Statistics of inhomogeneous media formed by nucleation and growth

Important statistical properties of inhomogeneous microstructures formed by nucleation and growth are established using line transects. A fundamental time-dependent equation has been derived for the probability of sampling only matrix phase by a random line transect in a system containing growing Poisson-distributed spherical nuclei. established that the probability of sampling matrix phase only measures simultaneously the product of two fundamental characteristics of inhomogeneity: the volume fraction of the matrix phase and the probability of existence in the matrix of a free path of specified minimum length. Increasing the number density of the nuclei and decreasing the size of the mean projection of the nuclei on a plane perpendicular to the line transect by the same factor does not change the mean and the variance of the free paths. also demonstrated that the distribution of the intercepts from the weaker phase is an important indicator regarding the risk of poor properties. Accordingly, a new approach is suggested for setting MFFOP reliability requirements which minimise the risk from premature fracture.