Space charge, elastic field, and dipole contributions to equilibrium solute segregation at interfaces

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Abstract
The interaction potentials between solute ions and grain boundaries in ionic solids are identified as (1) the electrostatic interaction between the charged solutes and grain boundaries, (2) the elastic energy due to the size misfit of solutes in the matrix, and (3) the dipole interactions between the solute-vacancy dipoles and the electric field in the grain-boundary region. We include these interaction potentials to evaluate the minimum free energy and the equilibrium solute and defect distributions in the grain-boundary region. Numerical calculations show that these interaction mechanisms, either acting individually or coupling with each other, lead to a nonuniform solute distribution near the grain boundary. Under certain conditions, both the elastic and dipole interactions can significantly modify the electrostatic potential near the boundary. Calculations also show that the grain-boundary segregation of an aliovalent solute can be induced or altered by another aliovalent solute of different size misfit with the matrix.