Re: [Ifeffit] Asymmetric error bars in IFeffit
Hi Scott, That's a pretty amazing use case. But I'm not sure I understand the issue exactly right. I would have thought the volume (r**3) was the important physical parameter, and that a 1000nm particle would dominate the spectra over 3nm particles. Or is it that you are trying to distinguish between 1 very large crystal or 100s of smaller crystals? Perhaps the effect you're really trying to account for is the surface/volume ratio? If so, I think using Matthew Marcus's suggestion of using 1/r (with a safety margin) makes the most sense. --Matt On Fri, Oct 22, 2010 at 3:23 PM, Scott Calvin dr.scott.cal...@gmail.com wrote: Hi all, I'm puzzling over an issue with my latest analysis, and it seemed like the sort of thing where this mailing list might have some good ideas. First, a little background on the analysis. It is a simultaneous fit to four samples, made of various combinations of three phases. Mossbauer has established which samples include which phases. One of the phases itself has two crystallographically inequivalent absorbing sites. The result is that the fit includes 12 Feff calculations, four data sets, and 1000 paths. Remarkably, everything works quite well, yielding a satisfying and informative fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to Ifeffit and Horae for making such a thing possible! Several of the parameters that the fit finds are characteristic crystallite radii for the individual phases. In my published fits, I often include a factor that accounts for the fact that a phase is nanoscale in a crude way: it assumes the phase is present as spheres of uniform radius and applies a suppression factor to the coordination numbers of the paths as a function of that radius and of the absorber-scatterer distance. Even though this model is rarely strictly correct in terms of morphology and size dispersion, it gives a first-order approximation to the effect of the reduced coordination numbers found in nanoscale materials. Some people, notably Anatoly Frenkel, have published models which deal with this effect much more realistically. But those techniques also require more fitted variables and work best with fairly well-behaved samples. I tend to work with messy chemical samples of free nanoparticles where the assumption of sphericity isn't terrible, and the size dispersion is difficult to model accurately. At any rate, the project I'm currently working on includes a fitted characteristic radius of the type I've described for each of the phases in each of the samples. And again, it seems to work pretty well, yielding values that are plausible and largely stable. That's the background information. Now for my question: The effect of the characteristic radius on the spectrum is a strongly nonlinear function of that radius. For example, the difference between the EXAFS spectra of 100 nm and 1000 nm single crystals due to the coordination number effect is completely negligible. The difference between 1 nm and 10 nm crystals, however, is huge. So for very small crystallites, IFeffit reports perfectly reasonable error bars: the radius is 0.7 +/- 0.3 nm, for instance. For somewhat larger crystallites, however, it tends to report values like 10 +/- 500 nm. I understand why it does that: it's evaluating how much the parameter would have to change by to have a given impact on the chi square of the fit. And it turns out that once you get to about 10 nm, the size could go arbitrarily higher than that and not change the spectrum much at all. But it couldn't go that much lower without affecting the spectrum. So what IFeffit means is something like the best fit value is 10 nm, and it is probable that the value is at least 4 nm. But it's operating under the assumption that the dependence of chi-square on the parameter is parabolic, so it comes up with a compromise between a 6 nm error bar on the low side and an infinitely large error bar on the high side. Compromising with infinity, however, rarely yields sensible results. Thus my question is if anyone can think of a way to extract some sense of these asymmetric error bars from IFeffit. Here are possibilities I've considered: --Fit something like the log of the characteristic radius, rather than the radius itself. That creates an asymmetric error bar for the radius, but the asymmetry the new error bar possesses has no relationship to the uncertainty it should possess. This seems to me like it's just a way of sweeping the problem under the rug and is potentially misleading. --Rerun the fits setting the variable in question to different values to probe how far up or down it can go and have the same effect on the fit. But since I've got nine of these factors, and each fit takes more than an hour, the computer time required seems prohibitive! --Somehow parameterize the guessed variable so that it does tend to have symmetric error bars, and then calculate
Re: [Ifeffit] Asymmetric error bars in IFeffit
