Figures of merit in full pattern decomposition

Since both Pawley and Le Bail full pattern decompositions are based on finding a least squares solution of Eq. 6.6, the problem may be considered solved and a pattern deconvoluted when the best possible fit between the 

therefore, of utmost importance to have certain numerical figures of merit that quantify the quality of the least squares fit and therefore, may be used to estimate the reliability of the extracted integrated intensities and observed structure factors. The following figures of merit are customarily used to characterize both the full pattern decomposition and Rietveld refinement quality. 

The Bragg residual, Rb (this figure of merit is quite important in Rietveld refinement but has little to no use during full pattern decomposition because only observed Bragg intensities are meaningful in both Pawley and Le Bail methods)  

In Eqs. 6.18 to 6.22, the following notations have been used n is the total number of points measured in the experimental powder diffraction pattern. 

All figures of merit except one (Eq. 6.20) include a contribution from the background. This raises an interesting problem about the reliability of profile reliability factors (pardon the tautology) when the correctness of the structural model is of concern, which will be further discussed in Chapter 7. 

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