Grain Boundary Segregation in Titanium Dioxide: Evaluation of Relative Driving Forces for Segregation
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Grain Boundary Segregation in Titanium Dioxide: Evaluation of Relative Driving Forces for Segregation Qinglei Wang, Guoda D. Lian and Elizabeth C. Dickey* Department of Materials Science and Engineering and the Materials Research Institute The Pennsylvania State University, University Park, PA 16802, U.S.A. *corresponding author: [email protected] ABSTRACT Solute segregation to grain boundaries is a fundamental phenomenon in polycrystalline metal-oxide electroceramics that has enormous implications for the macroscopic dielectric behavior of the materials. This paper presents a systematic study of solute segregation in a model dielectric, titanium dioxide. We investigate the relative role of the electrostatic versus strain energy driving forces for segregation by studying yttrium-doped specimens. Through analytical transmission electron microscopy studies, we quantitatively determine the segregation behavior of the material. The measured Gibbsian interfacial excesses are compared to thermodynamic predictions. INTRODUCTION Grain boundaries in ceramics influence many macroscopic material properties including grain growth1,2, high-temperature creep3,4 and dielectric response5. Electroceramics such as varistors and positive temperature coefficient of resistance thermistors derive their unique functionalities directly from grain boundary phenomena, while most others are at least influenced by local grain boundary behavior. While grain boundary segregation is believed to be well understood in metals, ceramic grain boundaries are more complex due to the charged nature of the defects. Several driving forces, including chemical, elastic and electrostatic, induce segregation of point defects to grain boundaries. The segregation behavior of isovalent solutes, where the segregation driving force results primarily from the misfit-induced strain energy of the solute ion, are relatively simple6. Electrostatic-controlled segregation is unique to ionic materials and is a consequence of equilibration of charged point defects with a surface or interface. This phenomenon has been studied since Frenkel first proposed a surface charge theory7 with notable advancements made by Lehovec8 and Kliewer9. In oxides, there are numerous experimental observations to support the existence of interfacial segregation in a number of systems, including Al2O33, ZrO22,10,11 and perovskites12,13. Understanding the driving forces behind interfacial segregation and the ultimate implications for physical properties are of extreme importance for developing next generation functional ceramics. Semiconducting TiO2 has been studied as a model system due to its well-known defect chemistry and relatively simple crystal structure. Space charge segregation of various dopants (e.g Zr, Sn1, Al, Nb, Ga14-16, Ca17) in TiO2 has been investigated. Ikeda and Chiang first proposed a space-charge segregation model for TiO2 with complementary theoretical and experimental studies14,15. Segregation models based on both electrostatic and elastic driving forces are more comple
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