Distortion of transmission spectra due to particle size
Hi all, I'm tracking down a piece of EXAFS lore which I think is incorrect. I've seen it said that you cannot compensate for the distortion introduced by large particle sizes by making the sample thicker. Certainly thick samples have their own set of issues (e.g. "thickness effects" from harmonics), but I've seen the claim that the mathematics of the distortions introduced by nonuniformity means that there is a particle-size distortion that is independent of thickness. This claim is sometimes accompanied by an equation giving chi_eff/chi_real as a function of particle size diameter D and various absorption coefficients. I've eventually traced this equation back to a paper by Lu and Stern from 1983, have walked through the derivation, and believe there is a flaw in the logic that has led to the erroneous--and widely quoted-- conclusion that thickness cannot compensate for particle size. The paper, for those who want to follow along, is K. Lu and E. A. Stern, "Size effect of powdered sample on EXAFS amplitude," Nucl. Instrm. and Meth. 212, 475-478 (1983). They calculate the intensity transmitted by a spherical particle, and from there calculate the attenuation in the normalized EXAFS signal for a beam passing through that particle. They then, however, extend this to multiple layers of particles by the following argument: "Finally, the attenuation in N layers is given by (I/I0)^N, where I is the transmitted intensity through one layer. Xeff for N layers is then the same as for a single layer since N will cancel in the final result." This is not the case, is it? It seems to me that their analysis assumes that the spheres in subsequent layers line up with the spheres in previous ones, so that thick spots are always over thick and thin spots over thin. It's little wonder, then, that making the sample thicker does not improve the uniformity according to that analysis. I've done a calculation for the effects of uniformity in a somewhat different way, and found that it is indeed true that multiple layers on particles show less distortion due to nonuniformity that a single layer of particles of the same size, just as one would intuitively imagine, and in contrast to Lu and Stern. Do you agree that the extrapolation to multiple layers in the original Lu and Stern paper is not correct, or have I misled myself somehow? --Scott Calvin Faculty at Sarah Lawrence College Currently on sabbatical at Stanford Synchrotron Radiation Laboratory P.S. None of this should be taken as an endorsement of overly thick samples! Harmonics and the like are a concern regardless of the uniformity issue.
Scott, I think you are correct in principle that more layers can reduce the thickness effect problem. If harmonics were not an issue, eventually if you pile up enough random layers, the thickness will be uniform. Whether this is useful in practice is another matter, but suspect it may not be when single particle absorption is large. Jeremy
-----Original Message----- From: ifeffit-bounces@millenia.cars.aps.anl.gov [mailto:ifeffit-bounces@millenia.cars.aps.anl.gov] On Behalf Of Scott Calvin Sent: Monday, November 22, 2010 1:46 PM To: XAFS Analysis using Ifeffit Subject: [Ifeffit] Distortion of transmission spectra due to particle size
Hi all,
I'm tracking down a piece of EXAFS lore which I think is incorrect.
I've seen it said that you cannot compensate for the distortion introduced by large particle sizes by making the sample thicker. Certainly thick samples have their own set of issues (e.g. "thickness effects" from harmonics), but I've seen the claim that the mathematics of the distortions introduced by nonuniformity means that there is a particle-size distortion that is independent of thickness. This claim is sometimes accompanied by an equation giving chi_eff/chi_real as a function of particle size diameter D and various absorption coefficients.
I've eventually traced this equation back to a paper by Lu and Stern from 1983, have walked through the derivation, and believe there is a flaw in the logic that has led to the erroneous--and widely quoted-- conclusion that thickness cannot compensate for particle size.
The paper, for those who want to follow along, is K. Lu and E. A. Stern, "Size effect of powdered sample on EXAFS amplitude," Nucl. Instrm. and Meth. 212, 475-478 (1983).
They calculate the intensity transmitted by a spherical particle, and from there calculate the attenuation in the normalized EXAFS signal for a beam passing through that particle.
They then, however, extend this to multiple layers of particles by the following argument:
"Finally, the attenuation in N layers is given by (I/I0)^N, where I is the transmitted intensity through one layer. Xeff for N layers is then the same as for a single layer since N will cancel in the final result."
This is not the case, is it? It seems to me that their analysis assumes that the spheres in subsequent layers line up with the spheres in previous ones, so that thick spots are always over thick and thin spots over thin. It's little wonder, then, that making the sample thicker does not improve the uniformity according to that analysis.
I've done a calculation for the effects of uniformity in a somewhat different way, and found that it is indeed true that multiple layers on particles show less distortion due to nonuniformity that a single layer of particles of the same size, just as one would intuitively imagine, and in contrast to Lu and Stern.
Do you agree that the extrapolation to multiple layers in the original Lu and Stern paper is not correct, or have I misled myself somehow?
--Scott Calvin Faculty at Sarah Lawrence College Currently on sabbatical at Stanford Synchrotron Radiation Laboratory
P.S. None of this should be taken as an endorsement of overly thick samples! Harmonics and the like are a concern regardless of the uniformity issue.
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I think you are correct in principle that more layers can reduce the thickness effect problem. If harmonics were not an issue, eventually if you pile up enough random layers, the thickness will be uniform. Whether this is useful in practice is another matter, but suspect it may not be when single particle absorption is large.
