Proton-conducting BaZrO3-doped electrolytes are considered as potential high temperature proton conductors due to their high ionic conductivity and electrical efficiency in the operating temperature range of solid oxide fuel cells. However, doping leads to a decrease in grain boundary conductivity and greatly limits its applications. Here, the charge transport properties of sub-micro and nano-BaZrO3 electrolytes were studied by in situ high-pressure impedance measurements and first-principles calculations. Mixed ionic-electronic conduction was found in both samples in the whole pressure range. Pressure-induced negative capacitance in the tetragonal phase of nano-BaZrO3 was observed, which was related to the space charge layer of grain boundaries as well as the electrostrictive strain of grains. The enhanced electrostrictive effect was attributed to the existence of polar nano-domains in nano-BaZrO3. Furthermore, the coincident imaginary part of impedance and modulus peaks on the frequency scale indicated a non-localized carrier conduction in the tetragonal phase of nano-BaZrO3. The grain boundary conductivity of nano-BaZrO3 was enhanced by four orders of magnitude, and the impedance response changed from a constant phase element to an ideal capacitance, which was accompanied by the cubic to tetragonal phase transition. At a switching frequency of 0.1 Hz, the real part of the dielectric function of nano-BaZrO3 increases sharply with frequencies from negative to positive values, exhibiting a plasma-like Drude behavior. Our results provide insight into the optimization and application of BaZrO3-based proton conductors in solid oxide fuel cells.

The increasing worldwide energy demand and the global warming-related concerns resulting from energy from conventional fossil fuel drive the desire for the generation of sustainable alternative energy. Because of the excellent chemical and thermal stability and high efficiency as well as fuel flexibility, the solid oxide fuel cells (SOFCs) have attracted much attention.1 However, SOFCs still face critical challenge due to their high operating temperature (above 750 °C),2 which causes high costs, differences in thermal expansion coefficients, and reactions between the cell components.3 

As one of the major components of an SOFC, the electrolyte plays an important role in reducing the operating temperature. For traditional oxide-conducting electrolyte materials [i.e., yttria-stabilized zirconia (YSZ)], the ionic conductivity drops dramatically at the reduced temperature, which results in poor performance and limits their application.4,5 Proton-conducting electrolytes exhibit higher electrical efficiency and ionic conductivity in the operating temperature range of SOFC.6 BaZrO3-doped perovskite-type electrolytes are considered as potential high temperature proton conductors with high mechanical strength, high proton conductivity,7 low thermal expansion coefficient,8 and good chemical stability.9 However, doping will introduce problems, such as electronic conduction, dopant segregation,10,11 the presence of blocking impurity phases,12 and shrinkage effect,13,14 leading to a reduction in grain boundary (GB) conductivity and thereby affecting the overall electrical performance of the electrolyte.

Pressure has long been recognized as a powerful and clean tool to adjust the crystal structure and properties of materials widely, which can effectively change the interaction between atoms, induce the redistribution of charges between atoms or at grain boundaries, and lead to the creation of new band structures or new interface states.15–18 For pure BaZrO3 (BZO), a cubic to tetragonal structural phase transition at 17.2 GPa has been clarified by high-pressure synchrotron x-ray diffraction measurements.19 However, as an important solid electrolyte, the pressure-modulated electrical transport properties of BZO are still ambiguous. An intensive study of the conductive and grain boundary behavior under high pressure is essential to explore the transport, recombination, and accumulation of the charges from non-equilibrium conditions to equilibrium conditions, and the ionic conductivity may be improved by pressure.

Furthermore, the grain size of materials plays a role in the conductivity since the space charge effect is enhanced in nanomaterials. Theoretically, if the grain size is significantly smaller than the Debye length, the conductivity of ions can increase by several orders of magnitude over that of micrometer materials.20,21 For example, the conductivity of BaTiO3 with a grain size of 35 nm is 1–2 orders of magnitude higher than that of micrometers.22 The nano-sized Sm0.5Sr0.5O3−δ promotes the movement of charges through the parallel grain boundaries and improves the overall grain boundary conductivity.21 Therefore, it is worth exploring the size effect of sub-micro and nano-BZO on the high-pressure transport properties.

