Evaluating the Rate-determining Steps of Oxygen Permeation in Ba_0.5La_0.5FeO_3−δ Perovskite

Abstract

Perovskite oxides obtained from Ba_1−xLa_xFeO_3−δ (BLF) are considered beneficial materials for electrodes of solid oxide fuel cells and oxygen permeation membranes because of their high oxygen permeability, which is a criterion of oxide ion (O²⁻)-electronic mixed conductivity. In this paper, the prime focus was to understand the oxygen permeation mechanism through surface exchange and bulk diffusion of the Ba_0.5La_0.5FeO_3−δ (BLF55) sample. The permeated oxygen flux displayed higher than that of the typical mixed conductor La_0.6Sr_0.4Co_0.2Fe_0.8O_3−δ (LSCF), which was explored simultaneously with corresponding oxygen chemical potentials employing an especial experimental setup. This study found that the surface exchange reaction on the oxygen-lean side was the rate-determining step (RDS) of the oxygen permeation below 800 °C, resulting from lower hole concentration on the oxygen-lean side surface. Enhancing the charge transfer from the surface oxygen by increasing hole concentration is a prime important strategy to improve the surface exchange reaction.

1. Introduction

The research focused on the mixed conductivity of electron and oxide ion through perovskites presents high attention across several application fields, for example, electrodes used in solid-oxide fuel cells (SOFCs), oxygen permeation membranes (OPMs), and catalysts for advanced oxidation processes.^1–5 Basically, when utilized as the application, ABO₃-type perovskites offer excellent chemical and thermal stability, high structural/compositional flexibility, and chemical as well as thermal robustness.^1,2,6 In particular, the mixed electron and oxygen-ion conducting (MEIC) Co and/or Sr-contained materials have many potentialities at reduced temperatures when used in the application. But, according to recent studies,⁷ the presence of Co and/or Sr leads to a number of challenging issues. Such as, Co-based materials show high combined thermal and chemical expansion coefficients owing to the changing redox state of Co. On the other hand, the segregation of Sr on the material surface and its reacting trend with extrinsic surface impurities limit their practical use.

Ba-Fe based perovskite is a possible candidate of SOFCs as Co/Sr free MEIC with high oxygen permeability,⁸ we also observed that Ba_0.5La_0.5FeO_3−δ (BLF55),⁹ which is free from Co and Sr, has high oxygen permeability (0.25 µmol/cm²/s) at 950 °C, comparable to that of La_0.65Ca_0.35FeO_3−δ (LCaF) (0.27 µmol/cm²/s).¹⁰ Thus, in comparison to La_0.6Sr_0.4Co_0.2Fe_0.8O_3−δ (LSCF),¹⁰ the BLF55 may have a high/comparable potential for the cathode of SOFCs, OPMs, etc. Although the oxygen permeation flux of BLF55 was investigated, the rate-determining step of oxygen permeation still remains unclear for the Ba-La based ferrites.

Figure 1 portrays a schematic diagram of oxygen permeation processes through the MEIC solid. In fact, oxygen permeates due to the difference in oxygen partial pressure (P_O2) between the membrane surfaces, where permeation follows from the high to low oxygen partial pressure side. Figure 1 clearly shows that permeation processes involved three steps; surface exchange at the high P_O2 side (A), bulk diffusion through a membrane (B), and surface exchange at the low P_O2 side (C). In step A, the oxygen adsorption or incorporation happened to diffuse over the sample surface and dissociate to form O²⁻ as the reaction Eq. 1.¹¹ The O²⁻ then transport through dense membrane following the step B. Finally, in step C, the permeated O²⁻ associates to form oxygen (O₂) following the reaction Eq. 2.¹¹ These three processes occurred consecutively and can be evaluated considering the especial experimental setup, discussed in the next section.   

\begin{equation} \text{O$_{2}$} \to \text{2O$_{\text{ads}}$} + \text{4e$^{-}$} \to \text{2O$^{2-}$} \end{equation} (1)

  

\begin{equation} \text{O$^{2-}$} + \text{O$^{2-}$} \to \text{O$_{2}$} + \text{4e$^{-}$} \end{equation} (2)

Figure 1.

