We present first-principles supercell calculations on ${\text{BaTi}}_{0.74}{\text{Zr}}_{0.26}{\text{O}}_3$, a prototype material for relaxors with a homovalent substitution. From a statistical analysis of relaxed structures, we give evidence for four types of Ti-atom polar displacements: along the $⟨111⟩$, $⟨110⟩$, or $⟨100⟩$ directions of the cubic unit cell or almost canceled. The type of a Ti displacement is entirely determined by the Ti/Zr distribution in the adjacent unit cells. The underlying mechanism involves local strain effects that ensue from the difference in size between the ${\text{Ti}}^{4+}$ and ${\text{Zr}}^{4+}$ cations. These results shed light on the structural mechanisms that lead to disordered Ti displacements in ${\text{BaTi}}_{1-x}{\text{Zr}}_x{\text{O}}_3$ relaxors, and probably in other ${\text{BaTiO}}_3$-based relaxors with homovalent substitution.

• Received 7 June 2010

DOI:https://doi.org/10.1103/PhysRevB.82.132102