In this work, we investigated the pressure-dependent charge transport properties of sub-micro and nano-BZO solid electrolytes by impedance spectroscopy measurements combined with first-principles calculations. Mixed ionic-electronic conduction was found in both samples within the studied pressure range. For the first time, pressure-induced negative capacitance in the nano-BZO was observed, accompanied by a structural phase transition. The negative capacitance was attributed to the space charge potential at grain boundaries as well as the electrostrictive effect in grains. More importantly, the grain boundary conductivity of nano-BZO was enhanced by four orders of magnitude, and the impedance response in the high-frequency region had a transition from a constant phase element (CPE) to an ideal capacitance element. The variation of ionic and electronic conductivity, dielectric properties, and space charge behavior with pressure were also discussed.

The studied sub-micro and nano-BZO samples were purchased from Alfa Aesar and Sigma Aldrich with the average size of 260 and 30 nm, respectively (see scanning electron microscopy results shown in Fig. S1 of the supplementary material). The impedance spectra of sub-micro and nano-BZO under selected pressures are plotted in Fig. 1 (see the Nyquist plots at each pressure in Figs. S2 and S3). For the sub-micro BZO, the spectra exhibit two parts: a straight line at a low frequency region and a semicircle at a high frequency region. The semicircle is attributed to the high-frequency vibration of electrons and/or ions around the rigid lattice while the straight line represents the typical Warburg diffusion process.23,24 These characteristics suggest that there exist both electronic and ionic conductions in sub-micro BZO in the whole pressure range. For the nano-BZO, when the pressure reaches up to 20.3 GPa, the impedance spectrum consists of a large semicircle above the Z′ axis and a small semicircle underneath [Fig. 1(d)], which is related to the charging and discharging process of the system (a non-Faraday process) and the inductive response (the Faraday process).

FIG. 1.

Impedance spectra (Z′, Z″, and frequency) of BZO at different pressures: (a) sub-micro BZO at 8.6 GPa, (b) sub-micro BZO at 27.3 GPa, (c) nano-BZO at 11.4 GPa, and (d) nano-BZO at 25.3 GPa. Red symbols represent curves against Z′, Z″, and frequency. Blue, green, and cyan symbols show the relationship between Z′, Z″, and frequency, respectively.

FIG. 1.

Impedance spectra (Z′, Z″, and frequency) of BZO at different pressures: (a) sub-micro BZO at 8.6 GPa, (b) sub-micro BZO at 27.3 GPa, (c) nano-BZO at 11.4 GPa, and (d) nano-BZO at 25.3 GPa. Red symbols represent curves against Z′, Z″, and frequency. Blue, green, and cyan symbols show the relationship between Z′, Z″, and frequency, respectively.

Close modal
FIG. 2.

The pressure-dependent bulk ionic conductivity (σbi), bulk electronic conductivity (σbe), grain boundary ionic conductivity (σgbi), and grain boundary electronic conductivity (σgbe) for the sub-micro BZO (a)–(d) and nano-BZO (e)–(h). The vertical dotted line indicates the phase transition from the cubic phase to the tetragonal phase.

FIG. 2.

The pressure-dependent bulk ionic conductivity (σbi), bulk electronic conductivity (σbe), grain boundary ionic conductivity (σgbi), and grain boundary electronic conductivity (σgbe) for the sub-micro BZO (a)–(d) and nano-BZO (e)–(h). The vertical dotted line indicates the phase transition from the cubic phase to the tetragonal phase.

Close modal
FIG. 3.

(a) The crystal structure of cubic-BZO. The green, gray, and red spheres represent Ba, Zr, and O atoms, respectively. Red spheres from a to k represent the O2− ions along the channel from sites a to k, with the minimized energy migration path of the cubic phase. (b) Calculated O2− migration energy barriers in the cubic phase along the path at different pressures. (c) The crystal structure (primitive cell) of tetragonal-BZO. Red spheres from a to g represent the O2− ions along the channel from sites a to g, with the minimized energy migration path of the tetragonal phase. (d) Calculated O2− migration energy barriers in the tetragonal phase along the path at different pressures.