Yes; it's a case of trying to distinguish between a few boulders and lots of pebbles; the total volume isn't the issue. What I'm looking at is something like surface/volume ratio, but with surface being path-dependent and gradual. For a nearest-neighbor path, only the top monolayer of atoms are on the surface. For a 5 angstrom path, the transition region from surface to core extends 5 angstroms in. But that more sophisticated definition of surface doesn't change the fact that the dominant dependence is 1/R, so that should address the issue. --Scott Calvin Sarah Lawrence College On Oct 25, 2010, at 4:43 AM, Matt Newville wrote: Hi Scott, That's a pretty amazing use case. But I'm not sure I understand the issue exactly right. I would have thought the volume (r**3) was the important physical parameter, and that a 1000nm particle would dominate the spectra over 3nm particles. Or is it that you are trying to distinguish between 1 very large crystal or 100s of smaller crystals? Perhaps the effect you're really trying to account for is the surface/volume ratio? If so, I think using Matthew Marcus's suggestion of using 1/r (with a safety margin) makes the most sense. --Matt ___ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Re: [Ifeffit] Asymmetric error bars in IFeffit
Scott, It is a strange result. Suppose you fit a bulk metal foil and vary the 1nn coordination number. You will not get 12 +/- 1000. You will get about 12 +/- 0.3 depending on the data quality and the k range, and on the amplitude factor you fix constant. Then, suppose you take your formula for a particle radius from your JAP article and propagate this uncertainty to get the radius uncertainty. That would give you a huge error because you are in the flat region of the N(R) function and R does bit affect N. The meaning of your large error bar is, I think, that you are in such a large limit of sizes that they cannot be inverted to get N and thus the errors cannot be propagated to find Delta R. Why don't you try to obtain N instead of R? You will get much smaller error bars and you can find the lower R limit from your N(R) equation (by plugging in N - deltaN you will find R - delta R). The right limit is infinity as you pointed out. Anatoly From: ifeffit-boun...@millenia.cars.aps.anl.gov ifeffit-boun...@millenia.cars.aps.anl.gov To: XAFS Analysis using Ifeffit ifeffit@millenia.cars.aps.anl.gov Sent: Fri Oct 22 16:23:08 2010 Subject: [Ifeffit] Asymmetric error bars in IFeffit Hi all, I'm puzzling over an issue with my latest analysis, and it seemed like the sort of thing where this mailing list might have some good ideas. First, a little background on the analysis. It is a simultaneous fit to four samples, made of various combinations of three phases. Mossbauer has established which samples include which phases. One of the phases itself has two crystallographically inequivalent absorbing sites. The result is that the fit includes 12 Feff calculations, four data sets, and 1000 paths. Remarkably, everything works quite well, yielding a satisfying and informative fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to Ifeffit and Horae for making such a thing possible! Several of the parameters that the fit finds are characteristic crystallite radii for the individual phases. In my published fits, I often include a factor that accounts for the fact that a phase is nanoscale in a crude way: it assumes the phase is present as spheres of uniform radius and applies a suppression factor to the coordination numbers of the paths as a function of that radius and of the absorber-scatterer distance. Even though this model is rarely strictly correct in terms of morphology and size dispersion, it gives a first-order approximation to the effect of the reduced coordination numbers found in nanoscale materials. Some people, notably Anatoly Frenkel, have published models which deal with this effect much more realistically. But those techniques also require more fitted variables and work best with fairly well-behaved samples. I tend to work with messy chemical samples of free nanoparticles where the assumption of sphericity isn't terrible, and the size dispersion is difficult to model accurately. At any rate, the project I'm currently working on includes a fitted characteristic radius of the type I've described for each of the phases in each of the samples. And again, it seems to work pretty well, yielding values that are plausible and largely stable. That's the background information. Now for my question: The effect of the characteristic radius on the spectrum is a strongly nonlinear function of that radius. For example, the difference between the EXAFS spectra of 100 nm and 1000 nm single crystals due to the coordination number effect is completely negligible. The difference between 1 nm and 10 nm crystals, however, is huge. So for very small crystallites, IFeffit reports perfectly reasonable error bars: the radius is 0.7 +/- 0.3 nm, for instance. For