To evaluate the electrochemical properties of dense BZY samples sintered at 1435, 1485, and 1535 °C for 15 h, EIS measurements were conducted in the temperature range 100 to 600 °C. Even though oxygen ions, protons, and holes are potential charge carriers in BaZrO
3-based proton-conducting oxide, at temperatures below 600 °C under a reducing atmosphere, the protons play a major role in the charge carrier, because the diffusion coefficient of protons is much higher than those of holes and oxygen ions [
29]. Therefore, in the present study, proton conductivity was measured under a reducing wet atmosphere (3% H
2 in Ar and
pH
2O = 0.03 atm). Cole–Cole plots are typically used to determine the grain (
Rb and CPE
b), grain boundary (
Rgb and CPE
gb), and electrode (
Relec and CPE
elec) contributions [
6,
7,
8,
13,
30,
31].
Figure 6 shows the Cole–Cole plots obtained for the sintered BZY samples.
Figure 6a shows that the grain arc could not be clearly distinguished in the temperature range of 400 to 600 °C, because of the frequency limit (1 MHz) of the impedance analyzer. Therefore, only the grain resistance was obtained from the real axis intercept at high frequency. In contrast, the grain arc was observed below 200 °C, as shown in
Figure 6b, which enables the grain capacitance to be determined.
Figure 6 also includes equivalent circuit fitting. In the equivalent circuit, a constant-phase element (CPE) was used for fitting of the depressed arc described by
, where
w is the frequency,
Y0 is the non-Debye capacitance, and
n is the phase-angle parameter of the constant-phase element. The capacitance of each arc contribution can be calculated using
, where
R0 is the resistance parallel to CPE.
Figure 7a plots the total proton conductivity of the BZY samples as a function of the inverse of the temperature. Among the BZY samples, the BZY sample sintered at 1435 °C exhibited a rather low conductivity compared to the other samples, throughout the entire temperature range. At 500 °C, total conductivity values of ((2.28, 1.15, and 2.01) × 10
−3) S∙cm
−1 were obtained for the sample sintered at 1485, 1435, and 1535 °C, respectively. The activation energies of the samples sintered at 1435, 1485, and 1535°C were 0.51, 0.52, and 0.44 eV, respectively, in the temperature range of 100 to 500 °C. The total conductivity of all of the BZY samples exhibited a change in slope at approximately 550 °C, because of the decrease in the concentration of protons in the BZY lattice [
17,
20]. The conductivity and activation energy values obtained in this study are consistent with the conductivity reported in the literature for BZY prepared by SSRS with a 1 wt.% NiO sintering aid (1.6 × 10
−3 S∙cm
−1) [
13]. Therefore, it could be concluded that the relatively high amount of NiO sintering aid used in this study had little impact on the total proton conductivity of the BZY in the temperature range (300 to 500) °C, except for the BZY sintered at 1435 °C. This suggests that the unincorporated Y
2O
3 phase plays a detrimental role in proton conduction, as indicated in the X-ray diffraction patterns (
Figure 4a), since the unincorporated Y
2O
3 results in the decrease of proton concentration of BZY. The conductivity values measured at temperature below 200 °C were much lower compared with those measured at a temperature higher than 200 °C (by a factor of ~5 to 12), which suggests that the effect of secondary and impurity phases (BaY
2NiO
5 and Y
2O
3) is apparent at temperatures below 200 °C.
Table 5 summarizes the conductivities obtained in this study, and those reported in the literature for BZY at temperatures between 500 and 600 °C under wet inert and reducing atmospheres. The comparison of total proton conductivities in this study and the literature indicates that 2 wt.% NiO sintering aid is not significantly detrimental for proton conduction in the BZY electrolyte.
The brick layer model is typically used to describe the physical properties of polycrystalline materials. The specific grain boundary conductivity is given by
, where
Rgb is the grain boundary resistance,
Cgb is the grain boundary capacitance,
Cbulk is the bulk capacitance,
L is the sample thickness, and
A is the electrode area. When the grain boundary capacitance cannot be extracted from the impedance spectra, the specific boundary conductivity is calculated using
, under the assumption that the grain boundary thickness and grain size remain effectively constant. Here,
δ is the grain boundary thickness, and
D is the grain size.
Figure 7b shows the grain conductivity and specific grain boundary conductivity of the samples as a function of the inverse of temperature. The conductivity data reported in the literature [
13] for BZY prepared by SSRS with a 1 wt.% NiO sintering aid are included for comparison. The grain conductivity was much higher than the grain boundary conductivity, which is consistent with the results reported in the literature for BaZrO
3-based proton-conducting oxides. The specific grain boundary conductivity obtained in this study was significantly lower than that reported for BZY prepared by SSRS with a 1 wt.% NiO sintering aid [
13] below 350 °C, whereas the grain conductivity was comparable. The significantly lower grain boundary conductivity obtained in this study might be due to the higher amount of the BaY
2NiO
5 secondary phase, resulting from the relatively high amount of the NiO sintering aid (2 wt.% NiO). This is consistent with the finding reported in the literature that the secondary phase is mainly segregated at the grain boundary by introducing a sintering aid [
32]. The activation energy values of the grain and specific grain boundary conductivities were in the ranges 0.33–0.39 and 0.35–0.45 eV, respectively, which is consistent with the values of 0.39 and 0.45 eV, respectively, reported in the literature for BZY prepared using SSRS [
13].
Table 6 shows the bulk dielectric constant (
εr), Debye length (
λ), and Mott–Schottky depletion length (
λ*) of BZY at 100 °C, calculated using
,
, and
, respectively. In these equations,
CH is the proton concentration of BZY (2.50 × 10
26 m
−3) estimated in the literature [
20]; Δϕ(0) is the barrier height at the center of the grain boundary, determined from
;
ε0 is the vacuum permittivity.
A is the area of the sample;
L is the thickness of the sample;
k is the Boltzmann’s constant; and e is the electron charge. It is generally believed that the arc in the high-frequency region exhibits a value for the proton-conducting oxide grain (
C = ~10
−11 F), and that the arc in the intermediate-frequency region exhibits a value for the grain boundary (
C = ~10
−9 F) [
6,
7,
8,
13,
30,
31] that is in agreement with this study. The bulk dielectric constants of BZY obtained in this study were higher than those (37–155) reported in the literature [
13,
31,
33,
34]. However, the Debye length, Mott–Schottky depletion length, and barrier height values obtained in this study were fairly consistent with the ranges of values of 0.26–0.35 nm, 0.5–1.4 nm, and 0.04–0.35 V, respectively) reported for BZY in the literature [
13,
33,
34].