Particle sizes and their distributions estimated from line‐ and point‐sampled intercepts. Including graphical unfolding

Abstract

SUMMARYInformation about particle size is currently obtained almost exclusively by the use of stereological methods which lead to estimates of the number distribution of linear particle size. The main point of this presentation is to stress the freedom to choose more appropriate parameters for size among a host of options, including particle surface area and volume. Moreover, particle size information may often be considered advantageously in terms of particle distributions based on structural characteristics rather than number distributions. Some of these other distribution types are correctly represented in samples of intercept lengths obtained by line‐ and point‐sampling, respectively. The known and quite simple theory of sampling intercepts is summarized and developed further in several different directions, including a derivation of the distribution of intercept length in ellipsoids, graphical unfolding procedures, and mean size estimators. The potential of the approach is illustrated—but not exhausted—by the existence of a general mean size estimator based on minimal assumptions regarding particle shape.