THE CHARACTERIZATION OF HOMOGENEOUS POLYH EDRAL MICROSTRUCTURES APPLYING THE SPATIAL POISSON-VORONOI TESSELATION COMPARED TO THE STANDARD DIN-50601

The development of high performance materials with tailored microstruc tures calls for a more complex description of the spatial microstructu re. Industrial standards for single phase polyhedral microstructures d eal only with the mean grain size which is determined by the mean numb er of intercept points per unit length of test line P-L Or by the mean number of grain sections per unit test area N-A. Both characteristic densities, P-L and N-A, represent different aspects of the microstruct ure and are therefore independent of each other. In the German standar d DIN 50 601 a reliable empiric relation is given to convert P-L into N-A by implication. This relation can be applied only if additional co nditions are fulfilled e.g. if the microstructure can be described by a spatial Poisson-Voronoi tesselation. The relation between P-L and N- A given in DIN 50 601 indicates that the Poisson-Voronoi tesselation i s an appropriate model for single phase polyhedral microstructures. Th is is of far-reaching importance for a complex characterization of suc h microstructures. For instance the mean number of grains per unit vol ume N-V can easily be calculated from measurements of P-L Or N-A. More over, the determination of other characteristic microstructural quanti ties which are usually difficult to recover becomes rather simple. Thi s is based on recent investigations of the Poisson-Voronoi tesselation . For simple use, the table of DIN 50 601 which gives relations betwee n the grain size number G, P-L and N-A has been extended. Now also the spatial intensity N-V as well as the mean spatial grain diameter d ca n be deduced if the Poisson-Voronoi model holds. The microstructure fo rmation in sintered materials is investigated as an example.