On the determination of grain-size distributions from intercept distributions

A matrix formulation for determining the spatial grain-size distribution of tetrakaidecahedral grains from linear-intercept data is developed. The truncation effect (which stems from the fact that the intersection of single-size grains by a test line gives rise to intercepts of different length) and the sampling effect (which results as a consequence of bigger grains being intersected more frequently than smaller ones) are separately taken into account. The derivation procedure of this formulation is applicable to any other convex shape, provided the linear intercept distribution for single-size grains of the corresponding shape is known. The percentage spatial grain-size distributions obtained by the formulation derived here are similar to those estimated by the Spektor's chord method for spherical grains.