Scattering properties and structure functions of Boolean models

The Boolean model is a successful short-range order model for ensembles of overlapping grains possessing many applications. Convex grains, randomly distributed in space with a certain density, are characterized by their SAS correlation function γ0(r). Characteristics, such as volume fraction c (porosity 1 − c) and sample correlation function γ(r) result.The function γ0(r) of unknown grains can be re-constructed from γ(r). Information on size and shape of the grains results. The chord length distributions of grain phase and matrix phase are analyzed. The latter distribution is an exponential distribution. The distribution law of the grain phase is determined explicitly, incorporating formulas for the moments.

Research highlights
► A random two-phase system can be described by two different CLDs.
► The SAS scattering pattern of a Boolean model result from the CLDs of the model.
► SAS structure functions of a Boolean model follow from the grain correlation function.
► The volume fraction of random two-phase systems is fixed by the CLD- moments.
► The CLD of the grain phase of a Boolean model is fixed by the scattering pattern.