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Page 4 of 14 Fujii et al. Microstructures 2023;3:2023045 https://dx.doi.org/10.20517/microstructures.2023.43

Figure 1. SEM images for undoped BaTiO ceramics with grain sizes of (A) 1.2 µm and (B) 76 µm and formulated BaTiO ceramics
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3
-2
-9
sintered at (C) 10 atm pO and (D) 10 atm pO .
2
2
[24]
amplifier, and a charge converter . An ac field frequency of 100 Hz was utilized. The ac field amplitude
was increased up to 4 kV/cm; the coercive fields are 4 kV/cm for air-sintered undoped BaTiO ceramics
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with 1.2 µm and 76 µm grain sizes, 3 kV/cm for undoped BaTiO ceramics sintered at 10 atm pO with a
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3
2
1.2 µm grain size, and 5 kV/cm for formulated BaTiO ceramics. The coercive fields were determined from
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polarization - electric field (P-E) loops measured by a custom-made measurement system at room
temperature, as shown in Figure 2.
For the model MLCCs, the ac field dependence of the dielectric properties was measured using an LCR
meter (4284A, Agilent Technologies Inc., Santa Clara, CA) with a frequency of 1 kHz. The ac field
amplitude was increased up to 12-15 kV/cm. The coercive fields of the samples were about 10-15 kV/cm.
The temperature dependence of the dielectric properties was measured upon cooling from 150 °C to
-150 °C or -180 °C, and the temperature of the samples was controlled by a furnace (DELTA 9023, Delta
Design, Poway, CA); the chamber was cooled with liquid nitrogen. The dielectric data were measured on
cooling to reduce artifacts associated with condensed moisture.

RESULTS AND DISCUSSION
Figure 3 illustrates the temperature dependence of the relative permittivity (ε') (prime) of a BaTiO ceramic
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sample as a function of ac field amplitude. Several points are immediately apparent. First, at temperatures
well above the Curie temperature T ~125 °C (i.e., measurements at 150 °C), where there should be no
c
ferroelectric domains, there are no domain wall contributions to the properties. As a result, the dielectric
permittivity shows very limited dependence on the amplitude of the ac electric field. As the temperature
drops to the Curie temperature (data at 125 °C), it is apparent that there is a finite field dependence of ε',
which may be due to persistent micropolar regions . Below T in the tetragonal ferroelectric regime (data
[28]
c
at 80 °C), there is a large population of mobile ferroelectric domain walls in the ceramics, and the
nonlinearity in ε' increases. Near any of the phase transitions (apparent as peaks in the permittivity data),
both the intrinsic polarizability and the domain wall contributions to the properties rise. The latter is clearly
apparent as enhanced dielectric nonlinearity (for example, the data set at 20 °C). Substantial dielectric