Testing stereological methods for the estimation of spatial size distributions by means of computer-simulated grain structures

The stereological problem for single phase polyhedral structures is discussed. Modified shape assumptions for the grains lead to improved estimations of the three-dimensional grain size distribution. Thus, the profile shapes carry additional information about the grain size. In contrast to the usual method of estimating the size distribution of the grains a new technique is proposed, exploiting size and shape information of the profiles observed in planar sections. The proposed methods are compared with the solution of the classical Wicksell corpuscle problem. For this reason, 3D microstructures are analyzed which have been simulated using the Monte Carlo method (or Q-state Potts model) of isothermal grain growth.