The intrinsic piezoelectricity of monoclinic Pb(Zr_1- Ti )O₃

The phase diagram of Pb(Zr_1- Ti )O₃ (PZT) is quite clear; however, the existence and intrinsic piezoelectricity of low-symmetry structures near the MPB (morphotropic phase boundary) remain subjects of considerable uncertainty. The impact of the MPB on the piezoelectric properties of PZT was investigated via first principles study. Different PZT structures were established by virtual crystal approximation (VCA). The density functional theory (DFT) with plane-wave basis set method was utilized to calculate the energy, elastic, and piezoelectric properties. The presence of the monoclinic phase in MPB was confirmed near x ∼ 0.53. This phase exhibited distinct piezoelectric properties. Although the coefficients d ₃₃ and d ₁₅ were lower, the maximum value of d ₃₁ reached -198.33 pm V^-1. By exhaustively exploring all possible structures at the MPB, we demonstrate that the intrinsic piezoelectricity of monoclinic structures is not the main contributor to the MPB effect. Further study shows that this is related to the hybridization between the O2p orbital and the d orbital of the central atom. Finally, analysis of the energy barrier along the polarization rotation paths implies a flattening of free energy in the monoclinic phase, suggesting a high intrinsic piezoelectric coefficient. The intrinsic piezoelectric properties of the monoclinic phase may bring new ideas to the study of the MPB effect.