[Ifeffit] Distortion of transmission spectra due to particle size

[Matthew Marcus]

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.
>
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