[Ifeffit] Calculation of the doping level

[Bruce Ravel]

On Wednesday, April 17, 2013 09:45:40 AM Dr. Dariusz A. Zając wrote:
> 1)
> I investigate the change of the Al:K edge XANES spectra for the 
> situation where I have Al in the centre and vary the distance to the 
> next Al. At the beginning I have only 1 Al in the centre. The 8A radius 
> consist 177 atoms: 86 Zn, 90 O and of course 1 Al.
> Can I simple say that my doping level in this situation is 1/177=~0.56 
> at% doping?
> But this could be also 1/88 if I will reduce the FMS to 6.2A, and the 
> calculation will give the same result. Is any physical limitation to 
> this calculation of doping level?


I think there is a small problem is what you wrote here.  The cluster
you describe is consistent with 0.56 at% doping but also with anything
smaller.  A more pedantically correct way of describing the cluster
you contrusted is that it is consistent with any physical situation in
which the Al dopants are, on average, separated by 8 A or more.  That
necessarily precludes any situation in which there is Al clustering of
any sort.

If you want to consider the effect of clustering on the XANES
calculation, you need first to consider the convergence of the
calculation of the host (albeit with the Al absorber) in cluster size.
That's not quite the same thing as the mean free path, although there
must be some relationship between the two.

First you have to figure out convergence as a factor of cluster size.
That is, make a calculation with FMS=4.0.  Then make one with FMS=5.0.
Then FMS=6.0.  Keep going until the calculation stops changing.  That
gives you a sense of what the sensitivity of the calculation could
possibly be to unclustered dopants.  That is, if the convergence
radius is 7.0 A, then the calculation is unlikely to be sensitive to
the presence of an Al atom at a diatance of 8.0 A.  With low doping
levels that, on the average, result in more distant Al atoms, I would
expect the computed spectra to be identical.


> 2)
> OK, lets add now another Al in the nearest Zn sphere - the XANES spectra 
> changes, as I expected. The doping level doubled from 1/177 to 
> 2/177=~1.13 at%. 

That's not what that means.  What you have done is to introduce
clustering.  You are now saying that Al atoms are paired, not that
they exist in higher concentration.  They may also exist in higher
concentrarion.  But, strictly speaking, that's not what the addition
of an Al in that place means.

> However, with the shifting of the second Al far away 
> from the 1st Al, I do not observe the change of the XANES spectra, up to 
> 4th sphere. With the 5th sphere (which is at ~6.5A) 

OK.  This is the follow-up to the point I made above.  The convergence
test on the host material sets an upper bound on how far away the
second Al atom can be and still be visible in the calculation.  You
are now probing that with an actual placement of the Al atom.


> I can observe the 
> tendency of the change of XANES spectrum toward this in point 1 
> (probably due to the limited size of the cluster).
> This means that with the change of the position of the second Al, I 
> change the free means path from ~3.22A for 1st Zn sphere to ~6.14A for 
> the 4th, this could be recalculated as the different doping level  from 
> ~5 at% to ~2 at%. Of course following the calculation from the point no. 
> 1 we have in both cases ~1.1 at%...

> My impression is that I should think in the way of the free means
> path, but maybe I'm wrong? - I would like to know your attitude.

MFP is relevant, but it is just a way of putting a number to a more
complicated effect.  The bottom line is that you want to understand
spectral trends as changes are made to the configuration used in a
Feff claculation.  To do that, you have to make a lot of Feff
calculations.

B


-- 

 Bruce Ravel  ------------------------------------ bravel at bnl.gov

 National Institute of Standards and Technology
 Synchrotron Methods Group at NSLS --- Beamlines U7A, X24A, X23A2
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