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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 415 records · Page 23

Joining of High Strength Low Ductility AA7055 by Friction Self-piercing Rivet

High strength aluminum (Al) alloy is one of higher specific strength materials for decarbonization in transportation industries. Because of low ductility at room temperature, conventional mechanical fastening such as self-piercing riveting produces cracks at the joint. In this work, we applied friction self-piercing riveting to join Al alloy (AA) 7055. No cracks were observed in the joints because of the improved local ductility of Al alloy by the generated frictional heat during joining step. Numerical modeling of joining process was applied to guide rivet geometry design and rivet material strength. Mechanical integrity of the AA7055 joints was assessed by lap shear tensile and cross-tension testing. Metallurgical characterizations revealed solid-state bonding formed not only between the rivet and surround Al materials, but also upper and lower Al sheets at the joint interface. Both solid-state bonding and mechanical interlocking between the flared rivet and bottom AA7055 sheet were the major joint mechanisms.

Lim, Yong Chae↗

AlGaN/GaN metal–insulator–semiconductor high electron mobility transistors (MISHEMTs) using plasma deposited BN as gate dielectric

AlGaN/GaN metal–insulator–semiconductor high electron mobility transistors (MISHEMTs) were fabricated on Si substrates with a 10 nm boron nitride (BN) layer as a gate dielectric deposited by electron cyclotron resonance microwave plasma chemical vapor deposition. The material characterization of the BN/GaN interface was investigated by X-ray photoelectric spectroscopy (XPS) and UV photoelectron spectroscopy. The BN bandgap from the B1s XPS energy loss is ~5 eV consistent with sp2 bonding. The MISHEMTs exhibit a low off-state current of 1 × 10 –8 mA/mm, a high on/off current ratio of 10 9 , a threshold voltage of –2.76 V, a maximum transconductance of 32 mS/mm at a gate voltage of –2.1 V and a drain voltage of 1 V, a subthreshold swing of 69.1 mV/dec, and an on-resistance of 12.75 Ω·mm. The interface state density (D it ) is estimated to be less than 8.49 × 10 11 cm –2 eV –1 . Gate leakage current mechanisms were investigated by temperature-dependent current–voltage measurements from 300 K to 500 K. The maximum breakdown electric field is no less than 8.4 MV/cm. Poole–Frenkel emission and Fowler–Nordheim tunneling are indicated as the dominant mechanisms of the gate leakage through the BN gate dielectric at low and high electric fields, respectively.

36 MATERIALS SCIENCE↗

Two-dimensional electronic–vibrational sum frequency spectroscopy for interactions of electronic and nuclear motions at interfaces

Significance Electronic–vibrational couplings are pivotal in many photo-induced processes at interfaces and surfaces. Two-dimensional electronic–vibrational sum frequency generation spectroscopy is a unique tool to decipher electronic–vibrational couplings for excited states of molecules at interfaces and surfaces, enabling the correlation of photo-induced electronic–vibrational manifolds with their subsequent time evolution of high-frequency vibrational modes. This technique is especially powerful to monitor ultrafast processes such as charge transfer, energy transfer, proton transfer, and proton-coupled charge transfer at interfaces and surfaces on a real-time basis.

Deng, Gang-Hua↗

Engineering Charge-Transfer States for Efficient, Low-Energy-Loss Organic Photovoltaics

Charge transfer (CT) between donors and acceptors following photoexcitation of organic photovoltaics (OPVs) gives rise to bound electron–hole pairs across the donor–acceptor interface, known as CT states. Although these states are essential to charge separation, they are also a source of energy loss. As a result of reduced overlap between electron and hole wavefunctions, CT states are influenced by details of the film morphology and molecular structure. In this work, we describe several important strategies for tuning the energy level and dynamics of the CT state and approaches that can enhance their dissociation efficiency into free charges. Furthermore, we provide an overview of recent physical insights into the key parameters that significantly reduce the Frenkel-to-CT energy offset and recombination energy losses while preserving a high charge-generation yield. Our analysis leads to critical morphological and molecular design strategies for achieving efficient, low-energy-loss OPVs.

