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Combined fitting of small‐ and wide‐angle X‐ray total scattering data from nanoparticles: benefits and issues
Author(s) -
Gagin Anton,
Allen Andrew J.,
Levin Igor
Publication year - 2014
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576714001046
Subject(s) - fourier transform , scattering , data set , algorithm , pareto principle , function (biology) , reciprocal lattice , curve fitting , parametric statistics , computational physics , small angle scattering , computer science , optics , physics , biological system , mathematics , mathematical optimization , mathematical analysis , statistics , evolutionary biology , diffraction , biology
Simultaneous fitting of small‐ (SAS) and wide‐angle (WAS) X‐ray total scattering data for nanoparticles has been explored using both simulated and experimental signals. The nanoparticle types included core/shell metal and quantum‐dot CdSe systems. Various combinations of reciprocal‐ and real‐space representations of the scattering data have been considered. Incorporating SAS data into the fit consistently returned more accurate particle‐size distribution parameters than those obtained by fitting the WAS data alone. A popular method for fitting the Fourier transform of the WAS data ( i.e. a pair‐distribution function), in which the omitted SAS part is represented using a parametric function, typically yielded significantly incorrect results. The Pareto optimization method combined with a genetic algorithm proved to be effective for simultaneous SAS/WAS analyses. An approach for identifying the most optimal solution from the Pareto set of solutions has been proposed.