Oxygen permeation processes through the MEIC oxide membrane.

It is of the utmost importance to know details of the oxygen permeation process in relation to the oxygen partial pressure gradient because these factors are necessary for developing new highly oxygen-permeable MEIC oxides. In this research, we paid attention on the detailed investigations of J_O2 and oxygen chemical potential through the BLF55 sample. This investigation could precisely suggest the foremost contribution(s) of rate-determining steps of oxygen permeation through the BLF55 sample. This detailed study of rate-determining steps would be the first report to provide a clear insight of oxygen permeation processes through the BLF sample.

2. Experimental Part

Ba_0.5La_0.5FeO_3−δ perovskite was prepared considering the steps of the citrate-based liquid mixing method.¹² High-pure oxide of BaCO₃ (99.9 %, Kojundo Chemical Laboratory Co. Ltd.) and nitrates of La(NO₃)₃·6H₂O (99.9 %, Fujifilm Wako Pure Chemical Corp.) and Fe(NO₃)₃·9H₂O (99.9 %, Fujifilm Wako Pure Chemical Corp.) were collected to prepare the particular stoichiometry. In addition to the citric acid, ethylene glycol was used as a fuel and complexant agent. The sample preparation process in this investigation was the same as the previous preparation of this BLF55 sample⁹ and our recent work.¹³ The obtained mixed solution was heated with a pyrex glass flasks to obtain a dark-red color gel at 100 °C. Employing continuous heat treatment, solid ash was obtained at 450 °C. The degreased temperature was 700 °C for 10 h under ambient air. Following the same procedure, the acquired black powder sample was calcined for 10 h at 1000 °C. Thereafter, the calcined powder was ball milled in presence of acetone and zirconia balls. Operating the uniaxial hydraulic pressing system, a green pellet membrane was designed by adjusting a pressure of 144 MPa for 2 minutes. For getting a uniform dense sample, cold isostatic pressure was executed for 2 minutes under the pressure of 300 MPa. Finally, the obtained pellet membrane was sintered at 1350 °C for 10 h under ambient air, confining temperature program rate of 5 °C/min.

Pure phase of the obtained perovskite sample was assured using the ordinary x-ray powder diffraction (XRPD) study. The x-ray powder diffractometer (RAD-C; Rigaku Corp.) with CuKα radiation (λ = 1.5418 Å = 154.18 pm) was considered to obtain room temperature XRPD data, where the voltage of 40 kV and current of 20 mA was considered. The recorded diffraction data was used for Rietveld refinement analysis to confirm the phase purity using freely accessible FULLPROF software.¹⁴ A systematic process of refinement was followed during the refinement.¹⁵

To confirm the homogeneous distribution of compositional atoms in sintered pellet sample, energy dispersive x-ray (EDX) analysis was considered. The polished surface was used for getting distributional information on the sample surface and cross-section was used for the distribution in sample depth.

Figure 2 represents the experimental setup for investigating the oxygen permeation through the membrane bulk and oxygen activity on both oxygen-rich and lean surfaces. A pellet sample (∼13 mmφ diameter) was set in between the alumina tubes, Figs. 2d and 2e. An Ag-ring was used for sealing the oxygen lean (upper) surface of the sample and exposed to a reduced atmosphere condition, where the oxygen partial pressure (P_l) was varied with the different He flow rates of 5–40 standard cubic centimeters per minute (sccm). The proper gas sealing was confirmed at 960 °C with the flow of 20 sccm helium (He) gas, where the lower surface was in contact with ambient air condition (P_h = 0.21 atm ≡ 21 kPa). The measurement was conducted at a temperature range of 950–700 °C. A gas chromatograph (Varian 490-GC, SpectraLab Scientific Inc., Canada) was used to monitor the oxygen permeation flux (J_O2) within the explored conditions. The J_O2 was estimated using the equations discussed in the literature.¹⁶

Figure 2.

