Dear all, Is there a physical limitation determining exafs bond distance resolution? Very often the equation r = pi / 2 deltak is quoted as a measure for bond distance resolution. But as i understand this equation is related to the fourier transform traditionally used for exafs analysis. If exafs fitting is done in k-space, on the raw exafs data without applying fourier or any other filtering transformation is there a physical limitation determining exafs bond distance resolution? This question comes down to the following practical problem. If one has a theoretical model developed using computational chemistry that predicts two different bond lengths within one shell, e.g. an octahedral metal center surrounded by 6 oxygen atoms and this shell is predicted to be split in three subshells for wich the bond length differs only 0.05 angstroms; and this model can be fit very well in k-space with the splitted shell, off course keeping the number of fit parameters below the nyquist criterion. Is there in such a case any physical reason not to fit the experimental data with the splitted shell , but with an averaged 6-atom shell with a larger Debye Waller factor? Best regards, Eric Breynaert
Eric,
Is there a physical limitation determining exafs bond distance resolution?
There is a physical limit in determining bond distances from EXAFS.
Very often the equation r = pi / 2 deltak is quoted as a measure for bond distance resolution.
The equation dr=pi/(2 *Delta k) gives the distance resolution: the ability to separately see two distances (here Delta k is the data range in k). This is not the same thing as the precision with which a single bond distance can be determined, which is generally quite a bit better than the "resolution". For Delta k ~= 15Ang^-1 (pretty good data), the resolution from the equation above is about ~= 0.1Ang. That is, one could expect to reliably detect a splitting of distances by ~0.1Ang. The precision in R from EXAFS experiments is typically 0.01Ang. This is typically determined by a combination of noise in the data and the accuracy of the phase shift calculations (say, from FEFF). For certain cases, it's entirely feasible to detect *changes* in bond distances with even better precision. One paper not so long ago (Pettifer, et al, Nature 435 pp78, 2005) claimed a precision of 10fm.
But as i understand this equation is related to the fourier transform traditionally used for exafs analysis. If exafs fitting is done in k-space, on the raw exafs data without applying fourier or any other filtering transformation is there a physical limitation determining exafs bond distance resolution?
Whether or not Fourier transforms are used in the analysis is "mostly" immaterial. That is, EXAFS is an interference technique, and we measure in k (or E) space to make statements about R space, so the limits are fundamental, not an artifact of the analysis tools. I say mostly because practical use of Fourier transforms (Fast Fourier Transforms with finite grids and extents) will impose additional restrictions on resolution and precision -- but these are typically finer than 0.1Ang for resolution and 0.01Ang for precision, and so are hardly ever a concern. As an example, FFTs in Ifeffit+Friends use a k-space grid of 0.05Ang^-1 and kmax of 102.4Ang^-1, and a grid in R-space of ~0.03Ang. This would limit resolution to about ~-0.03Ang, which might be a limiting factor if you have data to k~=50Ang^-1. It probably limits precision too, though I do not know to what extent.
This question comes down to the following practical problem. If one has a theoretical model developed using computational chemistry that predicts two different bond lengths within one shell, e.g. an octahedral metal center surrounded by 6 oxygen atoms and this shell is predicted to be split in three subshells for wich the bond length differs only 0.05 angstroms; and this model can be fit very well in k-space with the splitted shell, off course keeping the number of fit parameters below the nyquist criterion. Is there in such a case any physical reason not to fit the experimental data with the splitted shell , but with an averaged 6-atom shell with a larger Debye Waller factor?
My guess would be that the EXAFS could probably be fitted just as well with one distance and a slightly larger sigma2 as with 3 separate distances. But this would depend some on the data quality and it might be right at the resolution limits, so I'd recommend trying both models. Cheers, --Matt
This question comes down to the following practical problem. If one has a theoretical model developed using computational chemistry that predicts two different bond lengths within one shell, e.g. an octahedral metal center surrounded by 6 oxygen atoms and this shell is predicted to be split in three subshells for wich the bond length differs only 0.05 angstroms; and this model can be fit very well in k-space with the splitted shell, off course keeping the number of fit parameters below the nyquist criterion. Is there in such a case any physical reason not to fit the experimental data with the splitted shell , but with an averaged 6-atom shell with a larger Debye Waller factor?
My guess would be that the EXAFS could probably be fitted just as well with one distance and a slightly larger sigma2 as with 3 separate distances. But this would depend some on the data quality and it might be right at the resolution limits, so I'd recommend trying both models.
I think Matt is correct that the fits would be statistically indistinguishable. However, the paths have just enough distance difference that using a single shell will probably mess up your amplitude measurement.
Cheers,
--Matt _______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Jeremy Chemical Sciences and Engineering Division Argonne National Laboratory Argonne, IL 60439 Ph: 630.252.9398 Fx: 630.252.9917 kropf@anl.gov
On Tuesday 27 November 2007 12:02:57 Kropf, Arthur Jeremy wrote:
My guess would be that the EXAFS could probably be fitted just as well with one distance and a slightly larger sigma2 as with 3 separate distances. But this would depend some on the data quality and it might be right at the resolution limits, so I'd recommend trying both models.
I think Matt is correct that the fits would be statistically indistinguishable. However, the paths have just enough distance difference that using a single shell will probably mess up your amplitude measurement.
I agree, in substance at least, if not in vocabulary. At some point the split in distances will be large enough that a Gaussian is just not a good description of the actual partial pair radial distribution function. The Gaussian distribution that you use in that fit will have some centroid (i.e. bond length), some width (i.e. sigma^2), and some amplitude (i.e. coordination). Those three numbers will be quite valid in a statistical sense, but may be quite difficult to interpret in the context of the actual bi- or multi-modal distribution. I suspect "difficult to interpret" is what Jeremy means by "messed up". B -- Bruce Ravel ----------------------------------- bravel@bnl.gov National Institute of Standards and Technology Synchrotron Measurements Group, Beamlines X23A2, X24A, U7A Building 535A, Room M7 Brookhaven National Laboratory Upton NY, 11973, USA My homepage: http://xafs.org/BruceRavel EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/
participants (4)
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Bruce Ravel
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Eric Breynaert
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Kropf, Arthur Jeremy
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Matt Newville