Size distribution evolution equations in space-competing domain growth systems

Abstract

A model of microstructure development for phase transformations driven by nucleation and growth is presented. The model is based on a set of Fokker-Planck-like equations which allows us to compute the particle grain density distribution at any time during the transformation, provided that the nucleation and growth dependences on time and/or grain radius are known. The model is applicable to any kind of nucleation and growth protocols fulfilling the Johnson–Mehl–Avrami–Kolmogorov conditions, namely spatially random nucleation and isotropic growth. Comparison with stochastic (Monte Carlo) simulations is presented, giving quantitative agreement in all cases. This work shows the relationship between kinetic parameters and microstructure evolution as well as the accuracy of the developed model.

Acknowledgements

This work was funded by Comisión Interministerial de Ciencia y Tecnologia (grant MAT2001-0957) and Generalitat de Catalunya (grant 2001SGR00190). D. Crespo is supported by grant PR2002-0117 from the Ministerio de Educacion, Cultura y Deporte, Spain.

Notes

† Simulations were performed in a 256 × 256 × 256 cubic cell with periodic boundary conditions. In order to obtain acceptable statistics, each system is simulated 100 times and the populations obtained averaged.