Schematic layout for evaluating oxygen diffusion activity at sample surfaces: (a) sample with smooth surfaces; (b) Ag-ring for sealing; (c) ceramic ring to support sample; (d, e) He flow alumina tube, placed 1–2 mm above on the sample surface; (f, g) dense alumina tube for gas sealing; (h) box furnace; (i, j) cone shape YSZ oxygen sensor; (k, l) Pt paste to connect YSZ sensor and gold wire; (m, n) gold electrode; (o, p) gold wire; (q, r) multimeter for investigating EMF and (s) resin for gas sealing.

The oxygen sensor (yttria-stabilized zirconia, YSZ) was used to determine the oxygen chemical potential (OCP), Figs. 2i and 2j. The OCP on both oxygen lean and rich surfaces was simultaneously measured while investigating the J_O2 at different temperatures with a varying He flow rate. The electromotive force (EMF) between the gold electrode and YSZ sensor on the surfaces was recorded using a voltmeter (M3500A; PICOTEST Corp.), where data was considered for the temperature range of 950–700 °C with a 50 °C interval. At each temperature, the most stable data was noted for the flow rates of 5–40 sccm. In this study, two different thick samples (1.0 and 1.5 mm) were used. Using a similar experimental setup, our research group previously described the OCP for the LCaF membrane.¹⁷

The EMF measured by the YSZ sensor on the oxidized and reduced surfaces are denoted by E_s(rich) and E_s(lean), respectively. These two EMFs were generated due to dioxygen activity on the corresponding sides of sample surfaces and can be explained following the Nernst equation below^17,18   

\begin{equation} E_{\text{s(rich)}} = \frac{RT}{4F}\ln\frac{b_{1}}{b'_{1}} = \frac{\Delta \mu_{\text{O}2}^{\text{s(rich)}}}{4F} \end{equation} (3)

  

\begin{equation} E_{\text{s(lean)}} = \frac{RT}{4F}\ln\frac{b'_{2}}{b_{2}} = \frac{\Delta \mu_{\text{O}2}^{\text{s(lean)}}}{4F} \end{equation} (4)

Where b₁ and b₂ represent the dioxygen activity under ambient air and He gas atmospheres, respectively. The notations $b'_{1}$ and $b'_{2}$ indicate the dioxygen activity at the samples surfaces of oxygen-rich and oxygen lean, respectively. $\Delta \mu_{\text{O}2}^{\text{s(rich)}}$ indicates the OCP drop at the oxygen-rich surface and $\Delta \mu_{\text{O}2}^{\text{s(lean)}}$ signifies the OCP drop at the oxygen-lean surface. The Faraday and universal gas constants and temperature are represented in the equation by F, R, and T, respectively.

The bulk EMF (E_bulk) corresponds to the oxygen activity through the volume of a sample can be estimated by the equation^17,18   

\begin{equation} E_{\text{bulk}} = \frac{RT}{4F}\ln\frac{b'_{1}}{b'_{2}} = E_{\text{tot}} - E_{\text{s(rich)}} - E_{\text{s(lean)}} = \frac{\Delta \mu_{\text{O}2}^{\text{bulk}}}{4F} \end{equation} (5)

where $\Delta \mu_{\text{O}2}^{\text{bulk}}$ represents the OCP drop through the sample.