somewhat larger crystallites, however, it tends to report values like 10 +/- 500 nm. I understand why it does that: it's evaluating how much the parameter would have to change by to have a given impact on the chi square of the fit. And it turns out that once you get to about 10 nm, the size could go arbitrarily higher than that and not change the spectrum much at all. But it couldn't go that much lower without affecting the spectrum. So what IFeffit means is something like the best fit value is 10 nm, and it is probable that the value is at least 4 nm. But it's operating under the assumption that the dependence of chi-square on the parameter is parabolic, so it comes up with a compromise between a 6 nm error bar on the low side and an infinitely large error bar on the high side. Compromising with infinity, however, rarely yields sensible results. Thus my question is if anyone can think of a way to extract some sense of these asymmetric error bars from IFeffit. Here are possibilities I've considered: --Fit something like the log of the characteristic radius, rather than the radius itself. That creates an asymmetric error bar for the radius
Re: [Ifeffit] Asymmetric error bars in IFeffit
I don't think it's at all strange, Anatoly, and I think Matthew's solution is the right one--it seems obvious in retrospect that the parameter that Ifeffit should evaluate is 1/R, but apparently it wasn't obvious to me on Friday. :) As for obtaining N instead of R, the beauty of both of our algorithms is that they don't depend on finding N; they depend on finding the ratio of N's for different shells. Finding N accurately is notoriously challenging: you need some way of getting S02, you need to have the normalization right, and you're sunk if there are data quality issues like an inhomogeneous sample, uncorrected self-absorption, or significant beam harmonics. But finding the ratio of N for two or more different shells doesn't depend so strongly on any of those things. Since my method implicitly involves multiple ratios of coordination numbers, it is not so clear how to invert it. In any case, I expect Matthew's solution to work, and will pursue it further on Monday. --Scott Calvin Sarah Lawrence College On Oct 24, 2010, at 5:59 PM, Frenkel, Anatoly wrote: Scott, It is a strange result. Suppose you fit a bulk metal foil and vary the 1nn coordination number. You will not get 12 +/- 1000. You will get about 12 +/- 0.3 depending on the data quality and the k range, and on the amplitude factor you fix constant. Then, suppose you take your formula for a particle radius from your JAP article and propagate this uncertainty to get the radius uncertainty. That would give you a huge error because you are in the flat region of the N(R) function and R does bit affect N. The meaning of your large error bar is, I think, that you are in such a large limit of sizes that they cannot be inverted to get N and thus the errors cannot be propagated to find Delta R. Why don't you try to obtain N instead of R? You will get much smaller error bars and you can find the lower R limit from your N(R) equation (by plugging in N - deltaN you will find R - delta R). The right limit is infinity as you pointed out. Anatoly From: ifeffit-boun...@millenia.cars.aps.anl.gov ifeffit-boun...@millenia.cars.aps.anl.gov To: XAFS Analysis using Ifeffit ifeffit@millenia.cars.aps.anl.gov Sent: Fri Oct 22 16:23:08 2010 Subject: [Ifeffit] Asymmetric error bars in IFeffit Hi all, I'm puzzling over an issue with my latest analysis, and it seemed like the sort of thing where this mailing list might have some good ideas. First, a little background on the analysis. It is a simultaneous fit to four samples, made of various combinations of three phases. Mossbauer has established which samples include which phases. One of the phases itself has two crystallographically inequivalent absorbing sites. The result is that the fit includes 12 Feff calculations, four data sets, and 1000 paths. Remarkably, everything works quite well, yielding a satisfying and informative fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to Ifeffit and Horae for making such a thing possible! Several of the parameters that the fit finds are characteristic crystallite radii for the individual phases. In my published fits, I often include a factor that accounts for the fact that a phase is nanoscale in a crude way: it assumes the phase is present as spheres of uniform radius and applies a suppression factor to the coordination numbers of the paths as a function of that radius and of the absorber-scatterer distance. Even though this model is rarely strictly correct in terms of morphology and size dispersion, it gives a first-order approximation to the effect of the reduced coordination numbers found in nanoscale materials. Some people, notably Anatoly Frenkel, have published models which deal with this effect much more realistically. But those techniques also require more fitted variables and work