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At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Co 2 P-Pt Heterostructure Interfaces for Electrocatalytic Hydrogen Evolution

Pt-based electrocatalysts are effective for the hydrogen evolution reaction (HER); however, their limited ability to facilitate water dissociation and suboptimal hydrogen binding energy (H BE ) in alkaline electrolytes result in slow reaction kinetics, which hinders their cost-efficiency and practical applications. This study reports the synthesis of Co 2 P-Pt heterostructure nanorods using a seed-mediated growth method, producing a high density of Co 2 P-Pt interfacial sites. Density functional theory (DFT) calculations indicate that electronic interactions at these interfaces optimize H BE on Pt, while the interfacial sites promote water dissociation. The Co 2 P-Pt nanorods demonstrate an overpotential of 14 mV at 10 mA cm −2 for the HER, highlighting the potential of precisely engineered metal-metal phosphide interfaces for enhancing electrocatalytic efficiency.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Thin Cation-Exchange Layers Enable High-Current-Density Bipolar Membrane Electrolyzers via Improved Water Transport

With suitable water dissociation (WD) catalysts, bipolar membranes (BPMs) can efficiently dissociate water into H + and OH – at the junction between anion- and cation-exchange layers (AEL and CEL, respectively). First, however, water must be transported through the AEL or CEL and thus against the outward flow of hydrated H + and OH – . This is a challenge intrinsic to the BPM architecture and limits operation to current densities typically less than ~0.5 A·cm –2 . Here we explore how water transport affects durability and performance in reference alkaline and acidic membrane electrolyzers, and we use the insight gained to design BPMs with improved water transport. We demonstrate a thin-CEL BPM (2-μm Nafion CEL|~200 nm TiO 2 |~200 nm NiO + ionomer|50 μm Sustainion AEL) which maintains a pH difference of ~14 units between the anode and cathode for current densities of up to 3.4 A·cm –2 with a total water electrolysis voltage of ~4 V and an estimated WD overpotential of ~1.5 V. Finally, such high-current-density operation is crucial for key emerging BPM applications, including in water and carbon-dioxide electrolyzers and in (regenerative) fuel cells.

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

Amine-Assisted Ligand-Exchange Method to Enhance Photovoltaic Parameters in FAPbI3 Nanocrystal Solar Cells

Perovskite colloidal nanocrystals (PeNCs) have exceptional optoelectronic properties and phase stability, making them promising for photovoltaic applications. However, insulating ligands on PeNC surfaces limit the current density and reduce the power conversion efficiency (PCE) in PeNC solar cells (SCs). This study introduces an amine-assisted ligand-exchange (ALE) strategy using 3-phenyl-1-propylamine (3P1P) to effectively remove long ligands from PeNC films. ALE reduced long-chain ligand density without increasing the number of defect states and therefore reduced the exciton-binding energy of FAPbI3 NC films. These changes facilitated exciton dissociation and charge transport in FAPbI3 PeNC SCs. The facilitation of exciton dissociation was due to the increased magnetic dipole interaction between excitons after the ALE process. The use of ALE achieved FAPbI3 PeNC SCs that had an improved short-circuit current density of 17.98 mA/cm2 and a PCE of 15.56% with improved stability after the treatment and negligible hysteresis. This work provides new insight into engineering PeNC films.

amines↗
DOE OSTI2024

Asymmetric Bipolar Membrane for High Current Density Electrodialysis Operation with Exceptional Stability

Bipolar membranes (BPMs) enable isolated acidic/alkaline regions in electrochemical devices, facilitating optimized environments for electrochemical separations and catalysis. For economic viability, BPMs must attain stable, high current density operation with low overpotentials in a freestanding configuration. We report an asymmetric, graphene oxide (GrOx)-catalyzed BPM capable of freestanding electrodialysis operation at 1 A cm–2 with overpotentials <250 mV. Use of a thin anion-exchange layer improves water transport while maintaining near unity Faradaic efficiency for acid and base generation. Voltage stability exceeding 1100 h with an average drift of 70 μV/h at 80 mA cm–2 and 100 h with an average drift of −300 μV/h at 500 mA cm–2 and implementation in an electrodialysis stack demonstrate real-world applicability. Continuum modeling reveals that water dissociation in GrOx BPMs is both catalyzed and electric-field enhanced, where low pK a moieties on GrOx enhance local electric fields and high pK a moieties serve as active sites for surface-catalyzed water dissociation. These results establish commercially viable BPM electrodialysis and provide fundamental insight to advance design of next-generation devices.

