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

[22]
or piezoelectric response . Time dependence is also observed in cases where poorly poled piezoelectrics are
excited with unipolar waveforms, as is sometimes done in piezoelectric microelectromechanical systems. In
this case, the sample poles progressively during use, increasing the remanent piezoelectric coefficient but
decreasing the achievable strain during actuation due to progressive loss of the poling strain that is caused
by polarization alignment. It is also critical to note that these factors of microstructure, time, temperature,
and field are all inextricably linked such that the aging rates will depend on the amplitude of the field used
for their characterization .
[23]

This paper illustrates the temperature dependence of the domain wall contributions to the dielectric
properties of BaTiO ceramics, with an emphasis on the role of phase transitions, grain size, core-shell
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microstructures, and point defect concentrations in the response. The resulting temperature dependence of
the dielectric response is a complex interplay between these factors.

EXPERIMENTAL PROCEDURE
Samples
Undoped BaTiO ceramics were prepared using a BaTiO powder (BT02, with a Ba/Ti ratio of 0.996, Sakai
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Chemical Industry Co., Ltd., Sakai, Japan). To study the effect of grain size, BaTiO ceramics with grain sizes
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of 1.2 µm and 76 µm were prepared. The former was prepared by sintering a BaTiO compact at 1,300 °C for
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2 h and post-annealing the sintered body at 1,000 °C for 9.5 h , while the latter was prepared by sintering
[24]
the compact at 1,350 °C for 2 h . The grain sizes were measured from the microstructures of polished and
[25]
chemically etched ceramic surfaces observed by scanning electron microscopy (SEM). Figure 1A and B
shows the SEM images of the undoped BaTiO ceramics. Two grain lengths were measured for each grain,
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and the average of these two lengths was calculated for more than 90 grains. The grain size given is the
average of the two-length average, and the error bar for the grain size is the standard deviation. The grain
sizes were calculated to be 1.2 ± 0.5 µm and 76 ± 37 µm for the BaTiO ceramics sintered at 1,300 °C and
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1,350 °C, respectively. To study the effect of oxygen partial pressure (pO ) during sintering, BaTiO ceramics
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were sintered at 10 atm pO at 1,300 °C for 2 h . A microstructure similar to that of the undoped BaTiO
[24]
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ceramics sintered at 1,300 °C in air (10 atm pO ) was observed by SEM, and the grain size was 1.2 ± 0.4 µm.
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The dielectric properties were compared with those of the air-sintered BaTiO ceramics with a grain size of
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1.2 µm. Formulated BaTiO ceramics, which fulfill X7R specifications, were prepared using a BaTiO -based
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powder (EV540N, Ferro, Cleveland, OH, USA). The compact of the BaTiO -based powder was sintered at
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-2
1,300 °C for 2 h in the air (10 atm pO ) or at 10 atm pO . No reoxidation post-annealing was
[24]
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performed. Figure 1C and D shows the SEM images of the formulated BaTiO ceramics. Two formulated
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BaTiO ceramics had the same grain size of 0.5 ± 0.2 µm. The thickness of both undoped and formulated
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BaTiO ceramics was about 0.5 mm. For dielectric measurements, 100 nm thick Au electrodes were formed
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by sputtering. The details of the sample preparation and additional electric data are described elsewhere [24,25] .
The grain size effect was also studied for model multilayer ceramics capacitors (MLCCs). The size of model
MLCCs was 3.2 mm × 1.6 mm × 0.4 mm, and they consisted of ten 7.7-µm-thick BaTiO -based dielectric
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layers with X7R specifications and Ni internal electrodes. The grain sizes of the dielectrics were changed
from 0.28 ± 0.1 µm, 0.36 ± 0.1µm, and 0.39 ± 0.1 µm by changing the sintering temperature, while the
composition of the dielectrics was held constant. The details for the model MLCCs can be found in
Refs. [26,27] .
Measurement methods
For the undoped and formulated BaTiO ceramics, the ac field dependence of the dielectric properties was
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measured using a lock-in amplifier (SR830, Stanford Research Systems Inc., Sunnyvale, CA, USA), a voltage