Rietveld refinement theory

Of the 15 experimentally known phases of the higher oxides only five of them have been determined by X-ray and neutron diffraction using the Rietveld refinements method. To understand the thermodynamic behavior and phase reactions it is helpful to have a model of the undetermined structures. Using the experimental electron diffraction data it is possible to determine the symmetry of the unit cell and develops a transformation matrix between the fluorite and ten of the intermediate phases as shown in Table 2. The module theory provides a method for modeling the unknown structures of the homologous series of the lanthanide... 

The residual difference after a successful DDM refinement or/and decomposition can be considered as a scattering component of the powder pattern free of Bragg diffraction. The separation of this component would facilitate the analysis of the amorphous fraction of the sample, the radial distribution function of the non-crystalline scatterers, the thermal diffuse scattering properties and other non-Bragg features of powder patterns. The background-independent profile treatment can be especially desirable in quantitative phase analysis when amorphous admixtures must be accounted for. Further extensions of DDM may involve Bayesian probability theory, which has been utilized efficiently in background estimation procedures and Rietveld refinement in the presence of impurities.DDM will also be useful at the initial steps of powder diffraction structure determination when the structure model is absent and the background line cannot be determined correctly. The direct space search methods of structure solution, in particular, may efficiently utilize DDM. 

We calculated the covalency (fc) of lanthanon (Ln) to oxygen bond in the solid solution by the dielectric chemical bond theory of complex ionic crystals on the basis of the Rietveld refined crystallographic data and tried to show its underlying... 

The use of the bond valence concept to model the stmctures of perovskites is already well established and has been put to a number of practical uses over the last decade. The crystal structures obtained from modeling using bond valence concepts can be used for a variety of purposes including, but not limited to (1) starting points for Rietveld refinements, (2) an initial structure model for density functional theory (DFT) calculations, (3) estimate the structure stability of target compositions for the synthesis of new materials, and (4) investigating of the nature of the chemical bonding present in extended solids. The extensirai of this approach to pyrochlores. 

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