Thermodynamic state and kinetic process: Analysis of grain boundary excess in nano-scale grain growth

Derivation for grain boundary (GB) energy at thermodynamic equilibrium is reviewed. On this basis, the evolution of GB excess and bulk concentration with grain growth, and the relation between thermodynamic state and kinetic process have been discussed, for nanocrystalline materials. A concise description for the stop of grain growth is given in terms of thermodynamic and kinetic analysis.