Origin of the large piezoelectric activity in(1−x)Ba(Zr0.2Ti0.8)O3−x(Ba0.7Ca0.3)TiO3ceramics

Abstract

The diffusionless pseudobinary phase diagram, monodomain properties, and free energy of $(1\ensuremath{-}x)\mathrm{Ba}(\mathrm{Z}{\mathrm{r}}_{0.2}\mathrm{T}{\mathrm{i}}_{0.8}){\mathrm{O}}_{3}\text{\ensuremath{-}}x(\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3})\mathrm{Ti}{\mathrm{O}}_{3}$ are computed for comparison with experimental results. Specifically, the variation of the spontaneous polarization, anisotropy energy, and free energy with respect to temperature, composition, and polarization direction are discussed relative to the results of resonant piezoelectric measurements performed over a wide compositional range as a function of temperature. The phase angle, relative permittivity, piezoelectric and coupling coefficients, and elastic compliances were used to investigate relations between the computed and measured pseudobinary phase diagrams and the measured piezoelectric and elastic properties. It was found that ${d}_{33}$ values along the orthorhombic to tetragonal phase boundary are $\ensuremath{\sim}30%$ higher than those both along the rhombohedral to orthorhombic phase boundary and in the region where phases converge. It is shown that the reduction in anisotropy energy in these regions of the phase diagram is by itself insufficient to explain the measured properties. The highest small signal piezoelectric activity is found along the orthorhombic to tetragonal phase boundary due to a combination of reduced anisotropy energy, high remanent/spontaneous polarization, and increased elastic softening. The combined computed and experimental results are used to demonstrate that the interdependent behavior of these properties should be considered in the design of engineered piezoelectric ceramics.