Dear Jatin, There are many approaches for the first part of your question, how to find CNs for model clusters of different sizes and shapes. One approach is to read in the coordinates of each atom in the cluster into a program (my student wrote it but such programs may be out there on internet and available for download) that would calculate the pair distribution function for every atomic species (good also for compounds, not just monometallic clusters).
The advantage is that it can be used for disordered clusters, not just ideal fcc clusters. Then, the area of the PDF histogram peaks corresponding to a specific atomic shell can be calculated and these areas are the coordination numbers of those shells. This method is described in this paper, and I can send you the electronic copy if you'd like. D. Glasner and A. I. Frenkel Geometrical characteristics of regular polyhedra: Application to EXAFS studies of nanoclusters AIP Conf. Proc. 882, 746-748 (2007). How to handle multiple scattering paths that cannot be calculated by the PDF approach? The best chance that this multiple scattering analysis will work is if the clusters have fcc structure for which it is known that the most important ms paths are collinear. Most clusters have convex shape, at least the most commonly studied ones. For convex shapes, if any two points belong to the shape, the line connecting them belongs to the shape too. Hence, the CNs of double and triple scattering collinear paths that connect each atom and its 4th nearest neighbor (and an intervening atom), can be simply related to the CNs of single scattering paths to the 4th nearest neighbors. Those relationships are listed in the paper you cited. It is true that for bulk fcc structures other collinear paths contribute to the fit, and some non-collinear paths are important for the fit. But, those are negligible in clusters which are supposed to be somewhat distorted from ideal fcc structure and, hence, other ms paths are not expected to contribute much because their large degeneracies are lifted and they just cancel each other due to large static disorder in their lengths. hcp clusters also can be analyzed by this approach - there is a paper on that as well: A. M. Karim, V. Prasad, W. W. Lonergan, A. I. Frenkel, J. G. Chen, D. G. Vlachos Correlating particle size and shape of supported Ru/g-Al2O3 with NH3 decomposition activity J. Am. Chem. Soc., 131 , 12230-12239, 2009. Other codes were used, for example, in our recent paper: B. Roldan Cuenya, J. R. Croy, S. Mostafa, F. Behafarid, L. Li, Z. Zhang, J. C. Yang, Q. Wang, A. I. Frenkel Solving the structure of size-selected Pt nanocatalysts synthesized by inverse micelle encapsulation J. Am. Chem. Soc. 132, 8747-8756 (2010) There, we tried different shapes of fcc clusters (known to be synthesized as shape selective) until for a certain cluster shape and size, the set of model CNs plus the model cluster diameter matched well the experimental CNs and diameter (obtained by STEM but in your case you can try using Debye-Scherrer formula). It is the same principle of analysis as in the original JPCB paper you quoted but the code was different than in the AIP Conf Proc paper. The main comment if you are interested in trying this type of analysis is that you have to have a pretty good idea that your clusters are monodispersed and you do not have, for example, unreduced precursors or singly dispersed atoms on support in addition to clusters. If that's the case, XRD will miss it and you will not know what your EXAFS data mean, small clusters of the same size and shape, or a broader size distribution with a lot of unreduced atoms and small clusters. It is a long topic and we often discuss these methods at our short XAFS courses at BNL. The next one, by the way, will be on Nov. 13-15, and I will send a separate announcement to the list when the program is finalized. Hope it helps, Anatoly Sent from my Verizon Wireless 4G LTE Tablet -------- Original message -------- From: "Rana, Jatinkumar Kantilal" Date:07/15/2014 7:43 AM (GMT-05:00) To: ifeffit@millenia.cars.aps.anl.gov Subject: [Ifeffit] crystallite size determination by EXAFS Dear all, I have some questions regarding crystallite size determination by EXAFS. I am investigating a system where there is a formation of metallic Cu in the system. I could see the presence of metallic Cu in the sample by XRD and EXAFS. However, high resolution TEM does not show any evidence of metallic Cu, perhaps the crystallite size is much smaller than the resolving power of the microscope and/or these crystallites are highly disordered. Nevertheless, I thought of estimating the size of Cu crystallites by EXAFS. I know at least two approaches described by two prominent members of the mailing list, Scott Calvin and Anatoly Frenkel. The approach by Scott Calvin (http://link.aip.org/link/JAPIAU/v94/i1/p778/s1&Agg=doi) estimates crystallite size based on an assumption that they are spherical in shape. On the other hand, Anatoly Frenkel’s approach estimates both size and shape of crystallites based on the number of neighbors in each coordination shell obtained from EXAFS fit http://pubs.acs.org/doi/abs/10.1021/jp012769j I have questions about the second approach. I would like to know how to calculate the number of neighbors in various coordination shells as a function of cluster size for different shapes ? Conversely, if one knows the number of neighbors in various shells from EXAFS fits, then how to correlate those numbers to clusters of different sizes and shapes as discussed by Anatoly Frenkel. I know my questions are very specific, but I am sure many in the list would have already tried both these approaches and may provide some valuable insights. Many thanks in advance ! With best regards, Jatin ________________________________ Helmholtz-Zentrum Berlin für Materialien und Energie GmbH Mitglied der Hermann von Helmholtz-Gemeinschaft Deutscher Forschungszentren e.V. Aufsichtsrat: Vorsitzender Prof. Dr. Dr. h.c. mult. Joachim Treusch, stv. Vorsitzende Dr. Beatrix Vierkorn-Rudolph Geschäftsführung: Prof. Dr. Anke Rita Kaysser-Pyzalla, Thomas Frederking Sitz Berlin, AG Charlottenburg, 89 HRB 5583 Postadresse: Hahn-Meitner-Platz 1 D-14109 Berlin http://www.helmholtz-berlin.de
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