[Ifeffit] Distortion of transmission spectra due to particle size

[Kropf, Arthur Jeremy]

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 at millenia.cars.aps.anl.gov 
> [mailto:ifeffit-bounces at 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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