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BaTiO₃ is a well‐known ferroelectric material that was discovered before PZT in the 1940s during the World War II [11]. Before the emergence of PZT, BaTiO₃ had been the most important piezoelectric material, which has a higher piezoelectric coefficient d₃₃ = 120–190 pC/N than that of preceding piezoelectric materials such as triglycine sulfate (TGS), potassium dihydrogen phosphate (KDP), and quartz. BaTiO₃ undergoes a series of phase transitions, from cubic to tetragonal approximately at 130 °C, then to orthorhombic at 0 °C, and further to a rhombohedral crystal structure at −90 °C, as shown in Figure 2.2 [12].

Although BaTiO₃ is the first lead‐free piezoelectric compound, its Curie point (approximately 130 °C) is moderate, which limits its piezoelectric applications. Nevertheless, there are also many studies on lead‐free piezoelectrics based on BaTiO₃ [13, 14]. High piezoelectricity has been reported in pure BaTiO₃ single crystals [15, 16] and fine‐grained ceramics [17, 18]. In 2009, Liu and Ren reported a large piezoelectric response for the BaTiO₃‐based ceramic system with a d₃₃ coefficient >600 pC/N [19], which is comparable with soft PZT ceramics. The details will be given in Chapter 5.

BaTiO₃ is often used as a model ferroelectric material for fundamental studies because of its simple composition and rich phase structures. For example, early studies have been conducted to reveal the role of Pb from a comparison between BaTiO₃ and PbTiO₃ [20]. Both compounds have similar cohesive properties such as unit‐cell volume (0.0632 and 0.0642 nm³, respectively), yet with distinct ferroelectric behavior. PbTiO₃ has a high Curie temperature of 490 °C, and a large value of spontaneous polarization P_s (57 μC/cm²), whereas those of BaTiO₃ are much lower (P_s ~ 26 μC/cm²). PbTiO₃ has no low‐temperature phase transitions, whereas BaTiO₃ is known to have successive phase transitions, from the cubic structure to tetragonal, orthorhombic, and rhombohedral structure at low temperature. To explain why BaTiO₃ and PbTiO₃ show different ferroelectric behaviors, the studies have been focused on the difference in the chemical bonds of the two perovskite compounds. Kuroiwa et al. demonstrated through calculations that the Pb and O electronic states hybridize in tetragonal PbTiO₃, whereas the interaction between Ba and O is almost purely ionic in the tetragonal BaTiO₃, as shown by the charge‐density distributions of cubic and tetragonal PbTiO₃ and BaTiO₃ in Figure 2.3 [20]. It clearly revealed that no apparent difference can be seen between the cubic phases of PbTiO₃ and BaTiO₃, but between their tetragonal phases. Within the latter phases, the distributions in the Pb–O and Ti–O planes of PbTiO₃ are significantly different from those in the Ba–O and Ti–O planes of BaTiO₃. The electron‐density distribution around the Pb and O2 sites in tetragonal PbTiO₃ is quite anisotropic as shown in Figure 2.3c, i.e. extending toward the O2 and Pb, respectively. The electron densities of Pb and O2 are overlapped along the Pb–O2 direction in the tetragonal PbTiO₃. However, the electron densities around Ba and O are isotropic for tetragonal BaTiO₃, as shown in Figure 2.3a. These results indicate that the PbO bonds of tetragonal PbTiO₃ are covalent, although they are ionic in the cubic phase. By comparing Figure 2.3b,d, it is clear that the Ti in PbTiO₃ has a larger displacement than that in BaTiO₃, consistent with the fact that the spontaneous polarization of PbTiO₃ is larger than that of BaTiO₃. This provides clear evidence for the Pb–O hybridization in tetragonal PbTiO₃, which has been theoretically predicted as a key factor of much larger ferroelectricity of PbTiO₃ as a representative Pb‐containing ferroelectric compound than that of BaTiO₃ as a lead‐free counterpart.

Figure 2.2 Change in relative dielectric constants of BaTiO₃ ceramics as a function of temperature. Inserted are the crystal structures at the corresponding temperatures.

Source: Modified from Merz [12].

The aforementioned comparison between BaTiO₃ and PbTiO₃ indicates that partial covalent bonding due to the Pb–O hybridization should be responsible for the high performance of Pb‐containing piezoceramics. In lead‐free counterparts, Saito et al. also found that substituting Nb with Sb, which has higher electronegativity than the former, leads to further piezoelectric property enhancement in (K,Na)NbO₃‐based ceramics [10]; this is also because of the hybridization of covalency onto ionic bonding. In addition, Bi as a neighbor of Pb has a similar electronic structure with the latter, and can be used a modifier to enhance the contribution of covalent bonding.

Figure 2.3 Charge‐density distributions on (a) the (010) plane (Ba–O plane), (b) the (020) plane (Ti–O plane) of tetragonal BaTiO₃ at 300 K, compared to that of tetragonal PbTiO₃ at 300 K on (c) the (010) plane (Pb–O plane), and (d) the (020) plane (Ti–O plane).

Source: Reprinted with permission from Kuroiwa et al. [20]. Copyright 2001, American Physical Society.