Analysis of the fragments of a ‘dead leaves’ mosaic via a puzzle-fitting function Φ (r, L₀)

Abstract

The origin of homogeneous, randomly shaped particles embedded in a homogeneous medium can be analyzed by use of a puzzle-fitting function Φ. A well-defined range order L of the random medium is considered. The function Φ is defined in terms of the correlation function of the scattering experiment γ (r) of the whole particle ensemble and of the correlation function γ _P (r) of the isolated puzzle particles. It can be written Φ (r,L) = γ”(r)/[γ ′(r)·γ _P ′(r)]; (0 ≤ r < L). For fitting fragments (if all the puzzle particles belong to one and the same puzzle and fit together), Φ (0,L) = 1 is fulfilled, whatever the shape of the smooth grains of the ‘dead leaves’ tessellation which produces the fragments.

These relations have been checked for several model particle systems, as well as for an alloy system for L ₀ = 8 nm. Numerical details for a stable determination of Φ from the scattering experiment are included.