Split-Pearson VII

Peak shape function Pearson VII or split Pearson VII pseudo-Voigt... 

Asymmetry Individual using split Pearson VII Common for all peaks... 

By doing so, instead of k parameters for HW i.e. for each of k reflections) only three parameters are to be refined. The same is true for the (See Figure 4.14 with a curve of the parameters of a split-Pearson-VII function v. 29.)... 

Figure 4.14 Fitting of a measured, asymmetrical Si(l 11) reflection (points) by a Gaussian, a Lorentzian, and a split Pearson VII profile (full lines). Besides the not considered asymmetry (above and middle) the flanks above are too narrow (Gaussian) and in the middle too wide (Lorentzian. See also figure 4.17. (After Kern, 1992. )...

A widely used method is the separate handling of the left and the right peak moieties (split-Pearson VII or SP7). The peak heights and positions are taken as identical for both halves, but for half widths and slope parameters separate parameter sets are used i.e. two additional parameters per reflection, respectively parameter sets U,V,W and a,b,c for the left and right moieties each). 

Figure 4.16 Patterns of the changes of half widths (top) and of slope parameters m (bottom) for split Pearson VII profiles (SP7), which were taken with a Gninier camera for a PbN03 sample. By such curves the number of profile parameters to be refined can appreciably be reduced (After Brown and Edmonds, 1980. )...

The method most commonly used consists of considering that each diffraction peak corresponds to two half-Pearson VIIs or two half pseudo-Voigts each one defined on one of the two sides of the peak s maximum. This is called a spht-Pearson VII or a split pseudo-Voigt . The parameters that characterize each of the parts of the profile are independent and the resulting overall function is dissymmetric. 

---