Tailoring sodium and oxygen mixed-ion conduction in the A-site non-stoichiometric NaNbO_3-based ceramics

Domain: neuroscience
Published: 2026-02-09
Editorial outcome: major_revision

Abstract
Tailoring the electronic or ionic conduction properties of solid-state electrolytes with precision is essential to fulfilling the functional demands of electrochemical energy storage and conversion technologies. Here, the synergistic regulation of Na+ and O2− ions conduction in the Na 0.96xCa 0.04 Nb 0.96 Zr 0.04 O 3-δ conductor is achieved by the non-stoichiometric ratio strategy. Crystal structure and electrical property analyses reveal that all samples feature a Pbma orthorhombic structure. With rising Na content, the defect characteristics shift from vacancies to interstitials, the NbO 6 octahedra experience a change from being compressed to normal and then to being obliquely flattened, which leads to an expansion of the corresponding interstitials in the Na-O-Na and Na-O-Nb networks. By changing the structures of these three types of polyhedron and networks, the conduction channels of Na+ and O2− ions as well as electrons can be effectively regulated. The O2− ions are the main charge carriers for Na-deficient samples, stoichiometric samples feature the mixed O2− ions and intrinsic electrons, while Na⁺ ions become the dominant carriers for Na-excess samples. This work highlights the important role of lattice defects and oxygen octahedral distortions/twisting on the conductivity, offering insights into the design of and Na+/O2− ions migration pathways in solid-state ion conductors.

Introduction
Solid-state ion conductors as a class of advanced materials have broad applications in critical technologies such as all-solid-state batteries, solid oxide fuel cells, ion membranes, sensors and other advanced devices1–7. The architectures of solid-ion conductors are predominantly classified into two categories, the fluorite structure and perovskite structure8–13. It is worth noting that the perovskite structure with the general formula ABO3 exhibits an abundance of physical properties due to its unique crystal structure and tunability. Recent endeavors in exploring perovskite-structured functional ceramics have unearthed innovative ionic conductivity, spotlighting their remarkable application promise within the realm of solid-state ionic conductors14,15.

In perovskite-structured solid-state ionic conductors, a widely adopted strategy for enhancing ionic conductivity involves hetero-valent ion substitution8–10,16–20. Hetero-valent ion doping can introduce defects such as A/B-site and O vacancies, thereby enhancing the conductivity based on the vacancy mechanism16–20. On the other hand, A/B-site vacancies with high polarizability weaken the A-O/B-O bond strength, which is beneficial for enhancing the O2− ions conductivity. Li et al. achieved an O2− ionic conductivity approaching 0.01 S cm-1 by introducing Mg2+ ions at the B-site of Bi 0.5 Na 0.5 TiO 3 (BNT)-based ionic conductors8. It is known that the significant influence of defects in perovskite structure on the electrical properties is related to the behaviors such as oxygen octahedral distortion and torsion21–23. The symmetries of the perovskite-related lattice are key characteristics of oxygen octahedral distortion, tilting, and ordering, all of which are crucial parameters for improving ionic conductivity. Experiments on Ti doping of NaNbO 3 conducted by Gouget et al. provided compelling evidence for the significant influence of Nb(Ti)O 6 polyhedral deformation on ionic conductivity24. Since hetero-valent ion-modified NaNbO 3 perovskite typically involves two types of charge carriers, namely A-site cations and oxygen anions. A new question arises regarding the correspondence between the forms of oxygen octahedral deformation and the two types of charge carriers. In an effort to analyze this issue, many research works have analyzed the conductivity mechanism of NaNbO 3-based ceramics. NaNbO 3-based ceramics undergo abundant phase transitions and NbO 6 octahedral distortions in response to the variations in temperature and defect configurations. In the framework of the NaNbO 3 crystal structure, it is clear that O2− ions can migrate via the internal pathways of NbO 6 octahedra8,22,25,26. This implies a strong correlation between the variations in O2− ion channels and the inherent distortion of NbO 6 octahedra, which resonates with the proposition of Gouget and colleagues that elongated or flattened Nb(Ti)O 6 octahedra facilitate oxygen migration21. In contrast, lattice Na⁺ ions traverse the channels formed by the O atoms at the vertices of four NbO 6 octahedra, while interstitial Na⁺ ions may rely on the channels formed by the interstices of the Na-O-Na or Na-O-Nb networks27–29. There is a close connection between the changes in the Na+ ions channels and those caused by the distortion and torsion behaviors of the NbO 6 octahedra. The related perspective that Na+ ions pass through a triangular region formed by three O atoms, which is considered to be the bottleneck for Na⁺ ion diffusion, has been confirmed in the NaSICON-type materials30–32. Drawing on the understanding outlined above, elucidating the correlations between lattice defects, the distortion and torsional patterns of NbO 6 octahedra, and charge carriers in solid-state ionic conductors is of considerable significance for the defect-mediated modulation of electrical conductivity.

Here, the CaZrO 3 modified NaNbO 3 (Na 0.96 Ca 0.04 Nb 0.96 Zr 0.04 O 3) solid-state ionic conductor with a perovskite structure is employed as the research subject, and the physical mechanism of its conductivity was analyzed. This doping strategy effectively stabilizes the antiferroelectric Pbma phase, ensuring that Na0.96Ca0.04Nb0.96Zr0.04O3 adopts a single-phase structure at the onset and maintains its intrinsic electrical conductivity. Synergistic modulation of Na+ and O2− ions conduction in the Na 0.96xCa 0.04 Nb 0.96 Zr 0.04 O 3-δ (NCNZ-Nax, x=0.96-1.02) ceramics was successfully achieved by adjusting the non-stoichiometric ratio strategy. Crystal structure and electrical property analyses reveal that both stoichiometric and non-stoichiometric samples feature a Pbma orthorhombic structure. As Na content increases, defects transform from vacancies to interstitials. The NbO 6 octahedra undergo a change from being compressed to normal and then to being twisted and flattened, which leads to the expansion of the corresponding interstices of Na-O-Na and Na-O-Nb networks. The synergistic interaction between the flattened NbO 6 octahedra and oxygen vacancies serves as a critical determinant in the formation of O2− ion channels. Meanwhile, the expansion of the corresponding interstices of Na-O-Na and Na-O-Nb networks effectively enlarges the bottleneck for the migration of Na+ ions, thereby facilitating the establishment of Na+ ion channels, as depicted in schematic Fig. 1. Through the regulation of these channels, a coordinated control of the Na+/O2− ionic conductors is achieved. This work provides insights into the formation of Na+ and O2− ion migration channels in solid-state ion conductors.

Results
Phase and microstructure analysis
Figure 2 shows the XRD patterns of the NCNZ-Nax samples, all samples exhibit the same pure perovskite structure, and there is no diffraction peak of a second phase. This is consistent with the uniform grain distribution observed in the SEM/TEM images with no abnormal second-phase grains (Figs. S1 and S2). The only change is that as the Na content increases, the grain size grows. Significantly, a shift towards a lower angle is observed for NCNZ-Nax samples with increasing Na content in the expanded XRD pattern (Fig. S3). For the Na-deficient samples, both Na-vacancies and oxygen vacancies generated to maintain the charge balance can cause lattice shrinkage33–35. In case of excess Na, the excess Na enters the lattice interstice and causes the crystal lattice expansion. Similar phenomena were also found in the non-stoichiometric BNT-based ceramics14,15. In order to further understand the evolution of lattice parameters with variation of Na content, GSAS software was used to refine the XRD data36,37. It is found that the use of orthorhombic phase (Pbma) for refinement can obtain better refinement results (Fig. 2b), and the lattice constant a and c and gradually increase with the increase of Na content (Tables S1 and S2).

The refined data were imported into Diamond software to observe the local environment of the atoms. Due to the low number of O vacancies (V O••) and Na vacancies (V'Na) in the compound, it is impossible to accurately identify oxygen and Na sites that are partially occupied. The unit cell of the Pbma phase, as shown in Fig. S4, is composed of two symmetric parts (a−b−c− and a−b−c+), and the a−b−c− structural part is selected for analysis in Fig. 2c. The local environments of Nb5+ and Na+ ions for NCNZ-Na 0.96, NCNZ-Na 1.0 and NCNZ-Na 1.02 samples are shown in Fig. 2c and Fig. S5. For the Na-deficient samples, the average bond distances (~1.9940 Å) for d(Nb-O3) and d(Nb-O4) in the equatorial plane are shorter than those in the stoichiometric samples (~1.9941 Å), and there is a large difference between these bond distances and those in the stoichiometric samples. Meanwhile, d(Nb-O1) and d(Nb-O2) bond distances also decrease relatively, and the change in d(Nb-O2) is more significant. The phenomenon suggests the emergence of flattened NbO 6 octahedra21,25,26. In comparison to the Na-excess (NCNZ-Na 1.02) sample, a reduction is also observed in the bond distances d(Nb-O4), while an increase is noted in the bond distances d(Nb-O3). Concurrently, a decrease in both d(Nb-O1) and d(Nb-O2) is detected. The change in the equatorial plane is characterized primarily by increased asymmetry. The decrease in the distance d(Nb-O1/O2) between the apical oxygen atoms is in contrast to the increase in the unit-cell parameters. This finding unveils a substantial distortion and torsion within the NbO 6 octahedra, which in turn triggers alterations in the unit-cell parameters. Besides, the alteration of NbO 6 octahedra also leads to the expansion of the interstitial spaces within the Na-O-Na and Na-O-Nb networks (Fig. S6). Upon increasing the Na content from 1.0 to 1.02, notable changes in the cross-sectional interstitial distances were observed. In the Na-O-Na network, the d(Na-Na) distance increases from 3.894 Å to 3.896 Å, and the d(O-O) distance increases from 4.482 Å to 4.489 Å. The d(Na-Na) spacing varies modestly, whereas the NbO 6 octahedra change substantially, suggesting a strong correlation between unit-cell volume fluctuations and NbO 6 octahedra characteristics. In the Na-O-Nb network, the d(Na-Nb) distance grows from 3.378 Å to 3.379 Å, and the d(O-O) distance increases from 2.800 Å to 2.810 Å (Fig. S6). The expansion of the Na-O-Na and Na-O-Nb networks serves to diminish the migration energy barrier for Na+ ions. Under the influence of Na stoichiometry ratios, NbO 6 octahedra, Na-O-Na, and Na-O-Nb networks are tilted and flattened, leading to changes in O2−/Na+ ionic channels.

The atomic-scale microstructure of the NCNZ-Nax samples was examined along the [110] axis using high-resolution transmission electron microscopy (HR-TEM) and selected-area electron diffraction (SAED) (Fig. 3a–h). The atomic images were processed via Fourier transform and geometric phase analysis (GPA) to obtain a comprehensive understanding of the structure and strain distribution. All samples have an orthorhombic structure (Fig. 3a and e), the interplanar spacings of 3.84 Å and 3.85 Å correspond to the (040) crystal planes, and the interplanar spacing of 3.91 Å is related to the (101) planes. Compared with NCNZ-Na 1.0 sample, the distribution of A-site vacancies is represented by the occurrence of significant intensity variations between neighboring columns of atoms in the NCNZ-Na 0.96 sample34,38–41. The relatively weaker sites, which represent Na-vacancies, are marked with red triangles in Fig. 3c. The increase in atomic spacing along the [040] crystal direction in Fig. 3b compared to that in Fig. 3f also confirms the lattice strain phenomenon caused by the presence of Na-vacancies. Clearly, the GPA of NCNZ-Na 0.96 sample shows a stronger strain distribution along the xx and yy directions (Fig. 3d). In the strain mapping, the color change from dark blue to green and from orange to bright yellow represents compressive and tensile strains, respectively. The stronger tensile strain in the NCNZ-Na 0.96 sample is attributed to the presence of Na-vacancies, which cause significant lattice unit deformation. Due to the significant difference in nuclear charge values, it is difficult to identify the atomic columns of O-sites in HR-TEM images (Figs. 3b and 3f). Consequently, XPS was utilized to comprehensively analyze the surface chemical composition and variation of O-vacancies of the NCNZ-Nax ceramics. The O1s peak is deconvoluted into two distinct components, denoted as peak O1 and peak O2 (Fig. 3i–k). The O1 peak centered at approximately 529.5 eV can be ascribed to lattice oxygen, whereas the peak O2 at around 531.5 eV corresponded to oxygen vacancies34,42. A notable trend is observed: the concentration of oxygen vacancies increases markedly with decreasing Na content. In the NCNZ-Na 0.96 sample, the substantial presence of oxygen vacancies can be attributed to the generation of positively-charged oxygen vacancies to counterbalance the negatively-charged vacancies resulting from the Na-deficiency. Therefore, combining the above HR-TEM and XPS results, it is known that the synergistic effect between cation vacancies (V'Na) and oxygen vacancies (V O••) leads to significant lattice distortion.

