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The Chord Length Distributions of Selected Infinitely Long Geometric Figures--Connections to the Field of Small-Angle Scattering

Wilfried Gille
Organization: Martin-Luther-Universitšt Halle-Wittenberg, Halle, Germany
Department: SAS Laboratory
Journal / Anthology

Computational Materials Science
Year: 2001
Volume: 22
Page range: 318-332

Analytic expressions are summarized and the intrinsic behaviour of the chord length distribution and the small-angle scattering correlation function are investigated for the following eight infinitely-long geometric figures: S. plane stripe; Q. square rod; R. rectangular rod; N. elliptic needle; C. circular rod; O. hollow cylinder; H. hemicircular rod; T. triangular rod. There does not exist a power series expansion of the scattering intensity in the origin of any infinitely long figure, because of I(0) -> infinity. On the other hand, the asymptotic behavious of the SAS intensities for large scattering vectors is clearly defined by the shape parameters. This can be analysed by the use of so-called normalized porod plos P_1(h), which can be approximated by their asymptotic expansion P_1infinity(h). Deciding formulas for practical application in materials science are summarized in simple Mathematica patterns.

*Engineering > Materials and Metallurgical Engineering
*Mathematics > Geometry