The effect of solute atoms on grain boundary migration has been modelled on the basis of the idea that solute atoms will locally perturb the collective re-arrangements of solvent atoms associated with boundary migration. The consequence of such perturbations is cusping of the boundary and corresponding stress concentrations on the solute atoms which will promote thermal activation of these atoms out of the boundary. This thermal activation is considered to be the rate-controlling mechanism in boundary migration. It is demonstrated that the present statistical approach is capable of explaining, in phenomenological terms, the known effects of solute atoms on boundary migration. The experimental results on the effect of copper on boundary migration in aluminium, due to Gordon and Vandermeer, have been well accounted for. INTRODUCTIONIt has been known for a long time that impurity solid solution atoms have a tendency of segregation to grain boundaries, an effect which may strongly retard the grain boundary mobility and thus the kinetics of recrystallization and grain growth in pure metals, even when present in the ppm range. (commonly referred as the dissipation approach). Typical application examples for the force and dissipation approach are respectively [4][5] and [6]. In the force approach the solute drag is estimated by summing the forces that the solute atoms exert on the boundary and in the dissipation approach by evaluating the amount of free energy dissipated due to diffusion when the boundary goes through a volume containing one mole of material. Over the last decades, a lot of efforts have been made to generalize these approaches to a migrating phase boundary into a multi-component system [3,[7][8][9].Indeed in the initial treatment of the solute drag effect by Cahn and by Lücke and Stüwe [10] the equation used for evaluating the solute drag does not apply to phase transformations. It only applies to the migration of grain boundaries, i.e. to one phase materials.The force approach and the dissipation approach have both a sound physical basis and should therefore be equivalent. However the formula for calculating the solute drag for a migrating phase boundary into a multi-component system in steady-state conditions has been a subject of debates over the years and it was only recently that a valid expression has been found with a remarkable amount of empirical insight [11]. The general expression has also been derived in a deductive and completely independent way by applying the principle of maximum dissipation in [12].Even if in the recent years more complex situations than the one treated in the initial works of Cahn [2] and BACKGROUND THEORIESThe where m is the intrinsic boundary mobility (i.e. that corresponding to c = 0). The treatments by Cahn[2] and Lücke and Stüwe [10,23] are derived on the basis of the assumption that the effects on boundary mobility due to the cusp-formation resulting from the solute-boundary interaction can be neglected, the validity of this assumption is discussed belo...

The discrepancy between the classical grain growth law in high purity metals (grain size D / t 1=2 ) and experimental measurements has long been a subject of debate. It is generally believed that a time growth exponent less than 1/2 is due to small amounts of impurity atoms in solid solution even in high purity metals. The present authors have recently developed a new approach to solute drag based on solute pinning of grain boundaries, which turns out to be mathematically simpler than the classic theory for solute drag. This new approach has been combined with a simple parametric law for the growth of the mean grain size to simulate the growth kinetics in dilute solid solution metals. Experimental grain growth curves in the cases of aluminum, iron, and lead containing small amounts of impurities have been well accounted for.

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