Contribution of multiple scattering paths - basic question
Hello, I want to fit a cobalt-porphyrin for which I have an atom.inp-file and EXAFS experimental data at Co K-edge . I started with a simple sum of paths for all paths with a distance below 5 A and an amplitude above 10 (see attachment). If one compares experiment (black curve) with this first fit (red curve) the first shell peaks overlap quite nicely but not the second and third (fourier transforms of the single paths are also drawn as blue and red curves). Then I excluded four paths (the red ones) and did a second sum of path. Now the other shell peaks overlap as well (green curve). The four exluded paths are multiple scattering paths via one nitrogen and one carbon atom. I conclude that the extinction of the second shell peak in the first simulation is due to the fact that these paths have a different phase shift than the other paths with a similar frequency. Do I make a simple error (adjustments of the fitting parameters necessary?) or does that tell me something about the system? I appreciate any help. Regards, Gerrit
On Monday 09 May 2005 11:24, Gerrit Schmithals wrote:
Hello,
I want to fit a cobalt-porphyrin for which I have an atom.inp-file and EXAFS experimental data at Co K-edge . I started with a simple sum of paths for all paths with a distance below 5 A and an amplitude above 10 (see attachment). If one compares experiment (black curve) with this first fit (red curve) the first shell peaks overlap quite nicely but not the second and third (fourier transforms of the single paths are also drawn as blue and red curves). Then I excluded four paths (the red ones) and did a second sum of path. Now the other shell peaks overlap as well (green curve). The four exluded paths are multiple scattering paths via one nitrogen and one carbon atom. I conclude that the extinction of the second shell peak in the first simulation is due to the fact that these paths have a different phase shift than the other paths with a similar frequency.
Do I make a simple error (adjustments of the fitting parameters necessary?) or does that tell me something about the system? I appreciate any help.
I'll take a stab at this. I should mention that the image you sent did not reproduce very well on my computer. It was very hard to read, so my answer might be tainted somewhat by that. I think the simplest way to understand what you observed is to remember that when you do a sum of paths, you are doing so without any reference to sigma^2. It is quite possible, particularly in an organometallic thingie, that the MS paths will be quite strong in the sigma^2=0 Feff calculation, but quite weak in the real analysis due to their large sigma^2's. This seems reasonable. One might expect a MS path to be quite floppy in an organometallic. At finite temperature, that floppiness translates into a large sigma^2 which suppresses that contribution. I must say, though, that your data look to be a bit more complicated that that. Perhaps you have some interesting collinear MS paths which don't sigma^2 away while other, non-collinear MS paths do. The reason I say that is because the green line looks more like the data between 2 and 3.5, but the red looks more like the data at 4. Of course, I haven't seen the real or imaginary plots, so that might not really be the case... In any case, you are wise to proceed the way you have. It is a very good idea to begin any new analysis project by exploring the various contributions from Feff. You can learn a lot by doing so and that knowledge is very helpful as you start to actually fit the data. It is certainly a poor idea to jump right into the analysis without exploring the contributions from Feff in this manner. I think that being able to visualize the individual contributions in an easy manner is what makes Artemis competitive with other data analysis solutions out there. Good luck. I'll be interested to hear what other have to say. B -- Bruce Ravel ----------------------------------- bravel@anl.gov -or- ravel@phys.washington.edu Environmental Research Division, Building 203, Room E-165 Argonne National Laboratory phone and voice mail: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://feff.phys.washington.edu/~ravel EXAFS software: http://feff.phys.washington.edu/~ravel/software/exafs/
Gerrit, It is sometimes difficult to qualitatively compare |chi(R)|, especially if you haven't applied sigma2 values to the Feff paths. Also, I couldn't tell what k-weighting you used (it shouldn't matter too much, but some non-focussed triangle MS paths decay quickly, so that k-weighting of 2 or 3 can focus on the 'strong scattering'). But other than that, it does seem likely that the 'red paths' are cancelling the others, and are probably a better description of the data at least between 2.5 and 3.2 Ang (it might be worse beyond that, but it's hard to tell). And, yes, such destructive interference can definitely happen!! Of course, you'd probably want to do that more quantitavely, but it gives a reasonable place to start.... --Matt On Mon, 9 May 2005, Gerrit Schmithals wrote:
Hello,
I want to fit a cobalt-porphyrin for which I have an atom.inp-file and EXAFS experimental data at Co K-edge . I started with a simple sum of paths for all paths with a distance below 5 A and an amplitude above 10 (see attachment). If one compares experiment (black curve) with this first fit (red curve) the first shell peaks overlap quite nicely but not the second and third (fourier transforms of the single paths are also drawn as blue and red curves). Then I excluded four paths (the red ones) and did a second sum of path. Now the other shell peaks overlap as well (green curve). The four exluded paths are multiple scattering paths via one nitrogen and one carbon atom. I conclude that the extinction of the second shell peak in the first simulation is due to the fact that these paths have a different phase shift than the other paths with a similar frequency.
