When fitting the third cumulant, you should watch out for a couple of things. 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 On Mar 26, 2010, at 1:41 PM, ifeffit-request@millenia.cars.aps.anl.gov wrote:

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Today's Topics:

1. Anharmonic correction (Aaron Slowey) 2. Re: Anharmonic correction (Scott Calvin) 3. Re: Anharmonic correction (Frenkel, Anatoly)

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Message: 1 Date: Fri, 26 Mar 2010 10:13:56 -0700 From: Aaron Slowey To: ifeffit@millenia.cars.aps.anl.gov Subject: [Ifeffit] Anharmonic correction Message-ID: <9683660E-9ED8-4DBB-8E26-88586073B0F8@usgs.gov> Content-Type: text/plain; charset="us-ascii"

Dear XAFS community:

I am fitting Hg L3-edge EXAFS of what I think are mercury sulfide nanoparticles. I fit Fourier filtered 1st shell Hg-to-Sulfur pair correlations for 5 spectra and obtain interatomic distances (r) that are 0.2 angstroms shorter than a cubic HgS(s) (i.e., metacinnabar) and Hg-to-S coordination numbers (N) that range from 2.6 to 3.0 (compared to N = 4 for metacinnabar). Delta_E0 values are less than a few eV, so I think the r's are not 'incorrect' as far as these preliminary fits are based on harmonic atomic vibrations/Gaussian pair-distribution functions.

What intrigues me most about these data is that the fitted N's are consistent with the average 1st-shell Hg-S coordinations of 1 to 2 nm HgS clusters obtained by isotropically truncating the metacinnabar crystal lattice. In one case, I can also fit first-nearest Hg neighbors in the first shell, and this N is also consistent with a 1 nm HgS cluster.

My objective is to scrutinize the tentative conclusion that the mercury sulfides in the samples consist of 1 to 2 nm subunits (within a larger aggregate, as determined by DLS). For instance, while the fitted N's are consistent with nanoclusters, the assumption of a metacinnabar lattice to estimate N of nanoclusters is undermined by the shorter interatomic distances fitted to the data. This got me reading the work of Manceau and Combes from the late 1980s and Frenkel et al. (2001) J. Phys. Chem. B. In Frenkel's paper (p. 12691), they describe that they used a "third cumulant" to account for anharmonic corrections, but I'm not sure how exactly this is implemented.

It is something that you request in a feff.inp file, or is it a path parameter for IFEFFIT to include in its calculations?

I am using Artemis on Mac OS X 10.6 (thanks to iXAFS 2.1.1 beta!!) to execute FEFF 7 calculations and fit my data. I noticed parameters called "3rd" and "4th" in the path dialog; is "3rd" the same parameter as, for example, the sigma_sub_i_superscript_(3) term in eqn (2) of Frenkel et al. (2001)?

Thanks for reading this lengthy note...

Aaron

Branch of Regional Research, Water Resources U.S. Geological Survey Office (650) 329-5474 Lab (650) 329-4069 Fax (650) 329-4463 345 Middlefield Road, Mail Stop 466 Menlo Park, California 94025 http://profile.usgs.gov/aslowey