Thermodynamic theory of the lead zirconate-titanate solid solution system

Abstract

Abstract Compositions within the lead zirconate-titanate (PZT) solid solution system have been extensively used in polycrystalline ceramic form in a wide range of piezoelectric transducer application. However, the growth of good quality PZT single crystals for compositions across the entire phase diagram has not been accomplished. Due to the lack of single crystal data, an understanding of the properties of ceramic PZT has been limited. If the single domain (intrinsic) properties of PZT could be determined, then the extrinsic contributions (e.g., domain wall and defect motions) to the ceramic properties could be separated from the intrinsic contributions. The purpose of this research has been to develop a thermodynamic phenomenological theory to model the phase transitions and single domain properties of the PZT system. A two-sublattice theory, where each sublattice has a separate polarization, was used to account for the ferroelectric and antiferroelectric phases. An additional order parameter was also included to account for the tilting of the oxygen octahedra in the low temperature rhombohedral phase. The resulting energy function can be used to calcuate the phase diagram; spontaneous polarization, strain, tilt angle, and entropy change; and dielectric, piezoelectric, and elastic properties of the PZT system. Without single crystal data, the development of this theory was complicated and involved indirect methods of determining the coefficients of the energy function. To provide additional experimental data, a sol-gel method was used to prepare pure homogeneous powders of PZT compositions across the phase diagram. High temperature x-ray diffraction of these powders was used to determine the spontaneous strain which was related to the spontaneous polarization through the electrostrictive coefficients. These data were then used to determine some of the coefficients of the energy function, and to locate a second tricritical point between the cubic and tetragonal phases, where the transition changes from first to second order. The calculations from this theory are in good agreement with the available experimental data, and provide a method of predicting the intrinsic single domain properties of the PZT system. The extrinsic contributions of the properties of ceramic PZT can not be separated from these intrinsic contributions. This theory can also be used to study the effect of mechanical and electrical boundary conditions on the properties and phase stability, which will be useful in understanding ceramic materials. A future direction of this research is to extend the present theory into the lanthanum modified PZT system (PLZT) to further the understanding of relaxor type materials.