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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

X-ray chemical imaging for assessing redox microsites within soils and sediments

Redox reactions underlie several biogeochemical processes and are typically spatiotemporally heterogeneous in soils and sediments. However, redox heterogeneity has yet to be incorporated into mainstream conceptualizations and modeling of soil biogeochemistry. Anoxic microsites, a defining feature of soil redox heterogeneity, are non-majority oxygen depleted zones in otherwise oxic environments. Neglecting to account for anoxic microsites can generate major uncertainties in quantitative assessments of greenhouse gas emissions, C sequestration, as well as nutrient and contaminant cycling at the ecosystem to global scales. However, only a few studies have observed/characterized anoxic microsites in undisturbed soils, primarily, because soil is opaque and microsites require µm-cm scale resolution over cm-m scales. Consequently, our current understanding of microsite characteristics does not support model parameterization. To resolve this knowledge gap, we demonstrate through this proof-of-concept study that X-ray fluorescence (XRF) 2D mapping can reliably detect, quantify, and provide basic redox characterization of anoxic microsites using solid phase “forensic” evidence. First, we tested and developed a systematic data processing approach to eliminate false positive redox microsites, i.e., artefacts, detected from synchrotron-based multiple-energy XRF 2D mapping of Fe (as a proxy of redox-sensitive elements) in Fe-“rich” sediment cores with artificially injected microsites. Then, spatial distribution of Fe II and Fe III species from full, natural soil core slices (over cm-m lengths/widths) were mapped at 1–100 µm resolution. These investigations revealed direct evidence of anoxic microsites in predominantly oxic soils such as from an oak savanna and toeslope soil of a mountainous watershed, where anaerobicity would typically not be expected. We also revealed preferential spatial distribution of redox microsites inside aggregates from oak savanna soils. We anticipate that this approach will advance our understanding of soil biogeochemistry and help resolve “anomalous” occurrences of reduced products in nominally oxic soils.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Lewis Acid Site Engineering in Chromite Spinels Orchestrated Surface Reconstruction and Surpasses RuO 2 in Oxygen Evolution

Atomic-scale engineering of chromite spinels featuring redox-active tetrahedral A-sites and strong Cr–O covalency offers a promising route to superior platinum-group-metal-free oxygen evolution reaction (OER) catalysts. However, comprehensive studies addressing how cation substitution influences surface chemistry and governs OER activity and durability in chromite spinels remain limited. Here, in this work, a systematic investigation of the multicationic chromite series Ni x Fe y Cr 3−x−y O 4 is presented, identifying composition-dependent Lewis acidity as a descriptor of superior OER performance. It is further demonstrated that tuning surface acidity directly controls dynamic reconstruction processes and lattice-oxygen participation during spinel-based electrocatalysis. Following activation, the optimized Ni 0.8 Fe 0.3 Cr 1.9 O 4 catalyst delivers a current density of 10 mA cm −2 at an overpotential of 235 mV, surpassing RuO 2 , with excellent long-term stability. Integrating microscopic and spectroscopic analysis with operando impedance spectroscopy, it shows that activation generates an oxyhydroxide overlayer and reveals a previously unrecognized link between surface Lewis acidity and the growth kinetics and activity of these shells. Density functional theory calculations indicate that Fe incorporation at octahedral sites raises the O 2p-band center and lowers oxygen-vacancy formation energy, promoting lattice-oxygen activation and triggering reconstruction, yielding enhanced OER. This work integrates cation-driven surface-acidity modulation, acidity-governed reconstruction, and OER activity enhancement into a unified predictive framework for designing earth-abundant spinel-based catalysts.

operando impedance spectroscopy↗
DOE OSTI2022

Optical O 2 Sensors Also Respond to Redox Active Molecules Commonly Secreted by Bacteria

