[Ifeffit] calculating particle size from coordination numbers

[Scott Calvin]

Hi George,

Do you have a rough sense of the shape of your nanoparticles?

I've consistently found (and I think Anatoly Frenkel has as well) that these kinds of methods tend to underestimate the size of nanoparticles, and in fact give a "size" for bulk metals which suggests they're actually large-ish nanoparticles.

I've never been able to nail down why that is. The hypothesis that I used to favor is that EXAFS is emphasizing the small end of the size distribution, and so there's actually a low-end tail that is being measured. More recently I've started to wonder if it's related to the assumption that S02 is independent of R and k within the EXAFS region. It's been known since the 80's that this is not exactly true, and it seems possible to me that there's a slight systematic trend with R that gets confounded with the particle size effect. As I say, that's just a guess, but in any case the underestimate of particle size comes up quite often--I've discussed it in a number of papers.

Therefore, if you do have a sense of the shape of your nanoparticles (e.g. roughly spherical, or roughly raft-like), I'd suggest constructing a model that describes the morphology with a small number of free parameters. For a sphere-like shape, for instance, the only free parameter needed is the radius (and S02). Then calculate the effect on the coordination number as a function of those free parameters. Next, fit the copper foil using the model, and see what it finds for the free parameters-. Finally, apply to your nanoparticulate samples, setting S02 to the value you found for the foil using the model, and compare the results for the other free parameters, such as radius.

I suggest this procedure for several reasons:

*By using a relatively small number of free parameters, it reduces the ability of the fit to compensate for a host of other systematic errors by tuning each individual coordination number up and down.

*By comparing to the fit to the foil, and using the S02 for that fit, some kinds of systematic errors are more likely to apply equally to each fit, thus making the procedure useful for at least judging relative sizes.

*The procedure is relatively insensitive to the details of the shape of the nanoparticles; you don't have to get much further than "raft-like" or "sphere-like" to have it produce useful results.

Hopefully that helps!

--Scott Calvin
Sarah Lawrence College

On Oct 29, 2013, at 1:23 PM, Georges Siddiqi <gsiddiqi at gmail.com<mailto:gsiddiqi at gmail.com>> wrote:

Hi All,

I'm trying to use EXAFS data I have of Cu nanoparticles dispersed on SiO2 and ZnO to calculate their particle size.

Searching the archives, i've come by these topics and papers, which have helped immensely, but I'm still a little bit in the dark about the specifics of the fits:
http://www.mail-archive.com/ifeffit@millenia.cars.aps.anl.gov/msg02994.html
http://www.mail-archive.com/ifeffit@millenia.cars.aps.anl.gov/msg03430.html

http://pubs.acs.org/doi/full/10.1021/jp012769j
http://pubs.rsc.org/en/Content/ArticleLanding/1999/CP/a904654b#!divAbstract

So these discussions and papers make it clear that CNs for the 2nd or 3rd coordination shells will give a more accurate picture of the particle size (and even shape).  Also, just comparing SO2s between a foil and the sample isnt the most accurate.

My initial thought was to get a good fitting model on Cu foil, obtain coordination numbers which are very close to 1, then apply that same fitting model to the Cu nanoparticles (for the Cu-SiO2 species we have TEM data I can again calibrate myself with)

However, my specific problem is getting reasonable coordination numbers for the Cu foil.
- I can set the SO2 to 1 and get a very good fit for the data, but this is not useful for the nanoparticles
- I can give all paths the same SO2 variable, and get a fitted value close to 1, but this isnt useful for comparing first and second shell CNs, as the ratio will always be the same.
- And finally, when I try to give each scattering shell its own independent CN, I again get a good fit, but while the first shell SO2 is close to 1, the 2nd shell value is closer to 1.5

I've been playing with which variables are the same between paths, etc, and I can get more reasonable numbers, but the problem then becomes that I cant easily justify my fitting model.

Attached is my Artemis file for Cu foil.

Any help or suggestions with how to proceed (specifically with how to group variables) would be much appreciated.  I apologize in advance if i'm asking about a topic that's been covered extensively.

thanks,
Georges Siddiqui
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