[Ifeffit] DWF's for amorphous InP

[Matt Newville]

Dear Claudia,

> We think that restraining the DWF's might be a good approach.
> Unfortunately, the crystalline and amorphous systems do not have similar
> DWF's due to the large amount of disorder in the amorphous phase. From
> previous studies it is known, that the DWF of an amorphous semiconductor
> is roughly (!) twice the DWF of the crystalline phase. Hence, fixing the
> In-P DWF to twice the crystalline value (from a standard we also measured)
> would be a a first approach. My question is whether there maybe is a
> better way of relating/restraining the DWFs, as for example suggested by
> Crozier, Rehr and Ingalls (X-ray Absorption, Koningsberger and Prins,
> Wiley & Sons, 1988). They derive a formula for the DWF that contains the
> reduced mass and an integral over the projected density of states. If one
> could make a reasonable assumption about the integral (which is the
> problem) it would be possible to correlate the two DWF's. Or maybe there
> is another way to make an educated guess (by computing with FEFF or so).

If I might jump here, I think this question is closely related to the
one from Ricardo Faccio earlier today, and other questions about
standards and reference compounds we've seen recently.

It is generally difficult to get accurate and meaningful amplitude
(values for N and sigma2) from an a priori modeling of an EXAFS
spectrum.   There are many reasons for this, including experimental
problems (that is, measuring the amplitude of chi(k) with high
accuracy) and  theoretical problems (that is, understanding with high
accuracy all the physical terms other than N and sigma2 that influence
the amplitude of chi(k)).

It seems natural to want to improve the accuracy of N and sigma2
through "better modeling"  including trying different k-weights for
the fit.  This can even work to a small extent, and it is impressive
that it does work and that Artemis helps you do this easily.  But it
won't improve the accuracy of N and sigma2 by a lot.

But since you bring up some older work on Debye-Waller Factors and are
working on a classic EXAFS problem like site disorder  in an amorphous
semiconductor, I'd like to bring up a point that at one time was
taught earlier on in EXAFS analysis:
          Absolute measures of N and sigma2 have much larger uncertainties than
          relative measures of N and sigma2.

In the pre-FEFF days, very few people would measure a single spectra
and expect (dare) to publish N and sigma2 for it.  Instead, two
spectra would be measured with similar instrumentation, analyzed
together, and  N and sigma2 would be compared.   One common approach
was to vary the temperature, and if there was no phase change, N could
be assumed to be invariant, and you would extract the temperature
dependence of sigma2 (within a constant offset).    Another was to
measure a well-characterized crystal (say, crystalline InP) and
compare N and sigma2 between the two phases.   Even with FEFF, these
are good approaches.

The drawback to these approach are that they're limited to single
scattering and need a good reference sample and spectra with which to
compare your unknown.  But it would certainly be possible to analyze
spectra of amorphous semiconductor in this way.

The key is to look for relative differences. For sure, start by
modeling data for crystalline InP to get some idea of the thermal
component of sigma2 for the In-P bond.   Then, if at all possible,
measure InP at a few different low temperatures:  All the variation
between those spectra will be due to the thermal part of sigma2, not
the static disorder, and not N.   Once you get that far, you'll
probably want to do a multi-data-set fit constraining N for In-In and
In-P to be the same for all temperatures.

Hope that helps,

--Matt