  A formula of grain growth rate, based on a nonlinear capillarity-driven
relation, is derived to predict and interpret realistic growth processes in
polycrystalline systems. The derived formula reveals how the growth and
stagnation of grains dominated by the correlated parameters (temperature,
interfacial energy, step free energy, grain size and size distribution in
polycrystalline system etc.). Our study provide a conclusive model of the
growth and stagnation of grains, and thus offers helpful guides for the
microstructural design to optimize the properties of polycrystalline materials.
