Theoretical Investigations Of Structure Search, Piezoelectric Response And Band Structure In Pb_0.5Ba_0.5TiO₃ Alloys

In this work, we have carried out a systematic crystal structure search for Pb_0.5Ba_0.5TiO₃ alloys at different fixed pressure based on the particle swarming optimization algorithm implemented in the CALYPSO code, combined with the VASP and ABINIT calculations. The predicted elastically and dynamically stable ground-state and high-pressure Pb_0.5Ba_0.5TiO₃ phases are tetragonal ferroelectric and cubic paraelectric, respectively. Then, we have systematically investigated the structural property, piezoelectric effect and band structure of Pb_0.5Ba_0.5TiO₃ alloys.Firstly, compared with the single-crystal Pb TiO3 and Ba TiO3, we have systematically studied the structural, elastical and dynamical properties of tetragonal and cubic Pb_0.5Ba_0.5TiO₃ alloys, with a particular focus on the dynamic analysis of the pressure-induced sequent structural phase transitions in PbTiO₃. Meanwhile, our further structure predictions reveal that there are no stable tetragonal structures of Pb_0.5Ba_0.5TiO₃ at high-pressures of 130 GPa and 150 GPa.Secondly, in order to reveal the intriguing physical properties of tetragonal Pb_0.5Ba_0.5TiO₃, compared with the ferroelectric single-crystal PbTiO₃ and BaTiO₃, we have systematically investigated the polarization, piezoelectric strain and piezoelectric stress in tetragonal Pb_0.5Ba_0.5TiO₃ as a function of pressure. Our further investigations reveal that the mechanical and dynamical instabilities in tetragonal Pb_0.5Ba_0.5TiO₃ under pressure, which are associated with the softening behavior of c axis, are responsible for the pressure-induced colossal enhancements in piezoelectric response, and further emphasizes that the polarization rotation is not a necessary condition.Finally, the electronic structures of the typical d-electron metallic oxide ZrO₂ are studied using the standard hybrid density functional HSE06, which indicates the advantages of HSE06 to PBE in dealing with the electronic structure. Then we have systematically studied the electronic structure of tetragonal and cubic Pb_0.5Ba_0.5TiO₃ alloys under hydrostatic pressure using HSE06 method as a function of pressure. Compared with tetragonal PbTiO₃ and BaTiO₃, the underlying mechanism of d orbital influence on the band structure and band gap of Pb_0.5Ba_0.5TiO₃ are studied through analyzing the density of states and partial density of states.