The quantitative characterization of microstructure involves consideration of the topological properties of the physically distinguishable 3-dimensional regions (for example, phases or grains) which constitute it. The two topological properties of primary interest are the connectivity and number of separate regions. These topological concepts, their measurement, and their application in describing sinter bodies will be discussed.

The application of topological relationships to polycrystalline microstructure is extremely important in quantitative characterization of grain shape and boundary configurations. In this case, the properties of space filling, simply connected, polyhedral regions will be utilized to develop a consistent set of equations relating the number of grains, faces, edges, and vertices to the average configurations of these features. The implications and limitations upon polycrystalline aggregates which result from these equations will be presented. The measurement of these properties and their application in describing normal grain growth will also be discussed.