Estimation of the specific surface area of particle samples

We consider the statistical estimation of the specific surface area of particle samples, i.e., the total surface area of all particles divided by the total volume. In the engineering literature of particle statistics, there exist various estimators, for which no rigorous mathematical derivation is given. They are based on assumptions on relations between particle size, volume and surface area, which are not or only weakly empirically verified. In this study, we give a rigorous derivation of the most important estimators employing methods for marked point processes. There the particle sizes play the role of points and volumes or surface areas are the marks. On this theoretical basis, we discuss the role of a shape factor for particles, the so-called sphericity. In a case study, we analyse statistically a sample of fine rock material. This includes the consideration of some basic statistical assumptions as well as the quality of the specific surface area estimators.