Hi Hao, I haven't had time to look at your fits, but I have some generic responses to what you say below. It is typical of someone new to the field to chase r-factors. Don't do it! I could take any spectrum and any model and by floating enough variables, come up with a terrific looking r-factor...for a fit that's utter nonsense. At the risk of having another set of completely arbitrary criteria named after me <grin>, here's the guidelines I give undergraduates when I'm teaching the technique. (Note: these guidelines apply to decent-quality data. For cases like very dilute fluorescence, it's reasonable to expect statistical effects to inflate the R-factor a bit.) R-factor > 0.10: Serious problems with the fit. The underlying model may be incorrect. It's best at this stage to look at the spectrum for clues. Maybe the wiggles are qualitatively right, but shifted over or the wrong amplitude. Then the model may be OK, but things like the free parameters and constraints may need to be adjusted. On the other hand, the wiggles may be qualitatively wrong, in which case the underlying model must be seriously questioned. R-factor in the range 0.05 to 0.10: Underlying model may be correct, but there is likely some effect not being taken into account (for example: phase impurity, oversimplified sigma2 constraints, vacancies, etc., etc.). Alternatively, perhaps it's too wide a k-range, problems with background subtraction, or the like. I have occasionally published fits in this range, although always with an explanation of possible factors in the text of the article. R-factor in the range 0.02 to 0.05: Decently good match between fitted and actual spectra. There's still enough of a mismatch that, if the data is good quality, there are probably some issues with details of the model. At this point, R-factors are becoming less of a concern than the plausibility of the constraint scheme and the fitted parameters, the number of degrees of freedom, agreement with other source of information about the system, etc.. R-factor less than 0.02. Good match between fitted and actual spectra. Unless you're doing technical work on a very well-characterized sample (say, a piece of copper foil), there's no point in trying to reduce the R-factor any further. You're a lot better off with a constraint scheme that can be explained on physical grounds and an R-factor of 0.019, than, for example, introducing a parameter for the third cumulant of a fourth-nearest-neighbor in a metal to get an R-factor of 0.005. These are broad guidelines only; the R-factor has no meaning in a statistical sense, so what to expect is highly dependent on data quality. * * * OK--I've taken a very quick look at your fits to help answer your question about the k-weights. Your k-weight 2 and k-weight 3 fits are consistent, in that the error bars of corresponding parameters overlap. But the k-weight 2 fit has enormous uncertainties, and is thus pretty much useless. What good does it do you to find that n1 is 3.4 +/- 3.5? Presumably you knew that already. :) So in that sense the k-weight 3 fit is "better." But there are other problems: --the S02 is a bit high. Ideally it shouldn't be higher than 1.0. --You seem to be fitting too high an R-range. Going to 3 when your most distant path has an Reff of 2.4 is dangerous...depending on your substance there may be other stuff out there you're not accounting for. --The negative sigma2 that you're worried about is NOT a big problem, however. It is given as -0.003 +/- 0.008. So it could be positive according to the fitted results. --It looks like you set n2 to 0.175 based on some previous fit. Do you believe that's physically reasonable for your system? This business of running a fit, finding some parameters, and then running a fit on the same data fixing some parameters to values from a previous fit is at best dangerous, and at worst nonsense. That's different than the advice often given on this list, where you compare a fit with a parameter fixed to a suspected-prior-knowledge value to one where it is allowed to float. For example, saying "the chemists tell me this coordination number should be 6. I'll fix it at 6, and I'll let it float, and if the floated case doesn't seem better, I'll go back to fixing it at 6" is very different from "my first fit on this sample gave me a coordination number of 5.47 +/- 4.8. That's a big uncertainty, so I'll set the coordination number to 5.48 and proceed." Using the first procedure in a final, published fit is defensible, the second one is not. Hope that helps. --Scott Calvin Sarah Lawrence College At 01:48 PM 2/27/2007, you wrote:
I took your suggestion and have the amp and e0 the same for each path. In addition, I fixed the number axial U-O as 2. For the equatorial ligand, since the total coordination number is between 4 and 6, I guess the number of U-F as 2(that is n1), and def the number of U-O as (5-n1)(that is n2). Then I did the fit. The result showed the ss_2 is still negative. So I set the ss_2 as 0.003, did the fitting again. I don't know if it is ok to fix the ss_2=0.003. It seems the dr_1 change a lot.
In addition, I tried to do fitting in Kw=2 in stead of Kw=3. At this time, the ss_2 is positive, and from my understanding, it seems the modeling is more resonable for dr_1 and dr_2, but the R-factor is 0.023, a little bit larger than 0.02. How can I decide which one I should use, the Kw=3 or Kw=2? Is there anything I can do to improve the modeling?