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Wang et al. Microstructures 2023;3:2023023 https://dx.doi.org/10.20517/microstructures.2023.04 Page 5 of 10

[19]
leading to the emergence of smaller grain sizes . The breakdown field of ceramics is significantly
[18]
influenced by the grain size, with smaller grain sizes resulting in higher breakdown electric fields .
Therefore, the addition of SBTZ at low doping levels is advantageous for achieving high energy storage
properties. Specifically, when the SBTZ content is 0.07, 0.08, 0.09, and 0.1, the average grain sizes are
1.47 μm, 0.93 μm, 0.90 μm, and 1.22 μm, respectively.

Figure 3 depicts the dielectric behavior of (1-x)BNBT-xSBTZ ceramics over a temperature range of
35-400 °C and at frequencies of 1 kHz, 10 kHz, 1 MHz, 10 MHz, and 20 MHz, respectively. The curves
illustrate that the ceramics exhibit relaxation behavior with double dielectric peaks. The shape of the curves
remains consistent across varying SBTZ doping levels, with the dielectric peak T becoming broader,
m
indicating an enhanced relaxation characteristic . The second peak T , which corresponds to the
[20]
m
maximum dielectric constant (ε ), represents the relaxation of the rhombohedral-tetragonal phase
m
transition brought about by the polar nanoregions . As the doping level increases, the ε of the ceramics
[21]
m
tends to decrease, indicating a weakening of the ferroelectric properties. The low dielectric losses (tan δ) of
the samples demonstrate their excellent insulating properties, which play a crucial role in improving the
energy storage performance of ceramics.
In order to conduct a more thorough investigation into the relaxor transition in ceramics, an adaptation of
the Curie-Weiss Law was implemented, which can be expressed as follows:

where ε is the dielectric constant, T is the temperature, T is the temperature at which ε reaches its
m
maximum value ε , C is a constant, and is the diffuse degree. The value of γ ranges from 1 for typical
max
ferroelectrics to 2 for ideal relaxor ferroelectrics.
Figure 4 depicts the relationship between ln(T-T ) and ln(1/ε-1/ε ) for the examined samples. The
max
m
calculated value of γ ranges from 1.76 to 2.01, indicating a strong relaxation behavior of the sintered
ceramics.

The dielectric breakdown strength (DBS) of the ceramics was evaluated, as depicted in Figure 5A. By
[22]
utilizing the Weibull distribution as Equation (5-7) :

where i is the group number, X and Y are parameters in Weibull distribution functions, E is the DBS of
i
i
i
sample i, P is associated with dielectric breakdown, and n is the sum of specimens of each sample. The
i
electric field is ranged as Equation (8).