From a metabolic perspective, molecular oxygen (O 2 ) is arguably the most significant constituent of Earth’s atmosphere. Nearly every facet of microbial physiology is sensitive to the presence and concentration of O 2 , which is the most favorable terminal electron acceptor used by organisms and also a dangerously reactive oxidant. As O 2 has such sweeping implications for physiology, researchers have developed diverse approaches to measure O 2 concentrations in natural and laboratory settings. Recent improvements to phosphorescent O 2 sensors piqued our interest due to the promise of optical measurement of spatiotemporal O 2 dynamics. However, we found that our preferred bacterial model, Pseudomonas aeruginosa PA14, secretes more than one molecule that quenches such sen sors, complicating O 2 measurements in PA14 cultures and biofilms. Assaying supernatants from cultures of 9 bacterial species demonstrated that this phenotype is common: all super natants quenched a soluble O 2 probe substantially. Phosphorescent O 2 probes are often embedded in solid support for protection, but an embedded probe called O 2 NS was quenched by most supernatants as well. Measurements using pure compounds indicated that quenching is due to interactions with redox-active small molecules, including phena zines and flavins. Uncharged and weakly polar molecules like pyocyanin were especially potent quenchers of O 2 NS. These findings underscore that optical O 2 measurements made in the presence of bacteria should be carefully controlled to ensure that O 2 , and not bacterial secretions, is measured, and motivate the design of custom O 2 probes for specific organisms to circumvent sensitivity to redox-active metabolites.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Kinetic and X-ray Absorption Spectroscopic Analysis of Catalytic Redox Cycles over Highly Uniform Polymetal Oxo Clusters

Metal–organic framework materials (MOFs) offer an opportunity for investigating catalytic properties of polymetal oxo clusters that are highly well defined and uniform in nature, in contrast to other classes of catalysts that may exhibit a propensity toward active site heterogeneity. We report herein a kinetic and X-ray absorption spectroscopy (XAS) analysis of the two-electron oxidation of CO over divalent metal sites in MIL-100(M = Fe, Cr) (MIL = Materials of Institut Lavoisier) materials carrying μ 3 -oxo bridged trimers, and connect observations about the kinetic relevance of redox steps to density functional theory (DFT) predictions published previously. The high degree of uniformity evident from in situ titration measurements leads to a congruence in mechanistic inferences made from steady-state catalytic, transient stoichiometric, isotopic exchange, and isotopic tracer data that all point to a sequential mechanism comprised of separate oxidation and reduction half-cycle steps conjoined by an active oxygen intermediate. In situ XAS data reinforce mechanistic conclusions derived from kinetic analysis, and suggest that the active oxygen intermediate may be more appropriately characterized as an iron-oxyl (Fe 3+ –O – ) rather than an iron-oxo (Fe 4+ =O 2– ) species. The Cr analogue of MIL-100 exhibits contrasting rate features that can be rationalized using an identical sequence of steps as MIL-100(Fe), but with a highly dissimilar set of kinetic parameters that can also be validated using transient stoichiometric experiments. The larger coverages of active oxygen intermediates on MIL-100(Cr) are consistent with predictions from prior DFT studies that suggest more stable and less reactive active oxygen species for metals with lower d-electron counts, and point to metal identity as a lever for precisely controlling the kinetic relevance of oxidation and reduction half-cycles in catalytic redox sequences over polymetal oxo clusters. Importantly, the results presented point to the utility of developing broadly applicable structure–catalytic property relationships over MOF nodes specifically, and highly uniform catalysts more generally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Materials Design Directions for Solar Thermochemical Water Splitting

