Convex and concave successions of power-law decays in small-angle scattering

[摘要] The small-angle scattering (SAS) structure factor from a new model of a 3D deterministic fractal in which the relative positions and the number of structural units vary with fractal iteration number is calculated. It is shown that, depending on the relative positions of scattering units inside the fractal, we can obtain various types of power-law successions, such as: convex/concave - when the absolute value of the scattering exponent of the first power-law decay is higher/smaller than that of the subsequent power- law decay, or any combination of them (i.e. convex-concave or concave-convex). The obtained results can explain experimental SAS (neutron or X-rays) data which are characterized by a succession of power-law decays of arbitrary length.

[发布机构] Joint Institute for Nuclear Research, Dubna, Moscow region; 141980, Russia^1;Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest; RO-077125, Romania^2

[效力级别] 数学

[关键词] Absolute values;Iteration numbers;Power law decay;Relative positions;Small angle scattering;Structural unit;Structure factors;Types of power