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 gra in growth in a nanocrystalline material has a potentially strong influence on the kinetics of grain growth whenever grain-boundary migration is contro lled by solute (impurity) drag. As the grain-boundary area decreases, the c oncentration of solute or impurity atoms segregated to the boundaries is ex pected to increase rapidly, introducing a grain-size dependence to the reta rding force on boundary migration. We have modified the Burke equation-whic h assumes the drag force to be independent of the average grain size-to lak e into account a linear dependence of grain-boundary pinning on grain size. The form of the resulting grain-growth curve is surprisingly similar to Bu rke's solution; in fact, a constant rescaling of the boundary mobility para meter is sufficient to map one solution approximately onto the other. The a ctivation energies for grain-boundary motion calculated from the temperatur e dependence of the mobility parameter are therefore identical for both mod els. This fact provides an explanation for the success of Burke's solution in fitting grain-growth data obtained in systems, such as nanocrystalline m aterials, for which the assumption of grain-size-independent solute drag is incorrect. (C) 1999 Acta Metallurgica Inc. Published by Elsevier Science L td. All rights reserved.