But I would like to also make a complementary observation. For moderately disordered systems such as nanoscale samples, there's also no a priori reason to assume that the distribution is not skewed. In other words, the question of convergence isn't avoided by just ignoring higher cumulants!

3a) If the third cumulant refines to 0 to within the reported uncertainty and the other parameters don't move outside their original error bars, then the third cumulant is not needed; go back to fit 1.

3b) If the third cumulant refines to a nonzero value to within the reported uncertainty, then look at the value. If it violates the limit Grant gives, then it's not appropriate, but you need to find another way of dealing with the fit. (Sometimes you may have a splitting between two different path lengths that you haven't modeled, for instance.) If it is within Grant's limit, then proceed with the usual caution you accord to EXAFS fits. For example, evaluate the physical sensibility of parameters, the stability of the fit to small changes in the data ranges, etc..

Aaron -

There are a couple of things you should watch out for when fitting cumulants.

First, you should make sure in the fitting process that the third cumulant C3 doesn't get much more than twice C2^(3/2) (i.e. 2 sigma^3) - values much larger than that are probably unphysical, even if they happen to give you a better fit.

Second, the cumulant expansion loses its utility if it doesn't converge quickly enough. It's essentially an expansion in terms of order k*sigma, and if that approaches 1 the higher order cumulants may be large enough that convergence is questionable. If you are lucky and the effective distribution is Gaussian, or most of the variance is due to Gaussian broadening of a skewed distribution, it may converge OK, but that shouldn't be assumed a priori.

Grant Bunker

http://gbxafs.iit.edu
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