[Ifeffit] uncertainties in "relative" values

[Scott Calvin]

Hi all,

OK--this one's been puzzling me for a while, so I thought I'd see 
what you all had to say about it:

One of my students and I performed fits on some different samples of 
platinum nanoparticles to see if we could extract mean sizes by 
observing the reduction in coordination numbers as a function of 
absorber-scatterer distance (I and Anatoly Frenkel, among others, 
have done some past work in this area).

This worked OK: we extracted believable sizes that are consistent in 
some sense with what was seen via TEM and XRD (there are 
complications that arise because of polydispersion, but that's a 
story for another day).

But here's the issue: the uncertainties generated by Ifeffit in the 
particle size are fairly large compared to the difference between the 
best-fit values for different samples. These uncertainties are 
reasonable in the sense that varying details of the fits (e.g. 
k-range, k-weight, Debye-Waller constraint schemes, whether 
resolution and/or third cumulant effects are included, etc.) causes 
the best-fit values to jump around within the uncertainty range. Thus 
if a fit reports 15 +/- 4 angstroms for particle radius, I can 
construct fits with reasonable R-factors that yield best-fit results 
of 12 or 18 angstroms. This is perfectly sensible behavior. But we 
have also observed that as long as we use the same fitting details on 
all samples, that the fitted sizes of all samples move up or down 
together. In other words, if under one set of fitting conditions the 
best-fit radius for sample A is 15 +/- 4 angstroms while for sample B 
it is 17  +/- 5 angstroms, under another set of conditions the 
best-fit radii might be 18 +/- 6 and 20 +/- 7 respectively, but the 
size of B always comes out larger than the size of A. In addition, 
the relative sizes of A and B (and C and D and...) have since been 
confirmed by other methods (XRD, experiments involving mixtures of 
samples, etc.).

So it seems as if there should be a way to express the " uncertainty 
in the relative size" between the two samples...B is larger than A by 
13 +/- 5 %, for example, regardless of the absolute size the fits 
find. But so far the only way I've thought of for doing this is to 
look at all the fits we've tried that have yielded R-factors below 
some cut-off, and just sort of average all the results for the 
differences in size. That seems unsatisfactory, however, since the 
standard deviation depends intimately on whatever fitting details we 
just happened to try. It would be much better if there were some way 
to directly fit the difference in size for the two samples, but I 
haven't thought of a good way to do this yet.

Any ideas?

--Scott Calvin
Sarah Lawrence College
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