RANDOM MODELS FOR MORPHOLOGICAL ANALYSIS OF POWDERS

Models to estimate powder size distributions or fractions of components in a mixture of powders were developed and tested for various specimens. The models derived from the Boolean model and from the dead leaves models can be implemented on rough secondary electron scanning electron microscope images, obtained after minimal sample preparation. With the dead leaves tessellation, the size distributions of spherical particles or short fibres can be estimated either from the size distribution of intact grains, or from the area fraction measurement after binary erosions. With the dead leaves random function, there is no need for image segmentation. It provides data on the size and shape of a population of particles from an estimation of the distribution of grey-level images after erosions by convex structuring elements of increasing size. A version of these models for long fibres is developed for estimating their diameter distribution. Allowing for superposition of particles, the proposed methods enable an unbiased estimation of the size distribution and characterization of the shape of complex particles. The approach is illustrated by applications to spherical particles obtained by simulations and from scanning electron microscope micrographs.