Geometric limitations of nucleation and growth models: Revisiting the impingement assumption

The nucleation and growth process is known to control the kinetics of many important phase transformation processes. However, models of this process are often applied to systems, such as cements, which are different from the ones for which the models were originally developed. The applicability of the assumptions used in the development of these models to such systems has been questioned. One of the most common assumptions in nucleation and growth models is that the impingement between growing nuclei is proportional to the fraction of the untransformed volume. Through numerical simulations, this study investigates the validity of this assumption for various systems, including multiphase systems, different dimensionalities of growth and nucleation on boundaries of spherical particles. It is shown that although in some cases the models can be easily adapted for use in more complex systems, other systems are too complicated to be accurately represented by this simple rule.