Kinetics of volume and surface driven crystallization in thin films

A mathematical model of the crystallization process in a thin film is presented with the purpose to overcome the limitations of Kolmogorov-Johnson-Mehl-Avrami theory regarding finite-size systems. Two ways of nucleation are taken into account: at the film boundaries and in the bulk. The solution is obtained in terms of crystallization probability, which is the probability of a point inside the film to be included in the crystal at a given moment of time. It is shown that the characteristic feature of crystallization in finite-size systems is a non-uniform distribution of crystalline fraction.