I am glad the paper answered the question about r_poly.
That's a great question about Q_maxinst.
In terms of definition (which I think you know from that paper), Q_maxinst gives the highest Q-value that (along with Q_min) defines the range of I(Q) that the polynomial function is fit over. On the other hand, Q_max (along with Q_min) gives the range of the diffraction data that is Fourier transformed to obtain the PDF.
But what is maybe more valuable to you is to learn our workflow and how we use these two parameters in my group when we do data reduction, so I can share that here.
1) I select a representative dataset from all my data to play around with the analysis. It might be the lowest T data or the highest T, or whatever, but I choose one.
2) I use xPDFsuite, so I select it in xPDFsuite and click the 2D plot button. You can do something similar directly in PDFgetX3.
3) I set Q_maxinst and Q_max both to the maximum value so i can see all the data, and I select to plot I(Q) and F(Q) (but not S(Q) or G(r)). The most useful plot for what I will describe is F(Q) and I want it nice and big (I(Q) is a good sanity check, especially if there is a background being subtracted).
4) This allows me to see how BAD my data are. I look for glitches and very weird stuff that often happens at the edges of the data in the high-Q range. Then I identify a point on F(Q) to the left of the left-most nasty bad glitch (I don't worry so much about small glitches at this point). In xPDFsuite I use my cursor to find the Q value of that point I identified.
5) I set Q_maxinst to that value. The reason for this is that I want the polynomial to be fit over as wide a Q-range as possible, but I don't want the polynomial to try and fit nasty glitches that have nothing to do with the real signal. At this point I don't care about statistical noise. It can be as noisy as all heck, I am just caring about the glitches.
6) After I have set the Q_maxinst I then move the Q_max value around from lower to higher and see how it affects the PDF. At this point, I often change what I am looking at to be looking at F(Q) and G(r). Without changing Q_maxinst, I move Q_max around to get the right balance between resolution in my PDF (which wants higher Q_max) and reduction of noise (which wants lower Q_max). I can make good guesses based on just looking at F(Q), but the real measure is what the g(r) looks like. In F(Q) I am looking for signal-noise ratio, so I identify what I think is signal and I want it to be comparable to or higher than what I identify as noise. But since, esthetically, the appearance of noise depends on the binning, the better measure is how small the ripples look like in G(r).
7) this gets Q_max to the right ball-park, then I purposefully select a point for my final Q_max where the signal approaches or goes through the F = 0 line just to finalize things.
Hope it helps,