[Ifeffit] EXAFS mean free path in small particles

[Matt Newville]

Hi John,

> In the meantime, the self-energy can be adjusted in fits, e.g.
> to the mean free path. I'd be interested in hearing
> experimental evidence for the need for such corrections.

Yeah, I don't know of a very good experimental test for loss 
terms other than analyzing the heck out of good data.  

Trying the 10K Cu data, it turns out that I do get a better fit
to the first shell when adjusting all of {S02, Ei, ThetaD} than
when adjusting only {S02, ThetaD} and leaving Ei=0 (ie, using
only Feff's loss terms).

I get these results (using feff calculations from Feff 8.20):

|-----------------------------------------------------------------|
|Fit  S02       ThetaD    Ei        E0        dR       chi_reduced|  
|-----------------------------------------------------------------|
|#1  0.93(0.03) 271(12)  0.0( - ) 0.7(0.4) -0.003(0.002)  12.8    |
|#2  0.78(0.09) 300(23) -1.5(0.9) 0.7(0.3) -0.003(0.001)  10.9    |
|-----------------------------------------------------------------|

By refining Ei, reduced chi-square (not just chi-square!!) is
better and the refined Debye Temperature is closer to the
"known" value (315 K).  Ei is actually negative when refined,
which makes S02 smaller.  Curious, huh? 

Of course, S02 and Ei are very highly correlated (~0.97) but
both best-fit values have definitely moved away from the result
when Ei is set to 0.  It's seems pretty hard to say that the
"leave Ei=0" fit is better.

More details of this, including figures and all fit data, feff
files, and scripts are at
  http://cars9.uchicago.edu/~newville/Feff_MFP/

I have not done this with multiple temperatures, but that 
might be a slightly more robust test.

Cheers,

--Matt