Cellular Automata Modelling of Discontinuous Precipitation

Abstract

The fundamentals of discontinuous precipitation (DP) reaction modelling using a cellular automata (CA) method are presented. In the proposed CA model, cell states, internal variables, equations, and transition rules were defined to predict the manner of mass transport during DP reaction and to relate changes in the microstructure with corresponding changes in chemical composition. Furthermore, the concept of digital material representation (DMR) was introduced into the CA model, which allowed schematic images of the microstructure to be used as starting structures in the modelling of the DP reaction. The preliminary assumptions adopted in the proposed CA model for the DP reaction were verified by numerical simulations of the growth of discontinuous precipitates at a steady-state at the example of Al-22 at.% Zn alloy. The outcomes achieved from the CA simulations were presented in a different form than that most commonly used previously (single concentration profiles), namely as the 2D maps showing changes in Zn content accompanying the successive stages of growth of discontinuous precipitates. The model used for the description of the solute diffusion along of the reaction front (RF) allowed two-dimensional systems at the nano-scale to be treated within a reasonable simulation time. The obtained results indicate that the developed CA model was able to realistically simulate the DP reaction, which was confirmed by the visualisation of migrating RFs together with associated chemical composition changes in the microstructure.