Random local strain effects in the relaxor ferroelectric BaTi_1−xZr_xO₃: experimental and theoretical investigation

Abstract

We report an investigation of the local structure in homovalent-substituted BaTi_1−x Zr _x O₃ 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 BaTi_1−x Zr _x O₃, 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 BaTi_1−x Zr _x O₃ relaxors, and probably in other BaTiO₃-based relaxors with homovalent substitution.

Keywords:

• ferroelectrics
• relaxor ferroelectrics
• local structure
• pair distribution function
• X-ray absorption spectroscopy
• supercell ab-initio calculations

Notes

Notes

1. Note that due to the k-dependence of the phase shifts δ _c (k) and φ _i (k), the maxima of the FT modulii occur at distances which are different from the real ones.

2. Such a small static distribution of the Zr–O distances cannot be evidenced from the PDFs shown in Section 2, due to the overlap of the Ti–O and Zr–O contributions.

3. Local structure determinations by EXAFS can become model-dependent, especially when a large number of structural parameters are involved. In the present case, N _Zr, , , and the / buckling angles determine the amplitude of the FT modulus in the range [3.4–3.9 Å], which impedes the discrimination of angular and linear deformations of the Zr–O–Zr and Zr–O–Ti chains.