Electrical performance analysis
Temperature dependent XRD patterns (Fig. 4a) directly reveal the phase transition behavior in the NCNZ-Nax samples. It is observed that the NCNZ-Na 0.96 sample transitions from orthorhombic (Pbma, Pnmm, Ccmm) to tetragonal (P4/mbm) and then to cubic (Pm-3m) phases from room temperature to 700 °C. Unit-cell symmetry and volume changes are related to NbO 6 octahedra distortion and torsion. Besides, the temperature-dependent dielectric constant and loss are presented in Fig. 4b–g. In the temperature range from 300 °C to 600 °C, the NCNZ-Nax samples display two distinct phase transition peaks, corresponding to the transitions from the orthorhombic antiferroelectric Pbma (P) phase to the orthorhombic ferroelectric Pnmm (R) phase, and the tetragonal P4/mbm (T 2) phase to the cubic Pm-3m (U) phase, respectively43,44. Prominently, intense phase transition peaks of T 2-U (~560 °C) are observed in the NCNZ-Nax samples with increasing Na-deficiency (Fig. 4b–d). The formation of vacancies caused by Na-deficiency results in significant lattice contraction and oxygen octahedral distortion. These vacancies are highly susceptible to temperature variations, with significant changes in oxygen octahedral and unit-cell parameters as the temperature increases, thereby giving rise to distinct phase transition peaks. Differently, the characteristics of the T 2-U phase transition are further attenuated with increasing Na content (Fig. 4f and g). This is because interstitial Na+ ions compensate for lattice expansion caused by temperature increase. However, as the temperature increases, the interstitial Na+ ions are thermally activated and a more pronounced behavior of increased dielectric loss is observed in the T 2-U phase transition region (Fig. 4f and g).

Impedance spectroscopy tests were performed to investigate the conductance behavior of the NCNZ-Nax samples. However, the equivalent circuit modeling does not ensure correspondence between the electrical components and the underlying complex processes during spectral analysis. Also, it represents the global response at the cell level rather than representing the electrical transport phenomena at each component. The contributions from these distinct processes are buried in the impedance spectroscopy response. Therefore, the distribution of relaxation time (DRT) and the electrochemical characterization of the symmetrical (ECS) are combined for analysis, and a good fit is obtained. The DRT method reveals the dominant relaxations and their corresponding resistances as bounded by the log f axis and the distribution function. These resistances are inserted as constants in the modified ECS. Then the fitting dependencies are simulated to correctly describe the impedance data, and theoretical details can be found in the Supporting Information45–50. An example of such a fitting combined with detailed fragmentation of the spectra is given in Fig. 5a. Peaks with similar frequencies and lower intensities corresponding to DRT are regarded as RC (Resistor-Capacitance circuit) units, and the characteristic capacitance value C is fitted using Zview based on the capacitance value relationship formula (Eq. 1)51.

C = 1 / (2πf max R) (1)

As shown in Fig. 5a, the first semicircle corresponds to the grain effect of NCNZ-Nax ceramics. The characteristic capacitance value is 2.2458×10-11 F·cm-1 and the frequency at the maximum value of the semicircle is 1.06×106 Hz, which proves this statement. The second semicircle is composed of two arcs, each corresponding to an RC element. The characteristic capacitance of the first arc is 1.6990×10-10 F·cm-1 and the characteristic capacitance of the second arc is 1.3857×10-10 F·cm-1. Both of these arcs are attributed to the grain boundary effect, which is consistent with the result of the C’ spectra (Fig. S7b). Temperature-dependent capacitances of grain and grain boundary (Fig. S8) align well with the dielectric spectra (Fig. 4b–g). Notably, the capacitance of grain boundary is approximately 5×10-10 F·cm-1 and exhibit temperature independent, whereas the capacitance of grain decreases significantly as temperature increases (Fig. S8). The last polarization tail consists of four parts that can be classified into two categories. One with characteristic capacitances ranges from 3.9537×10-7 to 9.0655×10-7 F·cm⁻¹ and frequencies from 2860 to 274 Hz. The other with characteristic capacitances spans from 1.4754×10-6 to 1.3352×10-6 F·cm⁻¹ and frequencies from 42.8 to 8.7 Hz. The former category is associated with the ohmic contact resistance at the electrolyte/electrode interface or the high relaxation steps of the electrode fabrication process. In contrast, the latter category is ascribed to the electrode level, given its relatively larger capacitance and lower frequency. As depicted in Fig. 5b, a notable trend is observed that the impedance diminishes with the increment of Na-sites non-stoichiometry. This phenomenon strongly suggests that an augmentation of Na-site defects can effectively facilitate the ionic conductivity. In the DRT analysis (Fig. 5c), an intriguing behavior of the response peaks is revealed. As the Na content rises, the grain boundary response peak undergoes a significant shift. A jump movement towards a higher index occurs between the NCNZ-Na 1.0 and NCNZ-Na 1.01 samples. In contrast, the grain response peaks remain relatively stable, showing no significant alteration. These findings provide compelling evidence that the charge carriers in the solid-state ionic conductor are predominantly ions, and their characteristics are closely correlated with the varying Na content. When there is either a deficiency or an excess of Na, different distortion and torsion modes of the NbO 6 octahedra, in combination with Na-site defects and O-vacancies, collectively contribute to the observed behavior. This synergy not only influences the type of charge carriers (mainly O2− and Na+ ions), but also shapes the overall ionic conductivity of the NCNZ-Nax ceramics.

As the temperature rises, the resistance decreases for the NCNZ-Na 0.96 sample (Fig. 5d). This is attributed to the fact that at higher temperatures, a greater number of carriers can surmount the energy barriers and move freely. The same phenomenon is also observed in the impedance spectra of NCNZ-Na 1.0 and NCNZ-Na 1.02 samples (Fig. S9). Significantly, notable alterations of DRT profiles are observed in both the peak relaxation times (τ) and areas of the grain boundary response peaks with τ of 10-3 s to 10-5 s as the temperature ascends (Fig. 5f and Fig. S7a). The variation in the τ peaks serves as an indicator of the changes in the electrical response, whereas the peak area corresponds to the impedance of the associated process. By extracting the τ associated with the grain boundary relaxation peak and applying the Arrhenius equation for fitting, the activation energy (E a) can be determined 1.24 eV for the NCNZ-Na 1.0 samples (Fig. S10). The relaxation peak corresponds to a unique relaxation process within the conductor, and its associated relaxation time serves as the energy barrier that must be overcome during the conductance process. Interestingly, it can be observed that the τ of grain boundaries shifts towards higher index direction with increasing temperature for the NCNZ-Na 0.96 samples (Fig. 5e). The variation of grain relaxation time is similar to that of grain boundaries, and the response peak disappears above 540 °C (Fig. 5f). When correlated with the dielectric temperature spectra in Fig. 4, the temperature interval of 540°C–560°C aligns precisely with the position of the phase transition peak from the tetragonal phase T 2 to the cubic phase U.

To determine the changes in the dominant charge carriers as a function of Na content and temperature, impedance spectroscopy measurements under flowing nitrogen, air, and oxygen atmospheres were conducted52–54. As illustrated in Fig. 6a–c, all samples exhibit characteristic Warburg behavior, indicative of ionic conduction55. The transition from nitrogen to air to oxygen reflects a progressive increase in oxygen partial pressure. Notably, the significant variation in impedance observed in Fig. 6a and b with increasing oxygen partial pressure suggests a shift in the dominant charge carriers within the ceramics. Given that under an oxygen atmosphere, the conductivity is mainly attributed to O2− ions, while the Na⁺ ion conductivity is suppressed. In contrast, under a nitrogen atmosphere, it is evident that the NCNZ-Na 0.96 and NCNZ-Na 1.0 ceramics exhibit a mixed conductivity mode of Na+/e− based on their intrinsic properties. Subsequently, the total ionic conductivity is calculated by obtaining the resistance from the intercept of the semicircle with the x-coordinate (Fig. S11). The activation energy (E a) is evaluated using the Arrhenius method,

σ = σ 0 exp(−Ea / kT) (2)

Here, T denotes the temperature in Kelvin, and k stands for the Boltzmann constant23. The results of the calculations are depicted in Fig. 6d–f and Fig. S10. The consistency between the activation energy from fitting τ and σ shows the rationality and effectiveness of the DRT transformation analysis.

In the Arrhenius plots of NCNZ-Na 0.96 (Fig. 6d), a distinct relationship between σ values, oxygen partial pressure, and temperature is revealed. When the temperature is ≤540°C, a decrement in oxygen partial pressure leads to the highest σ value under a nitrogen atmosphere. Intriguingly, the σ values in air and oxygen environments are indistinguishable, strongly suggesting that O2− ions serve as the primary charge carriers in air, while the conduction of Na⁺ ions is effectively inhibited. At temperatures ≥560°C, the highest σ is observed in an oxygen-rich atmosphere. The σ values in air and nitrogen are comparable, with slightly higher ones under nitrogen. The E a decreases significantly in air and oxygen environments, and the transition point of E a precisely corresponds to the T 2-U phase transition of the NCNZ-Na 0.96 sample (Fig. 4b). This correlation indicates that the phase transition exerts a profound influence on E a, and the cubic U phase is highly favorable for O2− ions conduction. The shift of DRT peaks to higher indices in Fig. 5f offers further insights. It indicates a lower relaxation time and higher frequency, which is favorable for ion conduction. The Arrhenius plot of the NCNZ-Na 1.0 sample is presented in Fig. 6e. As the oxygen partial pressure decreases, the σ value under nitrogen is the highest, while the σ values under oxygen and air are observed to be the same, indicating that O2− ions and Na+ ions are the charge carriers in air and oxygen atmospheres. In a nitrogen atmosphere, the charge carriers are Na+ ions and e−. At 560 °C, the evidence of the charge carriers is observed. By comparing the Eₐ and σ values of the NCNZ-Na 0.96 and NCNZ-Na 1.0 samples, it finds that as the Na-deficiency increases, the σ values of O2− ions under oxygen and air atmospheres increase by nearly 100 times, which is much higher than the increase in the σ values of O2−/e− under a nitrogen atmosphere. Combined with the XRD analysis results, it is shown that the distortion and torsion modes of the NbO 6 octahedra under Na-deficient conditions are more favorable for O2− ions conduction. In addition, the Arrhenius plot of the NCNZ-Na 1.02 sample (Fig. 6f) shows a significant overall increase in σ under the condition of Na-excess, while the value of E a changes little under various atmospheres. The overlaps of the σ-T curves and impedance spectra (Fig. 6c) between the different atmospheres in the NCNZ-Na 1.02 samples allow us to determine that it is not the O2− ions that are responsible for the conductivity. Obviously, the E a values are not segmented over the entire temperature range and in different atmospheres. This is due to the fact that the excess sodium lead to lattice expansion, which makes the phase transitions smoother (Fig. 4g).

To delve deeper into the conductivity mechanism of NCNZ-Nax samples, a sandwich structure was devised. 8YSZ (8% yttria-stabilized zirconia) was employed to block Na+ ion conduction, thereby enabling a precise study of O2− ion transport24. The structure is illustrated in Fig. 7a and Fig. S12, depicting a sandwiched configuration. SEM images reveal that the sandwiched sample has a dense, homogeneous microstructure. The distinct compositional boundaries are observed at the interfaces between layers, suggesting no interdiffusion of elements. The observed homogeneous interfaces are conducive to O2− ions mobility. To quantitatively assess the contributions of Na+ and O2− ion conductivities, Eqs. 3 and 4 are employed to separately calculate their respective proportions of conductivity24,

t O2− = σ O2− / (σ Na+ + σ O2− + σ e−) = σ O2− / σ total (3)

t Na+ = σ Na+ / (σ Na+ + σ O2− + σ e−) = σ Na+ / σ total (4)

Here t quantifies the contribution of an individual ion to the total conductivity. The Na+ ion mobility can be determined by subtracting the O2− ion mobility from the total ionic mobility. Due to the small contribution of electronic conductivity, it is ignored here and the calculation process can be found in Fig. S13. Subsequent impedance spectroscopy analysis is conducted with varying Na content as shown in Fig. 7b–d.

Illustrated in Fig. 7b and c are the impedance spectra for NCNZ-Na 0.96 and NCNZ-Na 1.0, respectively. Notably, the impedance spectra for the sandwich pellet lack a polarization tail; a discrepancy is possibly attributed to variations in the low-frequency responses of yttria-stabilized zirconia and NCNZ-Nax at the electrode-electrolyte interface. The concordance of impedance spectra substantiates the validity of scrutinizing the conductivity mechanism and lends credence to the accuracy of the analytical outcomes. Furthermore, Fig. 7d reveals that the NCNZ-Na 1.02 sample manifests markedly diminished semicircles relative to the sandwich pellet, suggesting that the O2− ion conductivity is markedly inferior to the total conductivity. Utilizing Eqs. 3 and 4, the calculated values for the respective proportions of conductivity are t O2− = 8% and t Na+ = 92%. These results indicate that the charge carriers in NCNZ-Na 1.02 are Na+ ions. The curves of O2− and Na+ ions conductivity as a function of Na content (Fig. 7e) reveal that the conductivity modes can be classified into three types with the variation of Na content. They are O2− ions conductivity under Na-deficient conditions, the mixed O2− and e− conductivity at the stoichiometric component, and the Na+ ions conductivity under the presence of an excess of Na. Combined with the results of XRD analysis, the shrinkage of the equatorial plane and apical atoms of the NbO 6 octahedra, induced by sodium vacancies (V'Na) and oxygen vacancies (V••O) under Na-deficient conditions, leads to the formation of flattened NbO 6 octahedra (Fig. 2c). The structural change can lower the energy barrier for O2− ion conduction, thereby enhancing the O2− ion conductivity. Differently, when Na is in excess, the interstitial Na+ ions cause the equatorial plane of the NbO 6 octahedra to become flatter, the apical atoms to elongate, as well as leading to the expansion of the interstitial spaces within the Na-O-Na and Na-O-Nb networks (Fig. 7f, Fig. S6, and Table S3). For the Na-O-Na network, the d(Na-Na) distance expands from 3.894 Å to 3.896 Å, and the d(O-O) distance increases from 4.482 Å to 4.489 Å for the NCNZ-Na 1.02 compared to the stoichiometric component. Similarly, the d(Na-O) distance increases from 3.046 Å to 3.233 Å in the Na-O-Nb network (Fig. 7f). This expansion of the Na-O-Na and Na-O-Nb networks serves to diminish the Na+ ion migration energy barrier, leading to a significant increase in Na+ ion conductivity. Under the Na-site non-stoichiometric ratio strategy, the NbO 6 octahedra, Na-O-Na, and Na-O-Nb networks are tilted and elongated, leading to changes in the O2−/Na+ ion channels, which result in synergistic regulation of the ionic conductivity in the NaNbO 3-based solid-state ionic conductor.

