On Wednesday 07 March 2007 22:19, David Weedon wrote:

What are we doing when we make our own parameters? Are they a mixture of parameters from the EXAFS equation that we wish to evaluate in the fit, and if so why?

David, Many of your questions are actually the same question. Let me step back and try to offer up some of the big big picture. The simplest discussion of EXAFS is the single shell case, so let's start there. Matt gives a very nice derivation of the single-scattering exafs equation between pages 11 and 20 of this pdf file: http://xafs.org/Tutorials?action=AttachFile&do=get&target=Newville_Intro.pdf Jumping to the result, we see that the exafs equation is something like chi(k) = (N*S02*F(k)/2kR^2) * sin(2kr + phi(k)) * exp(-2k^2sigma^2) There is also a mean free path term and possibly some cumulants, but that equation has all the important stuff. The purpose of Feff is to compute the scattering amplitude and phase shift: F(k) and phi(k). R is the distance between the scatterer and the atom in the first shell. k is the wavenumber of the photoelectron, which is, of course, related to its kinetic energy (or energy in excess of the binding energy of the deep core electron). N is the coordination number, or number of atoms in the first shell. sigma^2 is a mean square deviation in R and so represents the disorder in the first shell. And S02 is an amplitude reduction factor that Matt talks about in that PDF file but which I won't discuss further here. There is also an energy shift term E0 which is used to align the k-grid of the theory with the k-grid of the data. If we do an analysis of our first shell data, then we are trying to figure out how many atoms are in the first shell, what their disorder is, and how many of them there are. In that case, it is natural to cast the problem insimple terms. N, R, and sigma^2 are the parameters of the fit. We modify those parameters until the theory best fits the data. And then we're done. What happens if, instead of having N atoms at a single distance R, you have some kind of splitting of the first shell, such that N/2 atoms are at a shorter distance R1 and N/2 of the atoms are at a longer distance R2? Well, the formalism that we use to understand the EXAFS says that contributions from different kinds of scatterers add. The contribution from atoms at distance R1 is evaluate using the equation above, as is the contribution from the atoms at R2. The total chi for this split shell, then, is chi(k) = chi1(k) + chi2(k) where chi1 and chi2 are evaluated using appropriate values of N, R, and sigma^2. Now consider trying to fit more than the first shell. The approach is, conceptually, exactly the same as what I have already described. You evaluate chi(k) for each kind of scatterer and add them up: chi(k) = sum over all paths [ chiN(k) ] As you can see from Scott's examples, which you have started working through, describing the first few shells of an EXAFS problem can involve many paths. It is not uncommon to use 10s of paths (or more) in a fit. At first glance, this is a catastrophe. We need to evaluate N, R, and sigma^2 for every path. If a fitting problem requires 15 paths, that means we have to evaluate 45 parameters. But our EXAFS data almost certainly does not contain that much information. There is no way to do a fit and evaluate 45 parametesr in a defensible way. We could throw up our hands and go home, but it's only 9:30 in the morning as I write this, so I'm not quite ready to do that ;-) Instead, let's try thinking differently about the problem. Perhaps this is a crystal so we can assert that we know N for each kind of scatterer. Perhaps, as in the case of our split shell, the split in distance is not so large and we can assert that sigma^2 must be the same (or with measured uncertainties) for each part of the split shell. Perhaps we are measuring a cubic crystal, so all chnages in bond length R can be expressed with a single parameter describing the bulk, isotropic expansion or compression of the lattice. The bottom line is that N, R, and sigma^2 might be the parameters of the EXAFS equation, but they do not have to be the parameters of the fit. That's the central concept of Ifeffit and, by extension, of Artemis. Instead of floating N, R, and sigma^2 in the fit, we float a set of abstract parameters and write N, R, and sigma^2 in terms of those parameters. Those relationships can be simple. For instance, we might have a sigma^2 parameters called "ss7" and use that as the sigma^2 parameters for path 7. Or we might, as Carlo suggested in his response to your email, use a correlated Debye model for the sigma^2 values. In that case, we would have two parameters: guess thetad 500 set temperature 300 and for each path for which we use the correlated Debye model, use sigma^2 for path N = debye(temperature, tehtad) The math expressions can be whatever they need to be. You get to use the binary operators ( + - * / ** ), common math and trig functions (sin, cos, exp, sqrt, and others), and a handfull of EXAFS-specific functions such as debye and eins. The point of all of this is to express your fitting model in a way that describes the data and to do so in a way that does throw a ridiculous number of floating parameters at the problem. That was really long, but hopefully helpful, B -- Bruce Ravel ---------------------------------------------- bravel@anl.gov Molecular Environmental Science Group, Building 203, Room E-165 MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007 Argonne National Laboratory phone and voice mail: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://cars9.uchicago.edu/~ravel EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/

On Wednesday 07 March 2007 22:19, David Weedon wrote:

After I hit the "Guess" button I cannot find the parameter "dr" on the list.  Am I correct in assuming that "dr" is some kind of reserved parameter name that should not be used in equations?

That's correct. "dr" is one of Ifeffit's so-called "program variables". It is usually ok to use a program variable name as the name of a parameter in a fit. Sometimes it's not. When I first discovered a situation where it was a bad idea to use a progarm variable name as a named fitting parameter, it took me a long time to troubleshoot the problem. So I decided that the best solution was to make Ifeffit's program variable names be reserved words in Artemis and to force you to select different words to use as the names of your parameters. I suppose this is an inconvenience (or possibly a freedom-of-speech issue!), but if you just get in the habit of typing "delr" instead of "dr", I think you'll manage.

From the Ifeffit document on the topic of program variables: http://cars9.uchicago.edu/~ifeffit/refman/node138.html

B -- Bruce Ravel ---------------------------------------------- bravel@anl.gov Molecular Environmental Science Group, Building 203, Room E-165 MRCAT, Sector 10, Advanced Photon Source, Building 433, Room B007 Argonne National Laboratory phone and voice mail: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://cars9.uchicago.edu/~ravel EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/