[Ifeffit] Multiple scattering path parameters

[Scott Calvin]

Hi Neil,

For some kinds of paths, the answer is unambiguously “yes.” For example, consider the path A -> B -> A -> B -> A, where A is the absorbing atom and B is another atom; i.e., the path has four legs and 180 degree angles between each leg. In that case deltaR_MS = deltaR_SS, and sigma2_MS = 4*sigma2_SS.

It’s also close to exact to assert that if a path is perfectly focussed (I think that’s what you’re calling “forward through”), that the deltaR is the same as the deltaR for single-scattering off the further angle, and likewise with sigma2. That’s not quite perfect, but its very close unless the disorder is very high.

But for most cases, the constraints imply a model of how the atoms are moving relative to each other. Is the motion independent? Completely correlated? Isotropic? In something like a monatomic metal, you can make a pretty good argument as to what the relative motion should be like. In more complicated materials such as oxides, however, it becomes more difficult (although qualitative educated guesses can certainly be made).

The good news is that in many of the cases where a physical model is not obvious, the multiple-scattering paths that are difficult to constrain (e.g. triangles) make relatively small contributions to the signal, and may be numerous as well. In that kind of case, I’ve done some work that suggests that the precise constraint scheme employed does not make much difference to the fit, but leaving those paths altogether does degrade the fit. In other words, any reasonable constraint scheme is better than the “constraint” of leaving off the triangle paths altogether.

That’s a little scary, I know. But the thing to do is to try a few different constraint schemes and just see if it changes your fits much. If it doesn’t, and it often doesn’t, then you don’t have to worry! You can also try to leave the smaller MS paths off altogether, and see if that makes a difference.

—Scott Calvin
Sarah Lawrence College

> On Jul 28, 2016, at 5:52 PM, Neil M Schweitzer <neil.schweitzer at northwestern.edu> wrote:
> 
> Are there standard ways of relating the parameters (deltaR and sigma^2) of multiple scattering paths to the parameters of the single scattering paths based on the type of MS path? For example, would deltaR_MS = deltaR_SS*2 if the MS was a “forward through” geometry? What about other geometries and paths that involve different types of atoms?
>  
> Neil
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