There are effectively two approaches to fitting x-ray diffraction patterns. In Rietveld fitting, peak positions are determined from a phase’s lattice parameters and intensities are determined from the crystallographic structure. In the second approach, individual peak fitting, which is also called sometimes called pattern deconvolution, both the peak positions and the peak intensity are treated as independent varied parameters. Peak profiles may or may not be treated as individual variables. GSAS-II implements both methods, where peak fitting is discussed in Chapter 17. In the late 1970’s Stuart Pawley developed a program he called ALLHKL that blended the two approaches. Peak positions were determined from lattice parameters, but peak intensities were fit directly as least-squares variable parameters. A bit of finesse was needed to decide when two reflections were too closely overlapped to deal with as individual reflections, but use of lattice parameters to determine peak positions is greatly advantageous when one has two closely-spaced peaks. Without that constraint, the peak tends to be fit as a single peak somewhere between the two actual positions. Note that in a Pawley fit, all of the usual parameters that determine background, peak positions and peak shapes can be refined in conjunction with the parameters, but care should be taken to only refine those terms after fairly good fits are obtained for reflection intensities. Parameters that determine peak intensities, such as atomic positions, texture or scale factors cannot be refined in a Pawley fit, of course.
The result of a Pawley fit provides an ideal fit to the crystallographic fit to a powder diffraction pattern, in that all reflection intensities are optimized to provide the best fit possible, which would match that of an ideal crystallographic model. The use of a Pawley fit provides a good starting point for fitting the non-crystallographic parameters, as has been discussed in Chapter 14. Likewise, as has been discussed in §13.3, at the final stages of a refinement project, a Pawley fit provides a measure for what R-factor or reduced \(\chi ^2\) value would be obtained in an ideal crystallographic fit, taking into imperfections in peak shapes, background fitting, etc. A Pawley fit can also be used to subtract out peaks from an impurity phase that has a known unit cell, but not a known structure, or for a phase that will not be fit well due to texture. Aluminum sample cans in neutron diffraction are an example of the latter case.
It should be noted that a Pawley reflection intensities are tied to the phase definition, so that if a phase is associated with more than one histogram, the same set of reflection intensities is used for all histograms. If you have very different types of datasets, this is probably not what you want do.
Setting up a Pawley fit in GSAS-II requires a few steps. First, you should look at the histogram(s) used in the phase to look at the data range that is needed, in my dreaded d-space units. You want to find the maximum d-space that includes the lowest Q peak across all histograms. Note that at the status line at the bottom of the GSAS-II graphics window, the \(2\theta \)/TOF position of the cursor is shown, along with the corresponding Q value and d-space values. Also do this for the high Q region, but be careful to stay very close to the minimum d-space. You will use these values to generate a list of reflections and you do not want to generate any reflections that are outside the region(s) where you are going to fit.
For the next step, use the “Select tab”/“Pawley Reflections” (or use the arrows on the tab bar to scroll to this tab). The data window will give you a hint for the next step, which is to use the Operations/“Pawley setup” menu command. The modal window shown in Fig. 20.4 will be opened. Select the “Do Pawley refinement” flag to be on, if that is not already set, and type in the range of as d-space values that you previously determined.
After closing the previous window by pressing OK, a window will be created, shown as Fig. 20.5, asking if you want to create a table of reflections to be used in Pawley fitting. Press the “Yes” button. (This step can be done manually using the Operations/“Pawley create” menu command.) This will also also the intensities of in this table to good starting values. (That step can be repeated at any point using the Operations/“Pawley estimate” menu command.) The window will now be filled with a list of reflections, as seen in Fig. 20.6. Note that in this window, double-clicking on the “refine” column label brings up a menu where the refine flag for all reflections can be set.
At this point, a refinement can be performed where the reflection intensities can be refined. Be sure to turn of refinement of all structural parameters, as well as any other parameters that change reflection intensities.
