  We present first-principles supercell calculations on BaTi0.74Zr0.26O3, 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 < 1 1 1 >, < 1 1 0 >, or < 1 0 0 >
directions of the cubic unit cell, or almost cancelled. 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 Ti4+ and Zr4+ cations. These results
shed light on the structural mechanisms that lead to disordered Ti
displacements in BaTi(1-x)Zr(x)O3 relaxors, and probably in other BaTiO3-based
relaxors with homovalent substitution.
