[Ifeffit] Fit in R and k space

[Michel Schlegel]

Hello everybody,

>Thinking about problems. You once told me that:
>
>>   Fitting in unfiltered
>>k-space also gives erroneous R-factors, as was recently
>>discussed here.
>
>would you give me a direction to the discussion about this point that I 
>can read?

Pardon my poor knowledge of EXAFS fitting and reliability of the results, 
but more generally, I wondered if EXAFS fitting in raw unfiltered k-space 
is always relevant.

Let me explain it; I do agree that in certain cases, when the whole 
structure is known and all EXAFS contributions well modelled by an 
ab-initio model (e.g., feff), you may well reproduce all oscillations of 
the EXAFS spectrum, and then fitting in raw k can be OK.

However, more often than wanted, the fitting is done with a structural 
model including only the first few shells. With these shells, we model not 
only the actual contributions from the neighboring shells, but also that 
from the more distant shells. Physically, it can be demonstrated that this 
would not be a problem if the EXAFS signal had a constant amplitude and 
would spread over an infinite range in k space. However: (a) EXAFS 
contributions have not a constant amplitude, and (b) they can be recorded 
over only a few Å-1. So maybe  (or even surely, I daresay), the 
contribution from non-modelled distant shells would affect the structural 
parameters from the modelled shells.

Finally, another issue - for which I would not lay out my neck, though - is 
the noise. In EXAFS, the signal to noise increases with k, and of course 
fitting in the raw k space is another way of dealing conveniently with the 
noise -or relative uncertainty, as we may name it. However, the FT is a way 
of filtering out some of this noise, and so maximise the signal from a 
shell. Likewise, fitting in filtered q-space may yield more accurate 
results, because some of the noise is filtered out. However, I concur that 
somehow the fact that the uncertainty on the high-q part of the filtered 
contribution os greater than in the low q-part should be implemented somehow.

So there are my own reflexions. Maybe some people have already worked on 
that, and there are some publications that I've missed (shame on me!). If 
that's the case, I would welcome any insight.

Best regards,

Michel Schlegel

-- 
Michel Schlegel
Commissariat à l'énergie atomique
CEN de Saclay, DEN/DANS/DPC/SCP/LRSI
Bat 391 - Piece 205B
F91 191 Gif-sur-Yvette Cedex, France
Ph:  +33 (0)1 69 08 93 84
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