14 SOLAR ENERGY↗

Thin-Film Paradigm to Probe Interfacial Diffusion during Solid-State Metathesis Reactions

We highlight a paradigm for studying complex reaction mechanisms that guide the synthesis of materials. Thin films of FeCl 2 and Na 2 S 2 were deposited to study the metathesis reaction to form FeS 2 and NaCl. In situ X-ray reflectivity was used to monitor the interface between materials, which revealed a slow, impeded reaction at high temperatures as compared to previous studies using powder samples. AC impedance and X-ray photoelectron spectroscopy provided insight into distribution of elements and conductivity of the phases present during the reaction, and phase-field modeling was used to elucidate the diffusion of ions throughout the thin-film bilayers. Here, the use of thin-film bilayers provides a simplified system to study solid-state metathesis reactions and highlights the complexity of diffusion at solid-state interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Kinetics of the Topochemical Transformation of (PbSe) m (TiSe 2 ) n (SnSe 2 ) m (TiSe 2 ) n to (Pb 0.5 Sn 0.5 Se) m (TiSe 2 ) n

Solid-state reaction kinetics on atomic length scales have not been heavily investigated due to the long times, high reaction temperatures, and small reaction volumes at interfaces in solid-state reactions. All of these conditions present significant analytical challenges in following reaction pathways. Herein we use in situ and ex situ X-ray diffraction, in situ X-ray reflectivity, high-angle annular dark field scanning transmission electron microscopy, and energy-dispersive X-ray spectroscopy to investigate the mechanistic pathways for the formation of a layered (Pb 0.5 Sn 0.5 Se) 1+δ (TiSe 2 ) m heterostructure, where m is the varying number of TiSe 2 layers in the repeating structure. Thin film precursors were vapor deposited as elemental-modulated layers into an artificial superlattice with Pb and Sn in independent layers, creating a repeating unit with twice the size of the final structure. At low temperatures, the precursor undergoes only a crystallization event to form an intermediate (SnSe 2 ) 1+γ (TiSe 2 ) m (PbSe) 1+δ (TiSe 2 ) m superstructure. At higher temperatures, this superstructure transforms into a (Pb 0.5 Sn 0.5 Se) 1+δ (TiSe 2 ) m alloyed structure. The rate of decay of superlattice reflections of the (SnSe 2 ) 1+γ (TiSe 2 ) m (PbSe) 1+δ (TiSe 2 ) m superstructure was used as the indicator of the progress of the reaction. Here, we show that increasing the number of TiSe 2 layers does not decrease the rate at which the SnSe 2 and PbSe layers alloy, suggesting that at these temperatures it is reduction of the SnSe 2 to SnSe and Se that is rate limiting in the formation of the alloy and not the associated diffusion of Sn and Pb through the TiSe 2 layers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Theory of the spin-Seebeck effect at a topological-insulator/ferromagnetic-insulator interface

The spin-Seebeck effect refers to voltage signals induced in metals by thermally driven spin currents in adjacent magnetic systems. We present a theory of the spin-Seebeck signal in the case where the conductor that supports the voltage signal is the topologically protected two-dimensional surface-state system at the interface between a ferromagnetic insulator (FI) and a topological insulator (TI). Our theory uses a Dirac model for the TI surface states and assumes Heisenberg exchange coupling between the TI quasiparticles and the FI magnetization. The spin-Seebeck voltage is induced by the TI surface states scattering off the nonequilibrium magnon population at the surface of the semi-infinite thermally driven FI. Our theory is readily generalized to spin-Seebeck voltages in any two-dimensional conductor that is exchange-coupled to the surface of a FI. Surface-state carrier-density-dependent signal strengths calculated using Bi 2 Te 3 and yttrium iron garnet material parameters are consistent with recent experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

ELaNa - Educational Launch of Nanosatellite Enhance Education Through Space Flight

