A regular solution model for impurity drag on a migrating grain boundary

We analyze the effect of solution thermodynamics on the mobility of grain boundaries in the presence of diffusing impurities within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation is performed within the framework of the regular solution model. The effects of non-ideality are largest when the impurities are attracted to the grain boundary and the deviation from ideality is positive. Positive deviations from ideality lead to enhanced impurity drag on the boundary and negative deviations lead to higher boundary mobility. When the impurities are attracted to the boundary, positive (negative) deviations from ideality produces larger (smaller) activation enthalpies for boundary migration (relative to the ideal solution). At large impurity concentrations, the activation enthalpy becomes impurity concentration independent. Decreasing impurity concentrations in ideal solutions and regular solutions with a negative deviation from ideality leads to a decrease in the activation enthalpy for migration.