[Ifeffit] delR versus thermal expansion A and first cumulant C1*

Leandro Langie Araujo leandrolangie at gmail.com
Wed Oct 5 22:02:22 CDT 2005


Matt,

first of all, thank you very much for your reply. It was pretty coherent 
and  did help to settle some conceptual mismatchs that were bugging me.
As for starting a wiki on this, looks like a good idea to me. Specially 
if there are more people interested on the topic.

 > Hope that helps, or at least keeps the conversation going....

Following your suggestion above, I'd like to make some more questions, 
if you don't mind.... ;)

>To first approximation, dR/R from EXAFS is similar to dA/A from
>diffraction.  Many people have equated these. In detail, and
>especially at high temperature, they are not the same.
>  
>
Ok, that's understood. I guess I didn't express myself propelry in the 
previous message, sorry. The thing is that Anatoly and John define their 
thermal net expansion as a(T)=<r-r0>, r0 being the minimum of the 
pair-potential and r the bond length at a given temperature. This made 
me think that their a(T) could be directly related to dR/R from EXAFS 
instead of dA/A from diffraction.  Does this sound correct to you?

>delR is the first cumulant, C1, and is equal to the first moment
>of the distribution.  It is the displacement from the starting
>center value, R0, Reff, etc.
>
>There is actually a subtlety in getting delR=C1 from EXAFS, as
>the EXAFS is not simply exponential in R, but also has a 1/R^2
>term and R dependence in the mean-free-path term.  These can be
>dealt with (and are dealt with in Ifeffit/Feffit), so that the
>delR, sigma2, third, and fourth *are* the cumulants of the
>atomic pair distribution.  But that's not your question (yet??).
>  
>
Well, I think you already saw where I am trying to go... I was pretty 
sure that the values of sigma2 and C3 I was getting from the fits were 
the "real" cumulants of the atomic pair distribution, but I wasn't so 
sure about delR, because of the 1/R^2 and lambda corrections. I believed 
they would be there, and now you reassured me.

The thing is, I have these temperature dependent EXAFS spectra from 10 
to 300K to analyze. If I try to analyze each at a time, I get reasonably 
values with small errors for sigma2, which are insensitive to small 
variations on the fitting conditions. But the values obtained for delR 
and C3 are pretty wonky, have big errors and vary a lot with small 
variations on the fitting conditions (like k-weights, windows, E0 
values,...).
So, I was trying to make a multiple dataset fit, with all of them 
together. And I was trying to do it the same way you (Matt) and some 
other people did, which involves writing the cumulants as functions of 
the pair potential constants and the temperature. This way, the number 
of free parameters is drastically reduced, as well as the uncertainties 
on the determination of delR and C3.
But, as my data is not on the "high T" limit (unlike most people), I 
cannot use the same equations that you have used. I was using Anatoly's 
equations instead [PRB48, 585, 1993], where there is no direct mention 
to a first cumulant, only to the linear thermal expansion given by 
a(T)=<r-r0>. Looking at some other papers (like [Troger et al., PRB49, 
888 (1994)], [Yokoyama, JSR6, 323 (1999)], [Van Hung and Rehr, PRB56, 
43, 1997]), I saw people treating the thermal evolution of the first 
cumulant as being given by a(T).
So, my question now is:
- How reasonable it is to represent the thermal evolution of delR by 
Anatoly and John's a(T)? Should any corrections be added when relating 
this two quantities?

Sorry for another over-sized messaged and thank you very much for your 
attention.

Cheers,
Leandro





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