*3.2. Dielectric Properties of Ceramics*

Figure 3 exhibits the temperature dependence of dielectric constant (*ε*r) and loss tangent (*tan σ*) of the oxide-modified SBT ceramics. As can be seen, all the samples show a dielectric anomaly around 540 ◦C, which can be related to the ferroelectric-paraelectric phase transition of the ceramics. The peak position is considered as the Curie temperature (*T*C). For the pure SBT (*T*<sup>C</sup> = 537 ◦C, Figure 3a), a sharp rise in the values of *ε*<sup>r</sup> occurred above 350 ◦C at low frequencies (100 Hz and 500 Hz), which can be attributed to the dielectric response of a large number of space charges to the external electric field. Moreover, its permittivity peaks are broadened and strongly dependent with frequency in terms of strength, and their positions seem to be also dependent with frequency as marked by the slightly oblique arrows. Therefore, this can be considered as a typical relaxed dielectric behavior, which is partially due to the compositional fluctuation in the crystallographic sites. In Figure 3b, SGBT exhibits a higher *T*<sup>C</sup> ~ 557 ◦C as well as a normal phase transition. This result may be attributed to the lattice distortion of the pseduo-perovskite structure since the bivalent strontium ions were substituted by the trivalent gadolinium ions at the *A*-site. The tolerance factor (*t*) which is used for evaluating the stability of ABO3-type perovskite structure can be calculated by the expression as follows [34]:

$$t = \frac{r\_{\text{A}} + r\_{\text{O}}}{\sqrt{2}(r\_{\text{B}} + r\_{\text{O}})} \tag{1}$$

where *r*A, *r*<sup>B</sup> and *r*<sup>O</sup> are the ionic radius of A, B and the oxygen ion, respectively. One-third of bivalent strontium ions (1.44 Å) and two-thirds of bismuth ions (1.30 Å) occupy the A site at the perovskite-like structure of pure SBT ceramics. According to the atomic percentage of the A-/B-site, the average ionic radius for Sr0.92Gd0.053Bi4Ti4O<sup>15</sup> could be reckoned as follows: *r*<sup>A</sup> = 1/3 (0.92*r*Sr2+ + 0.053*r*Gd3+) + 2/3 *r*Bi3+ = 1.33 Å (*r*Gd3+ = 1.107 Å), *r*<sup>B</sup> = *r*Ti4+ = 0.605 Å, *r*O2<sup>−</sup> = 1.40 Å. The tolerance factor of SGBT and SBT were calculated to be 0.96 and 0.97, respectively, according to Equation (1). The reduced tolerance factor indicates that the perovskite structure of SGBT is more stable; in this case, the phase transition from the ferroelectric state to the paraelectric state needs more energy, which corresponds to a higher *T*C. As can be seen from Figure 3c, *T*<sup>C</sup> of SCBT (531 ◦C) is less low than that of SBT, which could be attributed to the reduced stability of oxygen octahedron after adding CeO<sup>2</sup> into SBT, since the coordination number of introduced Ce4+ is smaller than that of Sr2+. The dielectric loss peak appearing around 500 ◦C at the low frequency of 100 Hz could be attributed to the space-charge relaxation as an extrinsic dielectric response [35]. The similar dielectric anomaly was also observed in cobaltmodified SBT [23]. The defect dipoles which are formed by combining space charges or ions with opposite charges may be slow to follow the external electric field, thereby contributing to the dielectric loss [36]. Therefore, the relaxation phenomenon reflected by the dielectric loss peaks or bumps in the wide temperature sweep can be related to the viscoelastic reorientation of defect dipoles following the external electric field at high temperature [37]. On the other hand, for all the oxide-doped compositions, the characteristic temperatures of permittivity peaks agree with that of loss peaks well. Especially, SCBT-Cr shows the most flat dielectric loss curve at 100 Hz, which indicates that the synergetic doping of CeO<sup>2</sup> and Cr2O<sup>3</sup> could significantly improve the temperature stability of the dielectric properties of SBT.

frequencies.

**Figure 3.** Temperature dependence of dielectric constant and loss tangent of the oxide-modified SBT ceramics at different **Figure 3.** Temperature dependence of dielectric constant and loss tangent of the oxide-modified SBT ceramics at different frequencies.
