[Ifeffit] Error in N (Number of Scatterers)

Matt Newville newville at cars.uchicago.edu
Wed Mar 9 16:18:04 CST 2016

On Wed, Mar 9, 2016 at 2:06 PM, Carolyn Carr <ccarr at chem.umass.edu> 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

> 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

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