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복잡계 이론물리 연구단
복잡계 이론물리 연구단
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Scattering from surface fractals in terms of composing mass fractals

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Title
Scattering from surface fractals in terms of composing mass fractals
Author(s)
A. Yu. Cherny; E. M. Anitas; V. A. Osipov; A. I. Kuklin
Publication Date
2017-06
Journal
JOURNAL OF APPLIED CRYSTALLOGRAPHY, v.50, no.3, pp.919 - 931
Publisher
WILEY-BLACKWELL
Abstract
We argue that a finite iteration of any surface fractal can be composed of mass-fractal iterations of the same fractal dimension. Within this assertion, the scattering amplitude of surface fractal is shown to be a sum of the amplitudes of composing mass fractals. Various approximations for the scattering intensity of surface fractal are considered. It is shown that small-angle scattering (SAS) from a surface fractal can be explained in terms of power-law distribution of sizes of objects composing the fractal (internal polydispersity), provided the distance between objects is much larger than their size for each composing mass fractal. The power-law decay of the scattering intensity I(q) ∝ qDs−6, where 2 < Ds < 3 is the surface fractal dimension of the system, is realized as a non-coherent sum of scattering amplitudes of three-dimensional objects composing the fractal and obeying a power-law distribution dN(r) ∝ r−dr, with Ds = −1. The distribution is continuous for random fractals and discrete for deterministic fractals. We suggest a model of surface deterministic fractal, the surface Cantorlike fractal, which is a sum of three-dimensional Cantor dusts at various iterations, and study its scattering properties. The present analysis allows us to extract additional information from SAS data, such us the edges of the fractal region, the fractal iteration number and the scaling factor.
URI
http://pr.ibs.re.kr/handle/8788114/3619
DOI
10.1107/S1600576717005696
ISSN
0021-8898
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > Journal Papers (저널논문)
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