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

[Leandro Langie Araujo]

Dear all,

I’m writing because I’ve been trying to analyze some thermal dependent 
EXAFS data for the first shell of a c-Ge sample and ended up in a 
conceptual confusion. If any of you could give me some help on this I’d 
be very grateful.

Whenever we fit an EXAFS spectrum with Artemis/IFEFFIT, we get a /delR/ 
value. As far as my (very) limited comprehension goes, /delR/ is the 
difference between the theoretical (FEFF8) bond length, /R0/, and the 
result of the best fit to my data, /R/, which gives the experimental 
bond length. So, this should be the /first cumulant/ of my distance 
distribution, right?

The net linear thermal expansion /A/ (as defined by Anatoly Frenkel and 
John Rehr in [PRB48, 585, 1993]) from an one-dimensional model seems to 
have been considered as equal to the temperature variation of the /delR/ 
values by several people, including Matt Newville (on his thesis). 
Following this approach, it is possible to relate the EXAFS cumulants 
(/delR/, /ss/, /C3/ and /C4/) of the distance distribution with the 
constants of an one-dimensional anharmonic effective potential, 
following a correlated Einstein model. I was going through this path...

… when I came across some papers (P. Fornasini and G. Dalba in [PRL82, 
4240, 1999; PRB70, 174301, 2004] and E. A. Stern in [J.Phys.IV 7, 
C2-137,1997]) where an issue is raised; it is said that the thermal 
evolution of the first cumulant /C1/* of the real distance distribution 
in a crystal (which was said to be equivalent to /delR/) is NOT equal to 
/A/, because in a crystal there are vibrations perpendicular to the bond 
direction which are not considered in the one-dimensional model. It is 
argued that the temperature dependence of these vibrations perpendicular 
to the bond direction give raise to a positive shift of the minimum of 
the effective pair potential, while the net thermal expansion /A/ 
accounts only for changes due to the asymmetry of the potential.

So, the main questions hammering my head are:
- does /delR/ include any contribution from vibrations perpendicular to 
the bond direction? Can really /delR/ and /C1/* be the same quantity?

- is the thermal evolution of /delR/ equal to the net thermal expansion 
/A/? Or should some correction for perpendicular vibrations be added to 
relate both quantities?

Sorry if I made it too long, but it was something hard to express in a 
few words…
Any help will be greatly appreciated.

Cheers,
Leandro