Phase field modeling for grain growth in porous solids

Concurrent evolution of grain size and porosity in solids is a technically important problem involving curvature-driven motion of grain boundaries and the pore motion by surface diffusion. A phase field approach comprising a system of Cahn–Hilliard and Allen–Cahn equations has been developed recently to tackle this problem. Through a formal asymptotic analysis, the current work demonstrates that the phase field model recovers the corresponding sharp-interface dynamics of the co-evolution of grain boundaries and pores; this analysis also fixes the model kinetic parameters in terms of real materials properties. As a case study, the model was used to investigate the effect of porosity on the kinetics of grain growth in CeO2 in 3D. It is shown that the model captures the phenomenon of pore breakaway often observed in experiments. Pores on three- and four-grain junctions were found to move along with the migrating boundary, while edge pores (on the boundary between two grains) were found to easily separate from the boundary. The simulations showed that pore breakaway leads to abnormal grain growth. The simulations also showed that grain growth kinetics in CeO2 changes from boundary controlled to pore controlled as the amount of porosity increases. The kinetic growth parameters such as the growth exponent and the rate constant (or equivalently the activation energy) were found to depend strongly on the precise amount and distribution of porosity, which reconciles the different experimental results reported for grain growth in CeO2.