> do you really have the > resolution even on > HRPD to see the diffuse scattering between Bragg peaks at > high Q ?
No we don't, but this is not the main point (by the way, we don't use HRPD for PDF, it doesn't go to sufficiently short wavelengths). The main reason to go to high Q is to avoid truncation errors. If you truncate S(Q), all your G(r) peaks will be convoluted with the Fourier transform of a step function, which is a sinx/x function. The width of the central peak is roughly 1/Qmax. If you use a wavelength of 0.5 A, this corresponds to about 0.08 A, or an equivalent B of 0.5. This in itself can be a problem when you want to look at sharp correlation features. Even worse, the "ripples" will propagate to adjacent PDF peaks, generating unphysical features. There are ways to suppress the ripples by convoluting the data with an appropriate smooth function rather than truncating them (these are extensively used in disordered materials work), but they all tend to broaden the features. You can also fit a model including the ripples (as in PDFfit) but it is clearly better not to have them if you are trying to exploit the model independence of PDF. Going to high Q does not solve all the problems. If the high-Q data are noisy, your truncation function will have higher frequency but also higher (and random) amplitude in the ripples, so there is always a compromise Qmax, depending on statistics. Finally, very high-Q data are quite difficult to normalise, because of the epithermal background. > You may > get better temperature factors with high-Q PDF refinement, > but you will > also do that with high-Q Rietveld. Generally, all crystallographic parameters come out worse from PDF refinements than from Rietveld on the same data sets. I think this is because you are trying to fit an average structure to something that contains correlations, so the fit is bound to be worse. You could fit a correlated model, but then you would not get "temperature factors" in the usual sense. > I also doubt that just because PDF uses data between the > Bragg peaks, then > it must be superior for seeing details not centered on atoms > in real space > in a crystal, eg the split atom sites in (In/Ga)As). You > might do just as > well with Bragg scattering if you use the result of Rietveld > refinement to > construct a Fourier map of the structure. Happily, a sampling of > reciprocal space (Bragg peaks) is sufficient to re-construct > the entire > density of a periodic structure in real space, not just point > atoms, to a > resolution limited only by Q. You are right. PDF is not always superior. It is the interpretation of the Fourier density in terms of correlated displacements that emerges uniquely from PDF, although you can often guess it right from the Fourier map in the first place. The case of Jahn-Teller polarons in manganites (La,Ca)MnO3 is quite illuminating. Several groups noticed that the high-temperature phase (above the CMR transition) has large DW factors for O. We showed that this affects primarily the longitudinal component along the Mn-O bonds, and guessed that this was caused by an alternation of short and long Mn-O distances. Simon Billinge showed the same thing quite convincingly from PDF data. Only the latter can be considered "direct evidence" (with some caveats). > But you do agree that in a PDF experiment you integrate over > energy, so > you only see an instantaneous snapshot of the structure... Yes, I agree with this and the fact that inelasticity corrections are an issue. Sometimes they are exploited to obtain additional information, and there is a claim that one can "measure" phonon dispersions with this method, but the issue is quite controversial. > > So while I am convinced of the interest of PDF for non-crystalline > materials, with short or intermediate range order, I am not > yet convinced > that you gain much from PDF refinement of crystalline > materials, where you > can also apply Rietveld refinement. I agree completely. The directional information gained from phasing and the fact of "locking in" to specific Fourier components is a major asset of Rietveld analysis. PDF is useful when correlated disorder is important (and large), even if superimposed on an ordered structure. Paolo Radaelli
