Random local strain effects in the relaxor ferroelectric BaTi1-xZrxO3: experimental and theoretical investigation

We report an investigation of the local structure in homovalent-substituted BaTi1-xZrxO3 relaxors by a combination of experimental and theoretical methods, namely neutron total scattering, X-ray absorption spectroscopy, and supercell ab-initio calculations. It is shown that unlike Zr atoms, Ti atoms are largely displaced in their octahedra, and are thus associated with strong local dipole moments. Besides, we give evidence that the difference in the size of Ti4+ and Zr4+ cations leads to a significant size mismatch of the Ti-O6 and Zr-O6 octahedra. When they link to form the perovskite structure of BaTi1-xZrxO3, the O6 octahedra undergo slight distortions in order to accommodate their different sizes. It is shown that they are compressed in the direction of Zr neighbors, and expanded in the direction of Ti neighbors. The polar Ti displacements, which are sensitive to the octahedral distortions, then become constrained in their orientation according to the local Zr/Ti distribution. Such constraints impede a perfect alignment of all the Ti displacements as existing in the classic ferroelectric BaTiO3. Our results shed light on the structural mechanisms that lead to disordered Ti displacements in BaTi1-xZrxO3 relaxors, and probably in other BaTiO3-based relaxors with homovalent substitution.