Profile fitting parameters integrated intensity

Toraya s Method. The WPPD as implemented by Toraya et al.11 decomposes the peak profiles and background functions to obtain the best fit to the experimental powder pattern of the individual pure phase data by least-squares refinement. The integrated intensities of the pure phases are then stored with the other refined parameters, such as the profile parameters and the unit-cell parameters of the phases to be quantified. During quantification step, the integrated intensity of the phase being quantified is scaled, as defined in Eq. (12.4), such that the total of the scale factors for the component phases sum to unity. The scale factors of the individual components are then refined by least-squares methods until a best fit is observed with respect to the pattern of unknown composition. 

We note that a figure-of-merit with fixed weighting parameter has been employed previously [85] in structure solution from powder diffraction data, although the figure-of-merit used in that paper differs in several respects from G(T) defined here. The figure-of-merit used in Ref. [85] did not consider normalized energy and normalized R-factor functions, and the R-factor was based on the use of integrated peak intensities rather than a whole-profile fit to the powder diffraction pattern. 

Depending on the quality of the pattern, profile fitting can be conducted in several different ways. They differ in how peak positions and peak shape parameters are handled, assuming that integrated intensities are always refined independently for each peak, and a single set of parameters describes a background within the processed range ... 

As briefly mentioned in the previous chapter, the determination of a crystal structure may be considered complete only when multiple pattern variables and crystallographic parameters of a model have been fully refined against the observed powder diffraction data. Obviously, the refined model should remain reasonable from both physical and chemical standpoints. The refinement technique, most commonly employed today, is based on the idea suggested in the middle 1960 s by Rietveld. The essence of Rietveld s approach is that experimental powder diffraction data are utilized without extraction of the individual integrated intensities or the individual structure factors, and all structural and instrumental parameters are refined by fitting a calculated profile to the observed data. 

---