Relation between the Volume-weighted and Number-weighted Grain Volume Distribution Function

Three-dimentional grain size distribution might be well described by a gamma or a lognormal distribution. On the basis of these two Kinds of distribution functions, the relationships of the characteristic parameters between the volume-weighted and the number-weighted grain volume distributions are derived theoretically and demonstrated experimentally. The method can be used to estimate the grain volume distribution parameters, such as the average grain volume and the coefficient of variation of grain volume distribution, from two-dimensional measurements on sections through polycrystas,