[Ifeffit] RE: Using more than one E0 correction

[Matt Newville]

Hi Wojciech,

> My question is the following: does anyone of you have some
> experience with such procedure? And if yes, shall than distinguish
> between the first shell of nearest neighbors and the rest of the
> atoms in terms of their E0 corrections (using 2 parameters)? Or
> perhaps one can use separate E0's for each path?

I'd say it's not usual to need more than 1 E0 parameter.  In some
cases, two distinct E0's (that is, outside their error bars) are
helpful in a fit.  I'm not sure there is a sensible way of
predicting which cases these would be, but it seems to have been
needed most clearly in solids with fairly ionic bonds.  And yes, it
generally ends up that using one E0 for the first shell and another
E0 for the rest of the paths is what ends up with distinct values.

I don't recall a case of needing more than two E0's, probably 
because the error bars just get too large.

> The second question concerns the background correction in Artemis:
> I was trying to find an easy explanation of what this procedure
> does during the fit but I guess I'm still somewhat confused how
> one can judge whether the spline co-refinement does the right job?

Sadly, I'm not sure how to judge whether it does a good job other
than by visual inspection.  The refinement method is pretty simple,
with only a few additional ingredients from a 'normal fit'.  First,
instead of modeling the measured XAFS chi(k) as Sum_of_Feff_Paths,
it models as
   chi_model(k) = Spline(k) + Sum_of_Feff_Paths(k)

The Spline(k) here (written as the *.kbkg array after the fit is
done)  has adjustable parameters (y-values through which the curve
must pass) spaced evenly in k.  The number of spline parameters is
  N_spline = 1 + 2*(kmax-kmin)*rmin / pi

The fit is then not between R=[rmin,rmax], but between R=[0,rmax]
The idea is that everything below rmin is 'background' and above 
rmin is 'data'.  In that way, rmin acts like Autobk's Rbkg.

In principle, the structural parameters should only affect the model
above Rmin, and the spline parameters only affect the model below
Rmin.  An important point is that because all the parameters are
refined together, we can determine their correlations: how does
changing the background affect E0, deltaR, N, etc, and have these
correlations included in the estimate of the uncertainties.

> Some people on this mailing list underline that one should avoid
> high correlations between fitting parameters and background
> parameters in order to make sure that the fit is correct. 
> But is it the only criterion? 

You can't avoid the high correlation between E0 and deltaR or
between N*S02 and sigma2.  I'd say that it's not that you want to
avoid high correlations, but that you want to understand their
impact on the analysis.  They definitely alter the uncertainties in
the fitted parameters.

The better criterion for whether a fit is believable ("making sure
the fit is correct" is a pretty high standard!!) is whether
chi_square is small, whether the model is reasonable, and whether
the adjusted parameters have some physical meaning and believable
values and uncertainties.  Sorry I can't be more specific than that.

> In some of my fits background line looks kind of constant over the
> entire R-range which was taken into the fit. Sometimes it becomes
> like a modulation peaking underneath some scattering paths' even
> if the background parameters don't correlate significantly with
> fitting parameters I have my doubts whether the result is
> trustful. Any hints about this procedure?

I'm not sure I understand you here.  The background looks constant
in R-space??  That does seem strange.  Can you give more details?

Hope that helps or is at least a start....

--Matt