Revisiting the phase diagram and piezoelectricity of lead zirconate titanate from first principles

Lead zirconate titanate $(\mathrm{PbZ}{\mathrm{r}}_{1\ensuremath{-}x}\mathrm{T}{\mathrm{i}}_{x}{\mathrm{O}}_{3},\phantom{\rule{0.16em}{0ex}}\mathrm{PZT})$ exhibits excellent piezoelectric properties in the morphotropic phase boundary (MPB) region of its temperature-composition phase diagram. However, the microscopic origin of its high piezoelectric response remains controversial. Here, we develop a machine-learning-based deep potential (DP) model of PZT using the training data set from first-principles density functional theory calculations. Based on DP-assisted large-scale atomic simulations, we reproduce the temperature-composition phase diagram of PZT, in good agreement with the experiment except for the absence of structural transition from R3c to R3m. We find that the rhombohedral phase maintains R3c symmetry with slight oxygen octahedral tilting with increase of temperature, instead of exhibiting R3m symmetry. This discrepancy could trace back to the lack of experimental measurements to identify such slight octahedral tilting. More importantly, we clarify the atomic-level feature of PZT at the MPB, which exhibits the competing coupling of ferroelectric nanodomains with various polarization orientations. The high piezoelectric response is driven by the polarization rotation of nanodomains induced by an external electric field.