Alan,
It is funny to switch roles and "argue" this from your side w/r to the papers we each published on the disorder in the Tl2Ba2CaC2O8 superconductor in the 80's (you worked on the problem with pretty much traditional methods while Takeshi Egami, Wojtek Dmowski and I developed methods for modeling the PDFs of crystals -- and we did come up with results in pretty good agreement). I would argue that the Bragg & diffuse scattering both reflect the average instantaneous atomic structure. In the case where PDF shows split sites and the Rietveld gives the high symmetry site, this is really a failure of our crystallographic modeling techniques, as the split model should really do a better job with the Bragg-only data, too. As Paolo pointed out before I could finish this e-mail, the place where the PDF is different from "crystallographic" results is that the former will reflect correlation in interatomic distances.But if you refine the full data with the same model, can there really be any fundamental difference, if in one case you simply do a Fourier transform to real space ?
in Rietveld refinement we throw away the non-Bragg peak data, where-as with PDF all scattering is included.
The other idea you raise, could one use the entire range of Q, up to 25 A-1 or even 50 A-1 in Rietveld to me raises a more profound question. In conventional use, the answer is probably no -- adding the "gentle wiggles" at high Q to a refinement provides almost nothing new. The reason for this is that Rietveld treats the background at high Q is an adjustable parameter. Thus, there are no termination errors in Rietveld, but the leverage of the high-Q data w/r to the ADPs is nearly zero once the peaks start to get quite broad due to extensive superposition -- where the computer (or user) draws the background curve is arbitrary. In "total scattering" the background is measured experimentally and "fixed." Perhaps in the quest for fundamental parameters, someone should develop a Rietveld code that uses additional background & empty container scans (as is done to obtain the PDF) so that instrumental background is derived rather than fit in Rietveld. Then we could then have ADPs on an true absolute scale (something more important IMHO than relating every blip in peak shape to something intrinsic to the instrument or sample.)
Finally, in the shameless self-promotion department. Simon and I just published a paper in Acta A on error analysis with models fit to PDFs. The results: s.u. from models fit to PDFs (if done right) are equivalent to those of Rietveld (for the same reasons why Bill David et al can do a Pawley fit and then get the same esd's by fitting to the extracted I's). However, s.u.'s from a PDF model fit values should be smaller, since it typically uses more data.
Brian
