Abstract
New derivation of the kinetics of isothermal phase transformation by using probability calculation has been introduced and demonstrated for the simple one-dimensional case, which yields conclusions for transformation with preferred nucleation at line defects. In contrast to the classical treatments, the present derivation starts from a finite discrete system and follows direct logic. With this method it is possible to determine the distribution function of nuclei and to investigate problems such as the many-nuclei correlation, superposition of more than one process, and various boundary conditions. Further analysis yields formulation for the rate of impingement and other details about the transformation. Combined with the analytical treatment, the specialized algorithm for Monte Carlo simulation of nucleation and growth has been developed. From the results of simulation the limitation of the continuous approach has been detected.
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