Dear Brian, It is 10:30 pm here, and I am supposed to be taking a day off tomorrow to be with my new grand-daughter :-) But I find PDF so interesting that I can't resist replying.
> I would argue that the Bragg & > diffuse scattering both reflect the average instantaneous atomic > structure. Yes. If you integrate over energy, the scattering function factors to a delta function in time, corresponding to an instantaneous snapshot of the spatial correlations. It is not a question of Bragg or diffuse scattering. > 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. Yes. The Bragg-only data is perfectly adequate for periodic structures - even those that contain two types of atoms disordered on the same site but with different co-ordinates - a split atom model, as Bob said. > 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. Hmm. The diffuse (non-Bragg) scattering contains information about short-range spatial correlations. Suppose we have a super-structure condensing as short range islands. This will produce diffuse super-lattice peaks that we will miss with Rietveld refinement. I suppose that PDF refinement might pick that up. > 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... > 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.) I thought that had been done by people non-constrained by beam-time allocation :-) So long as we are only looking for the periodic structure, and we are prepared to take the same care with Rietveld and PDF backgrounds, the methods should be equivalent. > Simon and I just published a paper in Acta A on error analysis with > models fit to PDFs. I'll have to read that, because I don't quite understand how you do the count statistics after the Fourier transform. I suppose it must be possible, since the liquids and amorphous people :-) do it. > 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). Well, that is an old chestnut that Cooper and Rollet used to oppose to Rietveld refinement. I think Rollet eventually agreed that Rietveld was the better method. Has Bill really gone back on that ? > However, s.u.'s from a PDF model fit values should be smaller, > since it typically uses more data. Typically but not necessarily ? Alan.
