[Ifeffit] several FEFF-questions
Bruce Ravel
bravel at bnl.gov
Mon Aug 11 08:48:07 CDT 2008
Eckhard,
I am sorry that you did not receive a response to your questions from
two weeks ago. The day your message appeared on the mailing list, I
was busy at the beamline. Ideally, the point of the mailing list is
to draw upon a wider pool of expertise so that if one person is
unavailable, another person steps up. It's a good idea....
As you can see I am responding to your original query rather than to
the follow up message you sent directly to me.
I am not certain that I can answer your questions fully, but I will
try.
> i read in the FEFF 8.4 manual, that the 6 modules are executed in
> ascending order. But now i'm confused concerning the modules 3 till
> 5. In module 3 the full multiple scattering is calculated. But only
> after this module the path enumeration (module 4) and the scattering
> amplitudes (module 5) are computed. I thought the path enumeration
> and the scattering amplitudes are required for calculation of the
> full multiple scattering? Why are these quantities calculated after
> the fms module? In my opinion this doesn't make sense.
You are not understanding things correctly. Full multiple scattering
is one way of computing the XAS function. A path expansion is another
way.
FMS is exact (within the limitations imposed by the approximations
made in the calculation, of course) in the sense that it computes all
orders of scattering within the cluster in one swoop. Because the
size of the angular momentum basis for the matrix algebra grows
quickly with energy, there is a practical limit in energy beyond which
FMS becomes computationally too expensive.
Path enumeration is inexact in the sense that at low k, it can be
shown that a path expansion is non-convergent. That is, near the
edge, you cannot possibly sum up enough paths to converge on the
result obtained by FMS. Fortunately the cost-per-path does not change
with energy and the number of paths required is quite modest away from
the edge. And, of course, the path expansion is useful for EXAFS
analysis. Even if you were willing to invest the resources to compute
FMS well above the edge, a path expansion would be more fruitful for
interpreting that part of the spectrum.
One strategy to computing the full spectrum (i.e. near the edge
through hundreds or thousands of volts above the edge) would be to
define a cross-over, using FMS before the cross-over and a path
expansion afterwards.
So, what does FMS need? FMS needs the potentials, which are computed
in the prior modules. Scattering amplitudes and phase shiftfs also
needs the potentials. So FMS needs modules 1 and 2. Scattering
functions need modules 1, 2, and 4. Computing the XANES requires FMS
or FMS+Scattering functions, depending on whether you are using the
cross-over strategy.
> Another question affects the paper (page 9 and 10) of Zabinsky et al
> (attached). In the section "path enumeration" (respectively one side
> bevor) he introduced the quantity r_tot = total path length and R =
> r_tot/2 = effective path length. My question is, what is the meaning
> of the effective path length? In my opinion r_tot is the way and the
> way back? And R < r_tot is the path length without negligible
> contributions (scattering amplitude,...), is this right?
I think you'll agree that, as long as we all agree on the ground rules
for the conversation, it doesn't actually matter whether we use R_tot
or R_tot/2. They don't differ in a significant way. If we agree and
do the right thing at all stages of the calculation, everything will
be cool.
That said, R_tot/2 is a much better choice. For a single scattering
path, R_tot/2 is the interatomic distance. The interatomic distance
is often the deliverable quantity in an EXAFS analysis. So, for SS
paths, R_tot/2 is the path of least confusion. For a MS path, R_tot/2
is the approximate position of the peak of the magnitude of the
Fourier transform of the MS path. This is only true when doing the
integral of Fourier transform of chi(k) over d(2k). That is the
widespread convention in EXAFS. It would be confusing, then, if the
language of XANES treated distance differently from the language of
EXAFS.
Conclusion: effective path length = yay!
> The next question concerns the XANES-Card. What is the meaning of k
> respectively xkmax? In my opinion k is the wavenumber (of the photo
> electron wave?) which occurs in the xmu.dat in the third column,
> isn't it?
According to the document (which is often a useful thing to consult)
http://leonardo.phys.washington.edu/feff/wiki/index.php?title=XANES
xkmax is the maximum k value of the XANES calculation. That is, the
FMS calculation will be made out to the energy corresponding to
k=xkmax.
HTH,
B
--
Bruce Ravel ------------------------------------ bravel at bnl.gov
National Institute of Standards and Technology
Synchrotron Methods Group at NSLS --- Beamlines U7A, X24A, X23A2
Building 535A
Upton NY, 11973
My homepage: http://xafs.org/BruceRavel
EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/
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