[Ifeffit] Distortion of transmission spectra due to particle size

[Matt Newville]

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