Hi Andrew, I’d add to this that it’s important to think about what it is that you are trying to figure out. At least with the systems that I’ve worked with, it is rare for the answer to that being “I would like to know the coordination number for this path.” Instead, it’s usually something like “I would like to know what fraction of the manganese ions are in sites octahedrally coordinated to oxygen as opposed to tetrahedrally coordinated,” or “I would like to know which of several possible ligands are attached to my central atom, and in what proportions.” Those questions can yield to clues aside from the coordination number alone. For example, the metal-oxygen bond lengths are significantly different for octahedral coordination than for tetrahedral coordination. If you’re trying to distinguish between ligands, sometimes you can include paths beyond the nearest-neighbor, and so on. I’ve often seen people who are first trying to learn EXAFS analysis think that the way to analyze their system is to first see what information they can get from a single nearest-neighbor path from a single sample under a single set of conditions. If they can’t get a precise result from that, they figure anything more complicated will yield even fuzzier results. But if you have some knowledge about your system, or about possible alternative models of your system, then that’s not the case. Comparing samples in some way, or employing more scattering paths, or measuring multiple edges and performing a combined fit, can reduce the uncertainties in fitted parameters. In your example of coordination number and sigma^2, one possibility is to measure the same sample at different temperatures. Of course, if you expect the sample might undergo a phase change or otherwise change structure with temperature, that won’t work very well. But if you expect the structure to be fairly stable over a range of temperatures, then the coordination number might be the same for all measurements, while the sigma^2 varies. A multiple-spectrum simultaneous fit can then help. Of course, every system, and every problem, is different. But I do think it’s important to think about your system and about what the scientific problem is that you’re trying to solve. Best, Scott Calvin Lehman College of the City University of New York

On Aug 23, 2018, at 12:13 PM, Bruce Ravel wrote:

On 08/23/2018 10:55 AM, Thomas, Andrew (AGW) wrote:

...

Hello, Does anyone have any suggestions for breaking the correlation between the coordination number and sigma^2? Specifically, is there a way to set a maximum or minimum value for parameters in a fit?

Matt is, of course, correct when he says that this correlation is inherent to EXAFS analysis and cannot be "broken". I would like to suggest a broader way of thinking about this sort of issue.

When you have a very well behaved analysis problem -- that is, something like my teaching example of FeS2, something for which the structure is pretty well known -- then your EXAFS analysis will yield defensible values for CN and sigma^2 without too much effort. They will still be correlated, but sensible numbers will tend to just fall out.

In a harder problem -- y'know something you are doing actual research on -- you often run into the situation where these correlations preclude a "fall right out" analysis. It is tempting to assert that the CN must be SOMETHING and the ss must be SOMETHING. That's true in a sense, but you have made a real measurement and are doing a real analysis with real measurement uncertainties. And you have to respect that.

When you are running into trouble in your EXAFS analysis -- big uncertainties, indefensible values, that sort of thing -- that is usually the program trying to tell you something about your analysis. Usually, that would mean that you want to know something that the data do not support (or do not support beyond some level of precision or accuracy). Or it might mean that your fitting model is not realized in the data -- that is, your model is missing some important feature and the bad fit results are the result of missing that important feature.

To summarize, I want to encourage you not to assert that you need to find a way to break the correlations. i want to encourage you think about what the wonky fit results are trying to tell you about your data or your fitting model.

That was kind of rambling, I admit. Hopefully it was helpful nonetheless....

B

-- Bruce Ravel ------------------------------------ bravel@bnl.gov

National Institute of Standards and Technology Synchrotron Science Group at NSLS-II Lead Beamline Scientist, 06BM (BMM) Building 743, Room 114 Upton NY, 11973

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