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X‐ray Rietveld Analysis with a Physically Based Background
Author(s) -
Riello P.,
Fagherazzi G.,
Clemente D.,
Canton P.
Publication year - 1995
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188989401037x
Subject(s) - rietveld refinement , scattering , bragg's law , polynomial , physics , computational physics , diffraction , mathematics , optics , materials science , mathematical analysis
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 ‐9006 PC 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 Y 2 O 3 and of α ‐Al 2 O 3 . 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.