The chord length distributions of selected infinitely long geometric figures - connections to the field of small-angle scattering

摘要

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) → ∞. On the other hand, the asymptotic behaviour 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-plots P_1(h), which can be approximated by their asymptotic expansion P_(1∞)(h). Deciding formulas for practical application in materials science are summarized in simple Mathematica patterns.