Interactions and chemistry of defects at the grain boundaries of ceramics

A thermodynamic approach is used to derive a defect chemistry formulation at the grain boundary of an ionic solid, Considering the elastic and/or electrostatic interactions between charged defects, the equilibrium electrostatic potential and the concentration of charged defects at the grain boundaries can be quantitatively predicted. The obtained result has general applicability at all levels of defect concentrations. Defect concentration at the boundary has been determined to critically depend on the interactions between defects, electrostatic potential, and segregation. These interactions, either acting individually or coupling with each other, lead to a nonuniform defect distribution near the grain boundary. Calculations also show that the grain-boundary segregation of an aliovalent solute is greatly affected by doping through the electrostatic or elastic interactions. The variation of the grain-boundary characteristics with the processing parameters, such as dopant concentration and temperature, is discussed in relation with the proposed model.