Statistical description of spherulite patterns

A statistical description of spherulitic morphology and its formation resulting from primary nucleation and radial propagation is presented. Two‐ and three‐dimensional cases are considered. The general formulas are valid for any time‐dependent mode of primary nucleation and can be modified for a time‐dependent propagation rate. Various distance distributions of boundaries and inner points of the final pattern and at intermediate stages of its formation as well as the degree of conversion and the distance correlation of primary nuclei are derived. Detailed derivations are carried out for three model modes of primary nucleation, athermal, thermal, and mixed. It is also shown that the degree of conversion from mixed‐mode nucleation does not follow the Avrami plot. The total surface of boundaries in bulk, total length of boundaries on a plane, and numbers of multiple boundary points are also calculated for all modes of primary nucleation. The relations are confirmed by computer simulation of primary nucleation and radial propagation of spherulites on a plane and in bulk.