Hi folks, Today I received one of the top-ten most asked questions. I am going to take a stab at answering it here in an archived forum. I am sort of hoping to get a discussion going and get several people's viewpoints. An Artemis user observed in her email that, in the EXAFS literature, people often publish values for coordination number. She asked how one obtains that using Artemis/Ifeffit. If only there were an easy answer to this question! It turns out that, in the EXAFS equation, there are two terms that directly affect the amplitude. One is N, the coordination number (or one might say "the path degeneracy"), and the other is S02, the so-called passive electron reduction factor. S02 is, according to popular wisdom, chemically transferable. This means that if you somehow have determined S02 for a given central atom in one compound, you can use this value for some other compound. While this may be true, particularly if a standard and a sample are measured back-to-back under identical experimental conditions, it is not a safe course of action. The problem is that lots of empirical effects can also change the measured amplitude. These may include things like detector response, sample inhomogeneity, and those annoying gremlins that sneak into the hutch when you're not looking. Assuming, though,that you know S02 and you are confident that empirical problems are a small factor, then the "S02" path parameter can often be interpreted simply as the coordination. If, however, you are not confident of S02 or of the smallness of the empirical effects, the situation is somewhat more complicated. A common assumption is that you should be able to determine S02 *and* coordination simultaneously from data. This is, at best, extremely difficult to do with statistical significance and, at worst, flatly impossible. If you are fitting only one shell of data, then it is certainly impossible. Why do I say that? Well, consider how coordination (N) and S02 enter the EXAFS equation: N * S02 * F(k) chi(k) = ------------------ sin( 2kR + delta(k) ) exp(-2ksigma^2) 2kR This is the generic formula. In Feff, Ifeffit, and Artemis, this is the the expression for chi(k) for a particular path. The data chi(k) is fit by evaluating this equation for one or more paths then summing them up. In that equation, note that N and S02 are both multiplicative factors. If your fit considers only one path, then N and S02 have *exactly the same effect* on the equation. They cannot be measured independently. In the absence of knowledge about either N or S02, the only thing you can do is measure the product (N*S02). How does one then report on coordination in a journal article? You have to somehow interpret the product (N*S02) and determine how much of that is N and how much is S02. There is no generic answer to how that is done -- it depends on the details of the sample and the experiment. To return to last week's silly posts about training monkeys -- it is yet another reason why data analysis requires a thinking human being. If you are fitting many shells or many data sets (the latter is something that Artemis does not yet allow you to do -- it's coming soon!), then you may have enough information in your data to uncouple the correlation between N and S02 and somehow fit them independently. Again, there is no generic way of doing so -- each situation is different. It is common to do as I suggested above and determine S02 from a well known standard that was measured at the same time as your sample. If there are no significant empirical effects in the sample that do not exist in the standard, then the value of S02 is probably useful for your unknown sample. Armed with that, it is much easier to then determine coordination. The discussion up to now has been conceptual. How are the amplitude terms handled in Artemis. Well, start by taking a look at a screenshot of the path page from a recent version of Artemis: http://feff.phys.washington.edu/~ravel/software/exafs/images/artemis/artemis... Note that there is an entry box labeled "N" and another labeled "S02". The one labeled "N is filled with the path degeneracy when the feffNNNN.dat file is imported. The one labeled S02 is intended to be filled with a math expression used to describe all remaining terms that may effect the amplitude. In the example shown, I have left N equal to the value from the feffNNNN.dat file and set S02 to a very simple math expression. The variable "amp" is being floated in this fit to copper foil data and used to evaluate the S02 term in the EXAFS equation for each path. In this case I am using knowledge of the system to uncouple N and S02. This is a copper foil, thus I am confident that the coordination is as expected from crystallography. I am also confident that the empirical effects are negligible. Whatever value amp ends up being, I will interpret that as S02. Now suppose I want to measure a nano-particulate copper oxide. In such a system, I may expect coordination to be reduced relative to the bulk oxide. For that, I may do the following: 1. Run feff using the crystal structure of bulk copper oxide. This will give me a copper/oxygen path to use to fit the first shell of my nanoparticle. 2. Read that feff path into Artemis along with my data 3. Set amp to the value determine from the copper foil (this is done by selecting "set" rather than "guess" from the appropriate optionmenu on the "Guess, Def and Set" page in Artemis. 4. For the first shell path, set N to 1 (rather than what ever value it was in the feffNNNN.dat file) 5. Set S02 for the first path to this math expression: n_first * amp 6. On the "Guess, Def and Set" page, define n_first as a guess parameter and choose a sensible starting value. The N and S02 part of the screenshot above will then look something like this: ___ ___________________________________ N |_1_| * S02 |_ n_first * amp ___________________| Here I have fixed amp to represent the known value of S02, I have set the N term in the EXAFS equation to be 1, and I have made a math expression, "n_first * amp", that will be evaluated and used for the S02 term in the EXAFS equation. n_first will be adjusted in the course of the fit and can be directly interpreted as a coordination number. Is this the only way of dealing with coordination? Certainly not. Is this the "official" way of measuring coordination? No. There isn't one. Every situation is different. Should you apply this example to every one of your analysis problems? No way! Did this example help you understand how N and S02 are used in Artemis and Ifeffit? I hope so. May this example be applicable to some analysis problem you run into at some point in your career? Quite possibly. Do you need to think hard about every analysis problem and figure out the best way to deal with the problem of N and S02 being coupled parameters? Absolutely! Hope that helps, Bruce -- Bruce Ravel ----------------------------------- ravel@phys.washington.edu Code 6134, Building 3, Room 222 Naval Research Laboratory phone: (1) 202 767 5947 Washington DC 20375, USA fax: (1) 202 767 1697 NRL Synchrotron Radiation Consortium (NRL-SRC) Beamlines X11a, X11b, X23b, X24c, U4b National Synchrotron Light Source Brookhaven National Laboratory, Upton, NY 11973 My homepage: http://feff.phys.washington.edu/~ravel EXAFS software: http://feff.phys.washington.edu/~ravel/software/exafs/