Hey Bruce, thanks a lot for your e-mail. The correlation between the coordination numbers and the DWF’s is exactly the problem. It is made worse by the overlap of the two peaks (In-P and In-In), allowing less free parameters for the fit to be physically reasonable. I was probably not specific enough with my question (apologies for that) so here some more information: Crystalline InP has a zinc blende structure with In tetrahedrally bonded to four P atoms and vice versa. However, this does not apply for the amorphous phase. The amorphous structure of compound semiconductors such as InP is characterized by structural as well as chemical disorder, i.e. the presence of “wrong” homopolar (In-In) bonds. The information we like to get from the EXAFS measurements (taken at the In K-edge) of the amorphous system are: (1) The total coordination number (though the total coordination number is around four, it is not yet clear whether it is exactly four, slightly over or slightly under coordinated.) (2) The percentage of the wrong (In-In) bonds. Due to the correlation between coordination number and DWF, varying ratios of the In-In and In-P DWS’s give varying In-In percentages even with the total coordination number being the same. Thus we need to apply constraints (as you said) 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). Hope that’s a bit more clear now. Many thanks, Claudia

On Thursday 29 March 2007 02:57, Claudia Schnohr wrote:

...

Hello everyone.

I am a PhD student and I have encountered a problem with analysing the EXAFS of amorphous InP.

For amorphous InP the first shell around an In atom is comprised of both P and In atoms. The In leads to a small peak in the R-spectrum that strongly overlaps with the bigger peak due to scattering from P. If I use two different Debye-Waller-factors, one for each scatterer, and let them both float during the fit I get weird values since the coordination numbers for both peaks have to be floated as well. Therefore, some restraint is needed for the DWF's.

Is there any correlation between the two DWF's following from theory or experiment that I could use to restrain my fitting parameters ? Are there other possibilities to handle such a situation ?

Many thanks in advance for your help,

Hi Claudia,

If I understand your explanation, I suspect that the problem is that your fit has more freedom in its parameters than the data can support. It is always the case that coordination number and sigma^2 are highly correlated. They are both terms that affect the amplitude of chi.

I doubt that the solution is somehow to constrain the sigma^2 values. Without doing some serious theory to figure out how those two values might be related, I would not know what constraint to apply. What would be a lot more reasonable would be to constrain the total number of atoms in the coordination shell. I don't know what kind of crystal InP forms, but I would assume that the In is either 4- or 6-coordinated with P in the crystal. It seems reasonable to enforce that coordination in the amorphous material. That is, require that the sum of In and P atoms in the first coordination shell be 4 (or 6 or whatever).

Make a guess parameter that describes the amount of the In:

set n = 4 # (or 6 or whatever) guess x_in = 0.1 def x_p = n - x_in

then define you sigma^2 parameters as before:

guess ss_in = 0.003 guess ss_p = 0.003

That reduces the number of parameters in the fit by one, enforces a physically reasonable constraint on the total number of parameters, and -- hopefully -- helps to stabilize your fit by removing one of the highly correlated guess parameters.

As I re-read what I wrote, it occurs to me that another reasonable constraint might be to require that sigma^2 for the In-P bond be the same in the amorphous material as in the crystal. Did you measure crystalline InP as well?

Hope that helps, B

-- Bruce Ravel ---------------------------------------------- bravel@anl.gov

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-- Claudia S. Schnohr Department of Electronic Materials Engineering Research School of Physical Sciences and Engineering The Australian National University Canberra, ACT 0200 AUSTRALIA

Hey Matt, thank you very much for your comments. Indeed, what we hope to determine from our measurements are relative differences between a number of samples measured in the same way (same beamline, same run etc) just as you have suggested. The problem with the amorphous samples is that due to the correlation between DWF and coordiantion number and due to the overlap of the peaks (In-In and In-P) different ratios of the two DWFs might still give the same (or at least a very similar) fit. Therefore, the fitting procedure might choose one ratio for sample A and another ratio for sample B even though their spectra look basically the same. That is why we thought to have some relation between the two DWFs would be handy and it is always worth a try to ask other people about their experiences :) At the moment, I try using different (multiple) k-weights and various k-ranges to see how the system behaves and hopefully I am able to pick a setting that allows for a good (reliable) fitting of the data even without assuming a relation between the two DWFs. Thanks again for your help, Claudia

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 _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit

-- Claudia S. Schnohr Department of Electronic Materials Engineering Research School of Physical Sciences and Engineering The Australian National University Canberra, ACT 0200 AUSTRALIA