Lucas, Éowyn↗
DOE OSTI2025

Comparing Advanced Bipolar Membranes for High-Current Electrodialysis and Membrane Electrolysis

Advanced bipolar membranes (BPMs) with low water-dissociation overpotential (ηwd) may enable new electrochemical technologies for electrolysis, fuel cells, acid–base synthesis, brine remediation, lithium-battery recycling, and cement production. However, these advanced BPMs have only been demonstrated in BPM water electrolysis (BPMWE) configurations where the BPM is under static compression by the porous-transport layers. It is important to study these BPMs in applications like electrodialysis where large degrees of static compression are not possible. We present a BPM electrodialysis (BPMED) platform to measure water-dissociation overpotential (ηwd) and compare BPMWE and BPMED systems. We show advanced BPMs with half the ηwd compared to commercial BPMs for BPMED while maintaining ∼90% current efficiency from 0.05–0.5 A cm–2. The BPMED ηwd values are, however, about 0.2 V higher at 0.5 A cm–2 than those for BPMWE. Regardless, these results show that BPMs developed and optimized in BPMWE applications are well-suited for next-generation high-current-density BPMED technologies.

Vulpin, Olivia T↗
DOE OSTI2020

Nanoconfinement of Molecular Magnesium Borohydride Captured in a Bipyridine-Functionalized Metal-Organic Framework

The lower limit of metal hydride nanoconfinement is demonstrated through the coordination of a molecular hydride species to binding sites inside the pores of a metal-organic framework (MOF). Magnesium borohydride, which has a high hydrogen capacity, is incorporated into the pores of UiO-67bpy (Zr6O4(OH)4(bpydc)6 with bpydc2- = 2,2'-bipyridine-5,5'- dicarboxylate) by solvent impregnation. The MOF retained its long-range order, and transmission electron microscopy and elemental mapping confirmed the retention of the crystal morphology and revealed a homogeneous distribution of the hydride within the MOF host. Notably, the B-, N-, and Mg-edge XAS data confirm the coordination of Mg(II) to the N atoms of the chelating bipyridine groups. In situ 11B MAS NMR studies helped elucidate the reaction mechanism and revealed that complete hydrogen release from Mg(BH4)2 occurs as low as 200 °C. Sieverts and thermogravimetric measurements indicate an increase in the rate of hydrogen release, with the onset of hydrogen desorption as low as 120 °C, which is approximately 150 °C lower than that of the bulk material. Furthermore, density functional theory calculations support the improved dehydrogenation properties and confirm the drastically lower activation energy for B-H bond dissociation.

Nanoconfinement, Metal Hydrides, Metal-Organic Fra↗
DOE OSTI2024

Low-Temperature Activation and Coupling of Methane on MgO Nanostructures Embedded in Cu 2 O/Cu(111)

Here, the efficient conversion of methane into valuable hydrocarbons such as ethane and ethylene at relatively low temperatures without deactivation issues is crucial for advancing sustainable energy solutions. Herein, AP-XPS and STM studies show that MgO nanostructures (0.2-0.5 nm wide, 0.4-0.6 Å high) embedded in a Cu 2 O/Cu(111) substrate activate methane at room temperature, mainly dissociating it into CH x (x = 2 or 3) and H adatoms, with minimal conversion to C adatoms. These MgO nanostructures in contact with Cu 2 O/Cu(111) exhibit unique reactivity, enabling C-C coupling into ethane and ethylene at 500 K, a significantly lower temperature than that required for bulk MgO catalysts (>700 K), with negligible carbon deposition and no deactivation. DFT calculations corroborate these experimental findings. The CH 4,gas → *CH 3 +*H reaction is a downhill process on MgO/Cu 2 O/Cu(111) surfaces. The activation of methane is facilitated by an electron transfer from copper to MgO and the existence of Mg and O atoms with a low coordination number in the oxide nanostructures. The formation of O-CH 3 and O-H bonds overcomes the energy necessary for the cleavage of a C-H bond in methane. DFT studies reveal that smaller Mg 2 O 2 model clusters provide stronger binding and lower activation barriers for C-H dissociation in CH 4 , while larger Mg 3 O 3 clusters promote C-C coupling due to weaker *CH 3 binding. All these results emphasize the importance of size when optimizing the catalytic performance of MgO nanostructures in the selective conversion of methane.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Toward the Observation of Dimagnesocene

