I think you're missing a key idea concerning this procedure. Both my method and Anatoly Frenkel's method for finding particle size rely on comparing the effective coordination for different paths. I am skeptical of EXAFS determinations of particle size using only one path, as coordination number is hard to tease out from other effects that suppress amplitude (sample quality, disorder, vacancies...). But the relative coordination number of different shells is more reliable.

If you're using Artemis, this is simple enough to do, as each path has a reff value (which is r in the formula you give), and you can define a guessed parameter R. (To do this right, you need to make sure that the r for multiple-scattering paths is the distance from the absorber to the furthest scatterer, not the half-path length. That means putting the value in "by hand" for those paths, rather than using reff.)

(If you want a really quick and dirty method, collect a reference for a bulk standard and for your sample, and multiply the FT of the bulk spectrum by the formula, adjusting R until you get a good match. The quick and dirty method doesn't handle multiple-scattering correctly, and has the usual problem of the fact that even for direct-scattering paths the peaks of the FT are shifted from actual absorber-scatterer distances. But it is model-free, which can be nice in some cases.)

By the way, the formula you've cited is derived for spherical particles. If they're kinda sorta spherical, it will still give a decent approximation and fit. But if the particles are needle-shaped or flat plates, then it doesn't work well. You either have to derive another formula, or look at Anatoly's papers, which have addressed a number of common morphologies.

So far, everything I've said applies to metals, and you asked about oxides. While most of this also applies to oxides, it's important to realize that the nearest-neighbor oxide paths are not suppressed at all; i.e. the formula doesn't apply until the first metal-metal path (but does apply to metal-oxide paths further out). This is because the surface of such particles is generally comprised of oxygen atoms, and the first scattering shell is thus fully populated no matter how small the particles are.

On Mar 8, 2010, at 1:45 PM, bill.schwartz@yale.edu wrote:

Hi Scott,

We met a couple of times at the EXAFS last two EXAFS workshops at BNL, for relative beginners like me.

I am attempting to determine the particle size of PdO particles supported on Alumina (3% PdO/Al2O3).

I am wondering if I can collect EXAFS data and use the formula in your 2003 Journal of Applied Physics paper(*) to estimate PdO particle size:

N_nano = [1-3/4(r/R)+1/16(r/R)^3]N_bulk

Here is a little more background:

PdO particles on metal oxide supports are generally smaller and more dispersed in comparison to Pd metal on the same support. Also, if PdO is reduced and then re-oxidized at varying temperatures, the re-oxidized PdO particle size varies with temperature, with higher oxidation temperatures resulting in smaller PdO particle size.

I have prepared a series of samples of 3% PdO/Al2O3, where the PdO has been been reduced and then re-oxideized at various temperatures, and I would like to use EXAFS to determine the coordination number of my various samples.

A major difference in my planned experiment compared to what you described in your paper is that you examined nickel metal, while I am looking at a metal oxide.

So my current questions are:

1) Is the above formula reasonable for determining bulk particle radius (R) of metal oxides?

2) If yes, then what is r, since scattering distance between Pd - Pd and Pd - O are different? Is it reasonable to average the distances?

3) Can N(nano) be determined by averaging the coordination numbers for the Pd-Pd and Pd-O paths?

Any guidance you can provide will be greatly appreciated.

Sincerely,

Bill

(*) Determination of crystallite size in a magnetic nanocomposite using extended x-ray absorption fine structure