[Ifeffit] Re: sigma squared

Bruce Ravel bravel at anl.gov
Thu Mar 31 14:48:47 CST 2005


Hi Karla,

These are excellent questions for the mailing list, so I am taking the
liberty of CCing my answers to the list.  That way, other people can
have a chance to answer your excellent questions.

On Thursday 31 March 2005 14:10, you wrote:
> Hello,
>     I am fairly new to EXAFS data analysis.  I am currently working on
> data that I collected from 10-ID at the APS.

Aha!  My new home!  I just collected my first spectra from that
beamline a couple of weeks ago. ;-)

> I have a couple of questions.  First, in Artemis, when I click on
> the "x" buttons to select my k- and r-ranges, the window never seems
> to correspond to where I clicked.  Is this a bug?

Probably not.  The default in Artemis is use a Kaiser-Bessel window.
The various strange words to describe FT windows ("Kaiser-Bessel",
"Hanning", "Welch", and so on) refer to different functional forms for
the window.  None of the functional forms will be 0 at the specified
boundary -- instead they all have window sills that extend a bit below
the boundary.  Thus, if you use the Kaiser-Bessel window, set kmin=2,
and dk=1, the window will become non-zero at about 1.5.

In short, it's not a bug.  It's an unexpected (for you, at least ;-)
feature of the functional form of the window.

Try setting dk or dr to 0 then replotting.  The FT may not look good,
but the window plotted by Artemis will be what I think you were
expecting.

> Second, why does Artemis allow a physical parameter like sigma
> squared to be negative?

There are a few ways I could answer this question.  I could talk about
how Artemis allows arbitrarily sophisticated fitting models where the
sophisticated user needs complete freedom to specify the fitting
model.  But that's a little abstract, so let's consider a slightly
more concrete example.

Suppose that your sample has some kind of oxygen-coordinated iron atom
and you have reason to believe that there is a high level of disorder
in the first coordination shell.  So you choose to run Feff using some
model compound that itself has much disorder in the first shell.  You
then use the first shell paths that came from the Feff calculation to
model your unknown data.  In this case a negative sigma^2 might be
telling you that your unknown has *less* disorder than you model
compound.

In more general terms, the negative sigma^2 is probably trying to tell
you something.  You should remember that sigma^2 is correlated to
other terms in the fit, most importantly to the various amplitude
terms, such as coordination number and S02.  If sigma^2 is negative,
then the fitten value for amplitude is probably to small.  A negative
sigma^2 will puff up the signal to compensate for the amplitude term
being rather too small.  If Artemis did not allow sigma^2 to go
negative, you might never know about this kind of problem.

So I would say that this too is a feature of the program and not a bug.

> Lastly, I have had a hard time figuring out these math expressions
> despite reading over the mailing lists.  Can you use the ">" sign so
> that sigma squared is always greater than 0?  How else can I write a
> math expression so that the fitting never gives me a sigma squared
> that is less than 0?  Any help would be greatly appreciated!

Using ">" won't work.  ">" is not a symbol in Ifeffit's math parser.

This is a topic that has come up many times over the past few years on
the mailing list.  In fact, I think that someone should write a FAQ
entry on this topic.

Here are a few suggestions:

1.  Guess a parameter like this: "guess  ss  0.003", then use it on
    the sigma^2 line of the path page like this: "abs(ss)".

2.  A very similar approach is to use the max function.  In the
    sigma^2 line of the path page, say this: "min(ss, 0)".  This can
    be improved slightly.  Doing this: "min(ss, 0.001)" constrains the
    sigma^2 for the path to be no smaller than 0.001.

3.  If you start reading the mailing list archives here:
       http://millenia.cars.aps.anl.gov/pipermail/ifeffit/2005-February/001650.html
    you will find a conversation between Matt and Scott about a way to
    impose a penalty for a sigma^2 being too small rather than forcing
    to be above a hard boundary.  Matt's scheme is kind of involved...

If you use any of these approaches, I would encourage you to do so
with hesitation.  As I mentioned above, the negative sigma^2 is not a
short coming of Ifeffit or Artemis.  Much more likely, it is useful
information that you should heed and use to figure out what
shortcoming in your fitting model is leading that to happen.

HTH,
B






-- 
 Bruce Ravel  ----------------------------------- bravel at anl.gov  -or-
						  ravel at phys.washington.edu
 Environmental Research Division, Building 203, Room E-165
 Argonne National Laboratory         phone and voice mail: (1) 630 252 5033
 Argonne IL 60439, USA                                fax: (1) 630 252 9793

 My homepage:    http://feff.phys.washington.edu/~ravel 
 EXAFS software: http://feff.phys.washington.edu/~ravel/software/exafs/






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