We have examined the electronic structure of C 5 H 5 MgMgC 5 H 5 , or dimagnesocene, using high-level coupled-cluster techniques. This research is suitable in light of the remarkable synthesis of the valence-isoelectronic diberyllocene by Boronski, Crumpton, Wales, and Aldridge. The Mg–Mg bond distance is predicted to be 2.758 Å, and the Mg–Mg bond dissociation energy is predicted to be 51.8 kcal/mol. Unique aspects to the present research is our characterization of the ionization energy and the electron affinity of this molecule, the energy of dissociation into two neutral cyclopentadienyl magnesium radicals, the determination of the neutral structure at the CCSD(T)/cc-pVTZ level, and the computation of the Raman intensities at the MP2/cc-pVDZ level. Apart from mass spectroscopy, the simplest means of experimental detection is gas-phase or matrix-isolated infrared spectroscopy, in which the A 2 ″ peak at 801 cm –1 should be the most prominent, with an intensity of 581 km/mol.

bond cleavage↗
DOE OSTI2024

Time-Resolved Probing of the Iodobenzene C-Band Using XUV-Induced Electron Transfer Dynamics

Time-resolved extreme ultraviolet spectroscopy was used to investigate photodissociation within the iodobenzene C-band. The carbon–iodine bond of iodobenzene was photolyzed at 200 nm, and the ensuing dynamics were probed at 10.3 nm (120 eV) over a 4 ps range. Two product channels were observed and subsequently isolated by using a global fitting method. Their onset times and energetics were assigned to distinct electron transfer dynamics initiated following site-selective ionization of the iodine photoproducts, enabling the electronic states of the phenyl fragments to be identified using a classical over-the-barrier model for electron transfer. In combination with previous theoretical work, this allowed the corresponding neutral photochemistry to be assigned to (1) dissociation via the 7B2, 8A2, and 8B1 states to give ground-state phenyl, Ph(X), and spin–orbit excited iodine and (2) dissociation through the 7A1 and 8B2 states to give excited-state phenyl, Ph(A), and ground-state iodine. The branching ratio was determined to be 87 ± 4% Ph(X) and 13 ± 4% Ph(A). Similarly, the corresponding amount of energy deposited into the internal phenyl modes in these channels was determined to be 44 ± 10 and 65 ± 21%, respectively, and upper bounds to the channel rise times were found to be 114 ± 6 and 310 ± 60 fs.

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

Coupling and Reactions of Lignols and New Lignin Monomers: A Density Functional Theory Study

This perspective summarizes and compares computational results for the thermodynamics of bond dissociation, coupling, and rearomatization for a number of noncanonical lignin monomer–lignol combinations that have been found to occur experimentally. The noncanonical lignin monomers discussed are tricin, caffeyl alcohol, 5-hydroxyconiferyl alcohol, and piceatannol. Among dimeric combinations, the results for bond dissociation are generally similar, but in cases for which trimers have been reported (tricin-lignol adducts), this value can be quite variable, with stereochemical and structural preferences. Among the adducts examined thus far, the energies associated with quinone methide formation and rearomatization are not dissimilar and would not impede subsequent polymerization. These fundamental studies may help to elucidate how lignin monomers are incorporated into the lignin polymer, provide leads for targeted genetic modification, and be of use in deconstruction for the production of commodity chemicals.

