A stochastic modeling method is presented for the analysis of nucleation and growth in a thin layer between two interfaces. In this layer, nucleation occurs randomly and growth stops at the interfaces after instantaneous growth. This halting of the growth causes non-random impingement because phantom crystallites in the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model shrink to an effective size. This stochastic model successfully deals with effective size using a factor γ which accounts for the overlap between a phantom crystallite and a crystallite. This leads to a phenomenological equation for non-random impingement: dX(t)/dVex = [1 - X(t)]i, where X(t) is the transformed fraction and Vex is the KJMA extended volume fraction. It is shown that the exponent is clearly expressed as i = 2 - γ. An analytical solution of the transformed fraction agrees very well with the numerical simulations.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Ceramics and Composites
- Polymers and Plastics
- Metals and Alloys