DIAMETER DISTRIBUTION OF SPHERICAL PRIMARY GRAINS IN THE BOOLEAN MODEL FROM SMALL-ANGLE SCATTERING

A method for determining the size-distribution density of small spheres which are arranged, without any interaction between them, at random positions in space and form an isotropic two-phase system is presented. In the case of higher volume fractions, frequent overlapping between the spheres is a logical consequence. This effect is an essential feature of the model itself and is well considered and observed. Stereological information, which contains all the necessary data about the unknown size distribution, is obtained from the angular intensity distribution (small-angle scattering experiment) of the particle system concerned. The resulting formula still includes, in a first representation, the volume fraction p as a free parameter. In a second step, a general analytical method for the determination of the volume fraction p from the set covariance of the considered random closed set is derived. Therefore, the unknown diameter distribution can be obtained in every detail, starting from the scattering curve of the sample, by way of two independent working steps.