Robust approaches for model‐free small‐angle scattering data analysis
Honecker, Dirk
Bersweiler, Mathias
Costo, Rocio
Kahmann, Tamara
Ludwig, Frank
Leiner, Jon
Jochum, Johanna K.
DOI: https://doi.org/10.1107/S1600576722004356
Persistent URL: http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/10220
Honecker, Dirk; 2Rutherford Appleton LaboratoryISIS Neutron and Muon FacilityChilton OX11 0QX United Kingdom
Bersweiler, Mathias; 3University of LuxembourgPhysics and Materials Science Research Unit162A avenue de la Faïencerie L-1511 Grand Duchy of Luxembourg
Costo, Rocio; 4Instituto de Ciencia de Materiales de MadridICMM/CSICC/Sor Juana Inés de la Cruz 3 Madrid 28049 Spain
Kahmann, Tamara; 5Technische Universität BraunschweigInstitute of Electrical Measurement Science and Fundamental Electrical Engineering and Laboratory for Emerging Nanometrology (LENA)Braunschweig 38106 Germany
Ludwig, Frank; 5Technische Universität BraunschweigInstitute of Electrical Measurement Science and Fundamental Electrical Engineering and Laboratory for Emerging Nanometrology (LENA)Braunschweig 38106 Germany
Leiner, Jon; 1Technische Universität MünchenHeinz Maier-Leibnitz Zentrum (MLZ)Garching D-85748 Germany
Abstract
The small‐angle neutron scattering data of nanostructured magnetic samples contain information regarding their chemical and magnetic properties. Often, the first step to access characteristic magnetic and structural length scales is a model‐free investigation. However, due to measurement uncertainties and a restricted q range, a direct Fourier transform usually fails and results in ambiguous distributions. To circumvent these problems, different methods have been introduced to derive regularized, more stable correlation functions, with the indirect Fourier transform being the most prominent approach. Here, the indirect Fourier transform is compared with the singular value decomposition and an iterative algorithm. These approaches are used to determine the correlation function from magnetic small‐angle neutron scattering data of a powder sample of iron oxide nanoparticles; it is shown that with all three methods, in principle, the same correlation function can be derived. Each method has certain advantages and disadvantages, and thus the recommendation is to combine these three approaches to obtain robust results.
Three different approaches are compared for determination of the correlation function from the small‐angle neutron scattering data of a powder sample of iron oxide nanoparticles.
Subjects
small‐angle scatteringcorrelation functions
Fourier transform
magnetic nanoparticles
modulation of intensity with zero effort
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