Stereological equations for phases within particles

Abstract

Summary Using data from sections, stereological equations can be used to estimate the volume‐weighted averages of both the volume and the volume‐squared of a set of particles. In mineral processing, the volume distribution of particles can be readily estimated using sieving, so it is uncommon to use stereological methods to determine the volume distribution of particles. A far more important application of stereology for mineral processing is to determine the volumetric grade distribution of minerals within particles. Different minerals or compounds within the particles are called phases. In this paper, stereological equations for estimating various volume‐weighted averages are modified so that they can be applied to phases within particles. From these equations, various volume‐weighted moments of the mineral grade distribution can be estimated. The equations are also modified so that the volume‐weighted covariance of different phases can also be estimated. The equations derived are studied numerically by simulating sections though a double‐capped sphere.