best with fairly well-behaved samples. I tend to work with messy chemical samples of free nanoparticles where the assumption of sphericity isn't terrible, and the size dispersion is difficult to model accurately. At any rate, the project I'm currently working on includes a fitted characteristic radius of the type I've described for each of the phases in each of the samples. And again, it seems to work pretty well, yielding values that are plausible and largely stable. That's the background information. Now for my question: The effect of the characteristic radius on the spectrum is a strongly nonlinear function of that radius. For example, the difference between the EXAFS spectra of 100 nm and 1000 nm single crystals due to the coordination number effect is completely negligible. The difference between 1 nm and 10 nm crystals, however, is huge. So for very small crystallites, IFeffit reports perfectly reasonable error bars: the radius is 0.7 +/- 0.3 nm, for instance. For somewhat larger
Re: [Ifeffit] Asymmetric error bars in IFeffit
The idea was that FEFF was not necessarily trustworthy to get the absolute answers, but was good enough to get the difference, say, between Al and Si, and Cu and Zn. In other words, experiment was the ground truth and FEFF used to extrapolate it to where it wasn't available. mam - Original Message - From: Frenkel, Anatoly To: ifeffit@millenia.cars.aps.anl.gov Sent: Friday, October 22, 2010 6:20 PM Subject: Re: [Ifeffit] Asymmetric error bars in IFeffit Matthew, if you relied on FEFF as one part of the complex calculation, where the other part was the experimentally extracted one, you could've as well done everything with just FEFF. Why didn't you? A. -- From: ifeffit-boun...@millenia.cars.aps.anl.gov ifeffit-boun...@millenia.cars.aps.anl.gov To: XAFS Analysis using Ifeffit ifeffit@millenia.cars.aps.anl.gov Sent: Fri Oct 22 18:01:17 2010 Subject: Re: [Ifeffit] Asymmetric error bars in IFeffit Another reason, from my point of view, is that FEFF wasn't accurate enough to use on its own without references. Also, it still can be argued that the process of data reduction and filtering produces distortions which aren't captured by using FEFF alone. Further, if one is comparing very similar systems, e.g. bulk and nano of the same stuff, then with the exception of multiple scattering, the one system should be an ideal reference for the other. A trick I used to do: Suppose, for instance, that I wanted to fit a shell of Zn surrounded by Si (not an actual case). There's no Si-rich zinc silicide to use as a reference, but it's not too hard to make theta-CuAl2, a compound in which all Cu atoms are surrounded by Al in the first shell (this was done). From this, amp and phase functions could be extracted which refer to Cu looking at Al (Cu-Al). Next, to transform this into the desired Zn-Si, I would do FEFF calculations on identical structures with the atoms changed around and take: A(Zn-Si, semi-empirical) = A(Cu-Al, expt)*[A(Zn-Si, FEFF)/A(Cu-Al, FEFF)] phi(Zn-Si, semi-empirical) = phi(Cu-Al, expt)+[Phi(Zn-Si, FEFF)-phi(Cu-Al, FEFF)] with A, phi being amplitude and phase for a given shell, and appropriate account being taken of the distance differences involved. This makes sense if you consider A~ = A*exp(i*phi) to be one of the factors in a complex chi~ such that chi = Im(chi~), and you're essentially making a correction to ln(A~). Yes, this was low-rent and subject to errors, but it seemed to make sense provided one didn't try to take it too far, for instance trying to change Al for Au or an oxide for a metal. Brings back memories, not all of them fond :-) mam - Original Message - From: Frenkel, Anatoly To: ifeffit@millenia.cars.aps.anl.gov Sent: Friday, October 22, 2010 2:38 PM Subject: Re: [Ifeffit] Asymmetric error bars in IFeffit On a related subject, now I understand why we use the concept of chemical transferability of amplitudes and phases by recycling the same FEFF path for different systems. The true reason is historic: back then it took one hour for one FEFF calculation Anatoly From: ifeffit-boun...@millenia.cars.aps.anl.gov ifeffit-boun...@millenia.cars.aps.anl.gov To: XAFS Analysis using Ifeffit ifeffit@millenia.cars.aps.anl.gov Sent: Fri Oct 22 16:23:08 2010 Subject: [Ifeffit] Asymmetric error bars in IFeffit Hi all, I'm puzzling over an issue with my latest analysis, and it seemed like the sort of thing where this mailing list might have some good ideas. First, a little background on the analysis. It is a simultaneous fit to four samples, made of various combinations of three phases. Mossbauer has established which samples include which phases. One of the phases itself has two crystallographically inequivalent absorbing sites. The result is that the fit includes 12 Feff calculations, four data sets, and 1000 paths. Remarkably, everything works quite well, yielding a satisfying and informative fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to Ifeffit and Horae for making such a thing possible! Several of the parameters that the fit finds are characteristic crystallite radii for the individual phases. In my published fits, I often include a factor that accounts for the fact that a phase is nanoscale in a crude way: it assumes the phase is present as spheres of uniform radius and applies a suppression factor to the coordination numbers of the paths as a function of that radius and of the absorber-scatterer distance. Even though this model is rarely strictly correct in terms of morphology and size dispersion, it gives a first-order approximation to the effect of the reduced coordination numbers found
