Hi Todd,
Allowing E0 to vary independently for each standard can be problematic. In
some cases, the shapes of the XANES spectra are quite similar, and the main
difference between spectra is the absorption energy. I always determine the
spectra of the standards with the same energy reference (and preferably on
the same beam line during the same run). I allow E0 to shift for the sample,
but not for the standards. Another way to do this is to have only one E0
shift for the standards and shift them all by the same amount.
I never force the sum of the weights to equal one, I do the normalization
after the analysis.
One little-mentioned problem I have found with LCF fitting is that using
data from different beamlines (and even the same beamlines at different
times) can be problematic due to the changes in spectrometer resolution. One
way to address that problem is to convolve the higher resolution spectrum
(spectra) with a Gaussian and/or a Lorentzian. Since I always use the same
energy reference standard, I convolve the higher resolution spectrum until
the spectra of the energy reference standards are as similar as possible. I
should note that, while convolving the spectra improves the fit, it does not
change the results other decreasing the uncertainties on the variables (in
my experience).
To be honest, I don't really care all that much about the quality of the fit
as an absolute number (e.g., the R-value) because noisy data will have a
high R-value if the data are not weighted by their uncertainty. Rather, I
care whether the results of the LCF pass the F-test, which provides the
likelihood that including a given standard actually improves the fit versus
improvement caused by uncertainty in the data. For example, if you are
fitting an unknown with three standards (A, B, and C), and the result of LCF
is 95% A, 4% B, and 1 %C, the F-test might give probabilities of 1E-8 for
A, 0.07 for B, and 0.23 for C, where the probability is that the improvement
to the fit is due to uncertainty in the data. In this case, A is certainly
present, C cannot be stated to be present, and B may be present (the general
criterion for the F-test is that the improvement to the fit is not due to
uncertainty in the data l if the probability is less than 0.05). A more
useful way to look at this is that the probabilities that A, B and C are
present are 99.99999999%, 93%, and 77%, respectively.
One way to make the absolute quality of the fit more useful is to determine
the uncertainty of each data point when the data is averaged. Then, the data
could be weighted during fitting and the weighted R-value could be
determined as is done for crystallography. I have never tried to do this
though.
Just my 2 cents.
Sincerely,
Wayne Lukens
On Mon, Oct 25, 2010 at 7:00 AM,
I have a general question for the group.
How do you conduct your LCF fitting routine? Do most people allow Eo to vary for the standards, or force the weights of all of the combinations to 1? How do people judge a significant improvement to the resulting goodness of fit parameters?
I am aware of most of the pitfalls associated with LCF analysis of XAFS data (over fitting data with too many standards, not having information to support the use of a standard in the fit, ect.). What I am really interested in is how people fit and judge the quality of a fit after collecting all of the necessary background information? Or, what is the process/routine people go through during LCF analysis?
I have looked at older threads on the IFEFFIT web page, but I was unable to find a description of the general process people follow. Additionally, if anyone is aware of a reference discussing the potential problems and/or solutions to fitting data using LCF that would be great.
All the Best
Todd
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