Do I make a simple error (adjustments of the fitting parameters necessary?) or does that tell me something about the system? I appreciate any help.
Regards, Gerrit
Hello, thank you Matt and Bruce for responding to my question so comprehensively. I have learned that it is quite possible that multiple scattering paths do not contribute to the spectrum because of their large mean square displacement. Is that due to the fact that the mean square displacements are large for all atoms and for multiple scattering paths with more atoms involved the mean square displacements are multiplied? I now tried different variable combinations but it seems that it is quite complicated to fit the material for higher R. That is probably due to the fact that up to 5A FEFF calculates about 260 paths, 2/3 of them being multiple scattering paths. I found that it is not satisfying to exclude all paths with an amplitude <10 because there are a lot of paths with a similar Reff and Phase shift that in sum contribute noticeably to the spectrum. One easy way to obtain a fit that is not too bad was to exclude all multiple scattering paths. I then fitted with just one mean-square-displacement and one amplitude for all paths (see attachment). The fit looks somewhat better for higher k-weights, I am not sure if this is a fact to worry about. For k-weight=2 the peak positions up to the third peak are not too bad, the broad peak around 4A is not resolved. I could probably argue that for higher R-values the contributions of multiple-scattering paths may not be neclegted. Cheers, Gerrit
On Thursday 12 May 2005 05:03, Gerrit Schmithals wrote:
I have learned that it is quite possible that multiple scattering paths do not contribute to the spectrum because of their large mean square displacement. Is that due to the fact that the mean square displacements are large for all atoms and for multiple scattering paths with more atoms involved the mean square displacements are multiplied?
Multiplied, eh? That doesn't sound quite right to me. When you measure the sigma^2 you are, as you say, measuring the mean square displacement about the nominal length of the path. A three-body path has many more modes of vibration (or degrees of freedom, if you prefer that language) than a two-body path. Each leg of the path has a mean square displacement, but there are also angular modes of motion. That is, the atoms are vibrating along the directions parallel to the line between them, but they are also vibrating in angle about the scattering angle. So you can imagine that atoms are connected by springs and there are springs restoring the angle between bonds. Picture something like this (this silly little picture won't make sense unless you look at it with a monospace font): O O \ / \-----/ \ / \ / X The springs represented by the slashes might be quite stiff, but the spring represented by the dashes might be quite floppy. This situation might result in a sigma^2 for the three-body path that is quite large compared to the two body sigma^2s.
One easy way to obtain a fit that is not too bad was to exclude all multiple scattering paths.
That might be ok. One way to explain that is to say that between the effects of sigma^2 and the sum of a large number of paths with different phases, the net effect of all those MS paths is to be reduced to small background signal. In general, what you have done so far is a good start to a complicated fitting problem. I am a big fan of the strategy whereby you start with the simplest model, see how it fits the data, then add complexity as the problem warrents. For a similar approach to the problem of a highly complex system, you might want to look through Shelly's presentation from last year's NSLS EXAFS school: http://cars9.uchicago.edu/xafs/NSLS_2004/Kelly.pdf The bit around page 25 is particularly relevant to this conversation. Good luck! B -- Bruce Ravel ----------------------------------- bravel@anl.gov -or- ravel@phys.washington.edu Environmental Research Division, Building 203, Room E-165 Argonne National Laboratory phone: (1) 630 252 5033 Argonne IL 60439, USA fax: (1) 630 252 9793 My homepage: http://feff.phys.washington.edu/~ravel EXAFS software: http://feff.phys.washington.edu/~ravel/software/exafs/
Thank you, Bruce for that detailed explanation. The link to the presentation was very useful - although I sometimes scan the CARS-pages for information I somehow missed that. Cheers, Gerrit
participants (3)
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Bruce Ravel -
Gerrit Schmithals -
Matt Newville