Features of the ferroelectric rhombohedral state in Ba(Ti_1−xZr_x)O₃ having the simple perovskite structure

Abstract

The crystallographic features of the ferroelectric rhombohedral (FR) state in Ba(Ti_1−xZr_x)O₃ (BTZ) have been investigated between 300 and 450 K mainly by transmission electron microscopy, with the help of the failure of Friedel’s law in electron diffraction. It was found that regions having ⟨001⟩_PC- and ⟨110⟩_PC-polarization components in the FR state were separately observed in dark field images, where the subscript PC denotes the paraelectric state. Based on the positional correspondence between regions with ⟨001⟩_PC and ⟨110⟩_PC components, the ferroelectric state for 0.11 ≤ x ≤ 0.17 could be explained as the nanometer-scale coexistence state consisting of fine FR and ferroelectric-tetragonal (FT) stripes, instead of the single FR state. In-situ observation also revealed that, when the temperature was lowered from the PC state, nanometer-scale polar (NP) regions with ⟨001⟩_PC and ⟨110⟩_PC components in the PC state were, respectively, coalesced into a banded structure with an average size of about 200 nm, and into fine stripes with that of about 30 nm. It is thus understood that the difference between the behaviors of the coalescences of NP regions with ⟨001⟩_PC and ⟨110⟩_PC components is directly associated with the appearances of both a complicated domain structure for x = 0.09 and the nanometer-scale coexistence state for 0.11 ≤ x ≤ 0.17.