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

Direct Conversion of Ethane to Oxygenates, Ethylene, and Hydrogen in a Noncatalytic Biphasic Plasma Microreactor

We selectively upgrade ethane (C 2 H 6 ) to ethanol (C 2 H 5 OH), methanol (CH 3 OH), and acetic acid (CH 3 COOH) in a catalyst-free, continuous, argon/water biphasic plasma microreactor. The water (H 2 O) evaporates and electron- dissociates into OH· radicals. OH· recombines with alkyl radicals, produced via electron dissociation of ethane, to generate the oxygenates that absorb into H 2 O. A plasma-assisted path, reminiscent of the low-temperature thermocatalytic ethane steam reforming, leads to significant H 2 coproduction. The gaseous stream also comprises CO 2 and C 2 H 4 . Up to 1.3 and 1 μmol min –1 of liquid C 2 H 5 OH and CH 3 OH are attained, respectively. Compared to CO 2 -assisted ethane plasma conversion, which produces many oxygenates with low selectivity, the carbon selectivity can range from >70% C 2 H 5 OH, CH 3 OH, and CH 3 COOH to 60% C 2 H 4 . Furthermore, the low carbon footprint, electrified, modular, intensified process using a reactive evaporation and separation plasma could pave the way for the valorization of underutilized shale gas resources in remote areas.

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

LixNiO/Ni Heterostructure with Strong Basic Lattice Oxygen Enables Electrocatalytic Hydrogen Evolution with Pt-like Activity

The low-cost hydrogen production from water electrolysis is crucial for practical deployment of sustainable hydrogen economy, but is often constrained by the lack of active and robust electrocatalysts from Earth-abundant materials. We describe here an unconventional heterostructure composed of strongly coupled Ni-deficient LixNiO nanoclusters and polycrystalline Ni nanocrystals, and its exceptional activities toward hydrogen evolution reaction (HER) in aqueous electrolytes. The presence of unique lattice oxygen species with strong Brønsted basicity is a significant feature, which spontaneously split water molecules and effectively accelerate the sluggish Volmer H-OH dissociation step in neutral and alkaline HER. In combination with the unpreceded level of intimate LixNiO and Ni interfacial junctions that produces abundant “hotspots” for promoted hydride coupling, the catalyst exhibited kinetic activities almost identical as Pt/C and decent long term stability in universal pH.

Lu, Ke↗
DOE OSTI2020

Mechanism of Methanol Decomposition over Single-Site Pt 1 /CeO 2 Catalyst: A DRIFTS Study

Single-site catalysts have drawn broad attention in catalysis because of their maximum atomic utilization and unique catalytic performance. Early work in our group has shown a 40-fold higher activity of methanol decomposition over single-site Pt 1 /CeO 2 catalyst than CeO 2 supported 2.5 nm Pt nanoparticles, while a molecular-level understanding of such enhancement is lacking. Herein, the reaction mechanism of methanol decomposition over Pt 1 /CeO 2 was carefully investigated using in situ DRIFTS, and a reaction pathway was proposed. Methanol molecules were dissociatively adsorbed on nanoceria support first, followed by the diffusion of as-formed methoxy species onto Pt single sites where the dehydrogenation occurs and results in the weakly bonded CO. The ease of methanol dissociative adsorption on nanoceria support and the tailored electronic property of Pt 1 via the metal-support interaction are believed to be strongly correlated with the high activity of Pt 1 /CeO 2 .

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

Redox-Induced Structural Reorganization Dictates Kinetics of Cobalt(III) Hydride Formation via Proton-Coupled Electron Transfer

