Phase field study of grain boundary effects on spinodal decomposition

We have developed a phase field model of a polycrystalline alloy by combining the Cahn–Hilliard model [J Chem Phys 28 (1958) 258] with a model of polycrystals due to Fan and Chen [Acta Mater 45 (1997) 3297]. We have used this model to study grain boundary (GB) effects on spinodal decomposition (SD) in two-dimensional (2D) systems. In binary A–B systems with constant atomic mobility, when the GB-energy $(\gamma\alpha)$ of the A-rich $\alpha$ phase is lower than that $(\gamma\beta)$ of the B-rich $\beta$ phase, decomposition starts by enriching the GB with species A, setting off a composition wave that produces alternating $\alpha$ and $\beta$ bands near the GB. Simultaneously, the grain interiors undergo normal SD. Thus, when decomposition ends, GB-bands coexist with grain interiors with spinodal microstructure. The number of GB bands is rationalized in terms of $(\gamma\beta - \gamma\alpha)$ and the rate of SD in the grain interior. Further, during decomposition, grain growth is effectively suppressed.