Solute segregation at grain boundaries in polycrystals with dominating mass transport by complexes

Isothermal segregation of an impurity from a finite-size grain to the interface or the external free surface under predominant mass transfer by (vacancy–impurity atom) complexes is studied at low temperatures. A modified equation is obtained for an impurity with the effective diffusion coefficient containing the diffusion coefficients of the impurity and complexes with different weights. The temporal evolution of the impurity concentration is determined for planar, spherical, and cylindrical grains (which are close in shape to conventional grains) in the case of a dilute solution at an arbitrary temperature. Simple algebraic equations are obtained for the impurity concentration at the interface as a function of time. These equations are also valid for a concentrated solution of the impurity at the interface. The kinetics of impurity redissolution, i.e., the enrichment or depletion of the interface with the impurity (the departure of impurity to the bulk of the grain) is considered.