Re: [Ifeffit] Asymmetric error bars in IFeffit
Some quantities, such as effective coordination numbers, are roughly linear in 1/size, so there's an argument for doing the coordinate transformation size-1/size. If you do that, then be sure to make things functions of abs(u) where u==1/size, because u0 is unphysical. Doing it this way also allows a simple way of testing for having it be bulk-like, by setting u=0. mam - Original Message - From: Scott Calvin To: XAFS Analysis using Ifeffit Sent: Friday, October 22, 2010 1:23 PM Subject: [Ifeffit] Asymmetric error bars in IFeffit Hi all, I'm puzzling over an issue with my latest analysis, and it seemed like the sort of thing where this mailing list might have some good ideas. First, a little background on the analysis. It is a simultaneous fit to four samples, made of various combinations of three phases. Mossbauer has established which samples include which phases. One of the phases itself has two crystallographically inequivalent absorbing sites. The result is that the fit includes 12 Feff calculations, four data sets, and 1000 paths. Remarkably, everything works quite well, yielding a satisfying and informative fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to Ifeffit and Horae for making such a thing possible! Several of the parameters that the fit finds are characteristic crystallite radii for the individual phases. In my published fits, I often include a factor that accounts for the fact that a phase is nanoscale in a crude way: it assumes the phase is present as spheres of uniform radius and applies a suppression factor to the coordination numbers of the paths as a function of that radius and of the absorber-scatterer distance. Even though this model is rarely strictly correct in terms of morphology and size dispersion, it gives a first-order approximation to the effect of the reduced coordination numbers found in nanoscale materials. Some people, notably Anatoly Frenkel, have published models which deal with this effect much more realistically. But those techniques also require more fitted variables and work best with fairly well-behaved samples. I tend to work with messy chemical samples of free nanoparticles where the assumption of sphericity isn't terrible, and the size dispersion is difficult to model accurately. At any rate, the project I'm currently working on includes a fitted characteristic radius of the type I've described for each of the phases in each of the samples. And again, it seems to work pretty well, yielding values that are plausible and largely stable. That's the background information. Now for my question: The effect of the characteristic radius on the spectrum is a strongly nonlinear function of that radius. For example, the difference between the EXAFS spectra of 100 nm and 1000 nm single crystals due to the coordination number effect is completely negligible. The difference between 1 nm and 10 nm crystals, however, is huge. So for very small crystallites, IFeffit reports perfectly reasonable error bars: the radius is 0.7 +/- 0.3 nm, for instance. For somewhat larger crystallites, however, it tends to report values like 10 +/- 500 nm. I understand why it does that: it's evaluating how much the parameter would have to change by to have a given impact on the chi square of the fit. And it turns out that once you get to about 10 nm, the size could go arbitrarily higher than that and not change the spectrum much at all. But it couldn't go that much lower without affecting the spectrum. So what IFeffit means is something like the best fit value is 10 nm, and it is probable that the value is at least 4 nm. But it's operating under the assumption that the dependence of chi-square on the parameter is parabolic, so it comes up with a compromise between a 6 nm error bar on the low side and an infinitely large error bar on the high side. Compromising with infinity, however, rarely yields sensible results. Thus my question is if anyone can think of a way to extract some sense of these asymmetric error bars from IFeffit. Here are possibilities I've considered: --Fit something like the log of the characteristic radius, rather than the radius itself. That creates an asymmetric error bar for the radius, but the asymmetry the new error bar possesses has no relationship to the uncertainty it should possess. This seems to me like it's just a way of sweeping the problem under the rug and is potentially misleading. --Rerun the fits setting the variable in question to different values to probe how far up or down it can go and have the same effect on the fit. But since I've got nine of these factors, and each fit takes more than an hour, the computer time required seems prohibitive! --Somehow parameterize the guessed variable so that it does tend to have symmetric error bars, and then calculate the characteristic radius and its error bars from
