The kinetics of thin films and crystal growth were extensively investigated by using geometrical stochastic approach. A significant contribution of this research lies in the theoretical and analytical extension of the classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) model. Specifically, the framework was adapted to account for the spatial correlation among nuclei – a crucial phenomenon that is both theoretically predicted and consistently observed in growth processes governed by adatom diffusion.

The proposed modeling architecture is rooted in the rigorous calculation of the ‘exclusion probability,’ derived through the application of m-point correlation functions. This statistical foundation proved to be a critical factor in determining other essential physical quantities, such as the evolution of the interface area between the transformed and parent phases, the dynamic nucleation rate, and the evolution of the Probability Density Functions (PDFs) related to nucleus size distribution.

One of the achievements of this work was the implementation of rate equations approach especially for thin film growth. This advancement not only bridges the gap between stochastic geometry and kinetic modeling but also provides a framework for the interpretation and description of experimental kinetic data in material science. This modeling has been applied to 3D phase transformations, as well as to thin film growth via Chemical Vapor Deposition (CVD) and in electrochemical systems.

Some publications:

• Connection between phantom and spatial correlation in the Kolmogorov–Johnson–Mehl–Avrami-model: A brief review -M. Tomellini, M. Fanfoni- Physica A 590 (2022), 126748
• Impact of seed density on continuous ultrathin nanodiamond film formation – M. Tomellini, R. Polini- Diamond and Rel. Mater.133 (2023) 109700
• Nucleation kinetics in phase transformations with spatially correlated nuclei – M. Tomellini- Physica A 676 (2025) 130882
• Fokker-Planck equation for the crystal-size probability density in progressive nucleation and growth with application to lognormal, Gaussian and gamma distributions – M. Tomellini, M. De Angelis- J. Cryst. Growth 650 (2025) 127970

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