The microstructural origin of the exceptionally high piezoelectric response of polycrystalline $\mathrm{0.5Ba}\left({\mathrm{Zr}}_{0.2}{\mathrm{Ti}}_{0.8}\right)O_3-0.5({\mathrm{Ba}}_{0.7}$${\mathrm{Ca}}_{0.3}){\mathrm{TiO}}_3$ is investigated using in situ transmission electron microscopy, in addition to a wide variety of bulk measurements and first-principles calculations. A direct correlation is established relating a domain wall-free state to the ultrahigh piezoelectric $d_{33}$ coefficient in this ${\mathrm{BaTiO}}_3$-based composition. The results suggest that the unique single-domain state formed during electrical poling is a result of a structural transition from coexistent rhombohedral and tetragonal phases to an orthorhombic phase that has an anomalously low elastic modulus. First-principles calculations indicate that incorporating ${\mathrm{Ca}}^{2+}$ and ${\mathrm{Zr}}^{4+}$ into ${\mathrm{BaTiO}}_3$ reduces the differences in structure and energy of the variant perovskite phases, and $\mathrm{0.5Ba}({\mathrm{Zr}}_{0.2}$${\mathrm{Ti}}_{0.8})O_3-0.5({\mathrm{Ba}}_{0.7}$${\mathrm{Ca}}_{0.3}){\mathrm{TiO}}_3$ is identified as unique because the variant phases become almost indistinguishable. The structural instability and elastic softening observed here are responsible for the excellent piezoelectric properties of this lead-free ceramic.

• Received 11 March 2014
• Revised 22 May 2014

DOI:https://doi.org/10.1103/PhysRevB.90.014103