Small-angle scattering from multiphase fractals
Small‐angle scattering (SAS) intensities observed experimentally are often characterized by the presence of successive power‐law regimes with various scattering exponents whose values vary from −4 to −1. This usually indicates multiple fractal structures of the sample characterized by different size...
Saved in:
Published in | Journal of applied crystallography Vol. 47; no. 1; pp. 198 - 206 |
---|---|
Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
5 Abbey Square, Chester, Cheshire CH1 2HU, England
International Union of Crystallography
01.02.2014
Blackwell Publishing Ltd |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | Small‐angle scattering (SAS) intensities observed experimentally are often characterized by the presence of successive power‐law regimes with various scattering exponents whose values vary from −4 to −1. This usually indicates multiple fractal structures of the sample characterized by different size scales. The existing models explaining the crossover positions (that is, the points where the power‐law scattering exponent changes) involve only one contrast parameter, which depends solely on the ratio of the fractal sizes. Here, a model that describes SAS from a multiphase system with a few contrast parameters is described, and it is shown that the crossover position depends on the scattering length density of each phase. The Stuhrmann contrast variation method is generalized and applied to experimental curves in the vicinity of the crossover point beyond the Guinier region. The contrast variation is applied not to the intensity itself but to the model parameters, which can be found by fitting the experimental data with the suggested interpolation formula. The model supplements the existing two‐phase models and gives the simple condition of their inapplicability: if the crossover point depends on the contrast then a two‐phase model is not relevant. The developed analysis allows one to answer the qualitative question of whether one fractal `absorbs' another one or they are both immersed in a surrounding homogeneous medium like a solvent or solid matrix. The models can be applied to experimental SAS data where the absolute value of the scattering exponent of the first power‐law regime is higher than that of the subsequent second power‐law regime, that is, the scattering curve is `convex' near the crossover point. As is shown, the crossover position can be very sensitive to contrast variation, which influences significantly the length of the fractal range. |
---|---|
Bibliography: | ArticleID:JCR2KS5387 ark:/67375/WNG-P2MSPB64-Z istex:FA1AF35BE38A9A4A8514B519847A9854746D3D87 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 1600-5767 0021-8898 1600-5767 |
DOI: | 10.1107/S1600576713029956 |