FIG. 3.

(a) The crystal structure of cubic-BZO. The green, gray, and red spheres represent Ba, Zr, and O atoms, respectively. Red spheres from a to k represent the O2− ions along the channel from sites a to k, with the minimized energy migration path of the cubic phase. (b) Calculated O2− migration energy barriers in the cubic phase along the path at different pressures. (c) The crystal structure (primitive cell) of tetragonal-BZO. Red spheres from a to g represent the O2− ions along the channel from sites a to g, with the minimized energy migration path of the tetragonal phase. (d) Calculated O2− migration energy barriers in the tetragonal phase along the path at different pressures.

Close modal

The impedance spectra were analyzed by the equivalent circuit method. In the inset of Fig. S4(a), due to the existence of the “dispersion effect,” the ideal capacitive element was replaced by a constant phase element (CPE), and the Warburg diffusion in the low frequency region was represented by the Warburg element. This circuit was applied to the nano-BZO below 20.3 GPa and to the sub-micro BZO in the whole pressure range (Fig. S5). For the nano-BZO, the constant phase element was changed by an ideal capacitive element above 20.3 GPa, and the semicircle underneath was represented by an inductance element [Fig. S4(b)]. The simulated results are consistent with the experimental data.

FIG. 4.

The grain boundary energies of the (a) cubic phase and (b) tetragonal phase under compression. Inset: schematic diagram for grain boundary (GB). The (111)(1¯10) GB for the cubic phase and the (100)(001) GB for the tetragonal phase. The blue lines indicate the borders of the primitive grain boundary cells.

FIG. 4.

The grain boundary energies of the (a) cubic phase and (b) tetragonal phase under compression. Inset: schematic diagram for grain boundary (GB). The (111)(1¯10) GB for the cubic phase and the (100)(001) GB for the tetragonal phase. The blue lines indicate the borders of the primitive grain boundary cells.

Close modal
FIG. 5.

(a) Space charge potential (Φ) of sub-mirco and nano-BZO at pressures. Schematic of the Schottky barrier model near the grain boundary region of the nano-BZO in (b) the cubic phase and (c) the tetragonal phase.

FIG. 5.

(a) Space charge potential (Φ) of sub-mirco and nano-BZO at pressures. Schematic of the Schottky barrier model near the grain boundary region of the nano-BZO in (b) the cubic phase and (c) the tetragonal phase.

Close modal

As displayed in Fig. 2, the variations of electrical transport parameters with pressure are obtained by fitting the impedance spectra. Two abnormities were observed at 15.8 and 20.3 GPa for sub-micro and nano-BZO, respectively, which are related to the structural phase transition from a cubic phase to a tetragonal phase,25 and the difference in the phase transition pressure is caused by the size effect.26,27 As shown in Fig. 2, the total electrical conductivity of sub-micro BZO in the cubic phase is higher than that of nano-BZO. According to the brick-layer model, the charge transport through the grain boundary is dominant in the samples with smaller grain size. However, a smaller grain size generally leads to a smaller grain boundary, which results in an increase in the atomic volume fraction on the grain boundary of nanomaterials and, thus, prevents the carrier transport. In the tetragonal phase, although the bulk conductivity of nano-BZO is lower than that of sub-micro BZO, the grain boundary conductivity of nano-BZO is obviously higher than that of sub-micro BZO, which is related to the appearance of inductive response. In the cubic and tetragonal phases, the bulk ionic conductivity (σbi) decreased with increasing pressure for both samples [Figs. 2(a) and 2(e)]. The bulk ionic conductivity is associated with the ionic concentration, the diffusion of ions, and the migration energy barrier. Based on the impedance spectra, the relative ionic diffusion coefficient (Di/D0), the transference number of O2− ions (ti) and electrons (te) are calculated [Figs. S6(a) and S6(b)]. As shown in Fig. 3, the energy barriers of O2− ions migration in sub-micro BZO at different pressures were calculated. The selection of the O2− migration path is based on the principle of the minimum energy barrier, which is along the z direction for cubic and tetragonal phases. However, the migration path is not the only one. If there is a strong enough voltage in other directions than can overcome the barrier, it will lead to O2− migration. In both cubic and tetragonal phases, the energy barriers increased with pressure. For sub-micro BZO, although the diffusion coefficient showed an increase in the cubic phase, the transference number decreased as the pressure increased. In the tetragonal phase, the diffusion coefficient decreased while te had a small increase with pressure. Therefore, it can be concluded that the migration energy barrier contributes dominantly to the decreased σbi with increasing pressure in both samples.

