Evolution equations and size distributions in nanocrystalline grain growth

Size effects observed in nanocrystalline grain growth are modelled by attributing a specific energy and finite mobility to each structural feature of a polyhedral grain. By considering grain growth as a dissipative process that is driven by the reduction in the Gibbs free interface, edge and vertex energy, a general grain evolution equation is derived that can be divided into nine types of possible growth kinetics. The corresponding self-similar grain size distributions are derived and compared with results from modified Monte Carlo Potts model simulations taking into account size effects in triple and quadruple junction limited grain growth.