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Comparison of extended x-ray absorption fine structure and Scherrer analysis of x-ray diffraction as methods for determining mean sizes of polydisperse nanoparticles
1.The term nanocrystal is used here for either a monocrystalline nanoparticle or a nanocrystalline inclusion within a matrix.
5.It is probable that data with lower noise levels could have been collected using synchrotron radiation. Our intention here is to compare crystallite size determination techniques commonly found in the literature; for this purpose, Scherrer analysis is generally performed using laboratory x-ray sources.
6.Some samples (primarily the mixed samples) were also analyzed using a Scintag XDS 2000 diffractometer to test for instrument variability. Samples analyzed on both instruments produced particle size measurements consistent to within the reported uncertainties.
7.A. West, Solid State Chemistry and Its Applications (Wiley, West Sussex, 1984).
8.JADE 6.1 (Materials Data, Livermore, CA, 2002).
14.699 independent points, 41 free parameters, and of freedom for the 12 samples according to the Nyquist criterion. The EXAFS -factor, a measure of mismatch between data and fit, was 0.03.
17.Relative to the first peak of the derivative of the energy spectrum.
18.The mean square radial displacements were initially allowed to vary for each sample, but were not found to differ significantly between samples; thus in the final fits all samples were fit to one set of same values: were found for the nearest, next-nearest, and more distant neighbors, respectively.
22.Note that, due to the difficulties posed by aggregation and polycrystallinity, observer bias was undoubtedly present for the TEM results.
23.The method used here is somewhat time-consuming and requires considerable specialized expertise. In cases in which EXAFS is already being used to determine other characteristics of the sample, however, an analysis of this type requires little additional effort. If an easier, quicker, and less accurate method is desired, a one parameter fit is appropriate.
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