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The chord‐length probability density of the regular 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/s1600576714011121
Subject(s) - chord (peer to peer) , mathematics , trigonometric functions , probability density function , algebraic number , inverse , trigonometry , mathematical analysis , combinatorics , geometry , statistics , computer science , distributed computing
The chord‐length probability density of the regular octahedron is separated into three contributions, relating to the pairs of facets opposite to each other or sharing an edge or a vertex. Each of these contributions is explicitly evaluated throughout the full range of distances and the final expressions only involve inverse trigonometric functions of elementary algebraic functions. Since the chord‐length probability density is proportional to the second derivative of the correlation function, knowledge of the chord‐length probability density makes the numerical evaluation of the associated small‐angle scattering intensity very fast and accurate.