Taking Bismuth Titanate (Bi₄Ti₃O₁₂) as a Aurivillius-type compound with m = 3 for example, the ion (W⁶⁺/Cr³⁺) doping effect on the lattice distortion and interlayer mismatch of Bi₄Ti₃O₁₂ structure were investigated by stress analysis, based on an elastic model. Since oxygen-octahedron rotates in the ab-plane, and inclines away from the c-axis, a lattice model for describing the status change of oxygen-octahedron was built according to the substituting mechanism of W⁶⁺/Cr³⁺ for Ti⁴⁺, which was used to investigate the variation of orthorhombic distortion degree (a/b) of Bi₄Ti₃O₁₂ with the doping content. The analysis shows that the incorporation of W⁶⁺/Cr³⁺ into Bi₄Ti₃O₁₂ tends to relieve the distortion of pseudo-perovskite layer, which also helps it to become more stiff. Since the bismuth-oxide layer expands while the pseudo-perovskite layer tightens, an analytic model for the plane stress distribution in the crystal lattice of Bi₄Ti₃O₁₂ was developed from the constitutive relationship of alternating layer structure. The calculations reveal that the structural mismatch of Bi₄Ti₃O₁₂ is constrained in the ab-plane of a unit cell, since both the interlayer mismatch degree and the total strain energy vary with the doping content in a similar trend to the lattice parameters of ab-plane.

A sort of tungsten/chromium(W/Cr) co-doped bismuth titanate (BIT) ceramics (Bi₄Ti_2.95W_0.05O_12.05 + 0.2 wt % Cr₂O₃, abbreviate to BTWC) are ordinarily sintered between 1050 and 1150 °C, and the indentation behavior and mechanical properties of ceramics sintered at different temperatures have been investigated by both nanoindentation and microindentation technology. Firstly, more or less Bi₂Ti₂O₇ grains as the second phase were found in BTWC ceramics, and the grain size of ceramics increased with increase of sintering temperatures. A nanoindentation test for BTWC ceramics reveals that the testing hardness of ceramics decreased with increase of sintering temperatures, which could be explained by the Hall–Petch equation, and the true hardness could be calculated according to the pressure-state-response (PSR) model considering the indentation size effect, where the value of hardness depends on the magnitude of load. While, under the application of microsized Vickers, the sample sintered at a lower temperature (1050 °C) gained four linearly propagating cracks, however, they were observed to shorten in the sample sintered at a higher temperature (1125 °C). Moreover, both the crack deflection and the crack branching existed in the latter. The hardness and the fracture toughness of BTWC ceramics presented a contrary variational tendency with increase of sintering temperatures. A high sintering tends to get a lower hardness and a higher fracture toughness, which could be attributed to the easier plastic deformation and the stronger crack inhibition of coarse grains, respectively, as well as the toughening effect coming from the second phase.

The origin of frequently observed ultrahigh electro-induced longitudinal strain, ranging from 1% to 26%, remains an open question. While recent studies have associated this phenomenon with bending deformation, the underlying mechanisms and the pronounced thickness dependence of the nominal strain have yet to be fully elucidated. Here, we demonstrate that the bending in piezoelectrics can be induced by a nonzero gradient of d_{31} across thickness direction. A scaling law (η_{3,nom}∝L^{2}E_{3}∇_{z}d_{31}/t) is derived to quantify the size dependence, thereby resolving longstanding ambiguities surrounding reported "giant" electrostrains. Simulations reveal that in standard perovskite piezoceramics, such as KNbO_{3}, a 0.69% concentration of oxygen vacancies can induce a 6.3 pC/N variation in d_{31} by suppressing polarization rotation, being sufficient to produce ultrahigh nominal strain in thin samples. Numerous factors, including gradients in defect concentration, composition, and stress, may lead to sufficient inhomogeneity in the distribution of d_{31}, suggesting electrobending may be a widespread phenomenon. This Letter presents a unified framework for understanding electrobending deformation, offering deeper insight into the mechanisms behind abnormally giant electrostrain responses in diverse piezoelectric systems and may encourage new engineering applications.