Stereological parameters of model polycrystalline structures built from polyhedra of various shape and size
Abstract
The five selected models of polycrystalline microstructure proposed by Williams (1979), built fiom polyhedra of various shape and size as well as a model of homogenous microstructure (a set of truncated octahedra of the same size) have been compared in this work. All the elements of the models containing approximately 18000 polyhedra have been entirely determined in 3-D space. On the basis of 8000 random plane section of the model microstructures (7000000 plane sections of polyhedra) the "statistical" and "geometrical" distributions ofparameters characterizing grain size and shape in 2-D space were evaluated. The studies indicated that "statistical" and "geometrical" distributions that describe both size and shape of grains in 3-D and 2-D space contain significantly different information concerning the model polycrystalline structures. It was shown that "geometrical" distribution of grain plane section area is more suitable for grain size evaluation of inhomogeneous granular structures than "statistical" one. It was stated-out that neither the distribution of number of sides of polygons obtained on plane sections of the model structures nor the distribution of polygons form factor are clearly related to the shape of polyhedra forming the model structures.