I think I agree with this. Among my beamline's users, a very common problem is preping samples that, as Matthew suggested, have boulders either on tape or in BN. If the individual particles/agglomerates are 10's of absorption lengths (which *is* a common problem among my users) then ignoring harmonics and stackin' 'em up won't help. So stacking as a solution to pinholes only works if the particles are small enough to begin with -- in which case it won't be that hard to make a good sample in the first place! B -- Bruce Ravel ----------------------------------- bravel@bnl.gov National Institute of Standards and Technology Synchrotron Methods Group at Brookhaven National Laboratory Building 535A Upton NY, 11973 My homepage: http://cars9.uchicago.edu/~ravel EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/
I think there is a confusion over what is being averaged. As an example, consider a layer of particles which are completely opaque, and let's say that the area fraction is 1/2. If the particles lined up, then the transmission would be 1/2 for any N, whereas if the layers were random, then you'd get a transmission of 1/2**N. The power law idea can be thought of in terms of probabilities. The transmission of a layer is the probability of a photon getting through. Now consider N layers which are unregistered. Then, for a photon to get through, it has to "roll the dice" N times, and the probability of transmission through each layer is independent, hence the (trans)**N law. That said, it is a common error for people to say things like "but I diluted the stuff 100x in BN; I should be immune to overabsorptiob and thickness effect because the edge jump in transmission is 0.01". Sorry, if the particles are mm-size, to give an extreme example, then you can dilute all you want and still not get the right answer. mam On 11/22/2010 11:45 AM, Scott Calvin wrote:
Hi all,
I'm tracking down a piece of EXAFS lore which I think is incorrect.
I've seen it said that you cannot compensate for the distortion introduced by large particle sizes by making the sample thicker. Certainly thick samples have their own set of issues (e.g. "thickness effects" from harmonics), but I've seen the claim that the mathematics of the distortions introduced by nonuniformity means that there is a particle-size distortion that is independent of thickness. This claim is sometimes accompanied by an equation giving chi_eff/chi_real as a function of particle size diameter D and various absorption coefficients.
I've eventually traced this equation back to a paper by Lu and Stern from 1983, have walked through the derivation, and believe there is a flaw in the logic that has led to the erroneous--and widely quoted--conclusion that thickness cannot compensate for particle size.
The paper, for those who want to follow along, is K. Lu and E. A. Stern, "Size effect of powdered sample on EXAFS amplitude," Nucl. Instrm. and Meth. 212, 475-478 (1983).
They calculate the intensity transmitted by a spherical particle, and from there calculate the attenuation in the normalized EXAFS signal for a beam passing through that particle.
They then, however, extend this to multiple layers of particles by the following argument:
"Finally, the attenuation in N layers is given by (I/I0)^N, where I is the transmitted intensity through one layer. Xeff for N layers is then the same as for a single layer since N will cancel in the final result."
This is not the case, is it? It seems to me that their analysis assumes that the spheres in subsequent layers line up with the spheres in previous ones, so that thick spots are always over thick and thin spots over thin. It's little wonder, then, that making the sample thicker does not improve the uniformity according to that analysis.
I've done a calculation for the effects of uniformity in a somewhat different way, and found that it is indeed true that multiple layers on particles show less distortion due to nonuniformity that a single layer of particles of the same size, just as one would intuitively imagine, and in contrast to Lu and Stern.
Do you agree that the extrapolation to multiple layers in the original Lu and Stern paper is not correct, or have I misled myself somehow?
--Scott Calvin Faculty at Sarah Lawrence College Currently on sabbatical at Stanford Synchrotron Radiation Laboratory
P.S. None of this should be taken as an endorsement of overly thick samples! Harmonics and the like are a concern regardless of the uniformity issue.
_______________________________________________ Ifeffit mailing list Ifeffit@millenia.cars.aps.anl.gov http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
Scott, I agree with Jeremy and Matthew. Layering very small (compared to an absorption length) spheres is exactly what "powder on tape" and mixing with a low-Z binder do, and that's why these are the preferred methods for turning a powder into a sample of uniform thickness. If the spheres are not small, then these techniques don't help. In fact, Lu and Stern show nicely that more layers of smaller particles is better than a few layers of thicker particles. I would say that is the main point of their work. Perhaps you read it differently.
"Finally, the attenuation in N layers is given by (I/I0)^N, where I is the transmitted intensity through one layer. Xeff for N layers is then the same as for a single layer since N will cancel in the final result."
This is not the case, is it? It seems to me that their analysis assumes that the spheres in subsequent layers line up with the spheres in previous ones, so that thick spots are always over thick and thin spots over thin.
I don't think they are making that assumption. I interpret that to mean only that I/I_0 (the attenuation integrated over the layer) is multiplicative, and so that ratios of Xeff (what we would probably call mu) are not distorted by having multiple layers. I think they are assuming that the layers are close to consistent in the amount of total material they have, but not how that material is distributed within or between layers.
It's little wonder, then, that making the sample thicker does not improve the uniformity according to that analysis.
I don't think that is a conclusion that Lu and Stern make. --Matt
participants (5)
-
Kropf, Arthur Jeremy -
Matt Newville -
Matthew Marcus -
Ravel, Bruce -
Scott Calvin