On the stagnation of grain growth in nanocrystalline materials

The stagnation of grain growth with solute segregation in nanocrystalline materials is often analyzed by using two kinetic models [J.E. Burke, Trans. Metall. Soc. AIME 180 (1949) 73; A. Michels, C.E. Krill, H. Ehrhardt, R. Birringer, D.T. Wu, Acta Mater. 47 (1999) 2143], in which it is supposed that solute drag stops grain growth. However, we show that the drag force in these kinetic models is not equivalent to the solute drag force, but to the reduced driving force due to the decrease in grain boundary energy.