[Ifeffit] choosing k-weight

[Bruce Ravel]

On Thursday 19 February 2004 08:17 pm, Peter Southon wrote:

> I'm wondering what principles you have to determine the appropriate
> k-weight to use for FTs. Until now I've used guidelines from a textbook by
> Teo, based on the Z of the backscattering atoms:
> Z > 57; kw = 1
> 57 > Z > 36; kw = 2
> Z < 36; n = 3

I have a couple of things to add to what Shelly and Scott have already
said on the k-weight topic.

I think it is important to understand the rationale behind the
guidelines Peter quotes from Teo.  Atoms with low Z number have
backscattering amplitudes (i.e. the F(k) function which Ifeffit reads
from the feffNNNN.dat file) that have a peak at low k and tail off to
almost nothing at high k.  For instance, O, N, and C backscattering
pretty much dies out above k=10.  On the other hand, atoms with high Z
numbers have rather small baskscattering amplitude at low k, but their
scattering carries on to extremely high k.  As an example, see
Rev. Sci. Inst. v.71 #6 (2000) p. 2422.  In figure 9, we see
oscillations on a rhodium foil K-edge spectrum out past 30 invAng.

So, the point of Teo's guideline is to try to "even out" the
oscillations.  That is, to try to make the oscillations near the end
of the fitted spectrum about the same size as the oscillations near
the beginning.  That way, every part of the data contributes to a fit
evenly, in some sense.  Thus, what Teo was really suggesting was to
choose a k-weight that does this for your data.  I think that is not
seeing the whole picture, however, as both Shelly and Scott have
already explained.

As Shelly suggested, Matt has taken a slightly different attitude in
Ifeffit (and Artemis, of course, follows that lead).  Ifeffit allows
you to choose the k-weight of your choice, but it also allows you to
choose 2 or more k-weights for your fit.  Thus the chi-square fitting
metric includes a sum over k-weights as well as a sum over data
points.  (See section 5.1 of
http://cars9.uchicago.edu/feffit/feffit.ps.  Eqn 5.1, then, becomes a
double summation.)  In Artemis, this is done by clicking more than one
k-weight button on the page with the data parameters.

As a final point, there is no reason that the k-weight *must* be an
integer.  If you are itching to k-weight your data by pi or by the
Euler-Mascheroni constant, Ifeffit and Artemis both allow you do
that. 

HTH,
B


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