Re: [Ifeffit] Asymmetric error bars in IFeffit
On a related subject, now I understand why we use the concept of chemical transferability of amplitudes and phases by recycling the same FEFF path for different systems. The true reason is historic: back then it took one hour for one FEFF calculation Anatoly From: ifeffit-boun...@millenia.cars.aps.anl.gov ifeffit-boun...@millenia.cars.aps.anl.gov To: XAFS Analysis using Ifeffit ifeffit@millenia.cars.aps.anl.gov Sent: Fri Oct 22 16:23:08 2010 Subject: [Ifeffit] Asymmetric error bars in IFeffit Hi all, I'm puzzling over an issue with my latest analysis, and it seemed like the sort of thing where this mailing list might have some good ideas. First, a little background on the analysis. It is a simultaneous fit to four samples, made of various combinations of three phases. Mossbauer has established which samples include which phases. One of the phases itself has two crystallographically inequivalent absorbing sites. The result is that the fit includes 12 Feff calculations, four data sets, and 1000 paths. Remarkably, everything works quite well, yielding a satisfying and informative fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to Ifeffit and Horae for making such a thing possible! Several of the parameters that the fit finds are characteristic crystallite radii for the individual phases. In my published fits, I often include a factor that accounts for the fact that a phase is nanoscale in a crude way: it assumes the phase is present as spheres of uniform radius and applies a suppression factor to the coordination numbers of the paths as a function of that radius and of the absorber-scatterer distance. Even though this model is rarely strictly correct in terms of morphology and size dispersion, it gives a first-order approximation to the effect of the reduced coordination numbers found in nanoscale materials. Some people, notably Anatoly Frenkel, have published models which deal with this effect much more realistically. But those techniques also require more fitted variables and work best with fairly well-behaved samples. I tend to work with messy chemical samples of free nanoparticles where the assumption of sphericity isn't terrible, and the size dispersion is difficult to model accurately. At any rate, the project I'm currently working on includes a fitted characteristic radius of the type I've described for each of the phases in each of the samples. And again, it seems to work pretty well, yielding values that are plausible and largely stable. That's the background information. Now for my question: The effect of the characteristic radius on the spectrum is a strongly nonlinear function of that radius. For example, the difference between the EXAFS spectra of 100 nm and 1000 nm single crystals due to the coordination number effect is completely negligible. The difference between 1 nm and 10 nm crystals, however, is huge. So for very small crystallites, IFeffit reports perfectly reasonable error bars: the radius is 0.7 +/- 0.3 nm, for instance. For somewhat larger crystallites, however, it tends to report values like 10 +/- 500 nm. I understand why it does that: it's evaluating how much the parameter would have to change by to have a given impact on the chi square of the fit. And it turns out that once you get to about 10 nm, the size could go arbitrarily higher than that and not change the spectrum much at all. But it couldn't go that much lower without affecting the spectrum. So what IFeffit means is something like the best fit value is 10 nm, and it is probable that the value is at least 4 nm. But it's operating under the assumption that the dependence of chi-square on the parameter is parabolic, so it comes up with a compromise between a 6 nm error bar on the low side and an infinitely large error bar on the high side. Compromising with infinity, however, rarely yields sensible results. Thus my question is if anyone can think of a way to extract some sense of these asymmetric error bars from IFeffit. Here are possibilities I've considered: --Fit something like the log of the characteristic radius, rather than the radius itself. That creates an asymmetric error bar for the radius, but the asymmetry the new error bar possesses has no relationship to the uncertainty it should possess. This seems to me like it's just a way of sweeping the problem under the rug and is potentially misleading. --Rerun the fits setting the variable in question to different values to probe how far up or down it can go and have the same effect on the fit. But since I've got nine of these factors, and each fit takes more than an hour, the computer time required seems prohibitive! --Somehow parameterize the guessed variable so that it does tend to have symmetric error bars, and then calculate the characteristic radius and its error bars from that. But it's not at all clear what