In this work, the synergistic regulation of Na+/O2− ionic conduction was effectively achieved in the Na 0.96xCa 0.04 Nb 0.96 Zr 0.04 O 3-δ solid-state ionic conductor by employing an A-site non-stoichiometric strategy. The correlation between the torsion and distortion patterns of NbO 6 octahedra and the conduction behavior of Na+ and O2− ions was elucidated. With rising Na content, the defect transformed from vacancies to interstitials. The NbO 6 octahedra underwent a change from flat to normal and then to twisted and flattened, which led to the expansion of the corresponding interstices of Na-O-Na and Na-O-Nb networks. The conduction channels of Na+ and O2− ions could be effectively regulated by the changes in the NbO 6, Na-O-Na, and Na-O-Nb polyhedral structures. Given this promising insight, a comprehensive re-evaluation of other perovskite-type materials is imperative, which provides guidance for designing and optimizing functional materials with tailored ionic and electronic transport properties.

Methods
Preparation of ceramics
Polycrystalline ceramics of Na 0.96xCa 0.04 Nb 0.96 Zr 0.04 O 3-δ (abbreviated as NCNZ-Nax, x=0.96, 0.98, 0.99, 1, 1.01, and 1.02) were prepared by a traditional solid-state reaction. Carbonate, Na2CO3 (99.8%), and CaCO3 (99.8%), and oxide, Nb2O5 (99.9%), and ZrO2 (99.99%) were purchased from Shanghai Aladdin Biochemical Technology Co., Ltd., CN, and used without further purification. The raw materials were dried in an oven at 180 °C for 8 h before weighing to reduce hygroscopic carbonates. Accurately weigh these reagents according to the molar ratio, and suspend them in ethanol, and then mill in a planetary ball mill for 12 h using zirconia balls. The following calcination was conducted in a covered alumina crucible at 850 °C for 2 h. To guarantee a homogeneous distribution, the calcined powders were ball-milled again for 12 h. The prepared powders have been uniaxially compacted into pellets (diameter 12 mm) with a pressure of ca. 25 MPa and pressed cold isostatically at 200 MPa. Finally, the pressed NCNZ-Nax pellets were covered with the same composition powders and then sintered at 1250~1350 °C for 2 h at a heating rate of 3 °C/min.

Characterization of ceramics
XRD patterns were recorded with a laboratory X-ray diffractometer (XRD, D8 ADVANCE, Bruker, Germany) using Cu Kα incident radiation (λ=1.54056 Å). Surface micromorphology, energy dispersive spectra (EDS), and selected area electron diffraction patterns (SAED) were investigated using HR-TEM (Talos F200X, FEI, USA) and field emission scanning electron microscopy (FE-SEM) (Nova NanoSEM 450, FEI, USA). Surface elemental states were studied by X-ray photoelectron spectroscopy (XPS, Axis Ultra DLD, Shimadzu, Japan).

