# [Ifeffit] The degeneracy and the coordination number

Scott Calvin scalvin at sarahlawrence.edu
Wed Dec 26 08:51:40 CST 2012

```Dear Zhaomo Tian,

This is an idiosyncrasy of Artemis/Ifeffit.

In the EXAFS equation, coordination number only appears multiplied by S02. Therefore it makes no sense to fit both S02 and N for a single path, as they would be 100% correlated.

Artemis' solution to this is to only allow you to fit S02, requiring you to interpret whether you are doing that to fit the actual value of S02, or to fit the coordination number.

To fit coordination number for the first shell, therefore, you need to know the value of S02.

Hopefully, examples will make this clearer. Suppose you know S02 = 0.90 (from, for example, fitting a standard).

One way to fit the first-shell coordination number would be to Set a parameter amp = 0.90 and guess a parameter N1 = 12. Then enter amp*N1 in the S02 box for path 1 in Artemis, and 1 in the N box.

Another way would be to Set amp = 0.90 and N1 = 12, and then enter amp*N1/12 in the S02 box and 12 in the N box.

There are, of course, other strategies that are also mathematically equivalent.

The key is that you must never put a variable in the N box, instead allowing the S02 box to do all the work of fitting.

--Scott Calvin
Sarah Lawrence College

On Dec 26, 2012, at 3:23 AM, Zhaomo Tian wrote:

Dear all,

I am confused about the degeneracy and the coordination number used in the Artemis program.
I want to get the coordination number of 1st shell of my copper sample, so I set a guess number N1=12(initial guess) as the coordination number which will vary during the fitting iteration, but when I am looking at the 1st path's parameters, there is another N appear which may stand for the degeneracy.The 1st path of copper model is single scattering, so the degeneracy N equals coordination number . But when I set N=12, the guessed N1 will have a value which is closed to 1, only when I set N=1, the guessed N1 will have a value which is closed to 12. It seems that N and N1 are reciprocals. But I think N actually equals N1 in the single scattering case.

So I am really confused, If I want to get coordination number of a shell in a fitting, how can I deal with floated coordination number and its path degeneracy N?

Thanks so much.
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