PARTICLE-SIZE, SHAPE AND ORIENTATION DISTRIBUTIONS - GENERAL SPHEROIDPROBLEM AND APPLICATION TO DEFORMED SI3N4 MICROSTRUCTURES

A general method is presented for solving stereological problems for p article systems consisting of spheroids having variable size, shape (a spect ratio) and orientation provided that the orientation has axial s ymmetry. The kernel function, which connects the probability density f unction (distribution) of the spheroids and that of the sectioning ell ipses on the observation planes along the symmetry axis, is calculated theoretically. The spatial distribution of the spheroids can be calcu lated from the experimentally measured planar data of the ellipses thr ough the inverse operation of the kernel function. Using this method, the spatial size, shape and orientation distributions of grains were c alculated in as-sintered and unidirectionally elongated silicon nitrid e samples consisting of rod-shaped beta-Si3N4 grains. The calculated s patial distribution shows that the aspect ratio remains almost constan t during the deformation although it appears elongated upon planar obs ervation owing to a superficial effect of grain alignment along the te nsile axis.