Electrical performance of ceramics
The working electrodes were manufactured by coating and sintering electronic paste. After sanding both sides of the ceramic sample to a flat surface, the sample was ultrasonically cleaned several times with ethanol. Then, Ag or Pt electronic paste was coated on both sides of the samples and cast at room temperature. Finally, the prepared electrodes were sintered at 850 °C for 15 min. The dielectric properties were tested in the temperature range from 25 °C~700 °C at different frequencies by using an LCR meter (Agilent E4980A, Agilent, Santa Clara, CA). AC impedance spectroscopy (IS) measurements were performed in different atmospheres (O2, air, and N2) by using an electrochemical workstation (CHI700e, CH Instruments Inc., China).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Although this script contains some interesting results there are many inconsistencies and a severe lack of rigour when it comes to presenting the data and providing information on how it was analysed. I outline my response in more details below and on this basis I have to suggest the script is rejected.\n(i) Composition and nomenclature are confusing. No explanation as to why the starting materials include 4% Ca and Ti on the A and B-sites of the lattice, respectively. Also If we start from the given formula Na Ca Nb Zr O then for x =0.96 we\nx 0.04 0.96 0.04 3-d\nhave a stoichiometric perovskite ABO , yet this is reported as being an Na-deficient\n3\nsample with Na and O vacancies and this is very confusing. The authors refer (I think)\nto x =1 being stoichiometric yet this would give a formula of A BO and infer either\n1.02 3.02\nan excess of A-site cations and oxygen ions (or conversely B-site vacancies). Taking\nthe A and O excess model, this begs the question if ABO perovskites are based on close\n3\npacking of AO layers how can we achieve an excess of A and O sites when no\n3\ninterstitial sites should be available in such a close packed lattice! (Presumably the\nlattice is therefore B-site deficient). I appreciate that small changes in stoichiometry\nassociated with A/B ratios can have a dramatic effect on the electrical properties of\nperovskites but this requires rationalisation within the context of the crystal lattice. Late\non in the script the authors suggest the presence of the A-site and O-vacancies in x =0.96\nis associated with volatilisation of Na O. This should come much earlier in the script,\n2\notherwise, there is substantial confusion about the changes in composition. It might be\nbetter for the authors to frame the changes in composition on a solid solution based on\na combination of Na NbO and CaZrO (at a level of 4 mol%) perovskites and\n1±x 3 3\nintroduce the fact that there is known non-stoichiometry in NaNbO and that there is\n3\n1\nadditional issues with Na O loss during ceramic processing. This would clarify several\n2\nissues at the outset regarding compositional design and give the reader a clear steer\nbefore the results are presented.\n(ii) Structural data from laboratory XRD. There is insufficient information given\npertaining to how the Rietveld refinements (RR) of the data were performed and of\nthe results obtained. This is important because the positions of the oxygen ions are critical\nto the arguments about the shape of the NbO octahedra and how that links to ion\n6\nmigration. Furthermore, where do the interstitial Na ions reside and what are the atomic\npositions? In the methods section it is therefore important that more information on the\nprocedure and strategy used in the RR of the data are provided. I assume ion sites were\nset to be fully occupied but what were the final (x, y, z) atomic positions of all the ions\nand what about the isothermal parameters; were they refined or fixed and what are the\nvalues? This is important data and must be included in the results. This is especially the\ncase given that XRD is relatively insensitive to light atoms such as O and Na, yet much\nis made of the final positions of these ions. Furthermore, there are no errors associated\nwith the values given in Table S1 and these need to be included. There is a typographical\nerror in the caption for Fig S3. It should be Na-O not Nb-O.\n(iii) Microscopy. I’m not an expert in TEM but this was convincing (to me at least)\nthat x = 0.96 contained more Na vacancies than x = 1.0 and the XPS showed there were\nvariations in oxygen content (both Fig 3). Given the heterogeneity in the electrical\nbehaviour (next section) of these materials and the interpretation provided, it would be\ngood to show some SEM/EDX of the materials to establish the presence of any core-\nshell distributions within the samples and also EDX profiles across grains to see any\nvariations in composition at the grain boundaries. This intermediate level of\nmicroscopic elemental analysis at the micron level is missing and needs to be included\nto aid the interpretation of the electrical data.\n(iv). The electrical characterization was extensive and performed by Dielectric\nSpectroscopy (DS), impedance spectroscopy (IS) using DRT and variable Po and ion\n2\nblocking measurements with YSZ; however, in many cases there was a lack of rigour\n2\n(eg DRT, more later), it was often difficult to see the ‘bulk’ response in the Z* plots\nbased on IS (Figs 5,6,7) and the interpretation between DRT and IS seems flawed, the\nPo analysis is confusing and there is no treatment of the electronic contribution in the\n2\nextraction of the transport numbers for O and Na in equations 4 and 5. I find the DS\ndata interesting but the authors should indicate if there is any change in T associated\nmax\nwith the P-R transition across the series of samples as this is a major event in these\nmaterials. They should also indicate what frequency was used in extracting the\ntemperature for the T to U transition. There are considerable space charge effects at\nthese temperatures and this may influence the values reported. The IS data are poorly\npresented, not well analysed and Im not convinced by the interpretation. It is very\ndifficult to see the bulk arc (called the first arc in the script) at high frequencies in any\nof the Z* plots yet this should be central to the analysis. Figures should be expanded to\nshow it in more detail and the extracted R and C values for it presented as a function of\ntemperature instead of a single analysis at 500 C. The extracted capacitance for this arc\nfor 500 C is given as 4 pF/cm which corresponds to a permittivity of ~ 40-50. This is\nan order of magnitude below the 300 -500 observed in the DS data at 500 C in Fig 4.\nGiven that the materials remain ferroelectric at 500 C, then a capacitance value of 4\npF/cm (no errors on this value provided) for the bulk is too low and physically\nunreasonable for NaNbO -based materials. The authors should plot out extracted C\n3\nvalues across the full data range and they should show some temperature dependence.\nBy tracking this onto the DRT (Fig 5 c and 6c) with a time constant of 10-6 s that is\nassociated with this grain response, it appears not to be thermally activated. It remains\nat this value between 400 to 600 C and this means that the ‘assigned’ bulk conductivity\nis not thermally activated!! This cannot be correct. The larger second arc (Fig 5) at 500\nC is deconvoluted into two components that are assigned as grain boundary\ncontributions based on C values of 0.17 and 0.14 nF/cm (no errors or showing of the\nfits based on the equivalent circuit, again illustrating poor rigour in the analysis). These\nC values correspond to permittivity of ~ 1500 to 2000 which are high but are more\nconsistent with ferroelectric bulk responses as opposed to grain boundary responses.\nestablish if they are bulk-like (and presumably temperature dependent) or grain\nboundary-like (presumably with little temperature dependence). These elements are\ntemperature dependent based on the DRT data and as the authors point out show\nsignificant changes at 540 C where there is a phase transition. Surely, it makes more\nsense that these elements associated with the large second arc are bulk (possibly core\nand shell?) rather than the grain boundaries? A full analysis of extracted R and C\nvalues across the full temperature range is required to ensure the analysis is robust and\nthe interpretation is consistent with the physical processes occuring within the materials as\nthey undergo phase changes. At this stage, its not worth interpretating the Po data until\n2\nthe basic IS data are fully analysed.\n(v). The DRT is simply provided in a figure and no indication of any fitting\nparameters are given-again illustrating poor rigour in information pertaining to data\nanalysis.\nFigure 9 based on transport numbers versus x makes some sense to me (at least for\nO). For x =0.96 there is sufficient Na O loss to create the level of oxygen vacancies that\n2\ndominate the conductivity and the presence of this soda loss is clear from TEM/XPS\ndata. For x =1.0 and 1.02 (which actually have excess Na based on the original formula),\nthe loss of soda probably still occurs but samples have much reduced levels of vacancies\nand therefore are close to being stoichiometric ABO3 with very low levels of vacancies\nand therefore ionic transport is low. The authors suggest that the sodium ion transport\nnumber is high in Figure 9 for x =1.02 but this might be linked to the lack of treatment\nof the electronic contribution to the conductivity used in equation 5 to estimate the\ntransport number for Na. I also refer back to my comments linked to composition in\nperovskites, where are the interstitial sites for A-site cations in the ABO lattice and can\n3\nthey located via diffraction (no evidence in this script)? I therefore find no-compelling\nevidence for high levels of Na ion transport in these materials. In addition, the authors\noften cite NASICON as an example where there is high Na ion migration. This is true\nbut they are based on framework structures where there are vacant sites and its possible\n4\nto use this sites to create interstitial ion conduction via selective doping.", "reviewer_2": "This paper is interesting, but the subject of mixed Na/O conduction in the same ‘NaNbO3’ perovskite lattice was already mentioned 5 years ago by these authors : Gouget, G. et al. Associating and tuning sodium and oxygen mixed-ion conduction in niobium-based perovskites. Adv. Funct. Mater. 30, 1909254 (2020). Reading the papers of Gouget et al. (ref 53 in this manuscript but also refs 21 and 22) , I consider that there are no original features in this paper submitted to Nature Comm, especially as there are other papers (refs 2& and 22) by the same team on the same class of materials. This paper should not be accepted in Nature Comm.", "reviewer_3": "Liu et al. reported the synergistic regulation of Na+ and O2- ions conduction in the NaNb3-based ionic conductor. By changing the structures of these three types of polyhedrons, the conduction channels of Na+ and O2- ions as well as electrons could be effectively regulated. This work is scientifically interesting and can be published after some revisions, and comments are listed below.\n1.The section of temperature-dependent dielectric responses. The author mentioned two phase transition peaks here. However, NaNbO3 has multiple phase transition characteristics within this temperature range. Are the phase transitions corresponding to these phase transition points accurate?\n2.The author mentioned that the type of carriers can be regulated by the non-stoichiometry of A-site elements, thereby achieving the transformation between P-type and N-type solid-state ionic conductors. When there is a sodium deficiency, it behaves as an oxygen ionic conductor. However, sodium deficiency also creates sodium vacancies. Why does the sodium ion conductivity deteriorate? Please explain.\n3.In Fig. 9d, both the samples with excess and deficiency show a sudden increase in conductivity at 2%. Please explain.\n4.The lattice expansion phenomenon of the Na-deficient sample analyzed by TEM is opposite to the cell volume contraction analyzed by XRD. Will this affect the conclusion?", "reviewer_4": "This research reports the variation of the conduction mechanism in NaxCa0.04Nb0.96Zr0.04O3-  perovskite ceramics through A-site nonstoichiometry. By adjusting the Na content from deficient to excess (i.e., x = 0.96–1.02), the dominant defect species changed, resulting in a transformation of the NbO₆ octahedral structure, from a flattened configuration in Na-deficient compositions to an obliquely elongated one in Na-excess compositions. Consequently, the dominant conduction mechanism shifted from O²⁻ ion conductivity (in Na-deficient samples), to mixed O²⁻ and electron (e⁻) conductivity (in stoichiometric samples), and finally to Na⁺ ion conductivity (in Na-excess samples).\nThe results are novel, and the insights obtained from this study are highly beneficial to the field of perovskite oxides. Rigorous experimental investigations and comprehensive analyses of the structural and electrical properties were conducted. However, there are some issues that need to be addressed:\n1. In the introduction, it is not clearly explained why the authors specifically chose “NaxCa0.04Nb0.96Zr0.04O3- ” as the base composition instead of pure NaNbO₃ or other potential NaNbO3-based ceramics. Please provide the rationale for choosing this composition in the revised manuscript.\n2. From Fig. 4, the εᵣ–T curves of all compositions (e.g., Na0.96, Na0.99, Na, Na1.01, Na1.02) at 1 kHz, 10 kHz, 100 kHz, and 1 MHz show good overlap from room temperature up to approximately 350 °C. Beyond this point, a sharp increase in both dielectric permittivity and dielectric loss is observed at 1 kHz and 10 kHz, most likely due to the thermally activated processes of defects at elevated temperature. However, for the Na0.98 composition, the εᵣ–T curve at 1 kHz exhibits dielectric peak that doesn’t overlap with other frequencies at TP-R (and higher temperature), which is distinctly different from the behavior of the other compositions.\nFurthermore, this composition shows the highest tan(δ) value, reaching approximately 30 at 600 °C, which is higher even than that of the Na0.96 composition. This observation appears to contradict the impedance spectroscopy results, which indicate that the Na0.96 composition has lower resistivity than that of the Na0.98 composition.\nThe authors are strongly encouraged to remeasure the dielectric data for the Na0.98 composition to confirm the accuracy and reproducibility of the results. Alternatively, an explanation should be provided to address this discrepancy.\n3. In Figure 7, it is highly recommended to include an expanded view of the high-frequency region to allow readers to clearly observe the semicircular arc corresponding to the grain response.\n4. The chemical formula “Na0.96xCa0.04Nb0.96Zr0.04O3-  ” should be changed to “NaxCa0.04Nb0.96Zr0.04O3- ” to be consistent throughout the manuscript."}, "author_response": "Response to Reviewers’ comments:\nIt is my great pleasure for your constructive comments and suggestions on our\nmanuscript. All revised contents were marked in red in the revision. Our responses to\nthe comments are as follows:\nReviewer #1 (Remarks to the Author(s):):\nAlthough this script contains some interesting results there are many\ninconsistencies and a severe lack of rigour when it comes to presenting the data and\nproviding information on how it was analysed. I outline my response in more details\nbelow and on this basis I have to suggest the script is rejected.