Simulation of phase transformation kinetics in thin films under a constant nucleation rate

• The Avrami exponent and rate constant change with the thickness of a film.
• The grain size distribution is predicted for phase transformation in thin films.
• The final grain size in the thin film depends on the film thickness.
• The characteristic length scale is determined by the grain size and film thickness.
• This characteristic length plays an important role on the growth dimensionality.

The classic framework of Johnson-Mehl-Avrami-Kolmogorov (JMAK) has been commonly used in studies of thin film phase transformation kinetics despite its inherent limitation to transformations that occur in finite size domains or via heterogeneous nucleation on surfaces. To address the effects of finite size and heterogeneous nucleation on a JMAK analysis, we employ the level-set method to simulate phase evolution in thin film systems. Isothermal transformations under a constant nucleation rate and isotropic interface growth, with both bulk and surface nucleation cases are considered for broad range of film thicknesses. In agreement with past work, we find that when the thickness of the film is sufficiently small or heterogeneous nucleation on surface is present, it is possible to have a non-constant Avrami exponent over the course of phase transformation. Our results also show that the rate constant varies with the film thickness in contrast to bulk phase transformations. Furthermore, we obtain the grain size distributions at the end of the transformation for various film thicknesses that vary strongly in shape for small changes in film thickness when the film thickness is on the order of the characteristic length. By analyzing this information and determining the change of the average grain size with film thickness, we find that, the film thickness relative to the characteristic length is a reliable indicator of the dominant growth dimensionality in thin film phase transformations.