Oxide chemistry and local structure of ${\mathrm{PbZr}}_x{\mathrm{Ti}}_{1-x}{\mathrm{O}}_3$ studied by density-functional theory supercell calculations

The ${\mathrm{PbZr}}_x{\mathrm{Ti}}_{1-x}{\mathrm{O}}_3$ (PZT) disordered solid solution is widely used in piezoelectric applications due to its excellent electromechanical properties. The disorder is caused by the random arrangement of B cations. To understand the relationship between properties of constituent atoms, local structure, and compositional phase transitions, we examine the response of the individual Pb atoms, B cations, and oxygen cages to the variation in the Zr/Ti arrangement and composition through first-principles density-functional-theory (DFT) calculations on a variety of PZT supercells. We use a statistical analysis of the relaxed DFT structures to identify crystal chemical structural motifs present in the Zr-rich rhombohedral, 50/50 monoclinic, and Ti-rich tetragonal phases of PZT and to examine the influence of composition variation on the motifs. We find that the distortions of the structure away from the ideal perovskite structure are governed by an interplay of bonding, electrostatic, and short-range repulsive interactions that depends on the B-cation arrangement. For Pb-atom displacements, there is a competition between electrostatic and bonding interactions that favor ordered collinear displacements, and local repulsive interactions that favor disorder. This competition is strongly affected by the changes in Zr/Ti composition and leads to compositional phase boundaries in PZT.