X-RAY RIETVELD ANALYSIS WITH A PHYSICALLY-BASED BACKGROUND

On the basis of known equations for calculating X-ray diffraction inte nsities from a given number of unit cells of a crystal phase in polycr ystalline material, as due to: (i) Bragg reflections; (ii) average dif fuse 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 'diso rder' as well as incoherent scattering. Instead of fitting the backgro und with a polynomial function, it becomes possible to describe the ba ckground by physically based equations. Air scattering is included in the background simulation. By this means, the refinement can be carrie d out with fewer parameters (six fewer than when a fifth-order polynom ial is used). The DBWS-9006PC computer program written by Sakthivel an d Young [(1990), Georgia Institute of Technology, Atlanta, GA, USA] ha s been modified to follow this approach and it has been used to refine the crystal structures of the cubic form of Y2O3 and of alpha-Al2O3. Peak asymmetry has been described by a function based on an exponentia l approximation. The results from refinements using polynomial physica lly based background function are, in terms of final structural parame ters and reliability indices, very dose to each other and in agreement with results reported in the literature. The reconstruction and optim ization of the background scattering by means of physically based equa tions helps the implementation in the Rietveld code of other possible specific diffuse scattering contributions, such as that due to an amor phous phase.