Fig. 3: Comparison between PbTiO3 and HfO2.
Cubic \(Pm\bar{3}m\) paraelectric (a) and tetragonal P4mm ferroelectric (b) phases of PbTiO3. The tetragonal phase presents two symmetry-inequivalent oxygen anions, colored differently and labeled by OI and OII, respectively. In panel b the arrow on the right marks the spontaneous polarization, which is essentially related to the upward displacement of the Pb and Ti cations with respect to the oxygen atoms (the arrows on the atoms mark such displacements). Panel c is a sketch of the tetragonal phase subject to a tensile η3 > 0 strain (the strain is exaggerated for clarity); the arrows on the atoms indicate how they react in response to the strain, as computed from first principles. Panels d–f are analogous to the previous three panels, but featuring the paraelectric (d) and ferroelectric (e) states of HfO2, and its longitudinal piezoresponse (f).
