Analysis of Randomly Shaped Puzzle-Fragment-Particles via their Chord Length Distribution

摘要

The chord length distribution (CLD) of an ensemble (E) of homogeneous, hard, compact, randomly shaped fragment particles F_i is studied. The practical problem whether such F_i can fit together like the pieces of a puzzle can be solved, based on the experimental information involved in a small-angle scattering (SAS) experiment. The sample material of such an experiment is the isotropic particle ensemble E, consisting of many separate F_i. Let L_0 be the maximum diameter of the largest piece (of the largest F_i). The one by one investigation of F_1, F_2, F_3 ... in a quasi-diluted arrangement (or in the separate state) yields the characteristic scattering pattern of E. This pattern fixes the mean CLD of the F_i. The approach is based on the construction of a 50 % volume fraction model from the F_i given. A fitting function Φ_(1/2)(r,L_0), (0 ≤ r L_0), has been introduced (limiting case r → 0+). If Φ_(1/2)(0+, 2 · L_0) = 1, the origin of the F_i is a destroyed mosaic. 'Dead Leaves' mosaics are a special case of the approach. Hereby, Φ_(1/2)(r) => Φ(r,L_0).