Grain growth in thin films with a fibre texture studied by phase-field simulations and mean field modeling

The evolution of fibre textured structures is simulated in two dimensions using a generalised phase field model assuming two forms for the misorientation dependence of the grain boundary energy. In each case, a steady-state regime is reached after a finite amount of grain growth, where the number and length weighted misorientation distribution functions (MDF) are constant in time, and the mean grain area A as a function of time t follows a power growth law A - A0 = ktn with n close to 1 and A0 the initial mean grain area. The final shape of the MDF and value of the prefactor k in the power growth law clearly correlate with the misorientation dependence of the grain boundary energy. Furthermore, a mean field approach is worked out to predict the growth exponent for systems with non-uniform grain boundary energy. The conclusions from the mean field approach are consistent with the simulation results. In previous studies on grain growth in anisotropic fibre textured systems, this steady-state regime was often not reached, which resulted in wrong conclusions on the growth exponent n and evolution of the MDF.status: publishe