Grain Growth in Thin Films with a Fibre Texture Studied by Phase-Field Simulations and Mean Field Modelling

Abstract

The evolution of fiber textured structures is simulated in 2 dimensions using a generalized phase field model assuming two forms for the misorientation, a steady-state regime is reached after a finite amount of grain growth, where the numer 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 = kt^n 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. From a quantitative point of view, the fraction of special boundaries obtained in simulations is quite sensitive to the number of possible discrete orientations. Furthermore, a mean field approach is worked out to predict the growth exponent for systems with nonuniform grain boundary energy. The conclusions from the mean field approach are consistent with the simulation results.