FIG. 6.

(a) Variation of inductance L and its reciprocal B with pressure. (b) Frequency dependence of the real part of the dielectric function at different pressures in the tetragonal phase of nano-BZO.

FIG. 6.

(a) Variation of inductance L and its reciprocal B with pressure. (b) Frequency dependence of the real part of the dielectric function at different pressures in the tetragonal phase of nano-BZO.

Close modal

The bulk electronic conductivity (σbe) at different pressures for sub-micro BZO and nano-BZO were shown in Figs. 2(b) and 2(f), respectively. In order to further analyze the conductivity, the bandgap was calculated (Fig. S7), which increased with increasing pressure in both phases. Normally, an increase in the bandgap will result in a decrease in conductivity. However, the bulk conductivity is also affected by te. te indicates the concentration of electrons involved in conduction, which is positively correlated with σbe. In Fig. S6(b), the te of sub-micro BZO in the cubic phase increased with pressure but decreased in the tetragonal phase. Thus, the increased σbe in the cubic phase was due to the increased te, and the decreased σbe in the tetragonal phase arose from the increased bandgap as well as the decreased te. For nano-BZO, te decreased with pressure in the cubic phase [Fig. S6(c)], so the increased σbe could be caused by the increased electronic mobility. While for the tetragonal phase, the increased bandgap played a dominant role in leading to the decreased σbe.

To better understand the carriers transport process at grain boundaries, the variation of grain boundary energy with pressure in both phases were calculated, as shown in Fig. 4. Generally, the grain boundary energy consists of two parts, namely, elastic distortion energy and chemical interaction energy. The former depends on the degree of grain boundary misorientation, while the latter depends on the chemical bond between the atoms on the grain boundary and the surrounding atoms. From the inset of Fig. 4, the number of atomic bonding at the grain boundaries remains almost unchanged. Therefore, for the two phases of BZO, the elastic distortion energy dominated the grain boundary energy and the variation of grain boundary energy with pressure reflects the change of the mismatch degree of grain boundaries with pressure. For both phases, the grain boundary energy increased rapidly with increasing pressure, which indicating the increase in mismatch degree. This conclusion is further substantiated by the HRTEM images of quenched samples from different pressures, as shown in Fig. S8. The average grain size of each phase of nano and sub-micro BZO was significantly reduced, and the density of grain boundaries increased with the increasing pressure, leading to the enhanced carrier scattering effect at grain boundaries. In the cubic phase, ti of sub-micro BZO decreased with increasing pressure but the ionic diffusion coefficient increased, leading to the increase in σgbi [Fig. 2(c)]. For the electronic transport, the increased te resulted in the increase in σgbe [Fig. 2(d)]. In the tetragonal phase, the increased grain boundary energy gave rise to a decrease in σgbi and σgbe, even though ti increased slowly with increasing pressure. The transference number of nano-BZO played a major role in the σgbi and σgbe of the cubic phase. The decreased grain boundary density weakened the carrier scattering in the tetragonal phase, which leads to the increasing of grain boundary conductivity [Figs. 2(g) and 2(h)].

It is worth noting that, when the phase transition was finished, the bulk conductivity of nano-BZO decreased and the grain boundary conductivity increased, which is different from the sub-micro sample. This could be related to the inductance in the tetragonal phase of nano-BZO. In the Faraday current process, the Faraday current If, which characterizes the reaction rate, is a function of the electric potential U, the unknown variable X (produces inductance), and the concentration CjS of the reactive particles (affects the reaction rate). The Faraday admittance can be deduced as (see the detailed derivation process in the supplementary material)

YXθ=1aB+jωB=1RL+jωL,
(1)

where YXθ is the Faraday admittance, a=(∂Ξ/X), Ξ=dX/dt is the change rate of the unknown variable X, B= (If/X)·(Ξ/U), RL=a/B, and L=1/B. According to Eq. (1), the inductance appeared only in the case of B > 0. That is, the unknown variable X should be proportional to the current If, and the change rate of X should be proportional to the electric potential U. Next, we will discuss the mechanism of inductive impedance in the tetragonal phase of nano-BZO.

