Crystallographic features of the relaxor state in the mixed ferroelectric system Ba(Ti_1-xZr_x)O₃

The relaxor state has been found in the mixed ferroelectric system Ba(Ti_1-xZr_x)O₃ around x = 0.35. To understand the nature of the relaxor state, the crystallographic features of the paraelectric (PC), ferroelectric, and relaxor states for 0.15 ≤ x ≤ 0.40 have been investigated mainly by transmission electron microscopy. It was found that a microstructure of the ferroelectric state for 0.15 ≤ x ≤ 0.28 consisted of banded structures with boundaries parallel to the {110}_PC and {100}_PC planes. Based on the Sapriel theory concerning ferroelastic transitions, it was understood that the banded structures were consistent with domain structures in the ferroelectric rhombohedral (FR) state having a polarization vector parallel to one of the <111> _PC directions. With the help of the failure of Friedel's law in diffraction, furthermore, polar regions having <001>_PC and <110>_PC components of a <111>_PC polarization vector were also found to be separately observed in the PC and relaxor states as well as the FR state. Then, in-situ observation for 0.29 ≤ x ≤ 0.40 made in this study indicated that the PC and relaxor states consisted of polar nanometer-sized regions having these two components. Based on this, the relaxor state in BTZ can be identified as an assembly of polar nanometer-sized regions, which were produced by the suppression of the (PC→FR) ferroelectric transition on cooling.