Matt, first of all, thank you very much for your reply. It was pretty coherent and did help to settle some conceptual mismatchs that were bugging me. As for starting a wiki on this, looks like a good idea to me. Specially if there are more people interested on the topic.
Hope that helps, or at least keeps the conversation going....
Following your suggestion above, I'd like to make some more questions, if you don't mind.... ;)
To first approximation, dR/R from EXAFS is similar to dA/A from diffraction. Many people have equated these. In detail, and especially at high temperature, they are not the same.
Ok, that's understood. I guess I didn't express myself propelry in the previous message, sorry. The thing is that Anatoly and John define their thermal net expansion as a(T)=<r-r0>, r0 being the minimum of the pair-potential and r the bond length at a given temperature. This made me think that their a(T) could be directly related to dR/R from EXAFS instead of dA/A from diffraction. Does this sound correct to you?
delR is the first cumulant, C1, and is equal to the first moment of the distribution. It is the displacement from the starting center value, R0, Reff, etc.
There is actually a subtlety in getting delR=C1 from EXAFS, as the EXAFS is not simply exponential in R, but also has a 1/R^2 term and R dependence in the mean-free-path term. These can be dealt with (and are dealt with in Ifeffit/Feffit), so that the delR, sigma2, third, and fourth *are* the cumulants of the atomic pair distribution. But that's not your question (yet??).
Well, I think you already saw where I am trying to go... I was pretty sure that the values of sigma2 and C3 I was getting from the fits were the "real" cumulants of the atomic pair distribution, but I wasn't so sure about delR, because of the 1/R^2 and lambda corrections. I believed they would be there, and now you reassured me. The thing is, I have these temperature dependent EXAFS spectra from 10 to 300K to analyze. If I try to analyze each at a time, I get reasonably values with small errors for sigma2, which are insensitive to small variations on the fitting conditions. But the values obtained for delR and C3 are pretty wonky, have big errors and vary a lot with small variations on the fitting conditions (like k-weights, windows, E0 values,...). So, I was trying to make a multiple dataset fit, with all of them together. And I was trying to do it the same way you (Matt) and some other people did, which involves writing the cumulants as functions of the pair potential constants and the temperature. This way, the number of free parameters is drastically reduced, as well as the uncertainties on the determination of delR and C3. But, as my data is not on the "high T" limit (unlike most people), I cannot use the same equations that you have used. I was using Anatoly's equations instead [PRB48, 585, 1993], where there is no direct mention to a first cumulant, only to the linear thermal expansion given by a(T)=<r-r0>. Looking at some other papers (like [Troger et al., PRB49, 888 (1994)], [Yokoyama, JSR6, 323 (1999)], [Van Hung and Rehr, PRB56, 43, 1997]), I saw people treating the thermal evolution of the first cumulant as being given by a(T). So, my question now is: - How reasonable it is to represent the thermal evolution of delR by Anatoly and John's a(T)? Should any corrections be added when relating this two quantities? Sorry for another over-sized messaged and thank you very much for your attention. Cheers, Leandro