On the Modeling of the Diffraction Pattern from Metal Nanocrystals
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METAL nanocrystals are a subject of study in several and quite different research fields, like clean energy production and biomedical applications, both requiring nanocrystalline metal surfaces to activate/ enhance oxidation.[1,2] In both cases, the key is controlling nanocrystal size and shape, to obtain a specific catalytic behavior and improve the performance. While nanotechnology actively pursues these important achievements, characterization techniques need to evolve to provide increasingly detailed information. Powder diffraction has so far lagged behind, as in many cases even in top level research studies just qualitative or partial information has been exploited: X-Ray Diffraction (XRD) line profiles are often analyzed in terms of peak width for a quick assessment of some characteristic length of the studied system.[3,4] Well known alternatives, much exploited in the cited studies, employ Transmission Electron Microscopy (TEM): spectacular pictures and detailed information can be obtained by high resolution TEM, and more specifically by HighAngle Annular Dark-Field imaging (HAADF),[5–7] although the analysis can hardly concern more than just a few nanoparticles. Sample preparation can result in a biased sampling of the statistical population (e.g., by excluding larger or smaller particles, or by focusing only on loose items and excluding agglomerates), and beam energy can degrade the specimen or promote phase transformations. XRD is a perfectly complementary technique, as it can support electron microscopy in providing a sound statistical basis: a typical powder diffraction analysis involves millions to billions of crystalline domains. However, much is still to be understood on the XRD from nanocrystalline materials.
As shown in this paper, the modern powder diffraction theory provides much better and more refined methods than the nearly centenary Scherrer equation and related integral breadth methods.[8,9] Methodologies proposed over the past decade evolved following two different schools of thought. According to the traditional paradigm (1), diffraction is studied in Reciprocal Space (RS); (a) diffraction peaks are described by suitable profile functions, just flexible ones (as in traditional profile fitting), or (b) model-based profile functions, for a direct evaluation of (nano)structural parameters.[10] As an alternative, (2) the Debye Scattering Equation (DSE) is based on the Direct Space (DS) representation of nanocrystals. This provides a detailed picture of the nanostructure, possibly down to the atomic level, although to the cost of a higher complexity and computational demand.[11–13] Differences between the two approaches have not been fully investigated so far, also because no simple and clear experimental cases are available for such a comparison. Atomistic models are convenient in this context: Molecular Dynamics (MD) can be used to build model systems of metal nanocrystals, then generate a corresponding powder diffraction pattern to be used as a plausible benchmark to compare RS and DS methods.[14] Besides co
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