[Ifeffit] fitting a specific k range

Bruce Ravel bravel at bnl.gov
Thu Dec 5 09:11:20 CST 2013


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 at bnl.gov

  National Institute of Standards and Technology
  Synchrotron Science Group at NSLS --- Beamlines U7A, X24A, X23A2
  Building 535A
  Upton NY, 11973

  Homepage:    http://xafs.org/BruceRavel
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