Chord length distribution of Voronoi diagram in Laguerre geometry with lognormal-like volume distribution

Abstract

The Voronoi diagram in the Laguerre geometry based on random close packing of spheres (RCP-LV diagram) has been found to be a better representation of polycrystalline structure than the conventional Poisson–Voronoi diagram. Stereology of the RCP-LV diagram with lognormal-like volume distribution has been investigated by the classical intercept count method. An improved five-parameter gamma distribution function is proposed to integrate the fact that probability density of the chord length remains non-zero as the chord length approaches zero. The proportional coefficient between the average grain size and the average chord length varies from 1.60 to 1.14 as the coefficient of variation of grain volume increases from 0.4 to 2.2. It is shown that there exists the possibility that not only the average grain size but also the grain size distribution can be estimated if the chord distribution characterization is fully explored with the aid of RCP-LV diagram simulation.