Nature of ferroelectric-paraelectric transition

Ferroelectric (FE) materials directly convert electrical energy to mechanical energy and are critical to applications such as sensors, transducers, and actuators. The giant electromechanical response is the manifestation of the critical point between the first-order and second-order ferroelectric- paraelectric (FE-PE) transitions. For the simple classic FE lead titanate (PbTiO ₃), it is commonly accepted that there is a critical point in the temperature-pressure phase diagram separating the first- and second-order FE-PE transitions at zero electric field. Here, we show that the FE-PE transition in PbTiO ₃ is second-order at zero electric field. We introduce the concept of the invariant critical points (ICP) among three phases, representing the stability of the PE phase with respect to two FE phases in a three-dimensional electric field-pressure-temperature phase diagram of PbTiO ₃. It is pointed out that the electromechanical response near ICPs is larger than that near the line of critical end points (LCEPs) between two phases.