[Ifeffit] calculating particle size from coordination numbers

[Georges Siddiqi]

Hi Scott,

thanks a lot for your detailed response!

Regarding your suggestions, I'm a bit unclear how I can implement this in
Artemis.  Is this approach similar to one of your papers:
http://scitation.aip.org/content/aip/journal/jap/94/1/10.1063/1.1581344
where you relate the nanoparticle coordination number to the bulk
coordination number via particle radius? (equation 4)

How can I do this in Artemis when there's other variables such as deltaE,
debye-waller factor and delr to worry about?

thanks,
georges


On Tue, Oct 29, 2013 at 7:31 PM, Scott Calvin <scalvin at sarahlawrence.edu>wrote:

> 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> 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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