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It is argued 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 a surface fractal is shown to be a sum of the amplitudes of the composing mass fractals. Various approximations for the scattering intensity of surface fractals are considered. It is shown that small-angle scattering (SAS) from a surface fractal can be explained in terms of a 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) ∝ q^{D_{\rm s}-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−τdr, with Ds = τ − 1. The distribution is continuous for random fractals and discrete for deterministic fractals. A model of the surface deterministic fractal is suggested, the surface Cantor-like fractal, which is a sum of three-dimensional Cantor dusts at various iterations, and its scattering properties are studied. The present analysis allows one to extract additional information from SAS intensity for dilute aggregates of single-scaled surface fractals, such as the fractal iteration number and the scaling factor.

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Portable Document Format (PDF) file https://doi.org/10.1107/S1600576717005696/vg5063sup1.pdf
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