On Wed, Mar 9, 2016 at 2:06 PM, Carolyn Carr wrote:

Hello Mailing List,

I have read papers describing that EXAFS has an error regarding N the number of scatters of +/- 20%.

To be clear, I think you mean an uncertainty of +/- 20%, not a systematic error in the value for N.

The only original reference I can see to support this is "The effect of statistical noise on structural parameters in EXAFS data analysis" by L. Incoccia, S. Mobilio (1984, Il Nuovo Cimento D). However, in the more recent D. C. Koningsberger review "XAFS spectroscopy; fundamental principles and data analysis" (2000, Topics in Catalysis) he cites an error of 5% for N (although the paper cites slightly varying error for different absorber-scatterer pairs).

Well, there are many references that discuss this. I can believe the 1984 paper you give is the first to state such an uncertainty. More importantly, the EXAFS literature is full of work reporting this range of uncertainty. N is typically uncertain to around 10%. Whether that's 5% or 20% depends on data quality and soundness of the proposed model. It's not 50%, and it's not 1%. Similarly, uncertainties in distances are typically around 0.02 Ang -- they can be as good as 0.005 Ang, and as bad as 0.05 Ang but are hardly ever as good as 0.001 Ang or as bad as 0.1 Ang. These are the typical uncertainties are not because someone said this is so but because they are what are typically found in actual analysis of real data.

Several months ago, I wrote to the mailing list regarding the difference of fitting in R- and k-space in Artemis and received several responses revealing that some comments made in the Koningsberger review are no longer valid in Artemis.

I can believe we have slightly different perspectives from that review.

In my literature search, I did not find additional papers describing the error inherent in N when fitting in Artemis. Since the paper cited by Koningsberger (X-ray-absorption fine-structure standards: A comparison of experiment and theory, G. G. Li, F. Bridges, and C. H. Booth, Physical Review B, 1995) utilized Feff6 for their theoretical standards and so does Artemis, is the error in N still the same? I was wondering if there is some literature that I have missed, or if the developers of the Demeter package can shed some light on this issue.

The uncertainty in N is more or less inherent to the method, though there are techniques that can be used to improve the uncertainties. A fairly substantial portion of that uncertainty is "absolute" (as opposed to "relative") in the sense that with Artemis one is comparing processed experimental data with a theoretical calculation. First, the data processing includes a scaling factor (the edge step) that is completely correlated with N, so uncertainties in the edge step translate directly to uncertainties in N. Getting the absolute value of the edge step to 1% is hard. Second, the theoretical calculation for the EXAFS amplitude is somewhat harder than the calculation for the EXAFS phase. This is because many-body-electron effects such as the inelastic mean-free-path and the S02 parameter are hard to calculate ab initiio, and almost exclusively alter the EXAFS amplitude. The amplitude also needs to account for disorder (sigma2 / Debye-Waller factor), but this is not usually the main limitation at the 10% level. It is perfectly reasonable to say that one can see relative changes in EXAFS amplitudes better than 10% for similar sets of data that is treated and modeled in a consistent manner. Actually, this approach can also be used to improve the certainty of relative changes in distances too. For example, one can use temperature-dependent data or some other changing external variable to see very subtle changes in coordination number of distances. --Matt