>> It is not a question of Bragg or diffuse scattering. > > Actually it is. Bragg scattering is equivalent to projecting all the > scattering density in the crystal onto a single unit cell divided by the > number of unit cells in the crystal and replicate that average unit > cell. In other words, you do a coherent configurational average (over > the correlation length of the probe).
No it's not :-) What I said was that the crystal lattice has nothing to do with Brian's statement that if you integrate over energy you get an instantaneous snapshot of the spatial correlations, which is true. More precisely, if you write down the general expression for scattering S(Q,w) it contains a term exp(iwt) so that if you integrate S(Q,w) over energy you can factor out a delta function in time Integral[exp(iwt)]dt. This applies to disordered materials as well as crystals - you don't need to introduce a lattice here. > Furthermore, because Bragg scattering is elastic, you also get a > coherent time average. This is not the way to look at it. Bragg scattering is simply all scattering that peaks at points in the "reciprocal lattice" that correspond to the long-range correlations called the "crystal lattice" in real space. Take the superstructure example again. Suppose the superstructure is condensing from a single zone-boundary soft mode eg a simple octahedral tilt in a perovskite. This will produce a slightly diffuse (in Q) and slightly inelastic, superstructure peak. A powder experiment (and most others) will integrate over energy, so will see just the spatial correlations, or an instantaneous snapshot. If you do a Rietveld refinement restricted to the Bragg peaks, you can either neglect the developing superstructure, in which case you won't see the octahedral tilt except as an anisotropic DW factor, or else you can double your unit cell to include the superstructure, in which case you will correctly model the correlated tilts - i.e. your model will then contain distances that are only present in the tilted structure. In the PDF method, you don't have to decide anything about the lattice a priori. This seems a strength, but it is also a weakness. The advantage is that you will naturally see the distances (peaks) that are only present in the tilted structure. The disadvantage is that you will have so many peaks that you probably won't be able to interpret them all unless you also (Rietveld) refine the structure :-) The whole point of Rietveld refinement is to reduce correlations by refining only parameters from a physical model. The fact that in crystallography you constrain your data to the reciprocal space points also helps :-) If you go to a more complex refinement without such constraints, you can expect to have problems with correlations. So I can see the interest of Fourier transforming the raw diffraction pattern to look for peaks that should not be there with your periodic model eg the split atom sites given as an example. But I am less sure that you will get a better result by refining a model to fit the PDF function, rather than modelling the split site or superstructure in Rietveld refinement. But I will try to convince myself otherwise :-) Alan.
