Pinning effect of second-phase particles on grain growth in polycrystalline films studied by 3-D phase field simulations

Three-dimensional simulations of grain growth in thin films containing finely dispersed second-phase particles were performed using a phase field model. The simulations show that although the growth behavior of the columnar grain structures in thin films is essentially two-dimensional, the interaction between the particles and the grain boundaries is three-dimensional. Grain boundaries can therefore more easily break free from the particles than in purely two-dimensional systems, resulting in fewer grain boundary–particle intersections and a larger final grain size. For a given volume fraction f_V and size of the particles r, the final grain size ${\overline{R}}_{\text{lim}}$ increases with film thickness. Moreover, it was found that particles located in the middle of the film are most efficient in pinning grain boundaries. A classical Zener type relation ${\overline{R}}_{\text{lim}}/r=K(1/f_{\text{V}}^b)$ cannot describe these effects.