[Ifeffit] EXAFS mean free path in small particles

[Matt Newville]

Hi Anatoly,

> In fact, Zhao and Montano say in p. 3403: "we would like to
> point out that based on the experimental results for noble
> metals [Cu, Au, and Ag] no evidence of a substantial change in
> the electron MFP value between bulk and small particles was
> found". That, to my mind, is an indirect but a fair reason to
> reuse bulk amplitudes, at least for Cu, Au and Ag.

I think this is a little unfair.  That experimental work done
prior to 1986 could not detect a change in MFP between bulk and
nanoparticles does not mean that there is not such an effect.

Zhao and Montano show (fig 1) large changes in the bulk plasmons
below 10 nm -- well before the surface plasmon dominates.  
These will also affect the MFP, as they show in fig 2, where the
MFP for 10nm and 3 nm are shown to be significantly different,
even though the surface plasmons are barely noticeable.

I'm not saying that Zhao and Montano are right, but I don't see
that it's obviously wrong.  And I sure don't like the idea of
saying that using the bulk MFP from Feff is OK for nano-Au, Cu,
and Ag, but not for nano-Al!

> I also think, if HRTEM and EXAFS agree, it says for itself
> (that bulk FEFF amplitudes are correct). If they do not agree,
> AND if other reasons for discrepancy can be ruled out (e.g.,
> broad size distribution, or electron-beam caused growth of
> particles), AND if the discrepancy is in the right direction
> (EXAFS-determined size is smaller than the HRTEM-determined
> size), then surface plasmon and other losses should be looked
> into. And, I agree, it is an important issue to be aware
> about.

I don't think the direction of the change in the MFP matters:  
if it changes with particle size, it will effect the EXAFS.  
Also, just to be clear: we know that the bulk Feff amplitudes
are NOT correct to better than 5%.

Since a lot of the interest in nanoparticles is precisely
because of their unique electronic properties and the idea that
"everything is different" for nanoparticles, it seems dangerous
to assert that some electronic properties can be modelled as
bulk properties without thinking about it.  And some of those
who did think about it (Zhao and Montano) concluded that the MFP
is different between bulk and nano particles.

I should say that the only analysis I've done on "nano"  
particles (10 years ago) showed slight differences in the Cu
K-edge EXAFS amplitude between bulk and 13nm (ie, huge!!) Cu
particles.  At the time we argued that the 13nm particles were
slightly more disordered, but still had an average coordination
of 12 (which was in dispute even if it seems obvious now).  But
we did not try to adjust the MFP....

--Matt