First discovered in 1959, the relaxor behaviour has become a major topic in materials science since the discovery of giant electromechanical responses in relaxor-based solid solutions [1]. The best properties are currently obtained with lead-containing relaxors (e.g. PbMg1/3Nb2/3O3). However, their toxicity raises environmental concerns, and a significant research effort is also concentrated on lead-free relaxors [2], such as BaTi1-xZrxO3.

Below the critical temperature Tc, classical ferroelectrics present a macroscopic polarisation. In the ferroelectric perovskite BaTiO3, this polarisation is due to displacements of Ba2+ and Ti4+ cations with respect to the O2- anions, which all occur in the same direction. Such displacements result in distortions with respect to the ideal cubic perovskite structure presented in Figure 101a. With increasing temperature, a sharp and frequency-independent divergence of the dielectric permittivity is observed at Tc, which corresponds to a structural phase transition: the ideal cubic perovskite structure is recovered. On the other hand, relaxors are characterised by a broad and frequency-dependent maximum of the dielectric permittivity as a function of temperature, which is not linked to a structural phase transition. In relaxor ferroelectrics, the polarisation is not macroscopic but local [3], due to cation displacements which are correlated on a nanometre scale only. Note that diffraction studies, which are sensitive to the average structure, suggest an apparently undistorted ideal perovskite structure in BaTi1-xZrxO3 relaxors at any temperature, because all local cation displacements are averaged to zero.

The mechanism that leads to the formation of polar nanoregions in relaxors is still unclear. In most studied relaxors, an aliovalent cationic disorder (e.g. Mg2+ and Nb5+ in PbMg1/3Nb2/3O3) is related to a random fluctuation of charges and thus to random local electric fields, which in turn break long-range ferroelectric correlations. Contrary to this, the relaxor BaTi1-xZrxO3 (0.25 ≤ x ≤ 0.5) presents a homovalent Zr4+/Ti4+ substitution on the octahedral sites, which cannot directly induce random electric fields. However, the difference in size of Zr4+ and Ti4+ cations (rZr4+/rTi4+ = 1.18) induces random elastic deformations, which could affect the displacement of the ferroelectrically active Ti4+ ions in their oxygen octahedra.

Fig. 101: a) The ideal perovskite structure, consisting of corner-linked oxygen octahedra. b) Modulus of the Fourier Transform of the k2-weighted EXAFS signal for BaZrO3 and BaTi0.65Zr0.35O3 at the Zr K-edge.

To investigate the local deformations induced by the Zr atoms in BaTi1-xZrxO3, X-ray absorption fine structure (EXAFS) experiments were carried out at the Zr K-edge in BaTi1-xZrxO3 samples (x = 0.25, 0.30, 0.35, and 1), on the BM30B-FAME beamline. The Fourier Transforms of the EXAFS signals of the BaTi0.65Zr0.35O3 relaxor and the end-member compound BaZrO3 are compared in Figure 101b. In the distance-range 1.2 – 2.3 Å, the analysis shows that the Zr-O distance measured by EXAFS is independent of x and equal to that measured in BaZrO3. On the other hand, the X-ray cubic cell parameter increases linearly with x (Figure 102a). The ZrO6 octahedra thus form rigid units, which do not fit to the average structure volume. In the distance-range 2.5 – 4.5 Å, a careful analysis of the multiple scattering contributions reveals a buckling of the Zr-O-Zr bonds, which is not present in a perfect cubic structure (Figure 102 c,d). Although a partial accommodation to the average structure is probably obtained through the latter deformation, the Zr-Zr distance is still approximately 2% larger than the average (Zr/Ti)-(Zr/Ti) distance deduced from X-ray diffraction (Figure 102b). Moreover, the chemical sensitivity of EXAFS allows us to evidence a tendency of Zr atoms to segregate in Zr-rich regions.

Fig. 102: Evolution of a) Zr-O and b) Zr-Zr distances with x: EXAFS results (circles), compared to a/2 and a deduced from X-ray diffraction (crosses). Schematic top views of the structure of BaTi1-xZrxO3 relaxors, according to either c) X-ray diffraction or d) EXAFS (the buckling angle is exaggerated for clarity).

From our results, one can conclude that the ZrO6 octahedra likely exert a significant tensile stress on the TiO6 octahedra at the interface of the Zr-rich regions. This tensile stress may generate particular Ti4+ local displacements (and thus local polarity). In this scenario, fluctuating local structural stress could then influence the formation of polar nanoregions in BaTi1-xZrxO3 relaxors, similarly to fluctuating charges in common relaxors.



[1] S.E. Park and T.R. Shrout, J. Appl. Phys. 82, 1804 (1997).
[2] L.E. Cross, Nature 432, 24 (2004); Y. Saito et al., Nature 432, 84 (2004).
[3] L.E. Cross, Ferroelectrics 76, 241-267 (1987); Ferroelectrics 151, 305-320 (1994).

Principal Publications and Authors

C. Laulhé (a), F. Hippert (a), J. Kreisel (a), M. Maglione (b), A. Simon (b), J.-L. Hazemann (c), V. Nassif (d), Phys. Rev. B 74, 014106 (2006)
(a) Laboratoire Matériaux et Génie Physique, CNRS-INP Grenoble (France)
(b) Institut de Chimie de la Matière Condensée de Bordeaux, CNRS Bordeaux (France)
(c) Laboratoire de Cristallographie, CNRS Grenoble (France)
(d) DRFMC/SP2M/NRS, CEA Grenoble (France)