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The small‐angle scattering structure functions of the single tetrahedron
Author(s) -
Gille W.
Publication year - 2003
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/s0021889803000177
Subject(s) - tetrahedron , interval (graph theory) , simple (philosophy) , mathematics , intersection (aeronautics) , polynomial , sequence (biology) , scattering , function (biology) , degree (music) , mathematical analysis , correlation function (quantum field theory) , combinatorics , geometry , physics , chemistry , quantum mechanics , philosophy , biochemistry , spectral density , epistemology , statistics , evolutionary biology , acoustics , engineering , biology , aerospace engineering
Basic properties of the SAS correlation function γ ( r ) and related functions are represented for a tetrahedron of edge length a . An interval splitting into four basic r ‐intervals in a sequence of cases for averaging the intersection volume between two tetrahedrons has been performed. Remarkably simple analytic expressions result in the first r ‐interval. Indeed, γ ( r ) is a polynomial of degree three. The coefficients are given explicitly. The asymptotic expansion I( h ) is compared with the exact scattering intensity I ( h ).