Two-electron, one-proton reactions of a family of [CoCp(dxpe)(NCCH 3 )] 2+ complexes (Cp = cyclopentadienyl, dxpe = 1,2-bis(di(aryl/alkyl)phosphino)ethane) form the corresponding hydride species [HCoCp(dxpe)] + through a stepwise proton-coupled electron transfer process. For three [CoCp(dxpe)(NCCH 3 )] 2+ complexes (dxpe = dppe (1,2-bis(diphenylphosphino)ethane), depe (1,2-bis(diethylphosphino)ethane), and dcpe (1,2-bis(dicyclohexylphosphino)ethane)), peak shift analysis was employed to quantify apparent proton transfer rate constants from cyclic voltammograms recorded with acids ranging 22 pK a units. The apparent proton transfer rate constants correlate with the strength of the proton source for weak acids, but these apparent proton transfer rate constants curiously plateau (k pl ) as the reaction becomes increasingly exergonic. The absolute apparent proton transfer rate constants across both these regions correlate with the steric bulk of the chelating diphosphine ligand, with bulkier ligands leading to slower kinetics (k plateau,depe = 3.5 x 10 7 M -1 s -1 , k plateau,dppe = 1.7 x 10 7 M -1 s -1 , k plateau,dcpe = 7.1 x 10 4 M -1 s -1 ). Mechanistic studies were conducted to identify the cause of the aberrant $k_PT^{app}$–ΔpK a trends. When the deuterated acids are employed, deuterium incorporation in the Cp ring is observed, indicating protonation of the CoCp(dxpe) species to form the corresponding hydride proceeds via initial ligand protonation. Digital simulations of cyclic voltammograms show ligand loss accompanying initial reduction gates subsequent PCET activity at higher driving forces. Together, these experiments reveal the details of the reaction mechanism: reduction of the Co(III) species is followed by dissociation of the bound acetonitrile ligand, subsequent reduction of the unligated Co(II) species to form a Co(I) species is followed by protonation, which occurs at the Cp ring, followed by tautomerization to generate the stable Co(III)-hydride product [HCoCp(dxpe)] + . Analysis as a function of chelating disphosphine ligand, solvent, and acid strength reveals that the ligand dissociation equilibrium is directly influenced by the steric bulk of the phosphine ligands and gates protonation, giving rise to the plateau of apparent proton transfer rate constant with strong acids. The complexity of the reaction mechanism underpinning hydride formation, encompassing dynamic behavior of the entire ligand set, highlights the critical need to understand elementary reaction steps in proton-coupled electron transfer reactions.

14 SOLAR ENERGY↗
DOE OSTI2022

Time-Evolving Chirality Loss in Molecular Photodissociation Monitored by X-ray Circular Dichroism Spectroscopy

In this work, the ultrafast photoinduced chirality loss of 2-iodobutane is studied theoretically by time- and frequency-resolved X-ray circular dichroism (TRXCD) spectroscopy. Following an optical excitation, the iodine atom dissociates from the chiral center, which we capture by quantum non-adiabatic molecular dynamics simulations. At variable time delays after the pump, the resonant X-ray pulse selectively probes the iodine and carbon atom involved in the chiral dissociation through a selected core-to-valence transition. The TRXCD signal at the iodine L 1 edge accurately captures the timing of C–I photodissociation and thereby chirality loss, c.a 70 fs. The strong electric dipole–electric quadrupole (ED–EQ) response makes this signal particularly sensitive to vibronic coherence at the high X-ray regime. At the carbon K-edges, the signals monitor the molecular chirality of the 2-butyl radical photoproduct and the spin state of the iodine atom. The ED–EQ response is masked under the strong electric dipole-magnetic dipole response, making this signal intuitive for the electronic population. The evolution of the core electronic states and its chiral sensitivity is discussed. Overall, the element-specific TRXCD signal provides a detailed picture of molecular dynamics and offers a unique sensitive window into the time-dependent chirality of molecules.

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

Deciphering the Olefin Isomerization-Polymerization Paradox of Palladium(II) Diimine Catalysts: Discovery of Simultaneous and Independent Pathways of Olefin Isomerization and Living Polymerization

