Microstructure characterization via stereological relations — A shortcut for beginners

Abstract

Stereological relations that can be routinely applied for the quantitative characterization of microstructures of heterogeneous single- and two-phase materials via global microstructural descriptors are reviewed. It is shown that in the case of dense, single-phase polycrystalline materials (e.g., transparent yttrium aluminum garnet ceramics) two quantities have to be determined, the interface density (or, equivalently, the mean chord length of the grains) and the mean curvature integral density (or, equivalently, the Jeffries grain size), while for two-phase materials (e.g., highly porous, cellular alumina ceramics), one additional quantity, the volume fraction (porosity), is required. The Delesse–Rosiwal law is recalled and size measures are discussed. It is shown that the Jeffries grain size is based on the triple junction line length density, while the mean chord length of grains is based on the interface density (grain boundary area density). In contrast to widespread belief, however, these two size measures are not alternative, but independent (and thus complementary), measures of grain size. Concomitant with this fact, a clear distinction between linear and planar grain size numbers is proposed. Finally, based on our concept of phase-specific quantities, it is shown that under certain conditions it is possible to define a Jeffries size also for two-phase materials and that the ratio of the mean chord length and the Jeffries size has to be considered as an invariant number for a certain type of microstructure, i.e., a characteristic value that is independent of the absolute size of the microstructural features (e.g., grains, inclusions or pores).