The E_tot can be calculated from the ambient air pressure (P_h) and the oxygen partial pressure (P_l) at a particular temperature recorded by gas chromatography as equation below^17,18   

\begin{equation} E_{\text{tot}} = \frac{RT}{4F}\ln\frac{P_{h}}{P_{l}} \end{equation} (6)

The total OCP drop ($\Delta \mu_{\text{O}2}^{\text{tot}}$) through the membrane can be expressed as^17,18   

\begin{equation} \Delta \mu_{\text{O}2}^{\text{tot}} = \Delta \mu_{\text{O}2}^{\text{bulk}} + \Delta \mu_{\text{O}2}^{\text{s(rich)}} + \Delta \mu_{\text{O}2}^{\text{s(lean)}} \end{equation} (7)

Based on the estimated OCP, an indication of the rate-determining steps (RDS) of oxygen permeability can be studied. Besides, using the OCP values, a critical parameter (B_c) can be defined as $B_{\text{c}} = \frac{\Delta \mu_{\text{O}2}^{\text{s(rich)}} + \Delta \mu_{\text{O}2}^{\text{s(lean)}}}{\Delta \mu_{\text{O}2}^{\text{bulk}}}$, $B_{\text{c}(\text{rich})} = \frac{\Delta \mu_{\text{O}2}^{\text{s(rich)}}}{\Delta \mu_{\text{O}2}^{\text{bulk}}}$ and $B_{\text{c}(\text{lean})} = \frac{\Delta \mu_{\text{O}2}^{\text{s(lean)}}}{\Delta \mu_{\text{O}2}^{\text{bulk}}}$. When 0 < B_c < 0.5, the RDS of J_O2 is dominated by oxygen bulk diffusion; when 0.5 < B_c < 1.5 (≈ 1), the RDS of J_O2 is controlled by both bulk diffusion and surface exchange of oxygen; and when B_c > 1.5, the RDS of J_O2 is governed by oxygen surface exchange.¹⁷

3. Results and Discussion

Figure 3a displays the XRPD pattern of the BLF55 sample. The crystalline structure was confirmed cubic perovskite without forming any irrelevant phase according to the ICSD database.¹⁹ Our previous study concerning synchrotron XRPD and literature also suggest a single phase formation.^20,21 The Rietveld refinement pattern of our previous synchrotron XRPD⁹ and the normal XRPD data (in this study) further assures the phase purity with cubic perovskite structure and Pm-3m phase of this sample, Fig. 3b. The estimated lattice constant is 3.9416(2) Å, which is comparable with the literature.²¹ Moreover, the low refinement parameters (χ = 1.44, R_wp = 19 %, R_p = 11.5 %) indicate admissible fitting. The high relative density (>95 %) and dense morphology of the prepared sample were also confirmed in our previous study of this sample.⁹

Figure 3.

(a) Room temperature XRPD outline of BLF55 and (b) corresponding Rietveld refinement pattern.

The homogeneous distribution of the atoms of the prepared sample was studied through EDX. To confirm the compositional homogeneity, EDX was performed on both the sample surface and cross-section. The surface EDX profile of this composition was reported in our earlier study.⁹ Figure 4 shows the EDX mapping layout of both surface and cross-section. The patterns look like almost similar and suggest the homogeneous distribution of compositional atoms on both surface and sample depth. In fact, there is no major agglomeration of atoms in the mappings. Thus, the depth homogeneity of atoms was confirmed in the prepared Ba_0.5La_0.5FeO_3−δ sample.

Figure 4.

EDX mapping on both surface and cross-section.

Figure 5a exhibits the Arrhenius layout of J_O2 for both thicknesses of BLF55. The J_O2 under a fixed pressure of ln P_l = −4.5 atm at higher temperatures than 800 °C was considered, where flux permeability was significantly reduced for the 1.5 mm sample relative to the permeability of the 1.0 mm sample. Inversely, below 800 °C, the slope of the 1.0 mm thickness sample displays a steeper. This unlike trend of flux between the two different thick samples suggests that the permeation RDS of the samples are not the same. Thus, to understand the difference between the two samples, a detailed RDS study is demanded.

Figure 5.

