[Ifeffit] Distortion of transmission spectra due to particlesize

[Kropf, Arthur Jeremy]

Scott,

You haven't totally convinced me, but clearly what we all need to do to
run powdered samples correctly is to use 2D detectors with pixels much
smaller than the absorption length and bin pixels of the same total
absorbance.

You heard it here first.

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: Tuesday, November 23, 2010 3:22 PM
> To: XAFS Analysis using Ifeffit
> Subject: Re: [Ifeffit] Distortion of transmission spectra due 
> to particlesize
> 
> 
> On Nov 22, 2010, at 2:55 PM, Scott Calvin wrote:
> 
> > But compare a monolayer of particles with a diameter equal to 0.4 
> > absorption lengths with four strips of tape of that kind 
> stacked. Do 
> > we really think the distortion due to nonuniformity will be 
> as bad in 
> > the latter case as in the first? In practice, I think many 
> > transmission samples fall in roughly that regime, so the question 
> > isn't just academic.
> 
> OK, I've got it straight now. The answer is yes, the 
> distortion from nonuniformity is as bad for four strips 
> stacked as for the single strip. This is surprising to me, 
> but the mathematics is fairly clear.  
> Stacking multiple layers of tape rather than using one thin 
> layer improves the signal to noise ratio, but does nothing 
> for uniformity.  
> So there's nothing wrong with the arguments in Lu and Stern, 
> Scarrow, etc.--it's the notion I had that we use multiple 
> layers of tape to improve uniformity that's mistaken.
> 
> A bit on how the math works out: for Gaussian distributions 
> of thickness, the absorption is attenuated (to first order) 
> by a term directly proportional to the variance in the 
> distribution. The standard deviation in thickness from point 
> to point in a stack of N tapes generally increases as the 
> square root of N (typical statistical behavior). This means 
> that the fractional standard deviation goes down as the 
> square root of N. In casual conversation, we would usually 
> identify a sample with thickness variations of +/-5 % as 
> being "more uniform" than one with thickness variations of 
> +/- 8%, so it's natural to think that a stack of tapes is 
> more uniform than a single one. But since the attenuation is 
> proportional to the variance (i.e.  
> the square of the standard deviation), it actually increases 
> in proportion to N. Since the absorption is also increasing 
> in proportion to N, the attenuation remains the same size 
> relative to the absorption, and the spectrum is as distorted as ever.
> 
> This result doesn't actually depend on having a Gaussian 
> distribution of thickness. if each layer has 10% pinholes, 
> for instance, at first blush it seems as if two layers should 
> solve most of the problem: the fraction of pinholes drops to 
> 1%. But those pinholes are now compared to a sample which is 
> twice as thick, on average, and thus create nearly as much 
> distortion as before. Add to this that there is now 9% of the 
> sample that is half the thickness of the rest, and the 
> situation hasn't improved any. I've worked through the math, 
> and the cancellation of effects is precise--a two layer 
> sample has the identical nonuniformity distortion to a one layer one.
> 
> (There is probably a simple and compelling argument as to why 
> this distortion is independent of the number of randomly 
> aligned layers for ANY thickness distribution, but I haven't 
> yet found it.)
> 
> * * *
> 
> For me personally, knowing this will cause some changes in 
> the way I prepare samples.
> 
> First of all, I'm going to move my bias more toward the thin 
> end. My samples are generally pretty concentrated, so signal 
> to noise is not a big issue. If I'm also not improving 
> uniformity by using more layers of tape, there's no reason 
> for me not to keep the total absorption down around 1, rather 
> than around 2.
> 
> Secondly, I'll approach the notion of eyeballing the 
> assembled stack of tapes for uniformity, whether with the 
> naked eye or a microscope, with more caution--particularly 
> when teaching new students. The idea that a sample which has 
> no evident pinholes is a better sample than one that does is 
> not necessarily true, as the example above with the single 
> layer exhibiting 10% pinholes as compared to the double layer 
> exhibiting 1% demonstrates. Stressing the elimination of 
> visible pinholes will tend to bias students toward thicker 
> samples, but not necessarily better ones.
> 
> 
> --Scott Calvin
> Faculty at Sarah Lawrence College
> Currently on sabbatical at Stanford Synchrotron Radiation 
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