Microstructure evolution during dendrite coarsening in an isothermal environment: 3-D cellular automaton modeling and experiments

Microstructure evolution of columnar dendrites during isothermal coarsening is simulated by a three-dimensional (3-D) cellular automaton (CA) model. The 3-D CA model incorporates the thermodynamics, and kinetics aspects influenced by the factors of temperature, composition, and interfacial weighted mean curvature. After quantitative validation through grid independence test and the liquid pool migration problem, the 3-D CA model is applied to simulate the dendrite coarsening phenomena caused by the simultaneous melting and solidification for a SCN-2.0 wt.% ACE alloy in an isothermal environment. Several typical features of dendrite coarsening occurring in the 3-D space are reproduced by the CA model, including melting of tertiary and small secondary branches, interdendritic groove base advancement, and coalescence of neighboring dendrite arms. The simulated dendritic microstructure compares well with the in situ experimental observation. Besides, the simulated specific surface area of the solid/liquid interface decreases with time following a power-law relation with an exponent of 1/3. The simulated distribution curve of the interfacial weighted mean curvatures becomes narrower with time, and the peak gradually shifts to zero, showing that the S/L interface is flattened during the isothermal dendrite coarsening. The average thickness of the primary dendrite arm and the secondary dendrite arm spacing (λ2) are found to increase with time, and the third power of λ2 shows a nearly linear relationship with time. The CA model not only visualizes morphological evolution of the dendrite arms, but also provides insight into the complex interaction among local melting/solidification, solute diffusion, and variation of weighted mean curvature in the 3-D space.