[Ifeffit] programming error in Hephaestus??

Matt Newville newville at cars.uchicago.edu
Fri Jun 1 10:29:54 CDT 2007


Hi Irmi,

This is not a programming error -- the cross sections in the various
tables that Hephaestus can use do vary, sometimes by as much as 10%.
That reflects the current (or perhaps "historic") uncertainty in the
absolute values of the actual cross-sections.

For EXAFS (and even XANES), the absolute values of the absorption
cross-sections rarely matters.  We're more interested in the variation
with energy over short energy scales, and are  almost always making a
differential measurement anyway.   We "never" (more later) take into
account the airpaths, thicknesses and compositions of x-ray windows,
and so on.   So for XAFS needs, knowing the absolute absorption to 10%
or so is fine.

If there are discrepancies between the tables, I would not know which
ones are more correct.  I believe the general wisdom is (where
"inaccurate" means ~10%):
  -   the Henke tables tend to be more suited for low energy, and may become
      inaccurate at  higher energies (and end at 30 keV).
  -   the Cromer-Libermann tables weren't really designed for mu, but
do an OK job.
  -   the McMaster tables use a single parameterized function for all
cross-sections, and
      is also fairly old.  They are efficient, but possibly inaccurate.
  -   the Chantler and Elam tables are probably the most accurate in general.

My understanding is that Chis Chantler (U.Melbourne) is actively
working on absolute measurements of absorption cross-sections,  but
that not many other groups are.  Perhaps your group is?

Now on to your questions:

> To make it short, I think I have found an error in the tool. In the tool
> "formulas" I took Kr, 30000 eV and get:
> the Absorbtion length: 15.031 cm (Resources Henke)
> : 14.431 cm (Resources Elam) which I also found in NIST Database
>
> then use the tool "Ion Chamber"
> put in Kr (only one gas), 10cm pathlength, 760 Torr, 30000 eV
> I got for Percentage absorbed: 48.58% (Resources Henke) which is correct
> I think: 39.22% (Resources Elam) which is wrong I think
> In my eyes the correct result for 14.431 cm Absorbtion length has to be:
> 49.99% absorbed photons.

Why do think one is correct and another wrong?  Have you measured it?
The measurement is not as easy as some might think....    It would
seem strange to me that the Henke tables are more accurate at its
highest energy point than all the other tables:

Kr at 30 keV
       Table        barns/atom
        Elam           2578.2
        McMaster    2601.7
        Henke         2475.3
        Chantler     2560.4
        C-L             2490.1

The range is ~5%, with Elam and Chantler in good agreement and Henke
the lowest value.

> It is critical for me, since the correct flux measured with the
> ionisation chamber goes directly in my results.

Then using tabularized data is something you'll want to avoid!  You
may want to think about how your measurements might be immune to
inaccuracies in the absolute flux....

> We investigated the detector response on monochromatic X-rays at HASYLAB of
> a widely used flat-panel detector in medicine.
>
> And I have also a question to you: Why do you use 30 eV/e- as ionization
> energy for the gases? Is there a reference for that?

I believe the ionization potentials are in the CRC, and also here
(from a quick google search):
  http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/ionize.html

When I do these calculations, I typically use 32eV  for all gases, so
that it nicely cancels the electron charge in coulombs.   Then again,
absolute accuracies that are better than 50% is not important to me.
 And again, to be much more accurate, I think you'd have to be careful
about other factors (gas purity, voltage dependence of total current,
space charge effects, harmonics, barometric pressure, and so on).

> In addition, don´t we have to take the room temperature into account not
> only the pressure, that means:
> Density(Temperature) = (273,15K/293,15K)*0.003749g/cm^3(at 273,15K)

That's right, the temperature is assumed to be "standard".  Again, if
the goal is high precision, one would need to take many factors into
account.

--Matt




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