Local structure and macroscopic properties in Pb Mg 1∕ 3 Nb 2∕ 3 O 3− Pb Ti O 3 and Pb Zn 1∕ 3 Nb 2∕ 3 O 3− Pb Ti O 3 solid solutions

We have examined the local structure of PbMg1∕3Nb2∕3O3PbTiO3 (PMN-PT) and PbZn1∕3Nb2∕3O3PbTiO3 (PZN-PT) solid solutions using density functional theory. We find that the directions and magnitudes of cation displacement can be explained by an interplay of cation-oxygen bonding, electrostatic dipole-dipole interactions, and short-range direct and through oxygen PbB-cation repulsive interactions. We find that the Zn ions move off center in the PZN-PT system, which also enables larger Pb and Nb∕Ti displacements. The off-centering behavior of Zn lessens PbB-cation repulsion, leading to relaxor-to-ferroelectric and rhombohedral-to-tetragonal phase transitions at low PbTiO3 content in the PZN-PT system. We also show that a simple quadratic relationship exists between Pb and B-cation displacements and the temperature maximum of the dielectric constant, thus linking the enhanced displacements in PZN-PT systems with the higher transition temperatures.