Structure-property relation in mesoscopic barium titanate and lead titanate

The last decade has witnessed great research efforts to miniaturize ferroelectric devices so as to integrate these components with semiconductor technology. Miniaturization requires the realization of microstructures in the mesoscopic size range (<500 nm) in which ferroelectric materials exhibit “size effects”. As the physical dimensions of a ferroelectric system are decreased, the stability of the polar phase diminishes. Below a certain size, called the critical crystallite size (CCS) ferroelectricity is known to vanish. However, the underlying reasons are not fully understood. As a result, the technological application of mesoscopic ferroelectric materials is limited due to performance and reliability problems arising from size effects.; In this study, structure-property relations in mesoscopic PbTiO ₃ and BaTiO₃ were investigated in terms of the factor(s) governing the intrinsic ferroelectric behavior in the <300 nm crystallite size regime. Phase pure perovskite particulate crystals were synthesized by the Pechini method and analyzed by a multitude of diffraction techniques including laboratory x-ray diffraction (room temperature and high temperature), synchrotron diffraction and differential scanning calorimetry. PbTiO₃ was employed as the prototype system to quantitatively determine the effects of crystallite size on the intrinsic ferroelectric behavior and properties with the aid of Devonshire's version of the Landau-Ginzburg free energy density formalism.; The CCS in PbTiO₃ was determined as 15 nm, whereas in BaTiO ₃ it is 67 nm. It was found that the CCS scales inversely with the transition temperature. Analysis of the microstrain indicates a multi-mono domain transition around 75 and 150 nm in PbTiO₃ and BaTiO₃, respectively. The enthalpy of the cubic-tetragonal transition decreases quasilinearly with decreasing crystallite size in the <100 nm range in either system. The observed decrease is attributed to the reduction in the number of pairwise dipole-dipole interactions constituting the cooperative ferroelectric ordering.; The Landau-Ginzburg analysis as applied to PbTiO₃ has revealed a decrease in the free energy density with decreasing crystallite size in the <100 nm size regime which was customarily taken as constant in several previous studies in the literature. Hence, crystallite size is, in fact, an additional thermodynamic coordinate that has to be included in the free energy expressions of a mesoscopic ferroelectric system.; Furthermore, an order of magnitude increase in the neighborhood of the CCS (15 nm) in the electrostrictive coefficients Q₁₁, Q₁₂ and Q_h is predicted. The asymptotic increase in the intrinsic electrostrictive response of PbTiO₃ is believed to caused by the anharmonicity of the lattice. Significant increase in piezocharge coefficients (d₃₃ and d₃₁) is also postulated. The analysis thus implies that the increase in electrostrictive coefficients largely compensates the decrease in spontaneous polarization with reduced crystallite size thereby increasing the piezoelectric response. Therefore, pronounced intrinsic piezoelectric activity can indeed be observed in the mesoscopic size range provided that the stability of the ferroelectric phase is preserved. In addition, it is postulated that PbTiO₃ becomes superparaelectric around 3 nm.