>> 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 or diffuse scattering. Your statement about integrating over energy is correct regardless of Bragg or diffuse scattering, but Brian's statement is not, at least in the context of the PDF/Bragg discussion, so "it is and it isn't" would have been a more appropriate statement on my part. It is true that in diffraction you measure the intermediate scattering function S(Q,t=0), but this is not the same thing as saying that you can then Fourier-transform any part of it you like to a G(x, t=0). To get a real-space function G(x) you have to integrate over the *whole* Q domain, and in doing so for Bragg scattering you set to zero everything that is outside the nodes of the RL. However, it is easy to see that this can be equivalent to setting an energy cut-off. This is because fluctuations in time and space are usually correlated, so by selecting an integration range in Q for you Bragg peaks, you also effectively select an integration range in energy. Your superstructure example shows it clearly: if you are far from the phase transition and the correlation length of your tilt fluctuation is 10 A, you would not see a Bragg peak there and you would get the time-average structure (without the superstructure). Clearly there is the limiting case of critical scattering very near the phase transition, where the fluctuating regions are so large that you effectively take a snapshot of each of them. There could even be a deeper point here to do with ergodicity, whereby you could show that coherent space average and coherent time average are effectively the same (I am not positive about this, though). The point I was trying to make is a different one. We are discussing about the difference between Bragg and PDF. If all the scattering is near the Bragg peaks, so that you integrate it all in crystallography, there is and there cannot be any difference between the two techniques. I am sure we are not discussing this case. The interesting case is when there is additional diffuse scattering. What I am saying is that if this diffuse scattering is inelastic, then PDF will reflect istantaneous correlations in a way that is missed by Bragg scattering. Let's look at the case of two bonded atoms again, with a bond length L, and lets this time assume that they vibrate harmonically in the transverse direction, and that the semi-axis of the thermal ellipsoid is a. The possible istantaneous bond lengths range from L to sqrt(L^2+4a^2) for an uncorrelated or anti-correlated motion, but is always L for a correlated motion. Bragg scattering will give you a distance of L between the two centres, which is only correct for correlated motion. It also provides information about the two ellipsoids, which is the same you would get by averaging the scattering density over time, regardless of correlations. Istantaneous correlations are only contained in the diffuse scattering, and are in principle accessible by PDF. Paolo Radaelli
