considering them as angular selective ®lters in the incident and diffracted beams. A general discussion is presented on the axial divergence aberration function with 2 for a range of standard instrument con®gurations. This work forms the basis of an accurate fundamental parameters approach to pro®le analysis and Rietveld re®nement.