One of NASA's missions is to attract and retain students in the science, technology, engineering and mathematics (STEM) disciplines. Creating missions or programs to achieve this important goal helps strengthen NASA and the nation's future work force as well as engage and inspire Americans and the rest of the world. During the last three years, in an attempt to revitalize educational space flight, NASA generated a new and exciting initiative. This initiative, NASA's Educational Launch of Nanosatellite (ELaNa), is now fully operational and producing exciting results. Nanosatellites are small secondary satellite payloads called CubeSats. One of the challenges that the CubeSat community faced over the past few years was the lack of rides into space. Students were building CubeSats but they just sat on the shelf until an opportunity arose. In some cases, these opportunities never developed and so the CubeSat never made it to orbit. The ELaNa initiative is changing this by providing sustainable launch opportunities for educational CubeSats. Across America, these CubeSats are currently being built by students in high school all the way through graduate school. Now students know that if they build their CubeSat, submit their proposal and are selected for an ELaNa mission, they will have the opportunity to fly their satellite. ELaNa missions are the first educational cargo to be carried on expendable launch vehicles (ELY) for NASA's Launch Services Program (LSP). The first ELaNa CubeSats were slated to begin their journey to orbit in February 2011 with NASA's Glory mission. Due to an anomaly with the launch vehicle, ELaNa II and Glory failed to reach orbit. This first ELaNa mission was comprised of three IU CubeSats built by students at Montana State University (Explorer Prime Flight 1), the University of Colorado (HERMES), and Kentucky Space, a consortium of state universities (KySat). The interface between the launch vehicle and the CubeSat, the Poly-Picosatellite Orbital Deployer (P-POD), was developed and built by students at California Polytechnic State University (Cal Poly). Integrating a P-POD on a NASA ELV was not an easy task. The creation of new processes and requirements as well as numerous reviews and approvals were necessary within NASA before the first ELaNa mission could be attached to a NASA launch vehicle (LV). One of the key objectives placed on an ELaNa mission is that the CubeSat and PPOD does not increase the baseline risk to the primary mission and launch vehicle. The ELaNa missions achieve this objective by placing a rigorous management and engineering process on both the LV and CubeSat teams. So, what is the future of ELaNa? Currently there are 16 P-POD missions manifested across four launch vehicles to support educational CubeSats selected under the NASA CubeSat Initiative. From this initiative, a rigorous selection process produced 22-student CubeSat missions that are scheduled to fly before the end of 2012. For the initiative to continue, organizations need to submit proposals to the annual CubeSat initiative call so they have the opportunity to be manifested and launched.

Skrobot, Garrett Lee↗

Volume 2: Explicit, multistage upwind schemes for Euler and Navier-Stokes equations

The objective of this study was to develop a high-resolution-explicit-multi-block numerical algorithm, suitable for efficient computation of the three-dimensional, time-dependent Euler and Navier-Stokes equations. The resulting algorithm has employed a finite volume approach, using monotonic upstream schemes for conservation laws (MUSCL)-type differencing to obtain state variables at cell interface. Variable interpolations were written in the k-scheme formulation. Inviscid fluxes were calculated via Roe's flux-difference splitting, and van Leer's flux-vector splitting techniques, which are considered state of the art. The viscous terms were discretized using a second-order, central-difference operator. Two classes of explicit time integration has been investigated for solving the compressible inviscid/viscous flow problems--two-state predictor-corrector schemes, and multistage time-stepping schemes. The coefficients of the multistage time-stepping schemes have been modified successfully to achieve better performance with upwind differencing. A technique was developed to optimize the coefficients for good high-frequency damping at relatively high CFL numbers. Local time-stepping, implicit residual smoothing, and multigrid procedure were added to the explicit time stepping scheme to accelerate convergence to steady-state. The developed algorithm was implemented successfully in a multi-block code, which provides complete topological and geometric flexibility. The only requirement is C degree continuity of the grid across the block interface. The algorithm has been validated on a diverse set of three-dimensional test cases of increasing complexity. The cases studied were: (1) supersonic corner flow; (2) supersonic plume flow; (3) laminar and turbulent flow over a flat plate; (4) transonic flow over an ONERA M6 wing; and (5) unsteady flow of a compressible jet impinging on a ground plane (with and without cross flow). The emphasis of the test cases was validation of code, and assessment of performance, as well as demonstration of flexibility.

