I was reading through Eric Mittemeijer's book 'Modern Diffraction Methods' when I found the following statement in the Rietveld chapter by Robert Dinnebier.

It is common practice to use orthogonal Chebyshev polynomials of higher order (typically 5–10) in combination with an 1/(2θi) term to describe a steep increase in the background at low scattering angle [...]. If higher-order polynomials are used, different types of correlations can occur, which require careful checking of the correlation matrix.

When I am usually describing my background in FullProf I use the '6-Coefficients polynomial function'. But this seems to cause more problems the more parameters I refine. So I switched to the 'Chebyshev polynomial' and refinded all 24 parameters (just to make sure). This caused a large jump in the X² from about 10 to 6.5 while the background was much better described.

My question is, although it is mentioned in the book, that Chebyshev is more common and I should be careful with using higher order polynomials, is this something I can use in general for my refinements? Can I just automatically assume for most x-ray determined backgrounds that using a Chebyshev polynomial with as many parameters refined as possible will give me useful results? By useful I mean good and especially 'allowed' results. Because sometimes FullProf refines parameters into regions where they are not defined like a negative η for the Pseudo-Voigt function.


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