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Modeling atomic structure at the nanoscale using the PDF: simulation studies of monoatomic nanoparticles



Katharine M. Mullen, Victor L. Krayzman, Igor Levin


The pair distribution function (PDF), as determined from total x-ray or neutron scattering, is a valuable probe of atomic arrangements in nanoparticles. Structural information in such experimental PDF data is convoluted with the effects of particle shape, size, extended defects, and internal substructure. We used synthetic PDF data generated for an ensemble of monoatomic nanoparticles having different degrees of displacive atomic disorder in the particle surface compared to the interior to explore a feasibility of reliably extracting key model parameters (i.e. a lattice constant, particle diameter, atomic displacement parameters for the interior and the surface, and thickness of the surface layer) from the experimental data in the absence of systematic errors. Several optimization algorithms were tested and a differential evolution algorithm was selected as the most reliable and accurate. Fitting synthetic PDF data using this algorithm was demonstrated to recover the correct set of parameters with relatively small uncertainty bounds. We further showed that this methodology allows for a reliable selection of the correct model among several alternatives. The approach described in this paper provides effective means for determining the amount of information that can be recovered via model fitting from experimental PDF data, if devoid from systematic errors. Software for nanoparticle simulation and model optimization is provided in open-source form, to allow reproduction and extension of our results.
Journal of Applied Crystallography


pair distribution function, nanoparticle modeling, differential evolution, global optimization


Mullen, K. , Krayzman, V. and Levin, I. (2010), Modeling atomic structure at the nanoscale using the PDF: simulation studies of monoatomic nanoparticles, Journal of Applied Crystallography (Accessed July 15, 2024)


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Created August 17, 2010, Updated February 19, 2017