The stereological method for studying grain structures is presented, it determines the interrelation between the size distributions of three-dimensional grains and their planar and linear sections. Method is applicable for both reconstruction and simulation of the 3D structures. The polyhedral shape of the grains is taken into account by means of the shape factors established for them. An original method to determine the distribution of plane sections from the certain grain-polyhedron to calculate the shape factors is presented. This method can be used to describe the shape of different structural components in many materials: steels, cast irons, concretes, rocks, ceramics, open-porosity materials, biofilms, foams, etc. The stereological method is also applicable to structures with spherical particles, for which the shape factors are equal to unity. The method makes it possible to create the standards of plane sections of grain structures and other structures with a previously known size distribution of 3D grains or particles.

A new method to create of the plane section standards of grain metal structures with a previously known size distribution of 3D grains is proposed. A quantitative analysis of G3, G4, G5 indices of the standard ISO 643:2012 was performed. The stereological modeling method taking into account the polyhedral shape of 3D grains was used to create new versions of plane section standards. Versions of 3D grains structures as the diameter size distributions of 3D grains, plane sections of which correspond to the main quantitative characteristics of existing G3, G4, G5 indices have been created. It was shown that these versions should contain 3D grain more than 1.5 times the mean diameter of the corresponding plane sections. Choosing the diameter size distributions of 3D grains, necessary for the standard, its possible to create a visual index as a picture, as it done on the existing standard, and also to give the parameters of 3D structure, plane section of which corresponds to this standard. Using a new approach to creating standards will increase the accuracy of the grain structure parameters determining.