Re: [Ifeffit] Asymmetric error bars in IFeffit
Another reason, from my point of view, is that FEFF wasn't accurate enough to use on its own without references. Also, it still can be argued that the process of data reduction and filtering produces distortions which aren't captured by using FEFF alone. Further, if one is comparing very similar systems, e.g. bulk and nano of the same stuff, then with the exception of multiple scattering, the one system should be an ideal reference for the other. A trick I used to do: Suppose, for instance, that I wanted to fit a shell of Zn surrounded by Si (not an actual case). There's no Si-rich zinc silicide to use as a reference, but it's not too hard to make theta-CuAl2, a compound in which all Cu atoms are surrounded by Al in the first shell (this was done). From this, amp and phase functions could be extracted which refer to Cu looking at Al (Cu-Al). Next, to transform this into the desired Zn-Si, I would do FEFF calculations on identical structures with the atoms changed around and take: A(Zn-Si, semi-empirical) = A(Cu-Al, expt)*[A(Zn-Si, FEFF)/A(Cu-Al, FEFF)] phi(Zn-Si, semi-empirical) = phi(Cu-Al, expt)+[Phi(Zn-Si, FEFF)-phi(Cu-Al, FEFF)] with A, phi being amplitude and phase for a given shell, and appropriate account being taken of the distance differences involved. This makes sense if you consider A~ = A*exp(i*phi) to be one of the factors in a complex chi~ such that chi = Im(chi~), and you're essentially making a correction to ln(A~). Yes, this was low-rent and subject to errors, but it seemed to make sense provided one didn't try to take it too far, for instance trying to change Al for Au or an oxide for a metal. Brings back memories, not all of them fond :-) mam - Original Message - From: Frenkel, Anatoly To: ifeffit@millenia.cars.aps.anl.gov Sent: Friday, October 22, 2010 2:38 PM Subject: Re: [Ifeffit] Asymmetric error bars in IFeffit On a related subject, now I understand why we use the concept of chemical transferability of amplitudes and phases by recycling the same FEFF path for different systems. The true reason is historic: back then it took one hour for one FEFF calculation Anatoly -- From: ifeffit-boun...@millenia.cars.aps.anl.gov ifeffit-boun...@millenia.cars.aps.anl.gov To: XAFS Analysis using Ifeffit ifeffit@millenia.cars.aps.anl.gov Sent: Fri Oct 22 16:23:08 2010 Subject: [Ifeffit] Asymmetric error bars in IFeffit Hi all, I'm puzzling over an issue with my latest analysis, and it seemed like the sort of thing where this mailing list might have some good ideas. First, a little background on the analysis. It is a simultaneous fit to four samples, made of various combinations of three phases. Mossbauer has established which samples include which phases. One of the phases itself has two crystallographically inequivalent absorbing sites. The result is that the fit includes 12 Feff calculations, four data sets, and 1000 paths. Remarkably, everything works quite well, yielding a satisfying and informative fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to Ifeffit and Horae for making such a thing possible! Several of the parameters that the fit finds are characteristic crystallite radii for the individual phases. In my published fits, I often include a factor that accounts for the fact that a phase is nanoscale in a crude way: it assumes the phase is present as spheres of uniform radius and applies a suppression factor to the coordination numbers of the paths as a function of that radius and of the absorber-scatterer distance. Even though this model is rarely strictly correct in terms of morphology and size dispersion, it gives a first-order approximation to the effect of the reduced coordination numbers found in nanoscale materials. Some people, notably Anatoly Frenkel, have published models which deal with this effect much more realistically. But those techniques also require more fitted variables and work best with fairly well-behaved samples. I tend to work with messy chemical samples of free nanoparticles where the assumption of sphericity isn't terrible, and the size dispersion is difficult to model accurately. At any rate, the project I'm currently working on includes a fitted characteristic radius of the type I've described for each of the phases in each of the samples. And again, it seems to work pretty well, yielding values that are plausible and largely stable. That's the background information. Now for my question: The effect of the characteristic radius on the spectrum is a strongly nonlinear function of that radius. For example, the difference between the EXAFS spectra of 100 nm and 1000 nm single crystals due to the coordination number effect is completely negligible. The difference between 1 nm and 10 nm crystals, however, is huge. So for very
