Hi Eugenio, To my eye, I strongly suspect there's real signal there. To confirm, try several different k-ranges and k-weights. If the feature persists, it is likely physical. (It may change size and shape to some extent.) --Scott Calvin Sarah Lawrence College On Aug 20, 2009, at 11:54 PM, Eugenio Otal wrote:

Hi, I have a sample of a pure Er2O3 (blue line in the attached graph) and a sample of doped ZnO with erbium that has segregated the same oxide (red line) by thermal treatmen. The signal for de segregated oxide gets noisy around k=9 because the sample is so diluted, but the radial distribution shows second shell signal, smaller than the pre oxide, but still a signal. My doubt is about how to know if the second shell is real and if that second shell can be useful to obtain information. Is there a criteria to know that? Some limit in k-space? Thanks, euG _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit

Dear Eugenio, There is a standard statistical test to answer just this problem, the F-test. To use the test, you first do the refinement including the contribution from the second shell and record chi-squared, which we will call c1, and the number of parameters, p1. Then you redo the fit without the second shell but keeping everything else the same including the k-weighting and the fit range; record the chi-squared, which we will call c2, and the number of parameters, p2. Finally, you will need the number of independent data points, which is the number given by ifeffit plus 2 (Stern’s rule), idp. Then you need to calculate F, which is given by F=(c2-c1)*(idp-p2)/[(p1-p2)*c1]. Using Excel, you can calculate the probability of F using FDIST(F,(p1-p2),(idp-p1)). This gives the probability that the improvement in chi-squared due to adding the second shell to the fit is due to noise in the data. The usual criterion for the F-test is that FDIST()<0.05, which means that the improvement in the fit due to including that shell is two sigma over the noise. I think it is OK to include the shell even if FDIST()>0.05, but you should report the probability that the improvement in the fit is due to random noise. This is a standard test in crystallography, where it is known as the Hamilton test. In short, the F-test tells you the probability that the improvement in the fit due to including a given shell is due to random error, or can be considered “real.” The F-test has one advantage of chi-squared tests in that it is a ratio of chi-squared of two fits, so the standard deviation of the data cancels. As with everything else, the F-test is model dependent and can give the wrong answer due to non-random errors such as problems with Feff. If you have "noisy" data, the F-test is probably pretty good; if you have data with little noise that goes high-k, I would be more careful applying it. The wikipedia entry on the F-test is OK, but used to have the formula wrong. There is a paper on using this test in EXAFS analysis: “A Variation of the F-Test for Determining Statistical Relevance of Particular Parameters in EXAFS Fits” Downward, L.; Booth, C. H.; Lukens, W. W.; Bridges, F. X-RAY ABSORPTION FINE STRUCTURE - XAFS13: 13th International Conference. AIP Conference Proceedings, Volume 882, pp. 129-131 (2007). Sincerely, Wayne -- Wayne Lukens Staff Scientist Lawrence Berkeley National Laboratory email: wwlukens@lbl.gov phone: (510) 486-4305 FAX: (510) 486-5596 Eugenio Otal wrote:

Hi, I have a sample of a pure Er2O3 (blue line in the attached graph) and a sample of doped ZnO with erbium that has segregated the same oxide (red line) by thermal treatmen. The signal for de segregated oxide gets noisy around k=9 because the sample is so diluted, but the radial distribution shows second shell signal, smaller than the pre oxide, but still a signal. My doubt is about how to know if the second shell is real and if that second shell can be useful to obtain information. Is there a criteria to know that? Some limit in k-space? Thanks, euG

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-- Wayne Lukens Staff Scientist Lawrence Berkeley National Laboratory email: wwlukens@lbl.gov phone: (510) 486-4305 FAX: (510) 486-5596