The sustainable, economical production of molecular hydrogen is a crucial component of a net zero-greenhouse-gas-emissions future. Solar thermochemical water splitting (STWS) offers a renewable route to hydrogen with the potential to help decarbonize several industries, including transportation, manufacturing, mining, metals processing, and electricity generation, as well as provide sustainable hydrogen as a chemical feedstock. STWS uses high temperatures generated from concentrated sunlight or other sustainable means for high-temperature heat to produce hydrogen and oxygen from steam. For example, in its simplest form of a two-step thermochemical cycle, a redox-active metal oxide is heated to ≈1700-2000 K, driving off molecular oxygen while producing oxygen vacancies in the material. The reduced metal oxide then cools (ideally with the extracted heat recuperated for re-use) and, in a separate step, comes into contact with steam, which reacts with oxygen vacancies to produce molecular hydrogen while recovering the original state of the metal oxide. Despite its promising use of the entire solar spectrum to split water thermochemically, the current estimated cost of hydrogen produced via STWS is ≈4-6× the U.S. Department of Energy (DOE) Hydrogen Shot target value of $1/kg. One contributing approach to bridging this cost gap is the design of new materials with improved thermodynamic properties to enable higher efficiencies. The state-of-the-art (SOA) redox-active metal oxide for STWS is ceria (CeO 2 ), due to its close to optimal, although too high, oxygen vacancy formation enthalpy and large configurational and electronic entropy of reduction. However, ceria requires high operating temperatures and its efficiency is insufficient. Therefore, efforts to increase the efficiency of STWS cycles have focused on further optimizing oxygen vacancy formation enthalpies and augmenting the reduction entropy via substitution or doping and materials discovery schemes. Examples of the latter include the perovskites BaCe 0.25 Mn 0.75 O 3 and (Ca,Ce)(Ti,Mn)O 3 . These efforts and others have revealed intuitive chemical principles for the efficient and systematic design of more effective materials, such as the strong correlation between the enthalpies of crystal bond dissociation and solid-state cation reduction with the enthalpy of oxygen vacancy formation, as well as configurational entropy augmentation via the coexistence of two or more redox-active cation sublattices. The purpose of this chapter is to prepare the reader with an up-to-date account of STWS redox-active materials, both the SOA and promising newcomers, as well as to provide chemically intuitive strategies for improving their cycle efficiencies through materials design – in conjunction with ongoing efforts in reactor engineering and gas separations – to reach the cost points for commercial viability. First, we will introduce the thermodynamics of STWS using a two-step, metal-oxide, thermochemical cycle with economics in mind. We also will compare the pros and cons of processes that do or do not involve phase changes. Second, we will describe the qualities that make ceria the SOA STWS redox-active material, as well as its limitations. Third, we will survey some of the most promising candidates to date in the search for materials to supplant ceria, emphasizing the post-ternary, metal-oxide-perovskite alloys. Lastly, we will enumerate and discuss the following materials design directions for STWS redox-active materials: crystal reduction potentials as a proxy for oxygen vacancy formation enthalpies, engineering the electronic and configurational entropy of reduction via f-shells and simultaneous redox, and vetting materials stability via temperature-dependent phase diagrams and melting-point prediction.

08 HYDROGEN↗
DOE OSTI2021

The role of oxygen in stimulating methane production in wetlands

Methane (CH 4 ), a potent greenhouse gas, is the second most important greenhouse gas contributor to climate change after carbon dioxide (CO 2 ). The biological emissions of CH 4 from wetlands are a major uncertainty in CH 4 budgets. Microbial methanogenesis by Archaea is an anaerobic process accounting for most biological CH 4 production in nature, yet recent observations indicate that large emissions can originate from oxygenated or frequently oxygenated wetland soil layers. To determine how oxygen (O 2 ) can stimulate CH 4 emissions, we used incubations of Sphagnum peat to demonstrate that the temporary exposure of peat to O 2 can increase CH 4 yields up to 2000-fold during subsequent anoxic conditions relative to peat without O 2 exposure. Geochemical (including ion cyclotron resonance mass spectrometry, X-ray absorbance spectroscopy) and microbiome (16S rDNA amplicons, metagenomics) analyses of peat showed that higher CH 4 yields of redox-oscillated peat were due to functional shifts in the peat microbiome arising during redox oscillation that enhanced peat carbon (C) degradation. Novosphingobium species with O 2 -dependent aromatic oxygenase genes increased greatly in relative abundance during the oxygenation period in redox-oscillated peat compared to anoxic controls. Acidobacteria species were particularly important for anaerobic processing of peat C, including in the production of methanogenic substrates H 2 and CO 2 . Higher CO 2 production during the anoxic phase of redox-oscillated peat stimulated hydrogenotrophic CH 4 production by Methanobacterium species. The persistence of reduced iron (Fe(II)) during prolonged oxygenation in redox-oscillated peat may further enhance C degradation through abiotic mechanisms (e.g., Fenton reactions). The results indicate that specific functional shifts in the peat microbiome underlie O 2 enhancement of CH 4 production in acidic, Sphagnum-rich wetland soils. They also imply that understanding microbial dynamics spanning temporal and spatial redox transitions in peatlands is critical for constraining CH 4 budgets; predicting feedbacks between climate change, hydrologic variability, and wetland CH 4 emissions; and guiding wetland C management strategies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

