Polarization-Induced Interface and Sr Segregation of in Situ Assembled La0.6Sr0.4Co0.2Fe0.8O3-δ Electrodes on Y2O3-ZrO2 Electrolyte of Solid Oxide Fuel Cells

Visualizing Interface Degradation of Solid Oxide Cell

Solid oxide electrolysis and fuel cells (SOEC/SOFC) can help achieve global net-zero carbon emissions. Understanding the degradation mechanisms of the cells and their components is crucial for enhancing longevity to ensure the cost-effectiveness of large-scale applications. Traditional degradation research relies on post mortem analysis, limiting our ability to elucidate dynamic changes and their separate contributions. The work introduces an operando environmental transmission electron microscope (ETEM) approach to investigate degradation processes in SOEC/SOFC. As a proof-of-concept, degradation experiments were conducted on cells composed of lanthanum-strontium-cobalt oxide (LSC) electrodes and an yttrium-stabilized zirconia (YSZ) electrolyte, where the symmetric LSC-YSZ-LSC cells are subjected to strong polarization, in 2.7 mbar O2, at an operation temperature of 700 °C inside an ETEM. The results highlight the capability of real-time monitoring of structural and compositional changes of active solid oxide cells through scanning transmission electron microscope imaging and electron energy loss spectroscopy analysis. Additional post mortem TEM and energy-dispersive spectroscopy confirmed previously reported decomposition of the negatively polarized LSC electrode and crack formation on the anodic side. Thereby, this work demonstrates the feasibility of using operando ETEM for in-depth, nanoscale observation of SOEC/SOFC degradation during cell operation.

Surface Chemistry Modulation of BaGd0.8La0.2Co2O6-δ As Active Air Electrode for Solid Oxide Cells

Modulation of the surface chemistry of air electrodes makes it possible to significantly improve the electrocatalytic performance of solid oxide cells (SOCs). Here, the surface chemistry of BaGd0.8La0.2Co2O6-δ (BGLC) double perovskite is modulated by treatment in an acidic citric acid solution. The treatment leads to corrosion on the surface of BGLC particles, and the effect is dependent on the acidity of the solution. As the acidity of solution is low, Ba cations are selectively dissolved out of the BGLC surface, while as the acidity increases, the corrosion becomes more homogeneous. The Ba surface deficiency remarkably increases the concentration of surface oxygen vacancies and electrocatalytic activity of BGLC. To avoid the loss of Ba-deficient surface during the conventional high temperature sintering process, a sintering-free fabrication route is utilized to directly assemble the Ba-deficient BGLC powder into an air electrode. A single cell with the surface Ba-deficient BGLC electrode shows a peak power density of 1.04 W cm-2 at 750 °C and an electrolysis current density of 1.48 A cm-2 at 1.3 V, much greater than 0.64 W cm-2 and 1.02 A cm-2 of the cell with the pristine BGLC, respectively. This work provides a simple and effective surface chemistry modulation strategy for the development of an efficient air electrode for SOCs.

Development of Nanostructured Lanthanum Strontium Cobalt Ferrite/Gadolinian-Doped Ceria Composite Electrodes of Solid Oxide Cells Formed by In Situ Polarization

In the development of nanoscale oxygen electrodes of high-temperature solid oxide cells (SOCs), the interface formed between the nanoelectrode particles and the electrolyte or electrolyte scaffolds is the most critical. In this work, a new synthesis technique for the fabrication of nanostructured electrodes via in situ electrochemical polarization treatment is reported. The lanthanum strontium cobalt ferrite (LSCF) precursor solution is infiltrated into a gadolinia-doped ceria (GDC) scaffold presintered on a yttria-stabilized zirconia (YSZ) electrolyte, followed by in situ polarization current treatment at SOC operation temperatures. Electrode ohmic and polarization resistances decrease with an increase in the polarization current treatment. Detailed microstructure analysis indicates the formation of a convex-shaped interface between the LSCF nanoparticles (NPs) and the GDC scaffold, very different from the flat contact between LSCF and GDC observed after heating at 800 °C with no polarization current treatment. The embedded LSCF NPs on the GDC scaffold contribute to the superior stability under both fuel cell and electrolysis operation conditions at 750 °C and a high peak power density of 1.58 W cm-2 at 750 °C. This work highlights a novel and facile route to in situ construct a stable and high-performing nanostructured electrode for SOCs.