This work elucidates a long-standing unexplained paradox commonly observed within the polymerization of α-olefin using palladium (Pd)(II)–diimine catalysts, in which isomerization and living polymerization of α-olefins are both observed. With a classical mechanistic understanding of these complexes, this behavior is often dismissed and interpreted as experimental error. Herein, we present a comprehensive mechanistic investigation into this phenomenon that supports the existence of a novel mechanistic pathway for Pd(II)–diimine complexes. Part one of the mechanistic study lays the foundation of the proposed mechanism, in which neutral Pd(II)–diimine complexes were found to exhibit a moderate to good catalytic activity for olefin isomerization of α-olefins despite the established notion that catalyst activation is required. Extensive experimental and computational studies reveal the possibility of a partial dissociation of the diimine ligand, which frees up one coordination site and enables coordination–insertion. This finding is significant as the coexistence of two reactive coordination sites at the palladium center becomes a valid proposal for the activated cationic Pd(II)–diimine complexes. In part two, we examined and validated the simultaneously observed α-olefin isomerization and living polymerization using the cationic Pd(II)–diimine catalyst, which supports the presence of two independent reaction pathways of isomerization and polymerization, respectively. Furthermore, the addition of a strong Lewis acid, such as AlCl 3 , accelerates the ligand dissociation and the consequential isomerization as it weakens the palladium–nitrogen bond through competitive binding. In part three, Lewis acid-triggered olefin isomerization-polymerization is employed to prepare living olefinic block copolymers and further synthesize novel polyolefin-polar block copolymers with unique architectures, distinct levels of branching, crystallinity, and polar functionality in a one-pot manner.

Catalysts↗
DOE OSTI2024

Unraveling Reactivity Differences: Room-Temperature Ring-Opening Metathesis Polymerization (ROMP) versus Frontal ROMP

Here, in this study, we explore the distinct reactivity patterns between frontal ring-opening metathesis polymerization (FROMP) and room-temperature solventless ring-opening metathesis polymerization (ROMP). Despite their shared mechanism, we find that FROMP is less sensitive to inhibitor concentration than room-temperature ROMP. By increasing the initiator-to-monomer ratio for a fixed inhibitor/initiator quantity, we find reduction in the ROMP background reactivity at room temperature (i.e., increased resin pot life). At elevated temperatures where inhibitor dissociation prevails, accelerated frontal polymerization rates are observed because of the concentrated presence of the initiator. Surprisingly, the strategy of employing higher initiator loading enhances both pot life and front speeds, which leads to FROMP rates exceeding prior reported values by over 5 times. This counterintuitive behavior is attributed to an increase in the proximity of the inhibitor to the initiator within the bulk resin and to whether the temperature favors coordination or dissociation of the inhibitor. A rapid method was developed for assessing resin pot life, and a straightforward model for active initiator behavior was established. Modified resin systems enabled direct ink writing of robust thermoset structures at rates much faster than previously possible.

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

Operando Characterization of Fe in Doped Ni x (Fe 1– x )O y H z Catalysts for Electrochemical Oxygen Evolution

Iron-doped nickel oxyhydroxides, Ni x (Fe 1– x )O y H z , are among the most promising oxygen evolution reaction (OER) electrocatalysts in alkaline environments. Although iron (Fe) significantly enhances the catalytic activity, there is still no clear consensus on whether Fe directly participates in the reaction or merely acts as a promoter. To elucidate the Fe’s role, we performed operando X-ray spectroscopy studies supported by DFT on Ni x (Fe 1– x )O y H z electrocatalysts. We probed the reversible changes in the structure and electronic character of Ni x (Fe 1– x )O y H z as the electrode potential is cycled between the resting (here at 1.10 V RHE ) and operational states (1.66 V RHE ). DFT calculations and XAS simulations on a library of Fe structures in various NiO y H z environments are in favor of a distorted local octahedral Fe(III)O 3 (OH) 3 configuration at the resting state with the NiO y H z scaffold going from α-Ni(OH) 2 to γ-NiOOH as the potential is increased. Under catalytic conditions, EXAFS and HERFD spectra reveal changes in p-d mixing (covalency) relative to the resting state between O/OH ligands and Fe leading to a shift from octahedral to square pyramidal coordination at the Fe site. XES measurements and theoretical simulations further support that the Fe equilibrium structure remains in a formal Fe(III) state under both resting and operational conditions. These spectral changes are attributed to potential dependent structural rearrangements around Fe. The results suggest that ligand dissociation leads to the C 4v symmetry as the most stable intermediate of the Fe during OER. This implies that Fe has a weakly coordinated or easily dissociable ligand that could serve to coordinate the O–O bond formation and, tentatively, play an active role in the Ni x (Fe 1– x )O y H z electrocatalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