A comprehensive study of pressure dependent phase transitions in ferroelectric PbTiO3, PbZrO3 and BaTiO3

Using first principles calculations, we investigate the pressure dependent polarization and phase transitions, based on the structural, electronic, piezoelectric and elastic properties in PbTiO3-P4mm, BaTiO3-P4mm, PbZrO3-R3m and BaTiO3-R3m. Under positive pressure, only PbZrO3-R3m does not exhibit a structural phase transition to paraelectric cubic and has a higher polarization than PbTiO3-P 4mm beyond 38 GPa. BaTiO3-P 4mm and PbZrO3-R3m show an isomorphic phase transition which is driven by the change in the bonding between A site and B-site atoms (Ba-Ti) and between the B-site and O-axial atoms (Zr-O), respectively. We quantitatively demonstrate the strong correlation of polarization with octahedral tilt in PbTiO3 and both phases of BaTiO3. The higher polarization in PbTiO3 and PbZrO3 under pressure is on account of the enhanced contributions from Pb atoms and the difference in their energy level shifts with respect to the Fermi level in comparison with that of Ba. We report that the anomalous enhancement in the polarization at negative pressures is a precursor of the onset of the mechanical instability in the material. The onset of mechanical instability is also the region of a node in piezoelectric constants d(ij).