Grain size distribution function for a one-dimensional system

Based on a newly developed method for studying the kinetics of the transformation based on nucleation and growth, an analytical solution for the grain size distribution function for the one-dimensional lattice is achieved, after the probability w(l) of finding two sites of distance I in one grain is determined and the relationship between w(l) and the grain size distribution function is established. A special algorithm of Monte-Carlo simulation, which is mainly developed for general problems of the transformation but also suitable for studying the topological relationship in the grain distribution, is introduced and results yielded are in excellent agreement with the analytical prediction. It is found in a one-dimensional system that the distribution function of the nuclei pair represents a good approach for the distribution function of the grain size.