Re: [Ifeffit] Asymmetric error bars in IFeffit
Matthew, if you relied on FEFF as one part of the complex calculation, where the other part was the experimentally extracted one, you could've as well done everything with just FEFF. Why didn't you? A. From: ifeffit-boun...@millenia.cars.aps.anl.gov ifeffit-boun...@millenia.cars.aps.anl.gov To: XAFS Analysis using Ifeffit ifeffit@millenia.cars.aps.anl.gov Sent: Fri Oct 22 18:01:17 2010 Subject: Re: [Ifeffit] Asymmetric error bars in IFeffit Another reason, from my point of view, is that FEFF wasn't accurate enough to use on its own without references. Also, it still can be argued that the process of data reduction and filtering produces distortions which aren't captured by using FEFF alone. Further, if one is comparing very similar systems, e.g. bulk and nano of the same stuff, then with the exception of multiple scattering, the one system should be an ideal reference for the other. A trick I used to do: Suppose, for instance, that I wanted to fit a shell of Zn surrounded by Si (not an actual case). There's no Si-rich zinc silicide to use as a reference, but it's not too hard to make theta-CuAl2, a compound in which all Cu atoms are surrounded by Al in the first shell (this was done). From this, amp and phase functions could be extracted which refer to Cu looking at Al (Cu-Al). Next, to transform this into the desired Zn-Si, I would do FEFF calculations on identical structures with the atoms changed around and take: A(Zn-Si, semi-empirical) = A(Cu-Al, expt)*[A(Zn-Si, FEFF)/A(Cu-Al, FEFF)] phi(Zn-Si, semi-empirical) = phi(Cu-Al, expt)+[Phi(Zn-Si, FEFF)-phi(Cu-Al, FEFF)] with A, phi being amplitude and phase for a given shell, and appropriate account being taken of the distance differences involved. This makes sense if you consider A~ = A*exp(i*phi) to be one of the factors in a complex chi~ such that chi = Im(chi~), and you're essentially making a correction to ln(A~). Yes, this was low-rent and subject to errors, but it seemed to make sense provided one didn't try to take it too far, for instance trying to change Al for Au or an oxide for a metal. Brings back memories, not all of them fond :-) mam - Original Message - From: Frenkel, Anatoly mailto:fren...@bnl.gov To: ifeffit@millenia.cars.aps.anl.gov Sent: Friday, October 22, 2010 2:38 PM Subject: Re: [Ifeffit] Asymmetric error bars in IFeffit On a related subject, now I understand why we use the concept of chemical transferability of amplitudes and phases by recycling the same FEFF path for different systems. The true reason is historic: back then it took one hour for one FEFF calculation Anatoly From: ifeffit-boun...@millenia.cars.aps.anl.gov ifeffit-boun...@millenia.cars.aps.anl.gov To: XAFS Analysis using Ifeffit ifeffit@millenia.cars.aps.anl.gov Sent: Fri Oct 22 16:23:08 2010 Subject: [Ifeffit] Asymmetric error bars in IFeffit Hi all, I'm puzzling over an issue with my latest analysis, and it seemed like the sort of thing where this mailing list might have some good ideas. First, a little background on the analysis. It is a simultaneous fit to four samples, made of various combinations of three phases. Mossbauer has established which samples include which phases. One of the phases itself has two crystallographically inequivalent absorbing sites. The result is that the fit includes 12 Feff calculations, four data sets, and 1000 paths. Remarkably, everything works quite well, yielding a satisfying and informative fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to Ifeffit and Horae for making such a thing possible! Several of the parameters that the fit finds are characteristic crystallite radii for the individual phases. In my published fits, I often include a factor that accounts for the fact that a phase is nanoscale in a crude way: it assumes the phase is present as spheres of uniform radius and applies a suppression factor to the coordination numbers of the paths as a function of that radius and of the absorber-scatterer distance. Even though this model is rarely strictly correct in terms of morphology and size dispersion, it gives a first-order approximation to the effect of the reduced coordination numbers found in nanoscale materials. Some people, notably Anatoly Frenkel, have published models which deal with this effect much more realistically. But those techniques also require more fitted variables and work best with fairly well-behaved samples. I tend to work with messy chemical samples of free nanoparticles where the assumption of sphericity isn't terrible, and the size dispersion is difficult to model accurately. At any rate, the project I'm currently working on includes a fitted characteristic radius
