The error bars generated in EXAFS fitting are an attempt to represent the uncertainty in the absolute value of each parameter. A large part of that uncertainty is often due to correlation with other variables; these correlations are listed in the log file.

Now suppose you have a sequence of data in which it is known that only one parameter should vary systematically. For example, suppose delE0 and delr for each temperature is unknown, but it is thought that delE0 does not change with temperature. (This is only an example! It certainly might, particularly if oxidation state changes.) The delr will have a large uncertainty, but much of that is due to the correlation with E0: they both could be higher or lower together. But if it is known that only delr is changing with temperature, then changes in delr that are smaller than the error bars may be detected and meaningful.

You'll also see people refer to the resolution of EXAFS data. They are talking about something like a Rayleigh criterion: how close can two bond lengths be and be distinguished as different bonds via EXAFS? But again, suppose it is known that there are two closely spaced bonds, even though they can't be resolved. If one changes relative to the other, it will change the MSRD (I.e. show up as a form of static disorder) if they are modeled as a single bond, and also change the "bond length" of the combined peak.

So there are plenty of cases where changes smaller than the error bars are meaningful. In general, though, they require additional knowledge about the system. If you know nothing about the system and see a systematic change in the bond length that is much less than the error bars, it might actually be a change in a correlated variable. Also, for very small changes, watch the third cumulant as a possible culprit! The third cumulant is often strongly dependent on temperature, and correlates with bond length. If you don't fit the third cumulant, you can think you have a bond length change when you don't--or even think it's changing in the opposite direction from what's happening.

Having said that, the fourth decimal point is very hard to pin down. While it's certainly possible to get a systematic effect over a series of spectra that shows up in the fourth decimal point, how do you know for certain it's not one of the other effects I've described? In other words, I'd say that it's possible to see a phase transition like that via EXAFS curve fitting, but it's difficult to know exactly what the structural change that's accompanying it is.

On Jul 25, 2008, at 7:58 AM, Bindu R. wrote:

Hi,

Could you please clarify me, up to what decimal place in the bond lengths obtained from EXAFS fitting is reliable?

If there are changes in the bond lengths in the fourth decimal place around the region of phase transition, can one consider this as a genuine one even though the error bars obtained from the EXAFS fitting are more than the variation in the bond lengths?

Regards
Bindu

Dr.Bindu R.
Visiting Fellow
BG-37
DCMP&MS
Tata Institute of Fundamental Research
Homi Bhabha Road
Colaba
Mumbai-400 005
India

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