Modelling the influence of grain-size-dependent solute drag on the kinetics of grain growth in nanocrystalline materials

The large relative change in total grain-boundary area that accompanies grain growth in a nanocrystalline material has a potentially strong influence on the kinetics of grain growth whenever grain-boundary migration is controlled by solute (impurity) drag. As the grain-boundary area decreases, the concentration of solute or impurity atoms segregated to the boundaries is expected to increase rapidly, introducing a grain-size dependence to the retarding force on boundary migration. We have modified the Burke equation—which assumes the drag force to be independent of the average grain size—to take into account a linear dependence of grain-boundary pinning on grain size. The form of the resulting grain-growth curve is surprisingly similar to Burke's solution; in fact, a constant rescaling of the boundary mobility parameter is sufficient to map one solution approximately onto the other. The activation energies for grain-boundary motion calculated from the temperature dependence of the mobility parameter are therefore identical for both models. This fact provides an explanation for the success of Burke's solution in fitting grain-growth data obtained in systems, such as nanocrystalline materials, for which the assumption of grain-size-independent solute drag is incorrect.