High-Entropy Surface Complex Stabilized LiCoO 2 Cathode

In this study, elevating the charge voltage of LiCoO 2 increases the energy density of batteries, which is highly enticing in energy storage implementation ranging from portable electronics to e-vehicles. However, hybrid redox reactions at high voltages facilitate oxygen evolution, electrolyte decomposition and irreversible phase change, and accordingly lead to rapid battery capacity decay. Here significantly improved high-voltage cycling stability of Mg-Al-Eu co-doped LiCoO 2 is demonstrated. It is found that element co-doping induces a near-surface high-entropy zone, including an innately thin disordered rock-salt shell and a dopant segregation surface. The high-entropy complex can effectively suppress oxygen evolution and near-surface structure deconstruction. The phase change reversibility between O3 and H1-3 and thermal stability of the cathode are greatly enhanced as well. As a result, the co-doped LiCoO 2 exhibits a remarkable cycling performance, retaining 86.3% and 72.0% of initial capacity over 800 and 2000 cycles, respectively, with a high cut-off voltage of 4.6 V. The feasible co-doping approach broadens the perspective for the development of stable lithium-ion batteries with high operating voltages.

25 ENERGY STORAGE↗
DOE OSTI2020

Methane combustion over Ni/Ce x Zr 1-x O 2 catalysts: impact of ceria/zirconia ratio

In this work, a series of Ce x Zr 1–x O 2 (x=1, 0.83, 0.17, 0) supports and 2 wt.% Ni/Ce x Zr 1–x O 2 catalysts were synthesized and evaluated for CH 4 oxidation. The Ce x Zr 1–x O 2 supports showed moderate activity (T 50 =519-638°C) with CO by-product formation. Additionally, nickel incorporation onto Ce x Zr 1–x O 2 lowered the T 50 to 438–477°C and eliminated the formation of CO. The results indicated that moderate Zr doping improved the support oxygen storage capacity (OSC) and reducibility of the catalyst at low temperatures (H 2 -TPR) leading to an enhanced CH 4 combustion turnover frequency: Ni/ZrO 2 <Ni/Ce 0.17 Zr 0.83 O 2 <Ni/CeO 2 <Ni/Ce 0.83 Zr 0.17 O 2 . The apparent activation energies of Ni/Ce x Zr 1–x O 2 catalysts (87-92 kJ/mol) were much lower than the ones of Ce x Zr 1–x O 2 supports and Ni/quartz sand (111-120 kJ/mol) indicating that CH 4 oxidation is facilitated when Ni is deposited on Ce x Zr 1–x O 2 . Moreover, stability tests with H 2 O and CO 2 showed that Zr doping can improve the catalyst stability, while H 2 O had a stronger reversible inhibition effect than CO 2 for CH 4 combustion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Two-Dimensional Conductive Ni-HAB as a Catalyst for the Electrochemical Oxygen Reduction Reaction

Catalytic systems whose properties can be systematically tuned via changes in synthesis conditions are highly desirable for the next-generation catalyst design and optimization. Herein, we present a two-dimensional (2D) conductive metal–organic framework consisting of M-N 4 units (M = Ni, Cu) and a hexaaminobenzene (HAB) linker as a catalyst for the oxygen reduction reaction. By varying synthetic conditions, we prepared two Ni-HAB catalysts with different crystallinities, resulting in catalytic systems with different electric conductivities, electrochemical activity, and stability. We show that crystallinity has a positive impact on conductivity and demonstrate that this improved crystallinity/conductivity improves the catalytic performance of our model system. Additionally, density functional theory simulations were performed to probe the origin of M-HAB’s catalytic activity, and they suggest that M-HAB’s organic linker acts as the active site with the role of the metal being to modulate the linker sites’ binding strength.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Detailed Characterization of an Annealed Reduced Graphene Oxide Catalyst for Selective Peroxide Formation Activity

