PiezoelectricPb(Zr0.5Ti0.5)O3: Interplay of atomic ordering, ferroelectric soft modes, and pressure

Abstract

Three ordered structures of piezoelectric $\mathrm{Pb}({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}){\mathrm{O}}_{3}$ (PZT) under hydrostatic pressure are studied using a first-principles pseudopotential approach. These three structures (namely, a tetragonal phase with Ti/Zr ordered along the pseudocubic [001] direction, a tetragonal phase and a rhombohedral phase, both with Ti/Zr ordered along the [111] direction) differ in atomic ordering and spontaneous polarization. The volume dependences of energy, polarization, and strain are calculated for each structure. We found: (1) The energy difference caused by atomic ordering is $\ensuremath{\sim}58\mathrm{meV},$ much larger than the energy difference $(\ensuremath{\sim}1\mathrm{meV})$ due to different spontaneous polarizations. Atomic ordering thus dominates the structural energetics of PZT. (2) For the PZT's with Ti/Zr ordered along the [111] direction, the tetragonal and rhombohedral phases are very close in energy (less than $1\mathrm{meV}),$ indicating a possible large piezoelectric response from rotating polarization. (3) Whereas pressure can dramatically suppress ferroelectricity, it will change but very little the relative stability of two ferroelectric phases. (4) The bulk moduli of three PZT phases are found to be close $(\ensuremath{\sim}154\mathrm{GPa}).$ (5) The tetragonal PZT with Ti/Zr ordered along the [001] direction will maintain a substantial polarization and strain at $\ensuremath{\sim}15\mathrm{GPa};$ it could be useful in making high-pressure ferroelectric devices. (6) The tetragonal and rhombohedral PZT phases ordered along the [111] direction have very different energy surfaces when strains are driven along their polarization directions. These two phases will thus have rather different normal piezoelectric responses.