External Voltage-Induced Restructuring of the Solid-State Electrode/Electrolyte Interface Revealed by X-ray Photoelectron Spectroscopy Depth Profiling Analysis

Solid/solid interfaces between electrodes and electrolytes play an important role in all-solid-state energy devices, while microscopic investigations of the buried interfaces remain challenging. Here, we construct metal|yttria-stabilized zirconia (YSZ)|Au model cells consisting of a metal film cathode (metal (M) = Au, Ni, and Ag), a single crystalline YSZ electrolyte, and a Au film anode, and use quasi in situ X-ray photoelectron spectroscopy depth profiling analysis to investigate the restructuring of buried interfaces between metal cathodes and YSZ. After applying 2.9 V at 500 °C, interfacial Zr4+ ions in the electrolyte are reduced and then interdiffuse with metal cathode overlayers, forming a miscible ZrM alloy interlayer. The interface restructuring degree follows the sequence of Au|YSZ|Au > Ni|YSZ|Au > Ag|YSZ|Au. Meanwhile, surface segregation of Zr on the cathode surface is also observed, whose degree follows the sequence of Ag|YSZ|Au > Ni|YSZ|Au > Au|YSZ|Au. Notably, the strong ZrM alloy formation enhances the interface restructuring but suppresses the Zr surface segregation. This work provides a fundamental understanding of the interfacial reaction at the buried electrode/electrolyte interface.

Facile Construction of Nanostructured Cermet Anodes with Strong Metal-Oxide Interaction for Efficient and Durable Solid Oxide Fuel Cells

Nanostructured anodes generate massive reaction sites to oxidize fuels in solid oxide fuel cells (SOFCs); however, the nonexistence of a practically viable approach for the construction of nanostructures and the retention of these nanostructures under the harsh operating conditions of SOFCs poses a significant challenge. Herein, a simple procedure is reported for the construction of a nanostructured Ni-Gd-doped CeO2 anode based on the direct assembly of pre-formed nanocomposite powder with strong metal-oxide interaction. The directly assembled anode forms heterointerfaces with the electrolyte owing to the electrochemical polarization current and exhibits excellent structural robustness against thermal ripening. An electrolyte-supported cell with the directly assembled anode produces a peak power density of 0.73 W cm-2 at 800 °C, while maintaining stability for 100 h, which is in contrast to the drastic degradation of the cermet anode prepared using the conventional method. These findings provide clarity on the design and construction of durable nanostructured anodes and other electrodes for SOFCs.

Heuristic Approach to Predict the Performance Degradation of a Solid Oxide Fuel Cell Cathode

The present work aims to predict the degradation in the performance of a solid oxide fuel cell (SOFC) cathode owing to cation interdiffusion between the electrolyte and cathode and surface segregation. Cation migration in the (La0.60Sr0.40)0.95Co0.20Fe0.80O3-x (LSCF)-Gd0.10Ce0.90O1.95 (GDC) composite cathode is evaluated in relation to time up to 1000 h using scanning transmission electron microscopy (STEM)-energy-dispersive X-ray spectroscopy (EDXS). The resulting insulating phase formed within the GDC interlayer is quantified by means of the volume fraction using a two-dimensional (2D) image analysis technique. For the very first time, the amount of the insulating phase in the GDC interlayer is quantified, and the corresponding performance degradation of the LSCF cathode is predicted. Mathematical relationships are established for the estimation of degradation due to surface segregation of the cathode. The ohmic resistance between the cathode and the GDC interlayer/electrolyte interface and the polarization resistance of the cathode, characterized by electrochemical impedance spectroscopy (EIS), show an excellent match with the predicted results. The combined degradation analysis and modeling for the cathode lifetime prediction provide a systematic understanding of the time-dependent cation migration and segregation behavior.