Recently, electrochemical hydrogen peroxide (H 2 O 2 ) generation from oxygen molecules has been extensively studied. Thus far, the best peroxide activity under alkaline conditions has been reported at the surface of a mild reduced graphene oxide annealed at 600 °C (mrGO-600). However, the detailed material information, such as chemical functionality and structural morphology, is unknown, which results in ambiguous debates on its catalytic active sites. Therefore, to solve this problem, we intensively characterize the structure of mrGO-600 to clarify the origin of its catalytic activity. Various characterizations, including X-ray photoelectron spectroscopy, Raman spectroscopy, infrared spectroscopy, near-edge X-ray absorption fine spectroscopy, and high-resolution transmittance electron microscopy coupled with in situ infrared spectroelecrochemistry, reveal that the annealing process generates not only various hole edge defects that are related to the ring ether group but also numerous point defects that result in a small-sized disconnected graphitic carbon region. These defects are believed to form a unique atomic level configuration in mrGO-600, which enables it to facilitate high peroxide-generated activity from oxygen molecules in an alkaline electrolyte.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Unveiling Synergetic Photocatalytic Activity from Heterometallic Ti/Ce Clusters

Titanium-oxo clusters, with their robust structure and suitable optical and electronic properties, have been widely investigated as photocatalysts. Heterometallic Ti/M-oxo clusters provide additional tunability and functionality, which enable systematic structure-activity investigations to elucidate reaction mechanisms and improve catalyst de-sign. Incorporating cerium into Ti-oxo clusters can provide additional redox (Ce IV /Ce III ) and oxygen harvesting ability, but to date only limited number of structurally defined titanium-cerium (Ti/Ce) clusters have been reported due to their synthetic challenges. Herein, we report the synthesis and photocatalytic properties of two structurally defined Ti/Ce-oxo clusters, Ti 8 Ce 2 (BA) 16 and Ti 9 Ce 4 (BA) 20 , as well as a TiCe-BA cluster with a calculated formula of Ti 20 Ce 9 O 36 (BA) 42 . Photocatalytic study of these clusters demonstrates that the amount of Ce 3+ species greatly impacts its photocatalytic oxidation performance, and their superior photocatalytic reactivity towards aerobic alcohol oxidation can be contributed to the synergistic effects of the multiple radical species generated upon light absorption. Furthermore, this work represents a significant milestone in the construction of stable Ti/Ce-oxo clusters, enriching the current library of known heterometallic Ti/M-oxo clusters, and providing a series of crystalline materials with great promise of photo-luminescence and photovoltaic chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

How Noninnocent Spectator Species Improve the Oxygen Reduction Activity of Single-Atom Catalysts: Microkinetic Models from First-Principles Calculations

Graphene-based single-atom catalysts are promising alternatives to platinum-based catalysts for fuel cell applications. Different transition metals have been screened using electronic structure methods by estimating onset potentials from the most endergonic elementary reaction step. Here, we calculate onset potentials for the oxygen reduction reaction on metal atoms embedded in N-substituted graphene di-vacancies by virtue of first-principles-informed microkinetic analysis. We find that for more oxophilic metals (Cr, Fe, Mn, and Ru), purely thermodynamic models systematically underestimate onset potentials. Furthermore, the oxophilic metals (Cr, Fe, Mn, and Ru) are oxidized under reaction conditions, leading to an increase in activity compared to their reduced state. Importantly, coadsorbed O m H n species actively participate in the reaction, which requires a dynamic treatment of spectator species. These findings highlight the limitations of thermodynamic analyses for electrocatalytic processes, which commonly assume the same oxidation state for each metal, and show that deviations between computational and experimental onset potentials cannot be solely attributed to the shortcomings of the electronic structure methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Non-Innocent Role of the Ceria Support in Pd-Catalyzed Halophenol Hydrodehalogenation

