[Ifeffit] sigma^2 values for multiple scattering paths (Scott Calvin); Re: Ifeffit Digest, Vol 92, Issue 4

Han Sen Soo hssoo at lbl.gov
Wed Oct 6 12:36:25 CDT 2010

Hello Scott,
Just to make sure I understand what you mean, are you saying that in your 3 atom system, the S1 and S2 atoms have relatively fixed locations but A may have large vibrational amplitudes in the A-S1 and A-S2 directions? So the round-trip 3 atom MS path has a small sigma^2 value since the variation in the A-S1-S2-A path is dictated by the more or less fixed S1 and S2 end-points (with minimal perpendicular contribution), whereas the 2 individual SS paths have large sigma^2 value due to the large A-S vibrations?

I tried setting the sigma^2 value to a reasonable number for the MS path and it appears to increase the R factor slightly and tries to maximize the floating degeneracy I set (with a restrain to be physically reasonable based on my model). It does not look as good but at least it seems more plausible. I will try out Shelly's suggestions to see if they work too. I guess what I wanted to find out is whether the model I included is telling me that something is terribly wrong.

Thank you all again for your responses!
han sen

On Oct 6, 2010, at 10:00 AM, ifeffit-request at millenia.cars.aps.anl.gov wrote:

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>   1. Re: sigma^2 values for multiple scattering paths (Scott Calvin)
> ----------------------------------------------------------------------
> Message: 1
> Date: Wed, 6 Oct 2010 09:39:49 -0700
> From: Scott Calvin <dr.scott.calvin at gmail.com>
> To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
> Cc: "Dr.Scott.Calvin at gmail.com" <Dr.Scott.Calvin at gmail.com>
> Subject: Re: [Ifeffit] sigma^2 values for multiple scattering paths
> Message-ID: <AB39966C-893D-4947-BED2-A26FC6534315 at gmail.edu>
> Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
> Although I agree with the main points that Bruce makes, I do want to  
> comment on one piece:
> On Oct 6, 2010, at 7:03 AM, Bruce Ravel wrote:
>> .
>> In no case can I understand a physical explanation for the the MS
>> sigma^2 being smaller than for the SS.
> Actually, there is a physical situation where something like that can  
> occur, although it sounds like it's not the one that Han Sen has.
> Consider an absorbing atom rattling around in a relatively fixed cage  
> or lattice. And then consider a linear (or near-linear) arrangement:
> S1 -- A -- S2
> One multiple scattering path that can sometimes have a sizable  
> contribution is A --> S1 --> S2 --> A. This path will have a sigma^2  
> that is a bit larger than the single-scattering path S1 --> S2 --> S1,  
> because of the perpendicular component of the motion of A.
> But it's quite frequently the case that S1 --> S2 --> S1 is not  
> modeled in a fit, because the S edge is not measured.
> On the other hand, the single scattering paths A --> S1 --> A and A -- 
>> S2 --> A ARE included in the fit. Those two have high sigma^2's,  
> because A is rattling around a lot.
> Under that circumstance, a multiple-scattering path included in the  
> fit may indeed have a lower sigma^2 than the single-scattering paths  
> included in the fit.
> The moral, of course, is that it's not hard to think physically about  
> what sigma^2 means for a multiple scattering path. If one appears to  
> have an "unphysically" small sigma2, then the explanation is probably  
> one of the ones given by Bruce or Shelly.
> One more thought on this. How much does it change your fit, Han Sen,  
> if you set the sigma^2 for the multiple-scattering path to some  
> "reasonable" value. If the scientific information you want from your  
> fit is not sensitive to exactly what sigma^2 the MS path gets, and is  
> not significantly different when given a "reasonable" value than when  
> allowed to find its "best-fit" value, then there's probably no need to  
> resolve the issue. In my experience, this is often the case with low- 
> amplitude MS paths: the fit is improved by their inclusion, but may  
> not be particularly sensitive to the details of their path parameters.
> --Scott Calvin
> Sarah Lawrence College
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