\n(i) Composition and nomenclature are confusing. No explanation as to why the\nstarting materials include 4% Ca and Ti on the A and B-sites of the lattice, respectively.\nAlso If we start from the given formula Na Ca Nb Zr O then for x =0.96 we\nx 0.04 0.96 0.04 3-d\nhave a stoichiometric perovskite ABO , yet this is reported as being an Na-deficient\n3\nsample with Na and O vacancies and this is very confusing. The authors refer (I think)\nto x =1 being stoichiometric yet this would give a formula of A BO and infer either\n1.02 3.02\nan excess of A-site cations and oxygen ions (or conversely B-site vacancies). Taking\nthe A and O excess model, this begs the question if ABO perovskites are based on close\n3\npacking of AO layers how can we achieve an excess of A and O sites when no\n3\ninterstitial sites should be available in such a close packed lattice! (Presumably the\nlattice is therefore B-site deficient). I appreciate that small changes in stoichiometry\nassociated with A/B ratios can have a dramatic effect on the electrical properties of\nperovskites but this requires rationalisation within the context of the crystal lattice. Late\non in the script the authors suggest the presence of the A-site and O-vacancies in x =0.96\nis associated with volatilisation of Na O. This should come much earlier in the script,\n2\notherwise, there is substantial confusion about the changes in composition. It might be\nbetter for the authors to frame the changes in composition on a solid solution based on\na combination of Na NbO and CaZrO (at a level of 4 mol%) perovskites and\n1±x 3 3\nintroduce the fact that there is known non-stoichiometry in NaNbO and that there is\n3\n1\nadditional issues with Na O loss during ceramic processing. This would clarify several\n2\nissues at the outset regarding compositional design and give the reader a clear steer\nbefore the results are presented.\n(ii) Structural data from laboratory XRD. There is insufficient information given\npertaining to how the Rietveld refinements (RR) of the data were performed and of\nthe results obtained. This is important because the positions of the oxygen ions are critical\nto the arguments about the shape of the NbO octahedra and how that links to ion\n6\nmigration. Furthermore, where do the interstitial Na ions reside and what are the atomic\npositions? In the methods section it is therefore important that more information on the\nprocedure and strategy used in the RR of the data are provided. I assume ion sites were\nset to be fully occupied but what were the final (x, y, z) atomic positions of all the ions\nand what about the isothermal parameters; were they refined or fixed and what are the\nvalues? This is important data and must be included in the results. This is especially the\ncase given that XRD is relatively insensitive to light atoms such as O and Na, yet much\nis made of the final positions of these ions. Furthermore, there are no errors associated\nwith the values given in Table S1 and these need to be included. There is a typographical\nerror in the caption for Fig S3. It should be Na-O not Nb-O.\n(iii) Microscopy. I’m not an expert in TEM but this was convincing (to me at least)\nthat x = 0.96 contained more Na vacancies than x = 1.0 and the XPS showed there were\nvariations in oxygen content (both Fig 3). Given the heterogeneity in the electrical\nbehaviour (next section) of these materials and the interpretation provided, it would be\ngood to show some SEM/EDX of the materials to establish the presence of any core-\nshell distributions within the samples and also EDX profiles across grains to see any\nvariations in composition at the grain boundaries. This intermediate level of\nmicroscopic elemental analysis at the micron level is missing and needs to be included\nto aid the interpretation of the electrical data.\n(iv). The electrical characterization was extensive and performed by Dielectric\nSpectroscopy (DS), impedance spectroscopy (IS) using DRT and variable Po and ion\n2\nblocking measurements with YSZ; however, in many cases there was a lack of rigour\n2\n(eg DRT, more later), it was often difficult to see the ‘bulk’ response in the Z* plots\nbased on IS (Figs 5,6,7) and the interpretation between DRT and IS seems flawed, the\nPo analysis is confusing and there is no treatment of the electronic contribution in the\n2\nextraction of the transport numbers for O and Na in equations 4 and 5. I find the DS\ndata interesting but the authors should indicate if there is any change in T associated\nmax\nwith the P-R transition across the series of samples as this is a major event in these\nmaterials. They should also indicate what frequency was used in extracting the\ntemperature for the T to U transition. There are considerable space charge effects at\nthese temperatures and this may influence the values reported. The IS data are poorly\npresented, not well analysed and Im not convinced by the interpretation. It is very\ndifficult to see the bulk arc (called the first arc in the script) at high frequencies in any\nof the Z* plots yet this should be central to the analysis. Figures should be expanded to\nshow it in more detail and the extracted R and C values for it presented as a function of\ntemperature instead of a single analysis at 500 C. The extracted capacitance for this arc\nfor 500 C is given as 4 pF/cm which corresponds to a permittivity of ~ 40-50. This is\nan order of magnitude below the 300 -500 observed in the DS data at 500 C in Fig 4.\nGiven that the materials remain ferroelectric at 500 C, then a capacitance value of 4\npF/cm (no errors on this value provided) for the bulk is too low and physically\nunreasonable for NaNbO -based materials. The authors should plot out extracted C\n3\nvalues across the full data range and they should show some temperature dependence.\nBy tracking this onto the DRT (Fig 5 c and 6c) with a time constant of 10-6 s that is\nassociated with this grain response, it appears not to be thermally activated. It remains\nat this value between 400 to 600 C and this means that the ‘assigned’ bulk conductivity\nis not thermally activated!! This cannot be correct. The larger second arc (Fig 5) at 500\nC is deconvoluted into two components that are assigned as grain boundary\ncontributions based on C values of 0.17 and 0.14 nF/cm (no errors or showing of the\nfits based on the equivalent circuit, again illustrating poor rigour in the analysis). These\nC values correspond to permittivity of ~ 1500 to 2000 which are high but are more\nconsistent with ferroelectric bulk responses as opposed to grain boundary responses.\nestablish if they are bulk-like (and presumably temperature dependent) or grain\nboundary-like (presumably with little temperature dependence). These elements are\ntemperature dependent based on the DRT data and as the authors point out show\nsignificant changes at 540 C where there is a phase transition. Surely, it makes more\nsense that these elements associated with the large second arc are bulk (possibly core\nand shell?) rather than the grain boundaries? A full analysis of extracted R and C\nvalues across the full temperature range is required to ensure the analysis is robust and\nthe interpretation is consistent with the physical processes occuring within the materials as\nthey undergo phase changes. At this stage, its not worth interpretating the Po data until\n2\nthe basic IS data are fully analysed.\n(v). The DRT is simply provided in a figure and no indication of any fitting\nparameters are given-again illustrating poor rigour in information pertaining to data\nanalysis.\nFigure 9 based on transport numbers versus x makes some sense to me (at least for\nO). For x =0.96 there is sufficient Na O loss to create the level of oxygen vacancies that\n2\ndominate the conductivity and the presence of this soda loss is clear from TEM/XPS\ndata. For x =1.0 and 1.02 (which actually have excess Na based on the original formula),\nthe loss of soda probably still occurs but samples have much reduced levels of vacancies\nand therefore are close to being stoichiometric ABO3 with very low levels of vacancies\nand therefore ionic transport is low. The authors suggest that the sodium ion transport\nnumber is high in Figure 9 for x =1.02 but this might be linked to the lack of treatment\nof the electronic contribution to the conductivity used in equation 5 to estimate the\ntransport number for Na. I also refer back to my comments linked to composition in\nperovskites, where are the interstitial sites for A-site cations in the ABO lattice and can\n3\nthey located via diffraction (no evidence in this script)? I therefore find no-compelling\nevidence for high levels of Na ion transport in these materials. In addition, the authors\noften cite NASICON as an example where there is high Na ion migration. This is true\nbut they are based on framework structures where there are vacant sites and its possible\n4\nto use this sites to create interstitial ion conduction via selective doping.\nResponse to Reviewer #1 comments:\nThank you very much for your comments and suggestions.\n(i) It is well known that two different phase structures exist in pure sodium niobate,\nantiferroelectric Pbma phase and ferroelectric P2 ma phase. This co-existence\n1\ncomplicates the analysis of the relationship between the crystal structure and electrical\nconductivity. To address this challenge, we introduced a minor amount of calcium\nzirconate (CaZrO ) as a dopant. This doping strategy effectively stabilizes the\n3\nantiferroelectric Pbma phase, ensuring that NaNbO adopts a single-phase structure at\n3\nroom temperature and reducing the influencing factors on electrical conductivity\nanalysis (J. Mater. Chem. C 2020, 17, 5681-5691, Dalton Trans. 2015, 44, 10763-10772\nand Appl. Phys. Lett. 2015, 107, 112904). We also added this point in the revised\nmanuscript.\nWe sincerely appreciate the valuable suggestions put forward by the reviewers. We\nmodified the formula from Na Ca Nb Zr O to Na Ca Nb Zr O to\nx 0.04 0.96 0.04 3-δ 0.96x 0.04 0.96 0.04 3-δ\nbetter reflect the design of the A-site non-stoichiometry. Through detailed analysis of\nthe crystal structure, it is believed that excess Na+ ions are located in the Na-O-Na and\nNa-O-Nb spatial networks. The designed Na-excess samples exhibit a significant\nenhancement in electrical conductivity and remarkable Warburg behavior\ncharacteristics of ionic conduction. The test results of the sandwich-structured samples\nconfirm the presence of Na+ ionic conduction (as shown in Fig. 7 a and b). Subsequently,\nthe contributions of electronic and ionic conductivities are determined by fitting the\nelectronic conductivity and ionic conductivity using an equivalent circuit.\nbetween the layers and EDS spectrum showing the elemental composition at the interface.\nImpedance spectra obtained from the conventional structure and sandwich structure for (b) NCNZ-Na ,\n(c) NCNZ-Na , and (d) NCNZ-Na samples, respectively. (e) Bar chart showing the Na+\n0.96 1.0 1.02\nand O2- ion conductivities of NCNZ-Na samples. (f) Schematic cross-sectional illustration of the\nx\nNa+ and O2- ion channels, along with the Na-O-Na and Na-O-Nb networks.\nHere, we attempt to emulate the more complex models using a simple equivalent\ncircuit composed of three parallel rails (Fig. S10a). At high frequencies, the ionic rail\nis conductive and the total resistance is equal to the parallel combination of the\nelectronic (R = d/σ A) and ionic (R = d/σ A) components (where σ is\nelec elec ion ion\nconductivity, d is sample thickness, and A is area). Along with the dielectric capacitance,\nC = εA/d, this generates the high frequency semicircle in the Z* plot (Fig. S10b). At\nBulk\nlow frequencies the ionic carriers have time to accumulate at the electrodes and, in the\ndc limit, the impedance approaches R (PCCP 2001, 3, 1668-1678 and Appl. Phys.\nelec\nLett. 2010, 96, 052906). Based on the standard model in Fig. S10b:\n𝑅 = (𝜎 +𝜎 )−1 (1)\n𝑖𝑜𝑛+𝑒𝑙𝑒𝑐 𝑖𝑜𝑛 𝑒𝑙𝑒𝑐\n𝑅 = (𝜎 )−1 (2)\n𝑒𝑙𝑒𝑐 𝑒𝑙𝑒𝑐\n𝜎 𝑅\nelec 𝑖𝑜𝑛+𝑒𝑙𝑒𝑐\nt = = (3)\nelec 𝜎 𝑅\ntotal 𝑒𝑙𝑒𝑐\nHere t quantifies the contribution of an individual ion to the total conductivity. R is the\nintercept of the fitted curve with the abscissa; σ is the electrical conductivity. According\nto the calculation results, the contribution of 𝑡 is approximately 8%.\nelec\nFig. S10 (a) An effective equivalent circuit used to model mixed conduction with ion, (b) simulated\nimpedance spectra. (c) Actual curve and fitted curve based on the test curve.\nThese results collectively support the existence of conductive Na+ ions in the\nlattice. Since the excess of Na+ ions is relatively small (only 2%×0.96) and it is\nimpossible to determine the position of Na+ ions in the ABO -type structure through\n3\nrefinement, we chose to quantify the space of the lattice interstices to prove the possible\nexistence of interstitial Na+ ions.\nRietveld refinement data clearly indicate that the Na-O-Na and Na-O-Nb networks\nexhibit expansion, as depicted in Fig. S6. Compared with the Na sample, all the edge\n1.0\nlengths of the Na-O-Na network in the Na sample exhibit elongation. This indicates\n1.02\nthe expansion of the Na-O-Na network and an increase in its interstitial space.\nMeanwhile, the Na-O-Nb network also shows a tendency towards enlargement. The\nalterations in the interstitial spaces of these networks within the conductive plane are\nillustrated in Fig. 7f. Upon increasing the Na content from 1.0 to 1.02, notable changes\noccurred in the cross-sectional interstitial distances. In the Na-O-Na network, the d(Na-\nNa) distance expands from 3.894 Å to 3.896 Å, and the d(O-O) distance increases from\n4.482 Å to 4.489 Å. Meanwhile, in the Na-O-Nb network, the d(Na-O) distance grows\nfrom 3.046 Å to 3.233 Å, while the d(Na-Nb) distance increases from 3.378 Å to 3.379\nÅ. This expansion of the Na-O-Na and Na-O-Nb networks serves to diminish the\n7\nmigration energy barrier for Na+ ions.\nFig. S6 The Na–O–Na and Na–O–Nb networks of the NCNZ-Na and NCNZ-Na samples.\n1.0 1.02\nTable S3 Ionic radii of Na and O ions.\nIons CN r/Å\n4 0.99\n6 1.02\nNa+\n8 1.18\n12 1.39\n2 1.21\nO2- 4 1.38\n6 1.40\nBased on the above insights, the spaces of the Na-O-Na and Na-O-Nb networks\nare quantified to observe the possibility of the existence of interstitial ions. The\n8\nintroduction of interstitial ions alters the local environment of surrounding ions, thereby\nchanging their coordination numbers. Consequently, when quantifying the spatial\ncharacteristics of the Na-O-Na and Na-O-Nb networks, we calculated the network\nspaces under various coordination numbers (Table S3) to assess the possibility of the\nexistence of interstitial ions:\nNa-O-Na network:\ni = d −2r (1)\nNa−Na (Na−Na) Na\ni = d −2r (2)\nO−O (O−O) O\nNa-O-Na network:\ni = d −r −r (3)\nNa−O (Na−O) Na O\nHere, i represents the interstitial space between two ions, d represents the inter-atomic\nspacing, and r represents the ionic radius. As shown in Fig. S6, the Na-O-Nb network\nis mainly restricted by the d(Na-O) interstices. Therefore, only the Na-O interstices are\nquantified here. The calculations show that the maximum value of i(Na-Na), which is\n1.878 Å, is greater than the minimum value of r(Na) 0.99 Å. Similarly, the maximum\nvalue of i(O-O), 1.098 Å, is also greater than the minimum value of r(Na) 0.99 Å.