The hydrodehalogenation (HDH) of halophenols is efficiently catalyzed by palladium supported on high-surface ceria (Pd/CeO2) under mild conditions (35 °C, 1 atm H2). A combination of NMR, diffuse reflectance infrared Fourier transform spectroscopy, Raman spectroscopy, and XPS studies and HDH kinetics of substituted halobenzenes suggests that the reaction proceeds mainly via a sequence of dissociative adsorption of phenolic hydroxyl onto the support, oxidative addition of the C–halogen bond to Pd, and reductive elimination to give phenol and hydrogen halide. The dissociative adsorption of the -OH group onto oxygen vacancies of the ceria support results in an electron-rich intermediate that facilitates the turnover-limiting reductive elimination step. In contrast, the direct pathway catalyzed by Pd without dissociative adsorption of the reactants on the support takes place at a slower rate. The mechanistic insights gained in this study were used to modify the reaction conditions for enabling HDH of recalcitrant halides such as fluorides and iodides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Universal Approach to Fabricating Graphene-Supported Single-Atom Catalysts from Doped ZnO Solid Solutions

Single-atom catalysts (SACs) have attracted widespread interest for many catalytic applications because of their distinguishing properties. However, general and scalable synthesis of efficient SACs remains significantly challenging, which limits their applications. Here we report an efficient and universal approach to fabricating a series of high-content metal atoms anchored into hollow nitrogen-doped graphene frameworks (M-N-Grs; M represents Fe, Co, Ni, Cu, etc.) at gram-scale. The highly compatible doped ZnO templates, acting as the dispersants of targeted metal heteroatoms, can react with the incoming gaseous organic ligands to form doped metal-organic framework thin shells, whose composition determines the heteroatom species and contents in M-N-Grs. We achieved over 1.2 atom % (5.85 wt %) metal loading content, superior oxygen reduction activity over commercial Pt/C catalyst, and a very high diffusion-limiting current (6.82 mA cm -2 ). Both experimental analyses and theoretical calculations reveal the oxygen reduction activity sequence of M-N-Grs. Additionally, the superior performance in Fe-N-Gr is mainly attributed to its unique electron structure, rich exposed active sites, and robust hollow framework: This synthesis strategy will stimulate the rapid development of SACs for diverse energy-related fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

First-Row Transition Metal Antimonates for the Oxygen Reduction Reaction

The development of inexpensive and abundant catalysts with high activity, selectivity, and stability for the oxygen reduction reaction (ORR) is imperative for the widespread implementation of fuel cell devices. Herein, we present a combined theoretical–experimental approach to discover and design first-row transition metal antimonates as excellent electrocatalytic materials for the ORR. Theoretically, we identify first-row transition metal antimonates–MSb 2 O 6 , where M = Mn, Fe, Co, and Ni–as nonprecious metal catalysts with good oxygen binding energetics, conductivity, thermodynamic phase stability, and aqueous stability. Among the considered antimonates, MnSb 2 O 6 shows the highest theoretical ORR activity based on the 4e – ORR kinetic volcano. Experimentally, nanoparticulate transition metal antimonate catalysts are found to have a minimum of a 2.5-fold enhancement in intrinsic mass activity (on transition metal mass basis) relative to the corresponding transition metal oxide at 0.7 V vs RHE in 0.1 M KOH. MnSb 2 O 6 is the most active catalyst under these conditions, with a 3.5-fold enhancement on a per Mn mass activity basis and 25-fold enhancement on a surface area basis over its antimony-free counterpart. Electrocatalytic and material stability are demonstrated over a 5 h chronopotentiometry experiment in the stability window identified by theoretical Pourbaix analysis. Furthermore, this study further highlights the stable and electrically conductive antimonate structure as a framework to tune the activity and selectivity of nonprecious metal oxide active sites for ORR catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