X-ray Rietveld Analysis with a Physically Based Background

On the basis of known equations for calculating X-ray diffraction intensities from a given number of unit cells of a crystal phase in polycrystalline material, as due to: (i) Bragg reflections; (ii) average diffuse scattering caused by thermal plus first-kind disorder; and (iii) incoherent scattering, a relationship has been found that ties, in the Rietveld analysis, the Bragg scale factor to a scale factor for `disorder' as well as incoherent scattering. Instead of fitting the background with a polynomial function, it becomes possible to describe the background by physically based equations. Air scattering is included in the background simulation. By this means, the refinement can be carried out with fewer parameters (six fewer than when a fifth-order polynomial is used). The DBWS-9006PC computer program written by Sakthivel & Young [(1990), Georgia Institute of Technology, Atlanta, GA, USA] has been modified to follow this approach and it has been used to refine the crystal structures of the cubic form of Y₂O₃ and of α-Al₂O₃. Peak asymmetry has been described by a function based on an exponential approximation. The results from refinements using polynomial physically based background function are, in terms of final structural parameters and reliability indices, very close to each other and in agreement with results reported in the literature. The reconstruction and optimization of the background scattering by means of physically based equations helps the implementation in the Rietveld code of other possible specific diffuse scattering contributions, such as that due to an amorphous phase.