Facile Approach for Improving the Interfacial Adhesion of Nanofiber Air Electrodes of Reversible Solid Oxide Cells

Nanofibers have great promise as a highly active air electrode for reversible solid oxide cells (ReSOCs); however, one thorny issue is how to adhesively stick nanofibers to electrolyte with no damage to the original morphology. Herein, PrBa_0.8Ca_0.2Co₂O_5+δ (PBCC) nanofibers are applied as an air electrode by a facile direct assembly approach that leads to the retention of most of the unique microstructure of nanofibers, and firm adhesion of the nanofiber electrode onto the electrolyte is achieved by applying electrochemical polarization. A single cell with the PBCC nanofiber air electrode exhibits excellent maximum power density (1.97 W cm^-2), electrolysis performance (1.3 A cm^-2 at 1.3 V), and operating stability at 750 °C for 200 h. These findings provide a facile means for the utilization of nanofiber electrodes for high-performance and durable ReSOCs.

Ultrafine, Dual-Phase, Cation-Deficient PrBa0.8Ca0.2Co2O5+δ Air Electrode for Efficient Solid Oxide Cells

Nanostructured air electrodes play a crucial role in improving the electrocatalytic activity of oxygen reduction and evolution reactions in solid oxide cells (SOCs). Herein, we report the fabrication of a nanostructured BaCoO₃-decorated cation-deficient PrBa_0.8Ca_0.2Co₂O_5+δ (PBCC) air electrode via a combined modification and direct assembly approach. The modification approach endows the dual-phase air electrode with a large surface area and abundant oxygen vacancies. An intimate air electrode-electrolyte interface is in situ constructed with the formation of a catalytically active Co₃O₄ bridging layer via electrochemical polarization. The corresponding single cell exhibits a peak power density of 2.08 W cm^-2, an electrolysis current density of 1.36 A cm^-2 at 1.3 V, and a good operating stability at 750 °C for 100 h. This study provides insights into the rational design and facile utilization of an active and stable nanostructured air electrode of SOCs.

Solid-State Electrochemistry and Solid Oxide Fuel Cells: Status and Future Prospects

Solid-state electrochemistry (SSE) is an interdisciplinary field bridging electrochemistry and solid-state ionics and deals primarily with the properties of solids that conduct ions in the case of ionic conducting solid electrolytes and electrons and/or electron holes in the case of mixed ionic and electronic conducting materials. However, in solid-state devices such as solid oxide fuel cells (SOFCs), there are unique electrochemical features due to the high operating temperature (600–1 000 °C) and solid electrolytes and electrodes. The solid-to-solid contact at the electrode/electrolyte interface is one of the most distinguished features of SOFCs and is one of the fundamental reasons for the occurance of most importance phenomena such as shift of the equipotential lines, the constriction effect, polarization-induced interface formation, etc. in SOFCs. The restriction in placing the reference electrode in solid electrolyte cells further complicates the SSE in SOFCs. In addition, the migration species at the solid electrode/electrolyte interface is oxygen ions, while in the case of the liquid electrolyte system, the migration species is electrons. The increased knowledge and understanding of SSE phenomena have guided the development of SOFC technologies in the last 30–40 years, but thus far, no up-to-date reviews on this important topic have appeared. The purpose of the current article is to review and update the progress and achievements in the SSE in SOFCs, largely based on the author’s past few decades of research and understanding in the field, and to serve as an introduction to the basics of the SSE in solid electrolyte devices such as SOFCs.

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Zirconia- and ceria-based electrolytes for fuel cell applications: critical advancements toward sustainable and clean energy production

Solid oxide fuel cells (SOFCs) are emerging as energy conversion devices for large-scale electrical power generation because of their high energy conversion efficiency, excellent ability to minimize air pollution, and high fuel flexibility. In this context, this critical review has focussed on the recent advancements in developing a suitable electrolyte for SOFCs which has been required for the commercialization of SOFC technology after emphasizing the literature from the prior studies. In particular, the significant developments in the field of solid oxide electrolytes for SOFCs, particularly zirconia- and ceria-based electrolytes, have been highlighted as important advancements toward the production of sustainable and clean energy. It has been reported that among various electrolyte materials, zirconia-based electrolytes have the potential to be utilized as the electrolyte in SOFC because of their high thermal stability, non-reducing nature, and high mechanical strength, along with acceptable oxygen ion conductivity. However, some studies have proved that the zirconia-based electrolytes are not suitable for low and intermediate-temperature working conditions because of their poor ionic conductivity to below 850 °C. On the other hand, ceria-based electrolytes are being investigated at a rapid pace as electrolytes for intermediate and low-temperature SOFCs due to their higher oxygen ion conductivity with good electrode compatibility, especially at lower temperatures than stabilized zirconia. In addition, the most emerging advancements in electrolyte materials have demonstrated that the intermediate temperature SOFCs as next-generation energy conversion technology have great potential for innumerable prospective applications.

