Re: [Ifeffit] errors in bond lengths

Something I've done for analyzing DWF on data taken at several temperatures is what I called 'consensus amplitude' fitting. Here, I fitted shells to k^n*chi[i](k) = exp(-2 dsig2[i] k^2) A(k) sin(phi(k)+2 dr[i]k) where i is the index to temperature, and the fit parameters are A(k), phi(k), dr[i] and dsig2[i]. The obvious ambiguity is solved by arbitrarily picking one i, say i=0, to have dsig2[0]=0 and dr[0]=0. This was done iteratively, starting with A and phi obtained by back-transforming the filtered shells. You can do this with multiple shells. In at least one case, this helped me separate two shells by their differing temperature dependence. Doing this treats the data 'democratically', not taking one of the spectra as a reference to which all others are fit. Also, it doesn't overemphasis the low-amplitude parts of the signal, which the log-ratio method could do. Refs: M. A. Marcus, M. P. Andrews, J. Zegenhagen, A. S. Bommannavar, P. Montano, "Structure and vibrations of chemically produced Au55 clusters", PRB 42,3312 (1990) M. Marcus (that was before I started using my middle initial), "Siting and dynamics of Cu impurity in Ti lattice", Solid State Commun. 38, 251 (1981) Not a lot of detail in those papers, I'm afraid. I did do more with this method way back when, but it doesn't seem to have made its way into the literature. Back then, I was so naive that I considered a conference proceeding to be as good as a PRL, so lost a lot of impact. mam On 4/12/2020 8:15 PM, Matt Newville wrote:

Hi George,

I think this will not be a different answer from Matthew's or Anatoly's answers, but just reiterate their points.  The Purans et al 2008 PRL from 2008 appears to use both non-linear fitting with Feff and EDA (which should give basically the same results as Artemis/Ifeffit/Larch, though I do not know in detail what error analysis is done), and the log-ratio method.  I think they also fit the resulting sigma2 (derived from the non-linear fit) to an Einstein model.

The log-ratio method can only determine relative changes in distance, coordination number, and sigma2.  The main motivation for using this method is that scattering factors in the EXAFS equation will cancel out (or mostly cancel out) when comparing two similar experimental spectra. In addition, it is often argued that data extraction errors (energy scale, background subtraction, etc) would tend to be the same for two experimental spectra and so would also mostly cancel out.  There usually isn't much analysis of what residual systematic errors happen with the log-ratio method.   The working idea is that the ratio of the log of isolated single-shell EXAFS chi(k) (or what we would call chi(q) in Artemis/Ifeffit/Larch)  amplitudes vs k**2 should be linear (intercept = Delta N, slope=Delta sigma2) and the phase difference vs k should also be linear (intercept=0 if E0 is truly unchanged, and slope = Delta R).  For anyone who actually plots those (even for spectra on the same sample), you will probably find that these are "linear-ish", clearly showing both "yeah, that could work" and also "maybe not perfectly".

But, if I'm reading this PRL correctly, it looks like they use the log-ratio method to compare sigma2 and R of spectra at the same temperature but with different isotopes. That does seem like a fine way to better determine the subtle differences between those spectra.

--Matt

On Sat, Apr 11, 2020 at 12:41 PM George Sterbinsky mailto:GeorgeSterbinsky@u.northwestern.edu> wrote:

Hello,

As is well known, EXAFS is more accurate at determining relative changes in bond lengths than absolute changes in bond lengths due to cancelation of systematic errors in relative comparisons. When comparing the relative changes in bond lengths determined from EXAFS fits, as one might for a temperature series for example, is it appropriate to use the uncertainties returned by Artemis?

My question arises in part from Phys Rev Lett vol. 100 pg. 055901 (2008), where the authors state that errors for changes in bond length in a temperature series were determined by empirical means rather than statistical means. This then raises the question as to if the authors believe that statistical means would overestimate the error. My inclination is to think that the uncertainties reported by Artemis would be appropriate because of the scaling by the square root of reduced chi squared. However, I want to see what others think about this before committing to it.

Thank you, George

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