Hi Aaron,
I find a nearest-neighbor third cumulant is frequently a useful
parameter for nanoscale materials. It's not just the anharmonicity of
individual bonds, it's also the anharmonicity of the distribution of
environments. In other words, in nanoscale materials there are core
atoms and surface atoms, atoms one monolayer below the surface, and so
on. (Or, in your case, read "interface" for "surface.") The atoms on
the surface may very well have interatomic distances a bit different
from those further in, and that distribution is often not symmetric,
for essentially the same reason that thermal vibrations are not
symmetric: it's energetically more favorable to stretch a bond from
equilibrium than to compress it by the same amount.
To use a third cumulant in Artemis, go to the Paths menu and check
"extended path parameters." The path dialogs will then include a blank
for "3rd," which is the third cumulant in the literature. It is then
used like any other path parameter. (Or, of course, you can access it
through IFEFFIT scripts, again using "3rd.")
--Scott Calvin
Sarah Lawrence College
On Mar 26, 2010, at 1:13 PM, Aaron Slowey wrote:
> 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
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