A Review of X-ray Photoelectron Spectroscopy Technique to Analyze the Stability and Degradation Mechanism of Solid Oxide Fuel Cell Cathode Materials

Nondestructive characterization of solid oxide fuel cell (SOFC) materials has drawn attention owing to the advances in instrumentation that enable in situ characterization during high-temperature cell operation. X-ray photoelectron spectroscopy (XPS) is widely used to investigate the surface of SOFC cathode materials because of its excellent chemical specificity and surface sensitivity. The XPS can be used to analyze the elemental composition and oxidation state of cathode layers from the surface to a depth of approximately 5–10 nm. Any change in the chemical state of the SOFC cathode at the surface affects the migration of oxygen ions to the cathode/electrolyte interface via the cathode layer and causes performance degradation. The objective of this article is to provide a comprehensive review of the adoption of XPS for the characterization of SOFC cathode materials to understand its degradation mechanism in absolute terms. The use of XPS to confirm the chemical stability at the interface and the enrichment of cations on the surface is reviewed. Finally, the strategies adopted to improve the structural stability and electrochemical performance of the LSCF cathode are also discussed.

Evaluation of LaxSr1−xZnyFe1−yO3−δ (x = 0.54, 0.8, y = 0.2, 0.4) as a promising cobalt free composite cathode for SOFCs

Cobalt free composite cathode materials with excellent fuel cell performance and thermal stability are reported as promising candidates for intermediate temperature solid oxide fuel cells (IT-SOFCs).

A critical review on nano-structured electrodes of solid oxide cells

Renewable energies from solar and wind power are playing an ever increasing role in meeting the tremendous global energy demand with substantially reduced carbon emissions, however, their intermittent nature poses...

Degradation Mechanisms of Solid Oxide Fuel Cells under Various Thermal Cycling Conditions

A critical issue to tackle before successful commercialization of solid oxide fuel cells (SOFCs) can be achieved is the long-term thermal stability required for SOFCs to operate reliably without significant performance degradation despite enduring thermal cycling. In this work, the impact of thermal cycling on the durability of NiO-yttria-stabilized zirconia-based anode-supported cells is studied using three different heating/cooling rates (1, 2, and 5 °C min^-1) as the temperature fluctuated between 400 and 700 °C. Our experiments simulate time periods when power from SOFCs is not required (e.g., as might occur at night or during an emergency shutdown). The decay ratios of the cell voltages are 8.8% (82 μV h^-1) and 19.1% (187 μV h^-1) after thermal cycling testing at heating/cooling rates of 1 and 5 °C min^-1, respectively, over a period of 1000 h. The results indicate SOFCs that undergo rapid thermal cycling experience much greater performance degradation than cells that experience slow heating/cooling rates. The changes in total resistance for thermally cycled cells are determined by measuring the R_pol of the electrodes (whereas the ohmic resistances of the cells remain unchanged from their initial value), signifying that electrode deterioration is the main degradation mechanism for SOFCs under thermal cycling. In particular, fast thermal cycling leads to severe degradation in the anode part of SOFCs with substantial agglomeration and depletion of Ni particles seen in our characterizations with field emission-scanning electron microscopy and electron probe microanalysis. In addition, the mean particle size in the cathode after thermal cycling testing increases from 0.104 to 0.201 μm for the 5 °C min^-1 cell. Further, the presence of Sr-enriched regions is more significant in the La_0.6Sr_0.4Co_0.2Fe_0.8O_3-δ cathode after fast thermally cycled SOFCs.

