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Fujii et al. Microstructures 2023;3:2023045 https://dx.doi.org/10.20517/microstructures.2023.43 Page 9 of 14

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Figure 8. Temperature dependence of the pseudo-Rayleigh parameters of the BaTiO ceramics sintered at 10 atm pO and the BaTiO 3
3
2
-2
ceramics sintered at 10 atm pO and post-annealed.
2
[24]
pinning of domain walls from weak pinning centers associated with the defect dipoles .
In most multilayer ceramic capacitors, the BaTiO is formulated to reduce the temperature dependence of
3
the permittivity and increase the reliability when base metal electrodes are utilized . It is thus interesting to
[35]
compare the temperature dependence of the extrinsic contributions of a formulated dielectric to that of
undoped ceramics. Figure 9 shows the ac field dependence of the dielectric properties of formulated BaTiO
3
-2
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[24]
ceramics sintered at 10 and 10 atm pO ; these samples showed core-shell microstructures . Above T , the
c
2
dielectric constant of both samples was independent of pO ; the permittivities of the two samples were
2
nearly identical in this regime due to the similar grain sizes (both samples had grain sizes of ~0.5 µm) and
the absence of a large concentration of mobile interfaces. As expected, provided that the samples are far
enough above T , there are few residual micropolar regions, and the nonlinear dielectric response of
c
formulated and undoped ceramics is similar. In contrast, below T , the irreversible contributions to the
c
permittivity were substantially suppressed in the formulated ceramics relative to the undoped materials. At
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-2
20 °C, the ac field dependence of the 10 atm pO sample was almost linear, while that of the 10 atm pO
2
2
sample was sublinear.
The dielectric responses were quantified using the pseudo-Rayleigh analysis, as shown in Figure 10. Below
T , the ε' 0.03kV/cm of the 10 atm pO sample monotonically decreased with temperature, while that of the
-2
2
c
10 atm pO sample showed a core/shell response. This is consistent with the temperature dependence of
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2
[24]
the small signal dielectric permittivity of the samples . With decreasing temperature, α' increased up to the
i
orthorhombic to rhombohedral phase transition and then decreased, which is consistent with the α' for the
i
small-grained undoped BaTiO ceramics (although the increase at the tetragonal to orthorhombic phase
3
transition was smeared). It was found that the difference of the α' between the formulated samples was
i
small above the T of the shell region. This suggests that the domain wall contributions are strongly
c
influenced by the shell region. Note that near room temperature, α' 2kV/cm and α' 0.5kV/cm of the 10 atm pO
-2
2
sample were similar, which corresponds to the Rayleigh behavior.