(a) Arrhenius layout of the J_O2 with ln P_l = −4.5 atm, where solid line indicates the deviation trend of data; the critical parameters B_c, B_c(lean), and B_c(rich) of (b) 1.0 mm and (c) 1.5 mm thickness samples for the He flow rate of 20 sccm.

Figures 5b and 5c reveal the changing trends of critical parameters B_c, B_c(lean), and B_c(rich) with a temperature of two different thickness samples. For both cases, B_c(lean) is much higher than that of B_c(rich) within the studied temperature range. On the other hand, both B_c and B_c(lean) values are close to unity (∼1) in all measured temperature conditions (except below 800 °C of 1 mm thick sample). This result suggests that the RDS of oxygen permeation is mixed controlled by bulk diffusion and surface exchange reaction for both samples. The MEIC oxides of LCaF¹⁷ and La_0.5Sr_0.5Fe_0.7Co_0.3O_3−δ²² also show a similar mixed controlled process of oxygen permeation. However, below 800 °C, the value of the parameters B_c and B_c(lean) are close to unity for the sample with a thickness of 1.5 mm but they are different for the 1 mm thick sample. In fact, the l mm thick sample shows that the B_c and B_c(lean) values are higher than 1.5 in the temperature range of 800–700 °C, signifying the surface exchange reaction is dominated on the lean side. Thus, 800 °C is possibly a critical temperature for the change of oxygen permeation RDS in BLF55 with a 1 mm thickness. It is considered that the time required for traveling of O²⁻ through the bulk of 1 mm sample is shorter compared to case of 1.5 mm thick sample. For the mixed controlled processes, both bulk diffusion and surface exchange rates are almost the same. The change of RDS of 1 mm sample below 800 °C signifies that the surface exchange reaction takes longer time compared to the bulk diffusion. This could be a critical change as discussed earlier. Moreover, the change of RDS with temperature also indicates that non-linear relation of oxygen permeability and OCP with temperature, which will be discussed later on in this study. But this RDS change also explains the temperature dependences of J_O2 between the two samples, as shown in Fig. 5a.

Figures 6a and 6b illustrate the relation of J_O2 with $\Delta \mu_{\text{O}2}^{\text{bulk}}/RT$ for the BLF55 sample, (a) 1 mm and (b) 1.5 mm thickness. No specific relation was obtained between the J_O2 and $\Delta \mu_{\text{O}2}^{\text{bulk}}/RT$ with a different flow rate of He, which indicates that J_O2 doesn’t follow Wagner’s equation for both thickness samples.¹⁷ Figures 6c and 6d display the relation between the B_c vs. $\Delta \mu_{\text{O}2}^{\text{bulk}}/RT$ for (c) 1 mm and (d) 1.5 mm thickness samples. In both cases, most of the data lie within B_c ≈ 0.5–1.5 and exceeds for 30–40 sccm. The absence of Wagner’s law concerning J_O2 with $\Delta \mu_{\text{O}2}^{\text{bulk}}/RT$ and the larger value of B_c (higher than 1.5) suggests that RDS is the mixed controlled or surface exchange reaction.

Figure 6.

Variation of J_O2 with $\Delta \mu_{\text{O}2}^{\text{bulk}}/RT$ for the (a) 1.0 mm and (b) 1.5 mm; and B_c with $\Delta \mu_{\text{O}2}^{\text{bulk}}/RT$ for the (c) 1.0 mm and (d) 1.5 mm thickness samples with different He flow rates of 5 to 40 sccm. The markers with red, blue, dark brown, pink, green, and dark yellow colors correspond to the temperatures of 950, 900, 850, 800, 750, and 700 °C, respectively.

