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The Isoscattering Points in X‐ray or Neutron Scattering Curves of One‐ and Two‐Dimensional Systems Measured by the Contrast‐Variation Method
Author(s) -
Kawaguchi T.
Publication year - 1995
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/s0021889894012197
Subject(s) - radius , bessel function , position (finance) , physics , integer (computer science) , contrast (vision) , optics , scattering , ideal (ethics) , function (biology) , point (geometry) , order (exchange) , half integer , x ray , mathematical analysis , mathematics , geometry , condensed matter physics , epistemology , philosophy , computer security , finance , evolutionary biology , computer science , economics , biology , programming language
The conditions for appearance of the isoscattering points of one‐ and two‐dimensional systems have been theoretically derived using the ideal models of oriented membranes and fibers. The position s * of the isoscattering point of a one‐dimensional system is given by s * = n /(2 R 0 ), where n is a positive integer and 2 R 0 is the thickness of the membrane. For a two‐dimensional system, the position s * is given by J 1 (2 πs * R 0 ) = 0, where J 1 is the first‐order Bessel function and R 0 is the radius of the fiber.