The local atomic distribution in tetragonal PZT

Expanding on the comprehensive research conducted by previous scholars, herein, we aim to elucidate the intrinsic piezoelectricity of tetragonal Pb(Zr_1-Ti)O₃ (PZT), by focusing on the local atomic distribution which was neglected for a long time, through the supercell approach based on colour symmetry. Density functional theory (DFT) was employed to perform first-principles calculations on the electronic, phononic structures and piezoelectricity of various tetragonal PZT supercells. Building upon the evaluation of the piezoelectric properties of 22 distinct distributions, classical Monte Carlo methods were utilized to explore the statistical macroscopic properties at the morphotropic phase boundary (MPB). The results reveal that at x = 0.5 and x = 0.55, the d₃₃ reached 957 pm V^-1 and 893 pm V^-1, respectively. The analysis of phonon vibration modes exposed significant disparity between different colour symmetries. The supercells of lower symmetry contain B-site atoms in asymmetric positions, and they exhibit softer vibrational frequencies in the phonon spectrum. These soft phonon vibration modes resulting from colour symmetry breaking were previously unknown. The weakening and reorientation of the covalent bonds between the O 2p and d orbitals were found in electronic structures. The free energy flattening in the polarization rotation path is the origin of the high piezoelectricity of this type of supercell. The analysis of the electronic structure is consistent with the experimental observations. Finally, colour symmetry proved to be an effective and accurate way to describe the local atomic distribution in supercells. It will also bring new perspectives to understanding the structure of domain walls, phase boundaries, etc.