The RDS of oxygen permeation through the membrane can further be analyzed by the OCP profile. Figure 7 shows the OCP at the different investigated temperatures with a He flow rate of 20 sccm. For the 1 mm thick BLF55 membrane, there was no significant change in OCP on the oxygen-rich side or through bulk in the investigated temperature range. But the OCP on the oxygen-lean side ($\Delta \mu_{\text{O}2}^{\text{s(lean)}}$) changed with temperature, where it is almost the same as $\Delta \mu_{\text{O}2}^{\text{bulk}}$ from 850–950 °C. This result indicates that the RDS of J_O2 is governed by the mixed regime of surface exchange and bulk diffusion within the temperature range of 850–950 °C. Moreover, at ≤800 °C, the OCP on the oxygen lean surface remarkably increased with lowering the temperature, indicating oxygen exchange is controlled by the oxygen lean surface. Because below 800 °C, O²⁻ surface exchange on the oxygen lean surface takes a longer time over the bulk diffusion. In fact, ∼800 °C could be a critical temperature for changing the OCP of the 1 mm thickness sample. The OCP values are close between 700 and 750 °C, indicating that the majority of changes in RDS occurred between 800 and 750 °C. Thus, the temperature of 800 °C can be concluded as the critical temperature concerning the RDS change, the same conclusion was also obtained in Fig. 5. Contrarily, for the 1.5 mm thick sample, both $\Delta \mu_{\text{O}2}^{\text{bulk}}$ and $\Delta \mu_{\text{O}2}^{\text{s(lean)}}$ are close within the investigated temperature range, indicating that the RDS of J_O2 is controlled by the mixed regime of surface and bulk diffusion for this thickness. This outcome further demonstrates that the RDS is mixed controlled for the 20 sccm He flow rate and supports earlier discussion.

Figure 7.

The outline of OCP through the BLF55 perovskite membrane with thickness of (a) 1 mm and (b) 1.5 mm within the temperature range of 700–950 °C.

The process of oxygen adsorption and desorption on the MEIC surface was discussed earlier.^17,23–25 Considering the Butler–Volmer formalism, the desorption of O₂ and the charge transfer mechanism can be understood using the equation below.²³   

\begin{equation} J_{\text{O2}} = A\left(\exp \left(\frac{1 - \beta}{2RT}\Delta \mu_{\text{O2}}^{\text{s}} \right) -\exp \left(\frac{-\beta}{2RT}\Delta \mu_{\text{O2}}^{\text{s}} \right) \right)^{1/(1-n)} \end{equation} (8)

where the constant A is involved with the oxygen surface exchange coefficient k and β reflects the asymmetric energy barrier for transporting solid/gas boundaries. $\Delta \mu_{\text{O}2}^{\text{s}}$ is OCP drop within the sample surface ($\Delta \mu_{\text{O}2}^{\text{s(lean)}}$ or $\Delta \mu_{\text{O}2}^{\text{s(rich)}}$) and gas. The parameter n is equivalent to $\frac{\Delta k}{\Delta \ln P_{\text{O}2}}$. If the value of OCP drop on surface is much higher compared to the RT, i.e., $\Delta \mu_{\text{O}2}^{\text{s}} \gg RT$, the above equation can be simplified as below   

\begin{equation} J_{\text{O}2} = A\exp \left(\frac{m}{RT} \Delta \mu_{\text{O}2}^{\text{s}}\right), \text{where}\ m = \frac{(1 - \beta)}{2(1 - n)} \end{equation} (9)

Taking log natural in both sides of the above equation,   

\begin{equation} \ln J_{\text{O}2} = \frac{m}{RT}\Delta \mu_{\text{O}2}^{\text{s}} + \ln A \end{equation} (10)

To study the oxygen surface exchange activity on the oxygen lean face, ln J_O2 vs. $\Delta \mu_{\text{O}2}^{\text{s(lean)}}$ plot was shown in Figs. 8a and 8b. Figures 8c and 8d show the B_c against $ \Delta \mu_{\text{O}2}^{\text{s(lean)}}/RT$. There is a sharp upturn of B_c values after 1.5, which signifies that the RDS of oxygen permeation changed from the mixed controlled to surface exchange due to the high flow rate of He gas. Comparing Figs. 8a and 8c; and Figs. 8b and 8d, a proportional relationship of Eq. 10 was obtained for the high value of B_c (greater than ∼1.5). In this condition, the obtained result also proposes that the RDS is surface exchange.