Microwave plasma rapid heating towards robust cathode/electrolyte interface for solid oxide fuel cells

Mixed electronic and ionic conductivity (MIEC) perovskite oxides hold promise as cathode with high oxygen reduction reaction (ORR) activity for solid oxide fuel cells (SOFCs) operating at reduced temperatures. However, these MIEC cathodes usually contain lanthanide or alkaline-earth elements at A-site. These elements tend to interact with yttria-stabilized zirconia electrolyte (YSZ) to form unwanted phases such as La₂Zr₂O₇ and SrZrO₃ at conventional electrode fabrication conditions (>800 °C). Such unwanted interfacial reaction severely degrades the cell performance. We present a new method to assemble SrCo_0.4Fe_0.5W_0.1O_3-δ (SCFW) directly onto YSZ by a highly efficient microwave plasma technique. Intimate contact between SCFW and YSZ phases can be achieved by ten-minute microwave-plasma treatment with no new phase formation. Consequently, the microwave-plasma fabricated interface exhibits a notably high ORR performance, showing an area-specific resistances of 0.11 Ω cm² at 600 °C, about two orders of magnitude better than the equivalent prepared via the conventional method. Our method is also effective in assembling other MIEC perovskite cathodes such as SrCo_0.5Fe_0.5O_3-δ and SrCo_0.8Nb_0.1Ta_0.1O_3-δ on YSZ electrolyte, achieving notable enhancement of the cathode performance. This study thus provides an effective and convenient method for synthesizing reactive and robust interfaces between two incompatible phases with minimized interphase interactions.

Nb and Cu co-doped (La,Sr)(Co,Fe)O3: a stable electrode for solid oxide cells

The stabilization of the cubic phase of LSCF co-substitution on the Fe site deposited on YSZ + GDC symmetrical cells to improve the performance.

Surface Segregation in Solid Oxide Cell Oxygen Electrodes: Phenomena, Mitigation Strategies and Electrochemical Properties

Abstract

Solid oxide cells (SOCs) are highly efficient and environmentally benign devices that can be used to store renewable electrical energy in the form of fuels such as hydrogen in the solid oxide electrolysis cell mode and regenerate electrical power using stored fuels in the solid oxide fuel cell mode. Despite this, insufficient long-term durability over 5–10 years in terms of lifespan remains a critical issue in the development of reliable SOC technologies in which the surface segregation of cations, particularly strontium (Sr) on oxygen electrodes, plays a critical role in the surface chemistry of oxygen electrodes and is integral to the overall performance and durability of SOCs. Due to this, this review will provide a critical overview of the surface segregation phenomenon, including influential factors, driving forces, reactivity with volatile impurities such as chromium, boron, sulphur and carbon dioxide, interactions at electrode/electrolyte interfaces and influences on the electrochemical performance and stability of SOCs with an emphasis on Sr segregation in widely investigated (La,Sr)MnO3 and (La,Sr)(Co,Fe)O3−δ. In addition, this review will present strategies for the mitigation of Sr surface segregation.

Graphic Abstract

Molten Salt Synthesis of High-Performance, Nanostructured La0.6Sr0.4FeO3-δ Oxygen Electrode of a Reversible Solid Oxide Cell

Nanoscale perovskite oxides with enhanced electrocatalytic activities have been widely used as oxygen electrodes of reversible solid oxide cells (RSOC). Here, La_0.6Sr_0.4FeO_3−δ (LSF) nanoscale powder is synthesized via a novel molten salt method using chlorides as the reaction medium and fired at 850 °C for 5 h after removing the additives. A direct assembly method is employed to fabricate the LSF electrode without a pre-sintering process at high temperature. The microstructure characterization ensures that the direct assembly process will not damage the porosity of LSF. When operating as a solid oxide fuel cell (SOFC), the LSF cell exhibits a peak power density of 1.36, 1.07 and 0.7 W/cm² at 800, 750 and 700 °C, respectively, while in solid oxide electrolysis cell (SOEC) mode, the electrolysis current density reaches 1.52, 0.98 and 0.53 A/cm² under an electrolysis voltage of 1.3 V, respectively. Thus, it indicates that the molten salt routine is a promising method for the synthesis of highly active perovskite LSF powders for directly assembled oxygen electrodes of RSOC.

Thermal and Plasma-Enhanced Atomic Layer Deposition of Yttrium Oxide Films and the Properties of Water Wettability

The atomic layer deposition (ALD) of yttrium oxide (Y₂O₃) is investigated using the liquid precursor Y(EtCp)₂(iPr-amd) as the yttrium source with thermal (H₂O) and plasma-enhanced (H₂O plasma and O₂ plasma) processes, respectively. Saturation is confirmed for the growth of the Y₂O₃ films with each investigated reactant with a similar ALD window from 150 to 300 °C, albeit with a different growth rate. All of the as-deposited Y₂O₃ films are pure and smooth and have a polycrystalline cubic structure. The as-deposited Y₂O₃ films are hydrophobic with water contact angles >90°. The water contact angle gradually increased and the surface free energy gradually decreased as the film thickness increased, reaching a saturated value at a Y₂O₃ film thickness of ∼20 nm. The hydrophobicity was retained during post-ALD annealed at 500 °C in static air for 2 h. Exposure to polar and nonpolar solvents influences the Y₂O₃ water contact angle. The reported ALD process for Y₂O₃ films may find potential applications in the field of hydrophobic coatings.

