Interaction of Solute Impurity with Grain Boundary: The Impurity Drag Effect

An equation of grain boundary motion in a binary polycrystal is derived. The derivation is based on minimization of free energy of the total systems. The equation takes into account an impurity segregation at the grain boundary, grain boundary curvature and energy.As an example, we apply this equation to the analysis of the impurity drag effect problem. It is shown, that the sign of the impurity effect on grain boundary velocity (delay or acceleration) does not depend on kinetic coefficients. The sign of the effect is determined by a thermodynamic function which combines the grain boundary segregation coefficient, the derivative of grain boundary energy with respect to absorbed impurity concentration, and the derivative of bulk free energy with respect to bulk impurity concentration.