Dear all, I always appreciate the big useful help from everyone. I have a basic question. I think a similar question has been arose long time ago. (But I lost the mail..) My sample has very small amount (under 1 wt%) and cluster size (< 1nm). The spectrum is always noisy at high k range, so I use usually k=2 to 10 or 12. It depends on the noise of the spectrum. Of course, if I go further down, it is better. My question is how low can I set the k range? Is there any minimum range for reliable result? Please let me get out of this dilemma... Thank you always. Steven
Hi Steven, I once published with k-ranges as small as 4-8. I think there are two related criteria you can look at off the bat to see if your k-range is definitely too small. One is, of course, the Nyquist criterion comparing independent points to variables being fit (automatically computed by IFEFFIT). This criterion assumes that information is "ideally packed" in the EXAFS signal, which it's not, so although fitting more variables than you have "independent points" according to this criterion is definitely bad, you really want to clear this criterion by a significant margin. The second (related) criterion is the resolution of different scatterers. A rule of thumb is that in order to resolve two different absorber-scatterer distances, you need to satisfy: kmax - kmin > pi/(2 x delta r) where delta r is the difference in absorber-scatterer distances you are hoping to resolve. You'll notice that with a k-range of 4-8, that means I couldn't resolve distances less than 0.4 angstroms apart... --Scott Calvin Sarah Lawrence College At 11:46 AM 4/27/2004 -0400, you wrote:
<fontfamily><param>Arial</param><smaller>Dear all, I always appreciate the big useful help from everyone. I have a basic question. I think a similar question has been arose long time ago. (But I lost the mail..) My sample has very small amount (under 1 wt%) and cluster size (<< 1nm). The spectrum is always noisy at high k range, so I use usually k=2 to 10 or 12. It depends on the noise of the spectrum. Of course, if I go further down, it is better. My question is how low can I set the k range? Is there any minimum range for reliable result? Please let me get out of this dilemma... Thank you always. Steven </smaller></fontfamily>__
Hi Steven, On Tue, 27 Apr 2004, Steven Sangyun Lim wrote:
My question is how low can I set the k range? Is there any minimum range for reliable result? Please let me get out of this dilemma...
Scott answered the question of how small "delta k" can be. It seems you might also be asking how low kmin can be. I'll try to answer that one: It depends on the details of the system, but using a kmin between 2 and 3Ang^-1 is a fairly safe value. Many people tend to stay on the conservative side of that (that is, kmin=3 or higher). Below kmin=2 (which is only 15eV above E0), the spectra can be heavily influenced by multiple-scattering, details of the background subtraction, and the selection of E0. In principle these XANES features could be modelled as part of the EXAFS if you trust the background function and either use enough paths or are very confident there are no contributions from multiple-scattering in that range. I believe some spectra for highly disordered metals really have analyzable EXAFS starting at k=1Ang^-1, but that seems to be the exception, not the rule. In practice, the cost in complexity is usually not worth the benefit in first shell information. --Matt PS: Scott's answer in a way that should be archived better: Hi Steven, I once published with k-ranges as small as 4-8. I think there are two related criteria you can look at off the bat to see if your k-range is definitely too small. One is, of course, the Nyquist criterion comparing independent points to variables being fit (automatically computed by IFEFFIT). This criterion assumes that information is "ideally packed" in the EXAFS signal, which it's not, so although fitting more variables than you have "independent points" according to this criterion is definitely bad, you really want to clear this criterion by a significant margin. The second (related) criterion is the resolution of different scatterers. A rule of thumb is that in order to resolve two different absorber-scatterer distances, you need to satisfy: kmax - kmin > pi/(2 x delta r) where delta r is the difference in absorber-scatterer distances you are hoping to resolve. You'll notice that with a k-range of 4-8, that means I couldn't resolve distances less than 0.4 angstroms apart... --Scott Calvin Sarah Lawrence College
participants (3)
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Matt Newville -
Scott Calvin -
Steven Sangyun Lim