The usual justification for using gaussians for peaks, aside from "it
works" is that there's inhomogeneous broadening over and above the
lifetime.  The usual justification for using an arctan for the step is
exactly the opposite.  Instrument broadening is often taken to be
gaussian.  Net result:  A (pseudo)Voight for peaks often works.  One
issue is what to do about the post-white-line peaks, which sometimes
are viewed as the first EXAFS wiggles.  Manceau has a nice paper about
S XANES  (I don't have the ref handy right now) in which he goes
through peak fitting and evaluates its uniqueness.
   mam

On Thu, Dec 8, 2016 at 5:40 AM, Matt Newville
<newville@cars.uchicago.edu> wrote:
> Hi Stephanie,
>
>
>
> On Wed, Dec 7, 2016 at 12:33 PM, Stephanie Laga <stephanie.laga@yale.edu>
> wrote:
>>
>> Dear all,
>>
>> I am trying to extract the % Ce(III) from some CeO2 nanoparticle XAS data.
>> I have been using moved the peak fitting function in Athena to model the
>> XANES with an arctan background function and a series of gaussians.
>>
>> Looking through the literature I haven't seen too many specifics to using
>> this approach (rationale for choosing the widths of peaks or how to define
>> the background function). Similarly, doesn't seem to be much rationale for
>> choosing a 4 vs 5 peak fit for the XANES.
>>
>> My main question is then...1) Is there a rational for picking the
>> background function, specifically the height and width (can I let the height
>> vary or should I be keeping a constant arctan through all samples)?
>>
>> Any advice is greatly appreciated!
>>
>> Stephanie
>>
>
> Matthew answered quickly, but sort of changed the subject, suggesting a
> different analysis (LSQ) and then discussing some of the pitfalls of that
> approach.  Your original question is still worth discussing.
>
> There is not a whole lot of justification in using one particular shape for
> the background.  A step broadened as arctan, error function are common and
> seem to work well. Each has some theoretical explanation in that the
> integral of a series of Lorentzian gives an arc-tangent function while the
> integral of a series of Gaussians will give the error function. (If this is
> wrong, can someone please correct?).  If you think as the above edge
> spectrum as a series of finely spaced individual transitions, then these
> functions have some justification.    Whether it actually works well in
> detail on a particular spectrum is a separate question.   FWIW, I've also
> seen people use (successfully) a single, very broad Lorentzian for the "main
> edge".
>
> The use of Lorentzians, Gaussians, Voigts, and PseudoVoigts is somewhat more
> justified in that those are how you would expect a single electronic
> transition to appear, especially broadened in the way(s) you'd expect a
> monochromatic X-ray beam to be energy broadened.  Using such functions is
> essentially asserting that there is a single electronic transition at that
> energy, and you want to know it's size and shape.  This is not wrong, but it
> does not inherently include any understanding of what that peak is. For
> pre-edge peaks, it's pretty well-justified, and works pretty well.  For
> peaks on or after the main edge or "white line", it's less justified because
> we know that EXAFS-like effects can be important.
>
> The biggest dangers in the peak-fitting approach are:
>    1) one always gets an answer, and that is rarely "no, this is not the
> right model to use".  In fairness, most linear algebra methods used for
> XANES analysis or really most other spectroscopies have the same feature.
>    2) interpretation of the results can be challenging, or at least it is
> hard to know when they are misleading.  Again, most linear algebra methods
> used for XANES analysis or really most other spectroscopies have the same
> feature.
>    3) it can sort of willfully ignore other parts of the spectra.  In
> fairness, we all do this sort of thing all the time.
>
> Hope that helps.  Peak fitting is not exactly "theoretical XANES analysis",
> but it is not always done in an ad-hoc manner out of ignorance either.
>
> Linear algebra techniques are completely justified too.
>
> Hope that helps,
>
> --Matt Newville
>
>
>

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