Theoretical and numerical investigations of the thermal transformation of finite size circular particles using a geometrical-probabilistic approach

The fundamental process underlying phase changes involving nucleation and growth are often described in terms of KJMA model. To interpret experimental results, it is of importance to keep in mind that this model relies on a few hypotheses. One of them states that the transformed material is of infinite size, avoiding edge effects. For finite specimen size, the model has to be revised as nucleus growth ceases at points where border is reached. In this work, the case of monodispersed circular particles is exhaustively analysed, using a geometrical approach with probabilistic elements. The transformed surface fraction is given in terms of mathematical equations when the nucleation takes place on the disk edge and on the disk surface. Analytical solutions are compared with Monte Carlo simulations and some experimental results.