Interfacial Segregation in Perovskites: I, Theory

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Abstract
Based on thermodynamic principles a theory for equilibrium interfacial segregation is proposed for perovskite materials, and this theory is applied to BaTiO3. An approach developed by Frenkel and refined by Kliewer and Koehler is extended to undoped ternary oxide materials such as BaTiO3. The approach uses regular solution approximations and considers space charge effects as the major driving force for segregation. The analysis based on this model indicates the presence of a negative space charge potential (−0.1 V at 800°C) at the surface of pure BaTiO3. The model also predicts cation enrichment at the interface. The thickness of the space charge layer decreases with increasing temperature, and calculated values agree well with experimental results. Since both elastic and electrostatic driving forces are important for dopant/impurity segregation, an approach where the grain boundary is considered to be a two‐dimensional phase, in equilibrium with the three‐dimensional phase of the grain, proves useful. Solving for the impurity/dopant segregation ratio is case specific and requires knowledge of the charge neutrality conditions as well as the strain energy contribution.