Reducing grain boundary, dislocation line and vacancy formation energies by solute segregation. I. Theoretical background

The Gibbs adsorption isotherm and Wagner’s definition of excess solute at surfaces and grain boundaries are both extended to include other crystalline defects, like dislocations and vacancies. By using a thermodynamic state function which is suitable for a partially open system, open with respect to solvent and closed with respect to solute atoms, a generalized Gibbs adsorption isotherm can be derived. Thus solute segregation to dislocations and vacancies gives rise to a reduction of their formation energies, too. The results of the presented treatment are compared with results stemming from statistical mechanics or computer simulations. Special attention is paid to the question whether defect energies might become zero or negative.