Automated stereology and uncertainty quantification considering spherical non-penetrating dispersions

Automated stereological methods are presented for approximating the 3D size distribution of unimodal or bimodal precipitate dispersions considering 2D and 1D measurements taken from polydisperse spherical non-penetrating particle dispersions. A method to quantify the uncertainty of the approximation as a function of the number of sampled particles is presented and demonstrated to experimental data. The derivation and verification of the analytical stereological expressions used are included. Two procedures are presented for estimating the 3D size distribution of bimodal particle populations depending upon the relative size of the two particle populations. If the particles can be characterised using micrographs of the same magnification, it is possible to estimate the volume fraction of each particle population. For cases where micrographs have been taken at different magnification, an estimate of the area fractions of the particle populations is needed to combine the datasets and allow for the approximation of the 3D size distribution. These methods are useful for use in determining the initial particle size distribution for use in modelling and determining the appropriate number of micrographs and particles to measure when characterising a precipitate dispersion.