From the perspective of the grain boundary, the influence on the unknown variable X can only be caused by the electrical potential generated in the space charge layer, since the applied voltage under each pressure is the same during the impedance measurements. According to the space charge layer model,28,29 the space charge layer will generate a built-in electric field that affects the charge transfer. The space charge potential Φ can be obtained with the following equation:

ρgbρb=exp(eΦkBT)2eΦ/kBT,
(2)

where ρb and ρgb represent the grain resistivity and grain boundary resistivity, respectively; e and kB refer to the elementary charge and the Boltzmann constant, respectively; T is 300 K. ρgb and ρb are derived from the sample geometry and the impedance measurements.

As shown in Fig. 5(a), in the cubic phase, the space charge potential of both samples decreased with pressure. In the tetragonal phase, the space charge potential of sub-micro BZO increased slowly while it became negative above 20.3 GPa for nano-BZO, and its absolute value also increased with increasing pressure. According to Eq. (2), the change of space charge potential of nano-BZO from positive to negative means that ρb > 2 ρgb. Therefore, the grain boundary conductivity became higher than the bulk conductivity after the phase transition, which can be interpreted by the double-Schottky barrier model [Figs. 5(b) and 5(c)]. This reveals that a pressure-induced negative to positive charge concentration transition of nano-BZO in the space charge layer accompanied the phase transition (see the detailed derivation process in the supplementary material).

Since the space charge potential is related to the charge density,30 the unknown variable X can be considered as the carrier concentration at the grain boundary. For the sub-micro BZO, the increased σgb in the cubic phase indicates that the carrier concentration X at grain boundaries increased. However, the space charge potential decreased in the cubic phase. The change rate of X is inversely proportional to the space charge potential and, therefore, no inductance is generated. The case in the tetragonal phase of sub-micro BZO is similar to in the cubic phase of nano-BZO. Notably, σgb of nano-BZO in the tetragonal phase increased while the space charge potential also increased. Therefore, the space charge potential is proportional to the change rate of carrier concentration X, which leads to the appearance of inductive impedance.

On the other hand, the change rate of the unknown variable X correlates with the electric potential, that is, with the electric field or the polarization. From the perspective of grain, the strain caused by electrostriction is a state variable related to the electric-field or polarization, so X can also be considered as the electrostrictive strain S. According to the electrostrictive effect of the dielectric material, when the material changes from the paraelectric phase to the ferroelectric phase, the generated S can be expressed as S=QP2, where Q is the electrostriction coefficient related to the polarization and P is the polarization induced by the electric-field. Generally, the electrostrictive effect is extremely weak and difficult to observe. However, when polar nano-domains (PNRs) appear in the crystal, the electrostrictive effect will be significantly enhanced.31 Upon compression, more defects were generated after the phase transition from a central symmetric paraelectric phase (cubic phase) to a lower symmetric ferroelectric phase (tetragonal phase). Under the arbitrary weak random electric-field, the spontaneous polarization in the tetragonal phase of nano-BZO will generate PNRs instead of a long-range ordered state.32 

As the space charge potential increases, the strain induced by electrostriction increases, contributing to ∂Ξ/∂U > 0. Simultaneously, as the electric potential U increases, the polarization also increases, resulting in (If)/∂X > 0. Therefore, B= (If/∂X)·(Ξ/∂U) > 0, the inductance impedance appeared. For the sub-micron BZO, since the size of the electric domain formed by the large particle size is also relatively larger, the response speed of the electric domain cannot keep up with the change in the electric field, and thus, it does not contribute to the electrostriction. This is the reason why no inductance phenomenon is observed. For the nano-BZO, the electrostrictive strain of the tetragonal phase is the state variable X which is responsible for the generation of inductance impedance. According to the fitting results, the pressure dependence of inductance L and its reciprocal B were obtained, as displayed in Fig. 6(a). The parameter B increased with increasing pressure, which indicates that the electrostrictive effect was enhanced by pressure. It should be noted that the negative real part of the dielectric function ε′ was observed at low frequencies in the tetragonal phase of nano-BZO, as shown in Fig. 6(b). With increasing frequency, the sample showed a plasma-like dielectric behavior, that is, ε′ increased sharply from negative values to positive values at a switching frequency of 0.1 Hz (see the detailed discussion in the supplementary material).