In Situ Formation of Er0.4Bi1.6O3 Protective Layer at Cobaltite Cathode/Y2O3-ZrO2 Electrolyte Interface under Solid Oxide Fuel Cell Operation Conditions

Bismuth-based oxides exhibit outstanding oxygen ionic conductivity and fast oxygen surface kinetics and have shown great potential as a highly active component for electrode materials in solid oxide fuel cells (SOFCs). Herein, a Nb-doped La_0.6Sr_0.4Co_0.2Fe_0.7Nb_0.1O_3-δ (LSCFNb) electrode with 40% Er_0.4Bi_1.6O₃ (ESB) composite electrode was successfully fabricated by decoration method and directly assembled on barrier-layer-free yttrium-stabilized zirconia (YSZ) electrolyte cells, achieving a peak power density of 1.32 W cm^-2 and excellent stability at 750 °C and 250 mA cm^-2 for 100 h. ESB decoration also significantly reduces the activation energy from 214 kJ mol^-1 for the O₂ reduction on pristine LSCFNb electrode to 98 kJ mol^-1. Further microstructural analysis reveals that there is a redistribution and migration of the ESB phase in the ESB-LSCFNb composite toward the YSZ electrolyte under the influence of cathodic polarization, forming a thin ESB layer at the cathode/YSZ electrolyte interface. The in situ formed ESB layer not only prevents the direct contact and subsequent reaction between segregated SrO and YSZ electrolytes, but also remarkably promotes the oxygen migration/diffusion at the interface for O₂ reduction reaction, resulting in a remarkable increase in power output and a decrease in activation energy. The present study clearly demonstrated the in situ formation of a highly functional and active ESB protective layer at LSCFNb cobaltite cathode and YSZ electrolyte interface via ESB-decorated LSCFNb composite cathode under SOFC operation conditions.

Highly Stable Sr-Free Cobaltite-Based Perovskite Cathodes Directly Assembled on a Barrier-Layer-Free Y2 O3 -ZrO2 Electrolyte of Solid Oxide Fuel Cells

Direct assembly is a newly developed technique in which a cobaltite-based perovskite (CBP) cathode can be directly applied to a barrier-layer-free Y₂ O₃ -ZrO₂ (YSZ) electrolyte with no high-temperature pre-sintering steps. Solid oxide fuel cells (SOFCs) based on directly assembled CBPs such as La_0.6 Sr_0.4 Co_0.2 Fe_0.8 O_3-δ show high performance initially but degrade rapidly under SOFC operation conditions at 750 °C owing to Sr segregation and accumulation at the electrode/electrolyte interface. Herein, the performance and interface of Sr-free CBPs such as LaCoO_3-δ (LC) and Sm_0.95 CoO_3-δ (SmC) and their composite cathodes directly assembled on YSZ electrolyte was studied systematically. The LC electrode underwent performance degradation, most likely owing to cation demixing and accumulation of La on the YSZ electrolyte under polarization at 500 mA cm^-2 and 750 °C. However, the performance and stability of LC electrodes could be substantially enhanced by the formation of LC-gadolinium-doped ceria (GDC) composite cathodes. Replacement of La by Sm increased the cell stability, and doping of 5 % Pd to form Sm_0.95 Co_0.95 Pd_0.05 O_3-δ (SmCPd) significantly improved the electrode activity. An anode-supported YSZ-electrolyte cell with a directly assembled SmCPd-GDC composite electrode exhibited a peak power density of 1.4 W cm^-2 at 750 °C, and an excellent stability at 750 °C for over 240 h. The higher stability of SmC as compared to that of LC is most likely a result of the lower reactivity of SmC with YSZ. This study demonstrates the new opportunities in the design and development of intermediate-temperature SOFCs based on the directly assembled high-performance and durable Sr-free CBP cathodes.