Eur. Phys. J. B 17, 371-383 (2000)
https://doi.org/10.1007/s100510070116

Chord length distributions and small-angle scattering

Department of Physics, Martin-Luther-University Halle-Wittenberg, SAS-Laboratory, Hoher Weg 8, 06120 Halle, Germany

Received: 15 March 1999
Revised: 26 April 2000
Published online: 15 October 2000

Abstract

Chord length distributions describe size, shape and spatial arrangement of geometrical objects (particles). The chord length distribution is in principle proportional to the second derivative of the correlation function of small-angle scattering. It is calculable from a relative measurement of the scattering intensity I(h). In structure research, the characterization of numerous particle systems can be achieved by comparing experimental chord distributions with theoretical ones, provided the latter are available with sufficiently high precision for a lot of fundamental, universal shapes. Both sides of this concept are exemplified: - the step from a relative measurement of the scattering intensity of an isotropic two-phase sample to the chord length distribution (errors in h_k and in I_k, limited h-interval, corresponding to the region (1-2) nm < r in real space, must be observed); as well as the geometric matter of calculation of chord distributions as fingerprints for basic geometric figures, including the non-convex case.