Stereology and simulation of heterogeneous crystalline media

Diverse sufficiently general stochastic models of heterogeneous stationary isotropic material structures are reviewed, constructed by means of stochastic simulations and subsequently sectioned by random planes and lines. In particular, a simple grain structure model (Poisson-Voronoi tessellation) is combined with a hard-core model of lens-like particles centred at the cell faces and edges and then examined in detail as an illustrative example. The partial one- and two-dimensional information gathered in sections by manual and computer analysis is treated by means of standard stereological procedures in order to obtain the estimates of 3D geometric characteristics of the original model. The accuracy and reliability of the standard metallographic procedures can be tested by comparing these estimates with the exact values known from simulations. Moreover, a simple method based on the simultaneous profile and chord counts is proposed to improve the standard grain size estimation strategy.