\nMoreover, the values of i(Na-O) range from 1.032 Å, which is larger than the minimum\nvalue of r(Na) 0.99 Å. This evidence confirms the existence of interstices in the Na-O-\nNa and Na-O-Nb structures that allow the passage of Na ions.\nIn summary, it is determined that there are ion channels in the perovskite-type\nstructure framework of NaNbO for Na+ ions to pass through, as shown in Fig. S6. The\n3\nsignificant Na⁺ ion conductivity behavior when there is an excess of Na+ ions at the A-\nsite is caused by interstitial ion conductivity. We added these results and discussions\nto the revised manuscript.\nRegarding the issue of Na O volatilization, we adopted the buried sintering\n2\nmethod to avoid volatilization when sintering the samples. Therefore, volatilization will\nnot be a significant influencing factor in this study. To avoid confusing readers, we have\ndeleted the content about Na O volatilization in the main text to ensure logical clarity.\n2\n9\n(ii) We sincerely appreciate the valuable suggestions put forward by the reviewers.\nIn response, we have supplemented the specific Rietveld data and presented them in\nTable S1 and S2. Meanwhile, we have corrected the errors in Fig. S5. The refinement\nwas carried out using the GASA software with the Pbma space group, and the error\nvalues are all within the ideal range. Since the content of interstitial Na ions is relatively\nlow (only 2%×0.96), the positions of interstitial Na ions cannot be clearly determined\nfrom the Rietveld data. We believe that the excess Na+ ions may be located in the Na-\nO-Na and Na-O-Nb networks (Fig. S6 and Table S3). The designed Na-excess samples\nexhibit a significant enhancement in electrical conductivity and remarkable Warburg\nbehavior characteristics of ionic conduction. The test results of the sandwich-structured\nsamples confirm the presence of Na+ ionic conduction (as shown in Fig. 7).\nSubsequently, the contributions of electronic and ionic conductivities are determined\nby fitting the electronic conductivity and ionic conductivity using an equivalent circuit\n(Fig. S10). After fitting calculations, ionic conductivity dominates with a value of 92%.\nMeanwhile, the interstitial spaces of the two networks are quantified, which shows the\npossibility of allowing Na+ ions to pass through. Therefore, interstitial Na⁺ ions exist in\nthese two network structures (the Na-O-Na and Na-O-Nb networks). We added these\nresults and discussions to the revised manuscript.\nFig. S5 Distortion of Na-O environments inNCNZ-Na (x = 0.96, 1 and 1.02) ceramics, respectively.\nx\nx\nCompound\nNa Na Na Na Na Na\nreference 0.96 0.98 0.99 1.01 1.02\nCrystal\nOrthorhombic\nsystem\nα/Å 5.5605(8) 5.5610(7) 5.5618(9) 5.5619(9) 5.5626(3) 5.5669(1)\nb/Å 15.5572(6) 15.5574(1) 15.5614(1) 15.5617(9) 15.5621(3) 15.5678(6)\nc/Å 5.5006(0) 5.5018(9) 5.5024(9) 5.5025(4) 5.5025(5) 5.5069(1)\nUnit cell\n475.84(4) 475.99(8) 476.23(8) 476.26(7) 476.33(8) 477.25(6)\nvolume/Å3\nSpace\nPbma\ngroup\nReduced χ2 1.70 1.79 1.97 2.09 1.51 1.93\nR (%) 5.82 5.73 4.25 4.82 2.11 5.55\nwp\nR (%) 6.45 7.95 6.73 8.24 6.01 8.47\np\nTable S2. Crystal structure parameters for the NCNZ-Na (x = 0.96 1.0 and 1.02)\nx\nSite Atom x/a y/b z/c Occ. U\niso\n4c Nb 0.2644(5) 0.1258(1) 0.2430(2) 0.96(-) 0.002(3)\n2a Na1 0.75(-) 0(-) 0.2570(1) 0.9216(-) 0.023(6)\n2b Na2 0.7803(4) 0.25(-) 0.2540(5) 0.9216(-) 0.038(5)\n2a O1 0.25(-) 0(-) 0.2951(8) 0.9808(-) 0.022(8)\n2b O2 0.2340(7) 0.25(-) 0.1711(5) 0.9808(-) 0.011(4)\nNa\n0.96 4c O3 0.0270(3) 0.1428(6) 0.5241(9) 0.9808(-) 0.010(1)\n4c O4 0.4580(1) 0.1108(7) -0.0449(4) 0.9808(-) 0.015(3)\n4c Zr 0.2644(5) 0.1258(1) 0.2430(2) 0.04(-) 0.029(6)\n2a Ca1 0.75(-) 0(-) 0.2570(1) 0.04(-) 0.080(1)\n2b Ca2 0.7803(4) 0.25(-) 0.2540(5) 0.04(-) 0.068(4)\n4c Nb 0.2624(8) 0.1256(1) 0.2436(5) 0.96(-) 0.004(2)\n2a Na1 0.75(-) 0(-) 0.2558(5) 0.96(-) 0.010(4)\n2b Na2 0.7785(4) 0.25(-) 0.2528(5) 0.96(-) 0.010(4)\n2a O1 0.25(-) 0(-) 0.3017(5) 1(-) 0.007(4)\n2b O2 0.2419(7) 0.25(-) 0.1777(5) 1(-) 0.007(4)\nNa\n1.0\n4c O3 0.0349(7) 0.1360(1) 0.5307(5) 1(-) 0.007(4)\n4c O4 0.4658(1) 0.1038(1) -0.0385(5) 1(-) 0.007(4)\n4c Zr 0.2624(8) 0.1256(1) 0.2436(5) 0.04(-) 0.008(9)\n2a Ca1 0.75(-) 0(-) 0.2558(5) 0.04(-) 0.008(3)\n2b Ca2 0.7785(4) 0.25(-) 0.2528(5) 0.04(-) 0.008(3)\n4c Nb 0.2645(6) 0.1254(1) 0.2447(5) 0.96(-) 0.004(7)\n2a Na1 0.75(-) 0(-) 0.2562(5) 0.96(-) 0.006(4)\n2b Na2 0.7809(4) 0.5(-) 0.2532(5) 0.96(-) 0.023(8)\nNa 2a O1 0.25(-) 0(-) 0.3035(5) 1(-) 0.006(2)\n1.02\n2b O2 0.2395(5) 0.5(-) 0.1823(5) 1(-) 0.004(6)\n4c O3 0.0325(5) 0.1434(1) 0.5353(5) 1(-) 0.019(7)\n4c O4 0.4627(1) 0.1088(9) -0.0331(6) 1(-) 0.006(7)\n11\n4c Zr 0.2645(6) 0.1254(1) 0.2447(5) 0.04(-) 0.027(4)\n2a Ca1 0.75(-) 0(-) 0.2562(5) 0.04(-) 0.026(4)\n2b Ca2 0.7809(4) 0.5(-) 0.2532(5) 0.04(-) 0.026(4)\n(iii) We sincerely appreciate the valuable suggestions put forward by the reviewers.\nIn response, we conducted a more detailed observation of the morphology and\nelemental distribution of the samples. The scanning electron microscopy (SEM) images\nof the non-stoichiometric and stoichiometric samples, as shown in Fig. S1, reveal a\nuniform distribution of grains. Notably, no obvious secondary phases are observed\nwithin the grains. To conduct a detailed examination of the internal structure and\nelemental distribution of the grains, transmission electron microscopy (TEM) analysis\nwas carried out. We prepared ion thinning samples and analyzed the morphology and\nelemental distribution at the grain positions using TEM and EDS, as shown in Fig. S2.\nThe analysis results indicate that the elements are uniformly distributed inside the\ngrains, and there are no characteristics of a second phase or core-shell structure. Besides,\na comprehensive review is conducted on the structural research of NaNbO -based\n3\nceramics with similar compositions. No reports are found regarding the presence of\ncore-shell structures in the components of such materials (J. Euro. Ceram. Soc. 2018,\n38, 4939–4945, J. Appl. Phys. 2015, 118, 174107, and Acta Mater. 2018, 161, 352-359).\nFig. S2 transmission electron microscopy (TEM) analysis reveals the morphology images and\ncorresponding energy dispersive X-ray spectroscopy (EDS) elemental distribution maps.\n12\n(iv) We sincerely appreciate the valuable suggestions put forward by the reviewers.\nIn response, we additionally measured the XRD patterns (Fig. 4) and dielectric spectra\nfrom room temperature to 700 °C to jointly characterize the phase transition of the\nNCNZ-Na samples. The analysis of the phase transition in the dielectric spectra mainly\nx\nrelies on the data at 10 kHz. By comparing with the temperature-dependent XRD\npatterns, we aim to determine the influence law of the phase transition on the electrical\nconductivity performances.\nFig. 4 (a) XRD patterns and structural transitions of NCNZ-Na with various temperatures. (b-g)\n0.96\nDielectric constant and loss of the NCNZ-Na ceramics as a function of temperature.\nx\nAfter replacing the electrode materials, we re-measured the impedance spectra\n(Fig. 5) of each sample and plotted the capacitance (C') curves as functions of\ntemperature (T) and frequency (f) (Fig. S7b). Herein, the fitting method of DRT is as\nfollows:\nDistribution of Relaxation Times\nThe method of the distribution of relaxation times (DRT) allows a separation of\nelectrochemical processes with different time constants which can be calculated from\n13\nmeasured impedance data. Thus, it allows a clearer look on the measured spectra and\nhelps to resolve processes which might not be detected otherwise. The numerical\nscheme follows a Levenberg-Marquardt algorithm. This is based on the fact that\nimpedance functions obeying the Kramers-Kronig relations (KK) can be represented as\na number of infinitesimal differential RC-elements. The underlying theory is discussed\nin detail in various references such as Electrochim. Acta 2017, 228, 652-658.\n∞\n𝛾(𝜏)\n𝑍(𝜔) = 𝑅 −𝑅 ∫ 𝑑𝜏 (7)\n0 𝑝𝑜𝑙 1+𝑗𝜔𝜏\n∞\n∫𝛾(𝜏)𝑑𝜏 = ∑𝑅 (8)\ni\ni=1\nThis classical approach has the drawback that data preprocessing is required to remove\nthe high-frequency region influenced by the cable’s inductance and the low-frequency\nregion representing the diffusion limitation. To better meet the requirements of the\nimpedance spectra, the general approach of Eq. (7) is expanded with an inductance L,\nmirroring the imaginary part of the impedance at high frequencies. A capacity\ncontributing to the impedance spectrum at low frequency, the ohmic resistance R\n0\ncauses by the bulk resistance of the electrolyte, a Warburg element and a capacitor\nrepresenting the diffusion processes. The Warburg element represents the diffusion\nbehavior for particles in micron range whereas the capacitor is added to model the\ndiffusion smaller particles in the nanometer range. Thus, the measured impedance data\nare fitted to the following equation:\n∞\n1 𝐴 𝛾(𝜏)\n𝑊\n𝑍 (𝜔) = 𝑗𝜔𝐿− − (1−𝑗)+𝑅 −𝑅 ∫ 𝑑𝜏 (9)\n𝑚𝑜𝑑𝑙𝑒 𝑗𝜔𝐶 √𝜔 0 𝑝𝑜𝑙 1+𝑗𝜔𝜏\nmultiplication and thus becoming a system of linear equations and adopting the form\ny=Ax:\n14\n1 1 𝜔1𝜏1 𝜔1𝜏𝑛\n⋯ ⋯\n1+(𝜔1𝜏1)2 1+(𝜔1𝜏𝑛)2 1+(𝜔1𝜏1)2 1+(𝜔1𝜏𝑛)2\n𝑍 𝜏 = ⋮ ⋱ ⋮ ∙𝛾+𝑗 ⋮ ⋱ ⋮ (10)\n𝑚𝑜𝑑𝑙𝑒\n1 1 𝜔𝑚𝜏1 𝜔𝑚𝜏𝑛\n⋯ ⋯\n[1+(𝜔𝑚𝜏1)2 1+(𝜔𝑚𝜏𝑛)2] [1+(𝜔𝑚𝜏1)2 1+(𝜔𝑚𝜏𝑛)2]\nDetails of the used numerical routine are described in.\nDue to the duration time and drifts in the system unwanted artifacts especially at\nlower frequencies might occur. To ensure that the measured impedance data match the\nKK-relation, they are transformed with the Z-HIT function which calculates the\nimpedance data Z(f) from the phase data 𝜑(𝜔) after the following approximation:\n𝜔0\n2 𝑑𝜑(𝜔)\n𝑙𝑛|𝐻(𝜔 )| ≈ 𝑐𝑜𝑛𝑠𝑡.+ ∫ 𝜑(𝜔)𝑑𝑙𝑛𝜔+𝛾 (11)\n0 𝜋 𝑑𝑙𝑛𝜔\n𝜔𝑠\nThe fitting results of DRT are shown in Fig. 5a. To further ensure the accuracy of DRT\nanalysis, the C'-f plots at several temperatures are displayed in Fig. S7b. The high-\ncapacitance plateau corresponds to the grain boundary response, the low capacitance\nplateau corresponds to the grain response, and both grain and grain boundaries exhibit\ntemperature dependence. The measured capacitance responses are in good agreement\nwith the fitting values, validating the rationality of the distribution of relaxation times\n(DRT) analysis.\nFig. 5 (a) Matching parts of the impedance spectra with the corresponding components of the DRT\n15\nfunction. (b) Nyquist plots of the NCNZ-Na ceramics at 500 ℃ and (c) the corresponding DRT\nx\ndiagram. (d) The Nyquist plots of NCNZ-Na\n0.96\nsamples at different temperatures, (e) normalized\nDRT curves.\nFig. S7 (a) DRT curves of the NCNZ-Na sample measured at various temperatures. (b) The C'\n0.96\nspectra for the NCNZ-Na sample.\n0.96\nFig. S8 (a and b) The Nyquist plots of NCNZ-Na and NCNZ-Na samples, (c and d) normalized\n1.0 1.02\nDRT curves at different temperatures.\nresponse shifts towards higher frequencies as the temperature increases, whereas the\nsemi-circle corresponding to the grain response gradually vanishes with rising\ntemperature. This behavior is consistent with the response peaks of grains and grain\nboundaries in the DRT analysis, which can be attributed to thermal activation. However,\ndue to the high degree of overlap between the grain boundary and grain response semi-\ncircles and the pronounced hindering effect from the grain boundaries, the semi-circle\nof the grain response at high frequencies is rather weak. Therefore, the DRT analysis\noffers a more intuitive way for observation. Additionally, Fig. S1 and S2 confirm the\nabsence of a core-shell effect. We added these results and discussions to the revised\nmanuscript.\n(v) To quantitatively analyze the contributions of ionic and electronic conduction and\ndetermine the types of charge carriers related to conduction, we fitted the electronic and\nionic conduction contributions of Na using the circuit and model shown in Fig. S10a\n1.02\nand b. The fitting results show that the contribution of electronic conductivity is only\n8%, as presented in “Analysis of the contributions of ionic and electronic conduction”\nbelow. Therefore, we neglected the contribution of electronic conduction in the main\nmanuscript.\nAnalysis of the contributions of ionic and electronic conduction\nFig. S10 (a) An effective equivalent circuit used to model mixed conduction with ion, (b) simulated\nimpedance spectra. (c) Actual curve and fitted curve based on the test curve.\ncomposed of three parallel rails (Fig. S10a). At high frequencies, the ionic rail is\nconductive and the total resistance is equal to the parallel combination of the electronic\n(R = d/σ A) and ionic (R = d/σ A) components (where σ is conductivity, d is\nelec elec ion ion\nsample thickness, and A is area). Along with the dielectric capacitance, C = εA/d,\nBulk\nthis generates the high frequency semicircle in the Z* plot (Fig. S10b). At low\nfrequencies the ionic carriers have time to accumulate at the electrodes and, in the\ndc limit, the impedance approaches R (PCCP 2001, 3, 1668-1678 and Appl. Phys. Lett.\nelec\n2010, 96, 052906). Based on the standard model in Fig. S10b:\n𝑅 = (𝜎 +𝜎 )−1 (1)\n𝑖𝑜𝑛+𝑒𝑙𝑒𝑐 𝑖𝑜𝑛 𝑒𝑙𝑒𝑐\n𝑅 = (𝜎 )−1 (2)\nelec 𝑒𝑙𝑒𝑐\n𝜎 𝑅\nelec 𝑖𝑜𝑛+𝑒𝑙𝑒𝑐\nt = = (3)\nelec 𝜎 𝑅\ntotal 𝑒𝑙𝑒𝑐\nHere t quantifies the contribution of an individual ion to the total conductivity. R is the\nintercept of the fitted curve with the abscissa. σ is the electrical conductivity. According\nto the calculation results, the contribution of 𝑡 is approximately 8%.\nelec\nThe significant contribution of Na⁺ ions to conduction is demonstrated through\ncalculations (Fig. S10c). The expansion of the two Na-O-Na and Na-O-Nb networks\n(Fig. S6 and Table S3), the presence of Na-ion conduction, and the weakening of\noxygen ion conduction are sufficient to prove that the conduction type when there is an\nexcess of Na is interstitial Na-ion conduction.\nReviewer: #2 (Remarks to the Author(s):\nThis paper is interesting, but the subject of mixed Na/O conduction in the same\n‘NaNbO ’ perovskite lattice was already mentioned 5 years ago by these authors:\nniobium-based perovskites. Adv. Funct. Mater. 30, 1909254 (2020). Reading the papers\nof Gouget et al. (ref 53 in this manuscript but also refs 21 and 22), I consider that there\nare no original features in this paper submitted to Nature Comm, especially as there are\n18\nother papers (refs 2& and 22) by the same team on the same class of materials. This\npaper should not be accepted in Nature Comm.\nResponse to Reviewer #2 comments:\nThank you very much for your comments and suggestions.\nGouget et al.'s work mainly focuses on adjusting NaNbO -based solid-state ion\n3\nconductors through doping and interlayer structure, and draws conclusions by\nanalyzing changes in unit cell parameters. Indeed, the behavior of mixed conductivity\nof Na+ and O2- ions in NaNb(Ti)O ceramics was revealed. However, it is known that\n3\npure NaNbO has a dual-phase (P2 ma and Pbma) structure at room temperature, which\n3 1\nexhibits antiferroelectric and ferroelectric characteristics respectively. This is\nunfavorable for analyzing the corresponding relationship between unit cell parameters\nand conduction forms. In this paper, we doped CaZrO to stabilize the antiferroelectric\n3\nphase structure (Pbma) of NaNbO , which allows for a more accurate determination of\n3\nthe changes in unit cell parameters corresponding to the variations in ionic conductivity.