About the Size Cut-Off Effect on Small-Angle Scattering by Stochastic Mass Fractals

Autor: O. V. Tomchuk, Leonid A. Bulavin, Mikhail V. Avdeev
Rok vydání: 2020
Předmět:
Zdroj: Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques. 14:S231-S234
ISSN: 1819-7094
1027-4510
DOI: 10.1134/s1027451020070484
Popis: There are several theoretical approaches for describing the cut-off effect on small-angle scattering curves of mass fractals because of the finite size of the scattering object (e.g., developed cluster of nanoparticles). The problem is to relate the power-law scattering, I(q) = Bq–D (corresponding to the fractal dimension D), at high q-values with the Gunier approximation, I(q) = G exp( $$ - R_{{\text{g}}}^{2}$$ q2/3), at low q-values. Various empirical or semi-empirical functions are used to cut-off correlations in the direct space with the following Fourier transform into the q-dependence of the scattered intensity. Then, the selected approach is verified by comparing the calculated intensity and the model or experimental scattering data. However, up to now no well-proven criterion of correctness was formulated. Here, we employed the fact that the parameters of the two scattering levels are D-dependent, which can be used as an additional test for the correctness of the above approaches. The analysis of the universal combined parameter $${{BR_{{\text{g}}}^{D}} \mathord{\left/ {\vphantom {{BR_{{\text{g}}}^{D}} G}} \right. \kern-0em} G}$$ as a function of D revealed different behavior for various models. The true dependence was obtained using the calculations for clusters generated by the algorithm, which allows regulating D. The simulated series of clusters with different sizes and packing densities gave the same predicted universal D-dependence of the combined parameter. The comparison showed that no theoretical data fit the simulations. One can see either principally different behavior, especially as D → 3, or some kind of renormalization is required. The given analysis is considered as a step towards understanding scattering by multiscale systems at a new level.
Databáze: OpenAIRE
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