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The structure factor in small‐angle scattering and the effect of deviation from spherical symmetry
Author(s) -
Hansen Steen
Publication year - 2011
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/s0021889811001075
Subject(s) - circular symmetry , structure factor , ellipsoid , symmetry (geometry) , volume fraction , physics , volume (thermodynamics) , scattering , atomic packing factor , spherical model , range (aeronautics) , rotational symmetry , function (biology) , small angle scattering , spheroid , condensed matter physics , geometry , classical mechanics , mathematics , chemistry , optics , materials science , nuclear magnetic resonance , mechanics , quantum mechanics , thermodynamics , in vitro , composite material , biology , biochemistry , evolutionary biology , astronomy
The effect of deviation from spherical symmetry is studied for the structure factor. This is done by combining the analytical expression for the excluded volume of an ellipsoid of revolution with the expression for the excluded volume correlation function for a sphere. This approach makes it possible to estimate the effect of small deviations from spherical symmetry as a function of axial ratio and volume fraction for relatively low volume fractions. The calculations are relevant for the case of short‐range potentials where the Percus–Yevick formula is frequently applied, and indicate that even minor deviations from spherical symmetry may lead to significant effects on the structure factor at low scattering angles.