[Ifeffit] E0 for bulk crystals and nanoparticles

[Bruce Ravel]

Hi Leandro,

I suspect you will get several answers to your excellent questions.
It's late as I type this and I am looking forward to seeing my pillow,
so I am going to respond to just one part of your email.

On Thursday 22 February 2007 20:59, Leandro Langie Araujo wrote:
> I've been reading some papers and I can find people who do set the
> [nanoparticle]'s deltaE0 to be the same as the crystalline foil as
> well as people who report different deltaE0s for NPs relative to the
> foil. This confuses me because by setting (or not) deltaE0 we
> directly change the correlated variables, delR and C3.

This really gets at the heart of why exafs analysis is difficult.  You
are certainly correct that the deltaE0 is highly correlated with delR
and C3.  That correlation is hard to avoid in a non-linear analysis
as all three terms effect the phase of the calculated chi(k).

Most of the tricks that we so-called experts yammer on about on this
mailing list have to do with ways of dealing with those strong
correlations that are physically sound and statistically defensible.
To continue with your example of comparing nanoparticles their bulk
analogs, one strategy taken to deal with these correlation is to
assert that some parameter will be the same in the bulk as at the
nanoscale.  By making that assertion -- or, if your prefer, by using
prior knowledge of the system -- we reduce the correlation by
supplying more information (perhaps in the form of a multiple data set
fit) or we remove the correlation by promoting that parameter from
"guessed parameter" to "parameter set according to prior knwoledge".

To be more specific, we might assert that the changes to the
electronic state of the nanoparticles compared to their bulk analog
are relatively small -- small enough that we can neglect the effect.
Saying that requires that one believes it.  It may be true for
metallic nanoparticles, but may not be true for, say, semiconductor
nanoparticles.  If you believe it to be true that the electronic state
doesn't change much, then you are well justified in asserting that the
E0 for carefully aligned data should be the same.  Otherwise, you
should lift that constraint and investigate how e0 might be different
for your nanoparticles.

So what should you do if you are not sure?  Well, one strategy might
be to do a multiple data set fit using carefully aligned bulk and nano
data.  Compare the fit using a constrained e0 to the fit where the two
e0s float freely.  If the free floating e0s make sense given what you
know about the electronics of the nanoparticles and they provide a
statistically significant improvement to the fit, then probably you
should have free floating e0s.  If you float the two e0s and they come
out the same (within their error bars, of course) then you probably
should reintroduce the constraint.

The whole time you are doing that, you need to be mindful that, as you
say, e0 is correlated to other parameters.  The fitting results need
to be both reasonable and defensible regardless of how you decide to
cast the problem.  "Reasonable and defensible" applied to all the
parameters, not just e0.

Hope that helps,
B




-- 
 Bruce Ravel  ---------------------------------------------- bravel at anl.gov

 Molecular Environmental Science Group, Building 203, Room E-165
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 Argonne National Laboratory         phone and voice mail: (1) 630 252 5033
 Argonne IL 60439, USA                                fax: (1) 630 252 9793

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