Derivation of the kinetics of phase transformations with nucleation and growth mechanism

The kinetics of phase transformation which follows a nucleation-and-growth mechanism was studied by using probability theory. From the calculation of the survival probability for each individual site, the general equation for describing the transformation kinetics, in which the nucleation and growth rates are considered as a function of time and space, is derived. In comparison to the classical derivation by Avrami, the new derivation is logical and transparent. The extension of the treatment by using the definition of the multiple-survival probability leads to the exact solutions of the time dependent grain size distribution functions during transformation. A new understanding of fundamental relationships for the microstructural analysis can be achieved by comparing different kinds of size distribution functions. By applying the principles of the analytical treatment to the simulation, model systems of vast size can be handled for very complicated transformation process.