Stereological analysis of grain size and grain shape applied to silicon nitride ceramics

The stereological estimation of the spatial grain size distribution from da ta obtained from planar sections of the microstructure has been subject of investigation already for a long time. The reason why stereological estimat ion is still an alive subject is due to the fact that numerical as well as statistical methods are involved and no clear criterion exists for the qual ity of the algorithms. The use of a crystallographically adequate shape ass umption for the grains reduces the bias of the estimation. The solution of the stereological equation based on this shape assumption requires a comput ation of the probabilities of the different cases of prism sections by mean s of computer simulation. The stereological method has been applied to two examples: (li the comparison of hot isostatic pressed and gas pressure sint ered silicon nitride microstructures and (2) the microstructural evolution during long term sintering. In both cases significant variations of the gra in population was quantified. Also considered in the method with adequate r eliability is the detection of "rare" large grains. In (1) some effect of g rain size and aspect ratio could be verified on the crack resistance. In (2 ) the growth of silicon nitride grain populations have been studied during sintering.