[Ifeffit] Linear combination fitting

mzhu at udel.edu mzhu at udel.edu
Wed Apr 8 19:11:06 CDT 2009


Hello Dominik,
  You explaination about LCF fitting is very clear. 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: Wed, 08 Apr 2009 23:20:32 +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 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
>>>> _______________________________________________
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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/
>>>
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>>> Ifeffit mailing list
>>> Ifeffit at millenia.cars.aps.anl.gov
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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/
>
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