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Small‐angle scattering studies of disordered, porous and fractal systems
Author(s) -
Schmidt P. W.
Publication year - 1991
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889891003400
Subject(s) - scattering , small angle scattering , fractal , small angle neutron scattering , neutron scattering , biological small angle scattering , scattering length , physics , power law , small angle x ray scattering , optics , fractal dimension , materials science , statistical physics , computational physics , mathematics , mathematical analysis , statistics
Small‐angle X‐ray and neutron scattering are important techniques for studying the structure of fractals and other disordered systems on a scale of lengths from about 10 to 2000 Å. This review begins with a brief outline of some properties of fractals. The small‐angle scattering from fractal systems is then discussed and the effect of polydispersity is considered. The intensity of small‐angle scattering from fractals and other disordered systems is often proportional to a negative power of the quantity q = 4 πλ −1 sin( θ /2), where θ is the scattering angle and λ is the X‐ray or neutron wavelength. From the magnitude of the exponent that describes this type of scattering, which is often called power‐law scattering, much important information can be obtained. Some situations in which power‐law scattering can be expected are described. To illustrate the scattering from fractals and disordered systems, several experimental investigations of mass‐fractal silicas and porous solids are reviewed and some calculations of the small‐angle scattering from model fractal systems are outlined.