Rietveld method pattern background

Le Bail s approach is also based on Eq. 6.6 and it differs from the Pawley s method in that the individual intensities remain unaltered during each least squares cycle. They are extracted from a total observed intensity of the pattern between the least squares cycles after subtraction of the background. The extraction is performed using a decomposition approach that has been employed in the Rietveld method since its development, in which intensity observed in every point of the powder pattern is divided among different reflections proportionally to their calculated intensities ... 

Moreover small variations in unit cell mlume and crystalline structure of ZSM-5 zeolite were observed to depend on the presence of adsorbates as water, xylene, benzene, etc (26-28). This makes thr previous statement to be considered with care when experimental conditions of XRD analysis, particularly water pressure, are not well controlled. As a matter of fact X-ray diffraction data have been used in a more complex manner by developing the well-known Rietveld method applied to powder X-ray diffraction pattern. By substracting the total integrated Bragg surface intensity to the background measured for a shuidard as silicon powder one may... 

Full profile refinement is computationally intense and employs the nonlinear least squares method (section 6.6), which requires a reasonable initial approximation of many fi ee variables. These usually include peak shape parameters, unit cell dimensions and coordinates of all atoms in the model of the crystal structure. Other unknowns (e.g. constant background, scale factor, overall atomic displacement parameter, etc.) may be simply guessed at the beginning and then effectively refined, as the least squares fit converges to a global minimum. When either Le Bail s or Pawley s techniques were employed to perform a full pattern decomposition prior to Rietveld refinement, it only makes sense to use suitably determined relevant parameters (background, peak shape, zero shift or sample displacement, and unit cell dimensions) as the initial approximation. 

Early data analysis attempted to extract values of the individual structure factors from peak envelopes and then apply standard single crystal methods to obtain structural information. This approach was severely limited because the relatively broad peaks in a powder pattern resulted in substantial reflection overlap and the number of usable structure factors that could be obtained in this way was very small. Consequently, only very simple crystal structures could be examined by this method. For example, the neutron diffraction study of defects in CaF2-YF3 fluorite solid solutions used 20 reflection intensities to determine values for eight structural parameters. To overcome this limitation, H. M. Rietveld realized that a neutron powder diffraction pattern is a smooth curve that consists of Gaussian peaks on top of a smooth background... 

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. 

---