[Ifeffit] Linear combination fitting

Wed Apr 8 16:20:32 CDT 2009

Dear Mengqiang,

> "If the component sum is close to 1, it means that no significant  
> component is missed in the LCF fitting."

I'd say that this statement is not generally true.

It basically goes back to another question: "Does the XANES portion  
(if fitting norm(E)) or the EXAFS portion (if fitting chi(k)) of a  
standard carry enough information for unambigously relating a single  
chemical compound to a unique spectrum, that additionally is linearly  
independent of all combinations of other possible spectra".

Chemical space is huge. This means, that there will be a case where  
two or more compounds map to very similar spectra (thus breaking the  
unambigiousity). There will also be a case where the weighted sum of  
spectra of compounds A+B+C... equal compound X (thus breaking linear  
independence). Both cases invalidate the statement.

A way of tackling this problem is by adding other information.  
Usually, when doing a LCF, one is working in a very limited  
composition space. If you have knowledge about the components of a  
chemical system, and maybe even about the phase diagrams of this  
system, you can be much more confident with selecting appropriate  
standards for the LCF.

After recording the standards for this system, you could then test for  
linear independence and for ambigiousity by trying to fit one standard  
with linear combinations of the other standards. For this, the  
combinatorial fitting tool of Athena is quite nice :-) If none of your  
standard spectra can be described by linear combinations of the other  
standards, you can be quite sure about the unique and independent  
mapping beween chemical compound and spectrum. In this case, I would  
also feel that after fitting an unknown compound from the same  
composition space, a residual close to unity most likely means that  
you've missed no important contribution.

Cheers,
dominik

Quoting mzhu at udel.edu:

> Hello Dominik,
>   Based on your reply about LCF analysis, is the following statement true?
>
>   "If the component sum is close to 1, it means that no significant  
> component is missed in the LCF fitting."
>
>   If it's true, could you please provide some reference articles for  
> that? Thanks.
>
> Best wishes,
>
> Mengqiang Zhu
>
>
>
>
>
>
> -----------------------
> Mengqiang Zhu
> Ph.D Candidate
> Environmental Soil Chemistry
> Department of Plant and Soil Sciences
> University of Delaware
> 152 Townsend Hall
> Newark, DE 19716
> http://ag.udel.edu/soilchem/zhu.html
>
>
> ---- Original message ----
>> Date: Tue, 07 Apr 2009 22:17:21 +0200
>> From: ifeffit-bounces at millenia.cars.aps.anl.gov (on behalf of  
>> Dominik Samuelis <d.samuelis at fkf.mpg.de>)
>> Subject: Re: [Ifeffit] Linear combination fitting
>> To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
>>
>> Dear Guvenc,
>>
>> Shelly and Scott have already replied to this issue, and I fully agree
>> with their points. Nevertheless, I'd like to add some points, that
>> generally apply to linear component fits.
>>
>> The huge discrepancy between chi(k) and norm(E) fit very likely is an
>> indication that your data is not sufficiently described by your
>> standards. It might be that you're either using a standard component
>> that is not present in your system, or that you have not only two, but
>> three or more components in your system.
>>
>> There is a number of ways to check which one could be the case. Very
>> often it helps to fit the system without the restriction that the
>> weights of the standards must sum to one. That way, you effectively
>> allow for the determination of a residual component during the fit. If
>> your system is sufficiently described by the standards, the weights of
>> the standards should sum to a constant value close to unity. The
>> difference to unity basically gives the residual.
>>
>> If you have a non-negligible (or even concentration-dependent)
>> residual, PCA might help you to determine how many standard components
>> actually are required to fit the system. Be aware, though, that the
>> interpretation of PCA results is somewhat complicated. If PCA shows
>> that you need 4 linearly independent quantities to fully describe your
>> system, it doesn't necessarily mean that your system has 4 components.
>> Even temperature differences between scans might manifest as an
>> additional "component".
>>
>> Cheers,
>> dominik
>>
>>
>> Quoting Guvenc Akgul <gakgul at aps.anl.gov>:
>>
>>> Dear all,
>>>
>>> I have done Ti doped ZnO EXAFS data analysis but I guess it  is
>>> getting mixture structure at high concentration for example 55% Ti
>>> doped ZnO.Also I done linear combination fit , but at  fitting space
>>> norm(E),ZnO weight is 0.779 and ZnTiO3 is 0.221 then I changed
>>> fitting space is chi(k)  ZnO weight is getting 25.2 and ZnTiO3 is
>>> getting 74.8 and it is not same like at fitting space norm(E) why?
>>>
>>> regards
>>>
>>> guven
>>> _______________________________________________
>>> Ifeffit mailing list
>>> Ifeffit at millenia.cars.aps.anl.gov
>>> http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
>>>
>>
>>
>>
>>
>> --
>> Dr. Dominik Samuelis
>> d.samuelis at fkf.mpg.de
>> Max-Planck-Institut für Festkörperforschung
>> Max Planck Institute for Solid State Research
>> Heisenbergstr. 1
>> 70569 Stuttgart
>> Germany
>> Phone +49-711-689-1769
>> Fax   +49-711-689-1722
>> Web   http://www.fkf.mpg.de/maier/
>>
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>
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-- 
Dr. Dominik Samuelis
d.samuelis at fkf.mpg.de
Max-Planck-Institut für Festkörperforschung
Max Planck Institute for Solid State Research
Heisenbergstr. 1
70569 Stuttgart
Germany
Phone +49-711-689-1769
Fax   +49-711-689-1722
Web   http://www.fkf.mpg.de/maier/