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The correlation functions of the regular tetrahedron and octahedron
Author(s) -
Ciccariello Salvino
Publication year - 2014
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/s1600576714014289
Subject(s) - tetrahedron , octahedron , autocorrelation , mathematics , algebraic number , function (biology) , pure mathematics , physics , mathematical analysis , geometry , quantum mechanics , ion , statistics , evolutionary biology , biology
The expressions of the autocorrelation functions (CFs) of the regular tetrahedron and the regular octahedron are reported. They have an algebraic form that involves the arctangent function and rational functions of r and ( a + br 2 ) 1/2 , a and b being appropriate integers and r a distance. The CF expressions make the numerical determination of the corresponding scattering intensities fast and accurate even in the presence of a size dispersion.