Triple junction controlled grain growth in two-dimensional polycrystals and thin films: Self-similar growth laws and grain size distributions

Triple junction controlled grain growth in two-dimensional nanocrystalline polycrystals is modeled by attributing to each structural feature of a polygonal grain a finite mobility. By considering grain growth as a dissipative process that is driven by the reduction of the Gibbs free interface energy, a general grain evolution equation is derived that separates into two types of possible self-similar growth kinetics. For the case of pure triple junction drag the influence of finite triple junction mobilities on metrical and topological properties is studied. Analytical expressions of the self-similar grain size distribution are derived, which compare very well with results from the modified Monte Carlo Potts model and front-tracking vertex dynamic simulations, taking into account size effects in triple junction limited grain growth. In addition, the analytical grain size distributions are used for a theoretical description of experimental data obtained in nanocrystalline thin films upon annealing.