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Form factor of rounded objects: the sections method
Author(s) -
Croset Bernard
Publication year - 2018
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/s1600576718007239
Subject(s) - gravitational singularity , amplitude , mathematical analysis , surface (topology) , form factor (electronics) , physics , simple (philosophy) , scattering , structure factor , singularity , mathematics , asymptotic analysis , geometry , classical mechanics , optics , quantum mechanics , condensed matter physics , philosophy , epistemology
An analytical method, the sections method, is developed to build a close link between the singularities of the surface of a body and the asymptotic behaviour of its amplitude form factor at large scattering vector, q . In contrast with a sphere, for which the asymptotic behaviour is in q −2 , surface singularities lead to both narrow regions, for which the amplitude form factor exhibits trailing behaviour, and extended regions, for which it exhibits a rapid decrease. A numerical study of a simple example, the fourfold truncated sphere, illustrates the usefulness of these analytical predictions.