Solute segregation transition and drag force on grain boundaries

We investigate solute segregation and transition at grain boundaries and the corresponding drag effect on grain boundary migration. A continuum model of grain boundary segregation based on gradient thermodynamics and its discrete counterpart (discrete lattice model) are formulated. The model differs from much previous work because it takes into account several physically distinctive terms, including concentration gradient, spatial variation of gradient-energy coefficient and concentration dependence of solute–grain boundary interactions. Their effects on the equilibrium and steady-state solute concentration profiles across the grain boundary, the segregation transition temperature and the corresponding drag forces are characterized for a prototype planar grain boundary in a regular solution. It is found that omission of these terms could result in a significant overestimate or underestimate (depending on the boundary velocity) of the enhancement of solute segregation and drag force for systems of a positive mixing energy. Without considering these terms, much higher transition temperatures are predicted and the critical point is displaced towards much higher bulk solute concentration and temperature. The model predicts a sharp transition of grain boundary mobility as a function of temperature, which is related to the sharp transition of solute concentration of grain boundary as a function of temperature. The transition temperatures obtained during heating and cooling are different from each other, leading to a hysteresis loop in both the concentration–temperature plot and the mobility–temperature plot. These predictions agree well with experimental observations.