First, a disclaimer--I haven't looked at the data Matt sent (it's a busy time of year!), but I disagree in a general sense with my reading of what Bruce wrote (perhaps I am reading it wrong). In particular, I disagree with this statement:
Given that you are fitting in q-space, it is completely unreasonable (from a numerical perspective) to expect that the fit could possibly reproduce a feature that you have (intentionally or otherwise) filtered out of the data.
To say that another way, given how you constructed the fit, you got a good fit. You made the fit in a way that it cannot possibly reproduce the feature you are asking about, thus your question is ill-posed.
To explain why, suppose I am fitting a standard--for the sake of a simple example, suppose it's copper. I include in my model paths out to 7 angstroms, including multiple-scattering paths, and use a Debye model for the MSRDs. It's possible to do a pretty good job in that kind of fit with just a few free parameters: S02, E0, an isotropic lattice expansion, and a Debye temperature. Now, suppose I perform the fit from 1 to 3.5 angstroms. Usually, the fit will do a pretty good job reproducing features well above 3.5 angstroms, because they're in the model (the paths are included) even though they're not in the fitting range. That's true for features in k-space that are caused by high-R paths too, of course.
In fact, that kind of fit is particularly valuable to me, because it strongly suggests I've got the model right--I've essentially hid the high-R data from the numerical routines, so if it fits that region well anyway, it's probably because the model itself is a good one.
While I defend that principle as a very important one, I'm not claiming it applies in Matt's case--it probably doesn't. To reproduce features at high-R, it IS necessary to have a model (i.e. paths) that cover the high-R contribution, and it sounds like Matt does not have those paths included in his model. But it's not necessary to FIT up to high R.
--Scott Calvin
Sarah Lawrence College
P.S. My least favorite warning that Artemis provides is the one that tells you that you're including paths outside the fitting region, for just this reason. It's easy enough to change the preferences so that Artemis doesn't give that warning, and it's usually one of the first things I have my students do when they're first learning to fit.
On Dec 5, 2013, at 10:11 AM, Bruce Ravel
Matt,
At the risk of coming off sounding a bit mean, I don't think you are asking a very well-posed question.
Examining the history of this project, I see that you are fitting in q space. Like Matt, this is not my favorite choice, but there is nothing horribly wrong about it, so long as you understand what you are doing.
What is problematic is your expectation that, in doing so, you should be better able to fit a particular feature in k space. If you examine the data in k and q space, you will see that the act of Fourier filtering the data (i.e. plotting in q space) has the effect of suppressing the wiggle at 5 inv. Ang. that you are asking about. Given that you are fitting in q-space, it is completely unreasonable (from a numerical perspective) to expect that the fit could possibly reproduce a feature that you have (intentionally or otherwise) filtered out of the data.
To say that another way, given how you constructed the fit, you got a good fit. You made the fit in a way that it cannot possibly reproduce the feature you are asking about, thus your question is ill-posed.
I think the deeper problem is that you don't have a deep grasp of what happens in Fourier analysis. So let's talk about that a bit.
When you do the transform from k to R-space, you are representing the frequency spectrum contained in the original data. Slow wiggling features in the original data give rise to the low-R (i.e. low-frequency) features in the chi(R) data. Fast wiggling features in chi(k) give rise to high-R features in chi(R). Your wiggle at 5 inv. Ang. looks to my eye like a pretty high frequency feature.
When you do the backwards transform from k to R with a restricted R range (in your case, from 1 to 3.5), you are filtering frequencies out of the data. The chi(q) data only contains those frequencies from the original chi(k) spectrum that fall in your R range.
What I am suggesting is that the wiggle in question is due to Fourier components beyond 3.5 Ang in chi(R).
So, how would you reproduce that feature in chi(k)? That's simple -- fit features in the data beyond 3.5 in chi(R). That is, do an actual good job of fitting the small signal from 3.5 to 5 Ang in R.
Of course, that's going to be difficult to do in a statistically robust manner because the signal is very small, there will be quite a large number of paths contributing to that region, and the parameterization of many paths for such a small signal is likely not to be very robust. EXAFS is hard!
Hope that helps, B
On 12/04/2013 02:17 PM, Matt Frith wrote:
Dear All,
I need some help in fitting an amorphous iron oxyhydoxide sample. I am having difficulty producing a good fit, particularly in the k=4-6 range. Fitting this region well is very important for me, because if I add another metal(+3 oxidation state) into my system, this is where I observe the most quantifiable changes (The shoulder @ 5 A^-1 and the min @ 5.6 A^-1). Thus far I have been unable to fit the shoulder well enough to make meaningful comparisons.
I have been fitting in kq with kmin=2.566 And kmax=10.877, and Rmin=1 and Rmax=3.5, and using the goethite O1.1, Fe.1, and Fe.3 paths. Attached is an Artemis file (P41_006_merge_norm_TRANS.fpj) for an amorphous Fe oxyhydroxide sample (Fe only, no other metals). The data was collected at the Fe K-edge.
*Is there a way to fit just this region (k~4-6 range) in k? If so what is the best method for doing this? If not, does anyone have suggestions as to how I can improve my fitting? Should I fit the data in k since the shoulder is less evident in kq?*
Thank you for your time.
Sincerely,
Matt Frith
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-- Bruce Ravel ------------------------------------ bravel@bnl.gov
National Institute of Standards and Technology Synchrotron Science Group at NSLS --- Beamlines U7A, X24A, X23A2 Building 535A Upton NY, 11973
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