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Efficient computation of the scattering intensity from systems of nonspherical particles

Journal article
Authors Rasmus Persson
Johan Bergenholtz
Published in Journal of Applied Crystallography
Volume 49
Issue 5
Pages 1524-1531
ISSN 0021-8898
Publication year 2016
Published at Department of Chemistry and Molecular Biology
Pages 1524-1531
Language en
Keywords small-angle scattering, form factor, structure factor, Monte Carlo
Subject categories Surface and colloid chemistry, Statistical mechanics


The analysis of the angle dependence of the elastic scattering of radiation from a sample is an efficient and non-invasive technique that is used in fundamental science, in medicine and in technical quality control in industry. Precise information on the shape, size, polydispersity and interactions of a colloidal sample is readily obtained provided an underlying scattering model, i.e. form and structure factors, can be computed for the sample. Here, a numerical method that can efficiently compute the form factor amplitude (and thus the scattering intensity) of nonspherical scatterers through an importance sampling algorithm of the Fourier integral of the scattering density is presented. Using the precomputed form factor amplitudes, the calculation of the scattering intensity at any particle concentration then scales linearly with the particle number and linearly with the number of q points for its evaluation. This is illustrated by an example calculation of the scattering by concentrated suspensions of ellipsoidal Janus particles and the numerical accuracy for the computed form factor amplitudes is compared with analytical benchmarks.

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