A model, based upon a phase-field approach to the study of grain-boundary segregation and solute drag, was proposed. It was shown that it was possible to model the dynamics of grain-boundary segregation to a stationary boundary, as well as solute drag on a moving boundary, using the same phase-field model. This was achieved by introducing a concentration-dependence of the height of the double-well potential in the Gibbs-energy expression. As the model was then able to treat the build-up of a concentration spike in the boundary, as well as its disappearance, this treatment was termed dynamic solute-drag theory.

Grain-Boundary Segregation and Dynamic Solute Drag Theory - a Phase-Field Approach. K.Grönhagen, J.Ågren: Acta Materialia, 2007, 55[3], 955-60