Strain-induced solute segregation at a grain boundary and the solute drag effect upon boundary migration were studied using a phase field model which integrated grain-boundary segregation and grain-structure evolution. The elastic strain energy of a solid solution due to the atomic size mismatch and the coherency elastic strain energy caused by the inhomogeneity of the composition distribution were obtained using Khachaturyan’s micro-elasticity theory. Strain-induced grain boundary segregation at a static planar boundary was studied numerically, and the equilibrium segregation composition profiles were checked against analytical solutions. A systematically study was then made of the effect of misfit strain upon grain-boundary migration with solute drag. A theoretical analysis which was based upon Cahn’s analytical theory showed that enhancement of the drag force with increasing atomic size mismatch resulted from an increase in grain-boundary segregation due to strain energy reduction and to misfit strain relaxation near to the grain boundary. The results were analyzed, on the basis of a theoretical analysis, in terms of elastic and chemical drag forces. The optimum conditions under which solute diffusivity maximized the drag force under a given driving force was identified.

A Phase Field Study of Strain Energy Effects on Solute–Grain Boundary Interactions. T.W.Heo, S.Bhattacharyya, L.Q.Chen: Acta Materialia, 2011, 59[20], 7800-15