In summary, we have investigated the pressure-dependent electrical transport properties of sub-micro and nano-BZO solid electrolytes. Both samples showed a mixed ionic-electronic conduction over the range of the applied pressure. The migration energy barrier played a dominant role in the bulk ionic conductivity, and the grain boundary energy increased with increasing pressure. Pressure-induced negative capacitance effect in nano-BZO was observed which was caused by the space charge concentration transition from negative to positive and the electrostrictive strain of grains. The enhanced electrostrictive effect was attributed to the existence of PNRs. The grain boundary conductivity of nano-BZO was improved by four orders of magnitude. The real part of the dielectric function showed a plasma-like Drude behavior, which increased sharply with frequency from negative to positive values at a switching frequency of 0.1 Hz. The impedance response of nano-BZO had a transition from a constant phase element to an ideal capacitance element. The coincident Z″ and M″ peaks on the frequency scale indicated the non-localized carrier conduction in the tetragonal phase of nano-BZO. All of these findings not only increase the understanding of relationship between the structure and conduction dynamics of BZO solid electrolytes, but also provide guidelines for designing and optimizing new BZO-based proton conductors in SOFCs.

See the supplementary material for experimental and theoretical methods, experimental data of BZO, including scanning electron microscopy (SEM) images, HRTEM images, Nyquist impedance plots, the equivalent circuit diagram, the ionic diffusion coefficient, and transference numbers of electrons and ions, the bandgap of BZO, the variation of Z″ and M″ with frequency, details of the derivation process of Faraday admittance, the cation/anion defect concentration at the space charge layer, and dielectric behavior.

This work was supported by the Science and Technology Plan of Youth Innovation Team for Universities of Shandong Province (Grant No. 2019KJJ019), the National Natural Science Foundation of China (Grant Nos. 11604133, 11874174, 62104090, and 11974154), the Natural Science Foundation of Shandong Province (Grant Nos. ZR2021QA087, ZR2021QA092, ZR2017QA013, ZR2022MA004, and 2019GGX103023), the Introduction and Cultivation Plan of Youth Innovation Talents for Universities of Shandong Province, the Research Funding of Liaocheng University (Grant Nos. 318012016, 318052103, and 318052104), and the Special Construction Project Fund for Shandong Province Taishan Scholars.

The authors have no conflicts to disclose.

Susu Duan: Data curation (equal); Formal analysis (equal); Writing – original draft (equal). Yanlei Geng: Software (equal); Validation (supporting). Jianfu Li: Formal analysis (equal); Methodology (equal); Software (lead); Writing – review & editing (equal). Xiaoli Wang: Formal analysis (supporting); Funding acquisition (equal); Software (equal); Writing – review & editing (equal). Yinwei Li: Formal analysis (supporting); Methodology (supporting); Writing – review & editing (supporting). Cailong Liu: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal). Qinglin Wang: Conceptualization (equal); Formal analysis (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Boyu Zou: Formal analysis (supporting); Validation (equal); Writing – review & editing (equal). Jialiang Jiang: Formal analysis (supporting); Validation (equal); Writing – review & editing (supporting). Kai Liu: Formal analysis (equal); Writing – review & editing (supporting). Guozhao Zhang: Formal analysis (equal); Methodology (supporting); Writing – review & editing (supporting). Haiwa Zhang: Formal analysis (equal); Writing – review & editing (supporting). Dandan Sang: Formal analysis (supporting); Funding acquisition (equal); Writing – review & editing (supporting). Zhenzhen Xu: Formal analysis (supporting); Software (equal); Validation (supporting).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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Supplementary Material