Self-Similar Grain Growth in Nanocrystalline Two-Dimensional Polycrystals and Thin Films

Grain growth in two-dimensional nanocrystalline polycrystals is modeled by attributing to each structural feature of a polygonal grain an own finite mobility and energy. By considering grain growth as a dissipative process that is driven by the reduction of the Gibbs free energy a general grain evolution equation is derived that separates into four types of possible self-similar growth kinetics, where for each case the influence of grain boundary and triple junction mobilities and energies on metrical and topological properties is studied. We find that the resulting analytical expressions compare very well with results from modified Monte Carlo Potts model simulations taking into account size effects in triple junction controlled 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.