[Ifeffit] Regarding calculations for scattering amplitude

[Maxim Boyanov]

Hi Pushkar,

 

We recently discussed a bit measuring particle size by interpreting coordination numbers obtained from fitting EXAFS data, also referring to the paper you mention:

 

http://millenia.cars.aps.anl.gov/pipermail/ifeffit/2015-August/thread.html#start

 

The basic idea is that surface atoms are not coordinated to other atoms on the outside (i.e., for your Pd foil the surface Pd atoms would have say 6-8 neighbors instead of 12 for the atoms on the inside) so when the particle size becomes less than a few nm the number of surface atoms become a significant proportion of the total number of atoms and you can now observe this undercoordination as a smaller amplitude (assumed to be due to average coordination number) of some coordination peaks in the FT. How you relate this average coordination decrease to particle size depends a bit on your system. Some approaches have been laid out in the literature, including the paper you mention. See the thread above for other. Some time back I used a “brute force” approach to calculate the average coordination vs size for a small particle of a certain crystal structure (see fig EA-7 in the supplementary material of Geochimica et Cosmochimica Acta 71 (2007) 1898–1912). I took the crystallographic structure and created the list of atom coordinates for a 10 nm spherical particle using the ATOMS program. I then wrote a simple program (which I can’t find now :-) to go through the list and calculate the average coordination for a certain shell by going to all atoms within a particle radius and counting the neighbors in each coordination shell of interest. The result is a graph of average coordination for that coordination shell vs radius, which you can then compare to the coordination numbers obtained in your fits of the EXAFS data to “read off” a particle size. This brute force approach takes into account the crystal structure of your material of interest and the slightly different surface density of atoms when you cut along different planes to create the particle. However, the improved accuracy from that will probably give you a difference in coordination number that is within the uncertainty of the coordination numbers in an EXAFS fit. You can use a spherical particle which is probably OK for your case with Pd, but you can also create say rod-shaped particles that emphasize certain crystallographic planes, depending on your case. 

 

Be aware of some of the issues raised by Scott in his email and in the thread in the link above when comparing EXAFS and TEM determined sizes. Another source of discrepancy may be the assumption that the EXAFS peak amplitude reduction is due only to a coordination number decrease. It is also conceivable that the strain in a 2nm particle gives a contribution to the Debye-Waller factor, potentially affecting the determination of the average coordination number by EXAFS. 

 

Overall, use particle size determinations as an estimate, regardless of the experimental or interpretation method used :-). More importantly, be aware of the pitfalls and their effect on the certainty of the conclusions you present. Unfortunately there doesn’t seem to be a recipe-like approach to the problem yet…

 

Best,

Max. 

 

 

 

 

 

From: Ifeffit [mailto:ifeffit-bounces at millenia.cars.aps.anl.gov] On Behalf Of pushkar shejwalkar
Sent: Thursday, January 21, 2016 3:02 AM
To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
Subject: [Ifeffit] Regarding calculations for scattering amplitude

 

Dear All,

   I sent a related question in the month of Dec but it seems that the question did not appeared on list because of mailbox being full, as we all have received an email. Since mailing list is started again I am sending this question once more.

My question is actually regarding finding out the nanoparticle size. In this respect, I am referring to Harris's work in which by using a simple equation we can roughly estimate the nanoparticle size

J. Appl. Phys., Vol. 94, No. 1, 1 July 2003

 Now the question is that in this paper and another paper I found online as well, it refers to Nnano and Nbulk. I am guessing that this is basically coordination number of nanoparticle and bulk. But my first question is how do I calculate it?? e.g. I am working on Pd K-edge. So should I fit Pd foil with Pd crystal data and get the CN? but that would be 12 anyways. So would Nbulk be 12 in that case? and what will be Nnano then?

In another context, CN is proportional to amplitude, so in that case is it directly proportional? as in, can I simply replaced in formula, Nbulk/Nnano with Amplitudebluk/amplitudenano? 

Third thing is that, if above is true then how should/can I calculated the amplitude? isnt that amplitude is always calculated by Feff? if so could someone help me with the procedure to do so? How will I know amplitude for nanoparticles, because I cannot have FEFF for nanoparticles, right?

I went through lot of material, however, so far my calculations give me a solution that is vaguely correlated to TEM images. The TEM value is about 2nm (rouhgly 20 angstrom). my current values I am getting by solving the equation by my current understanding is only 2Ao. about 10 times less. What I am doing is simply plotting the crude data in athena to get x(R) Vs radial distance graph, calculate A-3 for nanoparticles and bulk and using this as amplitudes. It is possible that I may be doing something totally irrelevant, so please help me in this aspect.

Thank you

Sincerely 

Pushkar

 

-- 

Best Regards,
Pushkar Shejwalkar.
Post-doctoral -Researcher,

Tokyo Engineering University,

Tokyo-to

Japan

 

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