Profile fitting parameters peak positions

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 ... 

Further aspects, pros and cons of WPPF, are discussed in Chapter 5. Here it is important to underline the fact that the validity of profile fitting is limited by the basic assumption of using an a priori selected profile function without any sound hypothesis that the specific functional form is appropriate to the case of study. The consequence of this arbitrary assumption can be quite different. For example, in most practical cases, profile fitting can provide reliable values of peak position and area, whereas the effects on the profile parameters are less known and rarely considered. The arbitrary choice of a profile function tends to introduce systematic errors in the width and shape parameters, which invariably introduce a bias in a following LPA, whose consequences can hardly be evaluated. It is therefore a natural tendency, for complex problems and to obtain more reliable results, to remove the a priori selected profile functions - leading to the following section dedicated to Whole Powder Pattern Modelling methods. 

The refinement method is the same as the one used in peak by peak fitting and the calculated profiles are chosen in the same way. Usually, the diagram is simultaneously refined over a large angular range, in order to significantly restrict variations in peak positions. Note that, with this approach, the values of the cell parameters can be directly determined. 

In this technique, structural parameters are refined to fit the overall profile of the powder, neutron-diffraction pattern, which is assumed to consist of Gaussian-shaped peaks, centered at the Bragg-angle positions. The data consist of the point-intensity counts over the angular scan, and overlapping peaks are treated separately, using their contributions to the point intensities. 

A difference Fourier map, calculated at this point, reveals an additional small electron density maximum in the tetrahedral cavity next to the partially occupied V2. Thus, it is reasonable to assume that the V2 site splits into two independent partially occupied positions with the coordinates, which distribute V atoms in a random fashion in two adjacent tetrahedral positions rather than being simply vanadium-deficient. We label these two sites as V2a (corresponding to the former V2) and V2b (corresponding to the Fourier peak). Refinement of this model slightly improves the fit. Subsequently, additional profile parameters (F, F , and sample displacement) were included in the refinement, followed by a typical procedure of refining the porosity in the Suortti approximation with fixed atomic coordinates and Ui o, and then fixing the porosity parameters for the remainder of the refinement. 

Figure 5 Time dependence of characteristic parameters ofSAXS profiles ofP(S-b-B) after a pressure jump from 600 to 800 bar, inverse of the normalized scattering peak maximum, (/ (l ois the peak intensity at the start of the experiment), maximum position, q, and peak width, Aq, as obtained from fits to the time dependent scattering intensity. The MST of the system is situated at approximately 600 bar with a transition range" of 200 bar. The lines are Avramiflts with an exponent of two as given in the insert and explained in the text.

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