ChapterĀ 14
Fitting Profile functions

As discussed before, to match the shapes of the peaks, you must reproduce the broadening effects of both the diffraction instrument and effects from the sample. What determines these broadening effects and how they are introduced into the fit will be the subject of this chapter.

For some studies, determining the broadening characteristics is only needed as a means to obtain a good fit to the pattern, allowing determination of lattice or structural parameters, and indeed this was the original goal when Hugo Rietveld developed his eponymous analysis process. However, the parameter values that are used to model the peak profiles can provide information on the sample at the microscale, which can be very important for understanding the properties of a material that are not intrinsic to the substance but rather depend on how the substance was processed. Traditionally, microscopic techniques are well suited to provide the most detailed information on things like crystallite size and morphology, but Rietveld analysis has an advantage in that it provides measures that represent the entire sample bulk. Bulk characterization of a sample by microscopy is typically a very tedious process. The downside of sample characterization from powder diffraction is that it requires careful work to separate sample from instrumental effects.

14.1 Peak broadening contributions convolute
14.2 Sources of instrumental broadening
14.2.1 Low-angle peak asymmetry
14.3 Sample broadening
14.3.1 Crystallite size broadening
14.3.2 Microstrain broadening
14.4 Approaches for peak fitting functions
14.5 Physically-Inspired Peak Shapes
14.6 GSAS-II Profile Implementation
14.6.1 GSAS-II Instrumental Profile Treatment
14.7 GSAS-II Sample Broadening Terms
14.7.1 GSAS-II Size Broadening Models
14.7.2 GSAS-II Microstrain Broadening Models
14.8 GUI Access to Sample Broadening Terms
14.8.1 Placing HAP parameters directly into data tree
14.9 GSAS-II Sample Broadening Visualization
14.10 Determining Instrumental Profile Terms
14.11 FPA Generation of Instrumental Terms
14.12 How to Refine Peak Profiles for a Sample
14.12.1 Refinement of sample terms only
14.12.2 Refinement of instrumental profile terms
14.13 Constraints on broadening terms
14.14 The Warren-Averbach Method
14.15 Parting words on Profile Fitting