\nIn addition, in terms of regulation methods, the non-stoichiometry at the A-site is\ndifferent from the doping at the B-site. The changes in the NbO octahedron induced\n6\nby the occupancy rate of A-site atoms in the unit cell show more relevance to the\nintrinsic crystal structure of NaNbO (Adv. Funct. Mater. 2020, 30, 2001840, and Chem.\nThe exploration of the conductance behavior of perovskite solid-state ionic\nconductors is carried out through Nyquist curve analysis. The electrochemical response\nprocess from high frequency to low frequency includes responses from the bulk phase,\ngrain boundaries, electrodes, etc. Currently, the main analysis method is to perform\nequivalent circuit fitting using Zview software. Nevertheless, some of the\nelectrochemical response Nyquist semicircles highly overlap, making it impossible to\ndetermine the number of CP elements in the equivalent circuit, which will affect the\n19\naccuracy of the analysis. In this study, the Nyquist curve is analyzed using the\ndistribution of relaxation times (DRT). The equivalent circuit model related to the\nelectrochemical process is accurately measured, and the test results are specifically\nanalyzed. By observing the area of the DRT curve and the frequency changes\ncorresponding to the peaks, the changes in grain and grain boundary conductance under\nvariations in composition and temperature can be effectively determined. For example,\nin the analysis of electrical conductivity changes, the grain response and grain boundary\nresponse in the Nyquist plot of NaNbO will partially overlap, and as the temperature\n3\nrises, the grain response will shift forward and gradually disappear. This is unfavorable\nfor analyzing the conduction change form through a single Nyquist plot. DRT provides\nan intuitive method for analyzing the law of unit-cell parameter changes caused by the\nvariation of electrical conductivity with composition, which is hidden under the Nyquist\ncurve.\nIn distinguishing the conductivities of oxygen ions, sodium ions, and electrons, we\nconducted a detailed analysis of the test results from aspects such as atmosphere design,\nstructure design, and equivalent circuit fitting. Among them, the contribution of ion\nconductivity and electron conductivity is distinguished by equivalent circuit fitting to\nensure the reliability of experimental results. Meanwhile, a hypothesis is proposed\nregarding the ion channels when there is an excess of Na+ ions and we quantify the\npossibility of these channels through calculations.\nBased on the above analysis, this work is highly innovation and practical\nsignificance in terms of composition design, crystal structure regulation, and ionic\nconductivity analysis.\nReviewer: #3 (Remarks to the Author(s):\nLiu et al. reported the synergistic regulation of Na+ and O2- ions conduction in the\nNaNb -based ionic conductor. By changing the structures of these three types of\n3\npolyhedrons, the conduction channels of Na+ and O2- ions as well as electrons could be\n20\neffectively regulated. This work is scientifically interesting and can be published after\nsome revisions, and comments are listed below.\n1.The section of temperature-dependent dielectric responses. The author\nmentioned two phase transition peaks here. However, NaNbO has multiple phase\n3\ntransition characteristics within this temperature range. Are the phase transitions\ncorresponding to these phase transition points accurate?\n2.The author mentioned that the type of carriers can be regulated by the non-\nstoichiometry of A-site elements, thereby achieving the transformation between P-type\nand N-type solid-state ionic conductors. When there is a sodium deficiency, it behaves\nas an oxygen ionic conductor. However, sodium deficiency also creates sodium\nvacancies. Why does the sodium ion conductivity deteriorate? Please explain.\n3.In Fig. 9d, both the samples with excess and deficiency show a sudden increase\nin conductivity at 2%. Please explain.\n4. The lattice expansion phenomenon of the Na-deficient sample analyzed by TEM\nis opposite to the cell volume contraction analyzed by XRD. Will this affect the\nconclusion?\nResponse to Reviewer #3 comments:\nThank you very much for your comments and suggestions.\n1. Sodium niobate exhibits multiple phase transitions spanning from room\ntemperature to 700 °C, encompassing crystal structures such as Pbma, Pnmm, Ccmm,\nP4/mbm, and Pm-3m. To accurately elucidate the correlation between the phase\ntransition behavior of the NCNZ-Na samples, supplementary X-ray diffraction (XRD)\nx\nmeasurements were conducted on the NCNZ-Na samples over the temperature range\nx\nfrom room temperature to 700 °C. The results are presented in Fig. 4a. Temperature\ndependent XRD (Fig. 4a) directly reveals phase transition behavior in NCNZ-Nax\nsamples. The NCNZ-Na sample transitions from orthorhombic (Pbma, Pnmm,\n0.96\nto 700 ℃. Unit-cell symmetry and volume changes, related to NbO octahedra\n6\ndistortion and torsion, significantly affect the ionic conductivity. Temperature-\ndependent dielectric constant and loss variations disclose conductivity relaxation\nassociated with these phase transitions. In the temperature range from 300 ℃ to 600 ℃,\nthe NCNZ-Na samples display two distinct phase transition peaks, corresponding to\nx\nthe transitions from the orthorhombic antiferroelectric Pbma (P) phase to the\northorhombic ferroelectric Pnmm (R) phase, and the tetragonal P4/mbm (T ) phase to\n2\nthe cubic pm-3m (U) phase, respectively. Distinct phase transition peaks are indicative\nof substantial changes in the crystal structure. Prominently, intense phase transition\npeaks of T -U (⁓ 560 ℃) are observed in the NCNZ-Na samples with increasing Na-\n2 x\ndeficiency (Fig. 4b-d). The phase transition temperature is basically consistent with the\nturning temperature of the conductivity change observed in Fig. 6, and it is considered\nto be the main factor influencing the conductivity change.\nFig. 4 (a) XRD patterns and structural transitions of NCNZ-Na with various temperatures. (b-g)\n0.96\nDielectric constant and loss of the NCNZ-Na ceramics as a function of temperature.\nx\n22\n2. The refined data are imported into Diamond software to observe the local\nenvironment of the atoms. Due to the low number of O vacancies (V·· ) and Na\nO\nvacancies (V' ) in the compound, it is impossible to accurately identify oxygen and Na\nNa\nsites that are partially occupied. The local environments of Nb and Na ions for NCNZ-\nNa , NCNZ-Na and NCNZ-Na samples are shown in Fig. 2c and Fig. S5. For\n0.96 1.0 1.02\nthe Na-deficient samples, the average bond distances (~1.9940 Å) for d(Nb-O3) and\nd(Nb-O4) in the equatorial plane are shorter than those in the stoichiometric samples\n(~1.9941 Å), and there is a large difference between the bond distances. This is\nconsistent with the observed reduction in the a and c lattice parameters (Table S1).\nMeanwhile, d(Nb-O1) and d(Nb-O2) bond distances also decrease relatively, and the\nchange in d(Nb-O2) is more significant. The phenomenon suggests the emergence of\nflattened NbO octahedra, a structural feature that is expected to facilitate the\n6\nconduction of oxygen ions. However, as shown in Fig. S5, regarding the d(Na-O)\nspacing in the NaO icosahedron related to the Na⁺ ion conductivity, the Na sample\n12 0.96\nexhibits an expansion trend compared with the Na sample, showing a change opposite\n1.0\nto that of the NbO octahedron. This might be the structural reason for the decrease in\n6\nthe Na⁺ ion conductivity. In addition, inspection of Fig. 6a and d reveals that the\nelectrical conductivity under a nitrogen atmosphere is markedly higher than that under\noxygen and air atmospheres, suggesting a strong correlation between the conductivity\nvariation and the oxygen partial pressure. An elevation in oxygen partial pressure is\nfound to facilitate oxygen-ion conductivity, a phenomenon intricately linked to the\nconcentration of charge carriers. Consequently, as the gaseous environment transitions\nfrom nitrogen to oxygen, the decline in conductivity can be ascribed to the alteration in\ncharge carrier concentration. A mutual suppression effect exists between Na+ and O2-\ncharge carriers. We added these results and discussions to the revised manuscript.\n3. In the crystal structures of solid-state ionic conductors, point defects play a\nmultifaceted role. They can induce structural distortions within the crystal lattice.\nSimultaneously, vacancies contribute to the establishment of migration pathways for\n23\ncharge carriers, thereby enhancing ionic conductivity. Nonetheless, a limited quantity\nof point defects can aggregate to create carrier trapping sites and defect dipoles. These\nstructural features act as impediments to ionic conduction and are thus detrimental to\nthe overall electrical conductivity of the material. In scenarios where the defect\nconcentration is relatively low, analogous structures may form, impeding the flow of\ncharge carriers and giving rise to an unexpected surge in electrical resistance or a\nsudden increase in a related conductivity associated parameter. However, as the\nconcentration of defects increases, this hindering effect dissipates, and ionic channels\nare established. Consequently, a sharp rise in electrical conductivity is observed.\n4. Transmission electron microscopy (TEM) is employed to examine the local\nunit cell features, whereas XRD is more suited for analyzing the overall lattice\ncharacteristics. At defect sites, the equilibrium of inter-atomic interactions surrounding\nvacancy positions is disrupted. Neighboring atoms, experiencing reduced inward\ndirected binding forces, relax towards the vacancies, leading to lattice expansion at\nthese sites. Nevertheless, local structural features can induce atomic elastic distortions.\nThese distortions generate long range stress fields that cause an increase in the inter-\natomic distances in remote regions.\nIn addition, a comprehensive understanding of the lattice parameters can be\nachieved through the refinement of XRD data. In contrast, TEM data only contain\ndiffraction information from specific crystal planes. Both types of data are related to\natomic spacing. The local environment diagrams of Na and Nb atoms obtained after\nXRD refinement are presented in Fig. 2 and Fig. S5. It can be observed that as the Na\noccupancy at the A-site decreases, the unit-cell parameters decrease. However, the\nasymmetry of the NbO octahedra and NaO icosahedra increases. This enhanced\n6 12\nasymmetry leads to an increase in the local atomic spacing, consequently inducing an\nenlargement of the spacing of certain crystal planes. For instance, as the Na occupancy\ndecreases, the d(Na1-O3) distance expands from 3.0465 Å to 3.1596 Å. This change is\nconsistent with the variation in crystal plane spacing observed in the TEM images. Thus,\ndespite these complex local and long-range effects, they do not undermine the validity\nof our analysis and subsequent judgment.\nx\nReviewer: #4 (Remarks to the Author(s):\nThis research reports the variation of the conduction mechanism in\nNa Ca Nb Zr O - perovskite ceramics through A-site non-stoichiometry. By\nx 0.04 0.96 0.04 3\nadjusting the Na content from deficient to excess (i.e., x = 0.96-1.02), the dominant\ndefect species changed, resulting in a transformation of the NbO octahedral structure,\n6\nfrom a flattened configuration in Na-deficient compositions to an obliquely elongated\none in Na-excess compositions. Consequently, the dominant conduction mechanism\nshifted from O2- ion conductivity (in Na-deficient samples), to mixed O2- and electron\n(e⁻) conductivity (in stoichiometric samples), and finally to Na⁺ ion conductivity (in\nNa-excess samples).\nThe results are novel, and the insights obtained from this study are highly\nbeneficial to the field of perovskite oxides. Rigorous experimental investigations and\ncomprehensive analyses of the structural and electrical properties were conducted.\nHowever, there are some issues that need to be addressed:\n1. In the introduction, it is not clearly explained why the authors specifically chose\n“Na Ca Nb Zr O - ” as the base composition instead of pure NaNbO or other\nx 0.04 0.96 0.04 3 3\n25\npotential NaNbO -based ceramics. Please provide the rationale for choosing this\n3\ncomposition in the revised manuscript.\n2. From Fig. 4, the εᵣ–T curves of all compositions (e.g., Na , Na , Na, Na ,\n0.96 0.99 1.01\nNa ) at 1 kHz, 10 kHz, 100 kHz, and 1 MHz show good overlap from room\n1.02\ntemperature up to approximately 350 °C. Beyond this point, a sharp increase in both\ndielectric permittivity and dielectric loss is observed at 1 kHz and 10 kHz, most likely\ndue to the thermally activated processes of defects at elevated temperature. However,\nfor the Na composition, the εᵣ–T curve at 1 kHz exhibits dielectric peak that doesn’t\n0.98\noverlap with other frequencies at TP-R (and higher temperature), which is distinctly\ndifferent from the behavior of the other compositions.\nFurthermore, this composition shows the highest tan(δ) value, reaching\napproximately 30 at 600 °C, which is higher even than that of the Na0.96 composition.\nThis observation appears to contradict the impedance spectroscopy results, which\nindicate that the Na0.96 composition has lower resistivity than that of the Na0.98\ncomposition.\nThe authors are strongly encouraged to remeasure the dielectric data for the\nNa0.98 composition to confirm the accuracy and reproducibility of the results.\nAlternatively, an explanation should be provided to address this discrepancy.\n3. In Figure 7, it is highly recommended to include an expanded view of the high-\nfrequency region to allow readers to clearly observe the semicircular arc corresponding\nto the grain response.\n4. The chemical formula “Na Ca Nb Zr O - ” should be changed to\n0.96x 0.04 0.96 0.04 3\n“NaxCa Nb Zr O - ” to be consistent throughout the manuscript.\n0.04 0.96 0.04 3\nResponse to Reviewer #4 comments:\nThank you very much for your comments and suggestions.\n1. It is well known that two different phase structures exist in pure sodium niobate,\n26\nantiferroelectric Pbma phase and ferroelectric P2 ma phase. This co-existence\n1\ncomplicates the analysis of the relationship between the crystal structure and electrical\nconductivity. To address this challenge, we introduced a minor amount of calcium\nzirconate (CaZrO ) as a dopant. This doping strategy effectively stabilizes the\n3\nantiferroelectric Pbma phase, ensuring that NaNbO adopts a single-phase structure at\n3\nroom temperature and reducing the influencing factors on electrical conductivity\nanalysis (J. Mater. Chem. C 2020, 17, 5681-5691, Dalton Trans. 2015, 44, 10763-10772\nand Appl. Phys. Lett. 2015, 107, 112904). We also added this point in the revised\nmanuscript.\n2. We extend our heartfelt gratitude to the reviewers for their invaluable suggestions.