HI Jatin, On Sat, Mar 21, 2015 at 8:06 AM, Rana, Jatinkumar Kantilal < jatinkumar.rana@helmholtz-berlin.de> wrote:

Dear All,

I have stumbled upon a question regarding correlationships between various parameters in EXAFS fitting. As we know, the parameters S02*N and sigma2 are highly correlated (where N is the number of nearest neighbors).

I would like to determine the number of nearest neighbors for a series of sample subjected to some treatment. I can do this by simply setting S02 to a value for a given absorber (based on the literature or my own measurements of some reference compounds) and letting N and sigma2 vary in a fit. However, the problem is the physical process which changes the number of nearest neighbors, also introduces structural disorder in samples. Thus, I always get the values of N overestimated due to its correlationship with sigma2.

By itself, the size of the correlation between any 2 variables should not bias the best-fit results. So, the high correlation of N and sigma2 should not always overestimate N. If you're consistently seeing N overestimated, it is probably not because sigma2 is also overestimated, but more likely to be due to some other reason. Like, if N is consistently too high, perhaps S02 is set artificially low.

I know of a method which can be used to breakdown the correlationship between S02 and sigma2 by setting a series of S02 values at different k-weights and refining the corresponding sigma2 as discussed in several literature. However, in this approach the explicit assumption is, S02 is the property of absorbing atoms and thus is independent of changes occurring inside the sample. In my case, however, both sigma2 and N vary with changes inside samples. Is there any way to break this correlationship ?

The idea of setting N*S02 and using different k-weights is sort cheating. By setting N*S02 you're purposely ignoring the correlation. Using multiple k-weights in a fit can lower the correlation on N*S02 and sigma2 somewhat, but it certainly does not break it. I've not seen a case where it makes a substantial reduction (say, below 0.5, and rarely below 0.75). That is, if you just check using a k-weight of 1,2, and 3 in Artemis, you'll likely see the correlation drop from something like 0.95 to 0.90 in the best cases -- hardly "breaking the correlation". Extending the k-range as much as possible (including to low-k) can also reduce the correlation, but again, only by small amounts. Like that for R and E0, N*S02 and sigma2 will be highly correlated even if you measure EXAFS to very high k and fit The correlation is basically endemic. But, correlation does not imply a bias. It can *allow* some bias to skew the results substantially, and increases the uncertainties in these values, but it is really not the ultimate cause of the results. --Matt