Figure 8.

Variation of ln J_O2 vs. $\Delta \mu_{\text{O}2}^{\text{s(lean)}}/RT$ for the (a) 1.0 mm and (b) 1.5 mm; and B_c with $\Delta \mu_{\text{O}2}^{\text{s(lean)}}/RT$ for the (c) 1.0 mm and (d) 1.5 mm samples under the condition of He flow rate of 5 to 40 sccm. The markers with dark brown, pink, green, and dark yellow colors correspond to the temperatures of 850, 800, 750, and 700 °C, respectively. The dotted lines indicate fitting.

The fitting by the Eq. 10 yields the parameter m, whenever B_c exceeds 1.5. From the different temperatures fitting of 1 mm thickness sample, the m value (corresponding slop) was 0.04, 0.019, 0.008, and 0.003 for the 850, 800, 750, and 700 °C, respectively. For the MEIC materials, the parameter n was studied within the range of 0.3–0.5.^23,25 A similar value of n was considered for the LCaF sample. Considering the same speculation of MEIC materials, the value of β was obtained ∼1. Similarly, for the 1.5 mm thickness sample, the m value yields 0.019, 0.023, 0.094, and 0.044 for the 850, 800, 750, and 700 °C, respectively. Moreover, the evaluated β value is ∼1. This value could be consistent because the value evaluated in the previous studies was 0 to 1.^23,25 The obtained β value of both thickness samples suggest that the concentration of holes is very low but oxygen vacancy is high at the oxygen lean surface of BLF55, in comparison to the LCaF sample.¹⁷

This fact can explain why the RDS of BLF with both thicknesses at 800 °C is a mixture of both bulk diffusion and surface exchange reaction, although the RDS of LCaF with 1 mm (1.2 mm) thickness is the mixture (the bulk diffusion), at the same temperature.

4. Conclusions

This study discusses the oxygen permeation through the Ba_0.5La_0.5FeO_3−δ membrane and its RDS. An experimental setup was considered that allows the evaluation of oxygen permeation RDS pursuant to the measurement of oxygen permeability along with oxygen chemical potential at sample surfaces. The oxygen activity investigation on both oxygen lean and rich surfaces indicates that RDS of oxygen permeation through membrane over 800 °C is controlled by a mixed regime of oxygen surface exchange and bulk diffusion, where the critical parameters B_c, B_c(lean), and B_c(rich) criteria were taken into account. In fact, the oxygen permeation processes are more or less similar for both 1 mm and 1.5 mm thickness samples above 800 °C. However, RDS clearly changed from the mixed regime to the surface exchange reaction for the 1 mm thickness sample. The β value estimated under the RDS of surface exchange reaction was close to unity indicating that RDS is charge transfer required for the oxygen molecule desorption on the lean side. The increase in hole concentration on this side is a significant key to improve the surface exchange reaction.

Acknowledgments

We thank the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan to support this research. This study received funds from the New Energy and Industrial Technology Development Organization (NEDO) (Grant Number JPNP20003).

CRediT Authorship Contribution Statement

Md Saiful Alam: Data curation (Lead), Investigation (Lead), Writing – original draft (Lead), Writing – review & editing (Equal)

Isao Kagomiya: Funding acquisition (Lead), Supervision (Lead), Writing – review & editing (Equal)

Ken-ichi Kakimoto: Resources (Supporting)

Conflict of Interest

There are no financial or personal conflicts of interest that might have seemed to affect the scientific activity described in this article.

Funding

New Energy and Industrial Technology Development Organization: JPNP20003

Footnotes

The content of this paper has been published by Md Saiful ALAM as a PhD thesis at Nagoya Institute of Technology in 2023.

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