\nIn response, we revisited the measurements for the compositions corresponding to\nNa and Na . The experimental outcomes indicate that both the dielectric response\n0.96 0.98\nand the loss curves of Na display notably higher values. Furthermore, the degree of\n0.96\noverlap in the frequencies of the dielectric peaks for Na is consistent with that\n0.98\nobserved in the other samples (as shown in Fig. 4). To clarify the correspondence\nbetween phase transitions and dielectric response peaks, we supplemented the study\nwith temperature dependent XRD patterns (Fig. 4a). This data directly reveals the phase\ntransition behavior in NCNZ-Nax samples. Specifically, upon heating from room\ntemperature to 700 °C, the NCNZ-Na0.96 sample undergoes a sequential phase\ntransition from orthorhombic (Pbma, Pnmm, Ccmm) to tetragonal (P4/mbm) and finally\nto cubic (Pm-3m) phases. The changes in unit-cell symmetry and volume, which are\nassociated with the distortion and torsion of NbO octahedra, have a substantial impact\n6\non electrical conductivity. By integrating these temperature dependent XRD data with\nthe corresponding data on the temperature dependent dielectric constant and loss,\nwe can precisely analyze the influence patterns of phase transition behavior as a function\nof composition and temperature. We added these results and discussions to the revised\nmanuscript.\n0.96\nDielectric constant and loss of the NCNZ-Na ceramics as a function of temperature.\nx\n3. We extend our sincere gratitude to the reviewers for their invaluable suggestions.\nIn response, we incorporated an enlarged illustration depicting the grain response\nwithin the high frequency regime into Fig. 6.\nFig. 6 The Nyquist plots of (a) NCNZ-Na , (b) NCNZ-Na , and (c) NCNZ-Na at various\n0.96 1.0 1.02\natmosphere, and (d-f) the corresponding Arrhenius diagram.\n28\n4. We extend our heartfelt gratitude to the reviewers for their insightful and\nconstructive feedback. In light of their suggestions, we have rectified the inaccuracy in\nthe chemical formula. Specifically, the original formula has been substituted with\nNa Ca Nb Zr O .\n0.96x 0.04 0.96 0.04 3\nBesides, some modifications were made in the revised manuscript.\n1) Adequate References were cited in the revised manuscript.\n2) We polished the whole manuscript carefully again and tried to avoid any\ngrammatical and formatting errors. All revised contents were marked in red in the\nrevised manuscript.\nWe greatly appreciate for Editors’ enthusiasms and Reviewer’s valuable comments,\nand hope that these corrections can meet them. Thank you very much.\nYours sincerely,\nZhiyong Liu\n29"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have made a good effort to appease my concerns about the stoichiometry and use of CaZrO3 (although the formula should be Nax not Na0.96x for X =0.96 to 1.02). The structural analysis is also much clearer however the presentation and interpretation of the electrical data by DRT and IS is still not convincing for me. The first point is that Figures 5 and 6 are too small to read easily and contain too much information. Secondly they there is a good fit between DRT and IS reponse (as shown in Fig 5 (a) based on open blue circles (IS) and red line (DRT); HOWEVER, the equivalentc circuit used for IS is based primarily on 5 RC elements but there are seven peaks in DRT so this cant be described as a fgood fit (if the expectation is that each RC element gives rise to a peak in DRT). R4C4 is indicated to give rise to a double peak in DRT and thgere is a peak at 10-1s in DRT that has no corresponding RC element. Thirdly, surely to compare the quality of DRT agreement to IS response would be to plot Arrhenius plots log(tau) vs 1/T) for the tau values from DRT in Fig 5 e to show the activation energies agree with those from IS in Fig 6. Finally, the insets in figure 6 are very small and its not clear to me what intercepts have been used to extract the values used in the Arrhenius plots. This is a shame as there is merit in this script but the lack of clarity in the electrical data makes it (in my opion) not worthy of publishing until this is sorted correctly. In my previous report I suggestd plotting the various capacitance values from the IS data versus temperature to try and assist with the assignment of the various arcs. The authors have not done this and I think this was an ommison on there part. As it stands, this script isnt worthy for publication in Nat Comms based on the presentation and analysis of the the electrical data.", "reviewer_3": "All issues have been satisfactorily addressed, and the manuscript is now suitable for publication.", "reviewer_4": "The authors have thoroughly addressed the comments raised by the reviewer. The inclusion of additional experiments, in-depth discussions, and relevant references has substantially strengthened the manuscript. I strongly recommend acceptance of this manuscript in its current form."}, "author_response": "According to the suggestions by reviewer, we submit our revised manuscript with the\ntitle “Tailoring sodium and oxygen mixed-ion conduction in the A-site non-\nstoichiometric NaNbO -based ceramics” to your journal as attached. All revised\n3\ncontents were marked in red in the revision. Our responses to the comments are as\nfollows:\nReviewer #1 Remarks to the Author (s):\nThe authors have made a good effort to appease my concerns about the\nstoichiometry and use of CaZrO (although the formula should be Nax not Na0.96x for\n3\nx =0.96 to 1.02). The structural analysis is also much clearer however the presentation\nand interpretation of the electrical data by DRT and IS is still not convincing for me.\n1. The first point is that Figures 5 and 6 are too small to read easily and contain too\nmuch information.\n2. Secondly they there is a good fit between DRT and IS response (as shown in Fig 5\n(a) based on open blue circles (IS) and red line (DRT); However, the equivalents\ncircuit used for IS is based primarily on 5 RC elements but there are seven peaks in\nDRT so this cant be described as a good fit (if the expectation is that each RC\nelement gives rise to a peak in DRT). R4C4 is indicated to give rise to a double peak\nin DRT and there is a peak at 10-1s in DRT that has no corresponding RC element.\n3. Thirdly, surely to compare the quality of DRT agreement to IS response would be\nto plot Arrhenius plots log(tau) vs 1/T) for the tau values from DRT in Fig 5 e to\nshow the activation energies agree with those from IS in Fig 6.\n4. Finally, the insets in figure 6 are very small and its not clear to me what intercepts\nhave been used to extract the values used in the Arrhenius plots. This is a shame as\nthere is merit in this script but the lack of clarity in the electrical data makes it (in\nmy opion) not worthy of publishing until this is sorted correctly.\n5. In my previous report I suggestd plotting the various capacitance values from the\nIS data versus temperature to try and assist with the assignment of the various arcs.\nThe authors have not done this and I think this was an ommison on there part. As it\n1\nstands, this script isnt worthy for publication in Nat Comms based on the\npresentation and analysis of the the electrical data.\nResponse to Reviewer #1 comments:\nThank you very much for your comments and suggestions.\n1. We sincerely appreciate the reviewers for their insightful comments. In\nresponse, we have revised Fig. 5 and 6 to present the Nyquist curves and DRT data\nmore clearly.\nFig. 5 a Matching part of the impedance spectra with the corresponding components of the DRT\nfunction. b Nyquist plots of the NCNZ-Na ceramics at 500 ℃ and c the corresponding DRT\nx\ndiagram. d The Nyquist plots of NCNZ-Na\n0.96\nsample at different temperatures. e Partial DRT curves\nof the NCNZ-Na sample measured at various temperatures and f normalized DRT curves.\n0.96\n0.96 1.0 1.02\natmosphere, and d-f the corresponding Arrhenius diagram.\n2. We extend our sincere gratitude to the reviewers for their constructive\ncomments. Guided by the frequencies of the relaxation peaks manifested in the\nDistribution of Relaxation Times (DRT), we designed a new equivalent circuit and\nconducted fitting. As shown in Fig. 5a, the first semicircle of the complex impedance\nspectra corresponds to the grain effect of NCNZ-Na ceramics. The characteristic\nx\ncapacitance value is 2.2458×10-11 F·cm-1 and the frequency at the maximum value of\nthe semicircle is 1.06×106 Hz, which proves this statement. The second semicircle is\ncomposed of two arcs, each corresponding to an RC element. The characteristic\ncapacitance of the first arc is 1.6990×10-10 F·cm-1 and the characteristic capacitance of\nthe second arc is 1.3857×10-10 F·cm-1. Both of these arcs are attributed to the grain\nboundary effect, which is consistent with the result of the C' spectra (Fig. S7b).\nTemperature-dependent capacitances of grain and grain boundary (Fig. S8) align well\nwith the dielectric spectra (Fig. 4b-g). Notably, the capacitance of grain boundary is\napproximately 5×10-10 F·cm-1 and exhibit temperature independent, whereas the\ncapacitance of grain decreases significantly as temperature increases (Fig. S8). The last\npolarization tail consists of four parts that can be classified into two categories: one\nwith characteristic capacitances ranging from 3.9537×10-7 to 9.0655×10-7 F·cm⁻¹ and\n3\nfrequencies from 2860 to 274 Hz. The other with characteristic capacitances spanning\nfrom 1.4754×10-6 to 1.3352×10-6 F·cm⁻¹ and frequencies from 42.8 to 8.7 Hz. The\nformer category is associated with the ohmic contact resistance at the\nelectrolyte/electrode interface or the high relaxation steps of the electrode fabrication\nprocess. In contrast, the latter category is ascribed to the electrode level, given its\nrelatively larger capacitance and lower frequency. We added these results and\ndiscussions to the revised manuscript.\n3. We are extremely grateful to the reviewers for their insightful comments. By\nextracting the relaxation time (τ) associated with the grain boundary peak and applying\nthe Arrhenius equation for fitting, the activation energy E can be determined:\naf\nτ = τ exp(-E /kT) (1)\n0 af\nHere, T denotes the temperature in Kelvin, and k stands for the Boltzmann constant. In\nthe context of the distribution of relaxation times (DRT), the relaxation peak\ncorresponds to a unique relaxation process within the conductor, and its associated\nrelaxation time serves as the energy barrier that must be overcome during this\nconductance process. The activation energy (E ) offers valuable insights into the energy\naf\nbarrier encountered by carriers during their migration. Subsequently, the total ionic\nconductivity and grain boundary ionic conductivity were calculated using the total\nresistance and grain boundary resistance, respectively, which were obtained from the\nintercepts of the grain boundary and grain semicircles with the x-axis (Fig. S11). The\nactivation energy (E ) is calculated using the Arrhenius method:\na\nσ = σ exp(-E /kT) (2)\n0 a\nHere, T denotes the temperature in Kelvin, and k stands for the Boltzmann constant.\nThe activation energy E derived from the fitting of conductivity serves as an indicator\na\nof the variations in the energy barrier that carriers must jump during their migration. As\nshown in Fig. S10, the values of E , total E , and grain boundary E obtained through\naf a a\nfitting the DRT grain boundary relaxation peak, total conductivity, and grain boundary\nconductivity are presented. The agreement between the values of the activation energies\naf a\nprovides evidence for the consistency and rationality of the relaxation time (DRT) and\nNyquist analysis distributions. Although grain boundaries are the primary factors\ninfluencing the total conductivity, the fact that the total conductivity is also influenced\nby grains leads to slight differences in their activation energies (Since the response data\nof grain boundaries disappear at high temperatures, the consistency issue is described\nby the values of the activation energies E and E obtained by fitting the relaxation time\naf a\nand conductivity of grain boundaries). We added these results and discussions to the\nrevised manuscript.\nFig. S10 Arrhenius plot corresponding to the bulk relaxation peak (DRT) and Nyquist plot.\n4. We would like to express our sincere gratitude to the reviewers for their\nvaluable comments. To enable readers to more clearly understand the specific process\nof impedance value extraction, we performed fitting using Zview. Meanwhile, we\nplotted the complete semicircles to allow readers to clearly identify the intercept\npositions. We added these results to the revised manuscript.\nFig. S11 Demonstration of the fitting of the intercepts of the Nyquist semicircles of NCNZ-Na\nx\nceramics with the x-axis.\n5\n5. We sincerely appreciate the reviewers for their insightful comments. The\ntemperature dependence of capacitance was investigated by utilizing the impedance\ndata corresponding to grains and grain boundaries (Fig. S11). For the separate analysis\nof the grain and grain boundary data, an equivalent circuit composed of two parallel\nRC elements was employed for fitting analysis. The impedance can be expressed by the\nfollowing equation:\n−1 −1\n1 1\n𝑍′ = ( +𝑗𝜔𝐶 ) +( +𝑗𝜔𝐶 ) (3)\n𝑅 𝑔 𝑅 𝑔𝑏\n𝑔 𝑔\n𝑀∗ = 𝑗𝜔𝐶 𝑍∗ (4)\nby combining with eq. (3) and (4) as follows:\n2 2\n𝐶 (𝜔𝑅 𝐶 ) 𝐶 (𝜔𝑅 𝐶 )\n𝑀′ = 0 ( 𝑔 𝑔 )+ 0 ( 𝑔𝑏 𝑔𝑏 ) (5)\n𝐶 2 𝐶 2\n𝑔 1+(𝜔𝑅 𝐶 ) 𝑔𝑏 1+(𝜔𝑅 𝐶 )\n𝑔 𝑔 𝑔𝑏 𝑔𝑏\n𝐶 𝜔𝑅 𝐶 𝐶 𝜔𝑅 𝐶\n𝑀\" = 0 ( 𝑔 𝑔 )+ 0 ( 𝑔𝑏 𝑔𝑏 ) (6)\n𝐶 2 𝐶 2\n𝑔 1+(𝜔𝑅 𝐶 ) 𝑔𝑏 1+(𝜔𝑅 𝐶 )\n𝑔 𝑔 𝑔𝑏 𝑔𝑏\nCombination of the electric modulus formalisms since each parallel RC element gives\nrise to a semicircle in the complex plane (M´ vs. M´´) is shown in Fig. S8a-c. The high\nfrequency arcs of complex plane are associated with Cg-1+Cgb-1, whereas the low\nfrequency intercepts are Cgb-1. The temperature dependences of the grain and grain\nboundary capacitance values obtained from fitting at various temperatures are shown\nin Fig. S8d-e. The curve of the grain capacitance value changing with temperature is\nconsistent with the trend of the dielectric spectra in the Fig. 4b-g, while the change of\nthe grain boundary capacitance with temperature remains relatively stable. Meanwhile,\nthe dielectric constant calculated from the grain capacitance is consistent with the\nvalues in Fig. 4b-g. These results indicate that the grains are ferroelectric, while the\ngrain boundaries are non-ferroelectric, and they can be distinguished from the\ncapacitance data: the grain boundary effect manifests as temperature-independent\ncapacitance, whereas the grain effect shows significant temperature dependence.\nx\n1.0, 1.02) ceramics.\nBesides, some modifications were made in the revised manuscript.\n1) Adequate References were cited in the revised manuscript.\n2) We polished the whole manuscript carefully again and tried to avoid any\ngrammatical and formatting errors. All revised contents were marked in red in the\nrevised manuscript.\nWe greatly appreciate for Editors’ enthusiasms and Reviewer’s valuable comments,\nand hope that these corrections can meet them. Thank you very much.\nYours sincerely,\nZhiyong Liu\n7"}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have done a good job this time in responding to previous comments about IS and DRT analysis. The figures in the script are clearer and the additional SI on the analysis is useful."}, "author_response": ""}]

Decision letter