Elmiligui, Alaa↗

Local probe of bulk and edge states in a fractional Chern insulator

The fractional quantum Hall effect is a key example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order and time-reversal symmetry breaking. Recently, a lattice analogue of the fractional quantum Hall effect at zero magnetic field has been observed, confirming the existence of a zero-field fractional Chern insulator (FCI). Despite this, the bulk–edge correspondence—a hallmark of a FCI featuring an insulating bulk with conductive edges—has not been directly observed. In fact, this correspondence has not been visualized in any system for fractional states owing to experimental challenges. Here we report the imaging of FCI edge states in twisted MoTe 2 (t-MoTe 2 ) using microwave impedance microscopy. By tuning the carrier density, we observe the system evolving between metallic and FCI states, the latter of which exhibits insulating bulk and conductive edges, as expected from the bulk–boundary correspondence. Further analysis suggests the composite nature of the FCI edge states. We also observe the evolution of edge states across the topological phase transition as a function of interlayer electric field and reveal exciting prospects of neighbouring domains with different fractional orders. Furthermore, these findings pave the way for research into topologically protected one-dimensional interfaces between various anyonic states at zero magnetic field, such as gapped one-dimensional symmetry-protected phases with non-zero topological entanglement entropy, Halperin–Laughlin interfaces and the creation of non-abelian anyons.

Imaging techniques↗

Surface Josephson plasma waves in a high-temperature superconductor

Abstract Electron density oscillations with acoustic dispersions and sustained at boundaries between different media provide information about surface and interface properties of heterostructures. In ultrathin metallic films these plasmonic excitations are heavily damped. Superconductivity is predicted to reduce dissipation allowing detection of these resonances. Emerging low-loss interface Cooper-pair waves have been studied before, however, the observation of surface-confined Josephson plasmons in highly anisotropic superconductors has remained elusive. Here, we report on generation and coupling to these excitations in an ultrathin single-crystal film of high-temperature superconductor La 1.85 Sr 0.15 CuO 4 . The film becomes brighter than Au below the critical temperature when probed with sub-gap THz photons. We show that the enhanced signal in the superconducting state, which can be visualized with a spatial resolution better than λ/3000, originates from near-field coupling of light to surface Josephson plasmons. Our results open a path towards non-invasive investigation of enhanced superconductivity in artificial multilayers, buried interface states in topological heterostructures, and non-linear phenomena in Josephson devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Precipitation behavior of Widmanstätten O phase associated with interface in aged Ti2AlNb-based alloys

Highlights: • Ball milling tunes the morphology of primary O phase in Ti{sub 2}AlNb alloys. • The interface of Widmanstatten B2 and O affects the hardness of the alloys. • The entire precipitation process of Widmanstatten O phase is reported. - Abstract: Ti{sub 2}AlNb-based alloys, spark plasma sintered from ball-milled octahedral Ti-22Al-25Nb powder, are aged for 0–3 h in this study. Ball milling tunes the morphology of primary orthorhombic (O) phase to be columnar, and improves the mechanical properties of the alloys. The evolution of the Widmanstätten O phase, which brought main precipitation strengthening effect, is then investigated during the ageing process. The hardness of the alloys is improved by an increasing content of O phase and the reduced width of the Widmanstätten O phase; in addition, the length of Widmanstätten O phase also brings positive effect on the hardness, which indicates that the hardness is strongly coupled with the interface of the Widmanstätten O precipitates and B2 matrix. By means of transmission electron microscopy observation, the precipitation of O initials with an amorphous state, followed by a coherent interface between (110){sub B2} and (002){sub O}, which is destroyed to be semi-coherent and incoherent during the next ageing stage.

36 MATERIALS SCIENCE↗

RISMC industry application #1 (ECCS/LOCA). Core characterization automation: Lattice codes interface for PHISICS/RELAP5-3D

The United States Nuclear Regulatory Commission (U.S. NRC) is currently proposing rule-making “10 CFR 50.46c” to revise the loss-of-coolant-accident (LOCA) and emergency core cooling system (ECCS) acceptance criteria to include the effects of higher burn-up on cladding performance. The key implications of this proposition are that the cladding performance cannot be evaluated anymore as separated from other disciplines, but needs to be evaluated in a coupled manner with other physics. The Risk-Informed Safety Margin Characterization (RISMC) Pathway initiated several programs at Idaho National Laboratory (INL) to support the industry in the transition to the new rule. One of these programs is the Industry Application #1 (IA1). IA1’s goal is to develop an Integrated Evaluation Model (IEM) called LOCA Toolkit for the US (LOTUS). This tool connects five major disciplines involved in LOCA analysis, among them is (automated) core design (CD-A). Here, this paper focuses solely on the design of LOTUS' CD-A module as well as a demonstration application of the CD-A module to a generic Pressurized Water Reactor (PWR). The demonstration of the other LOTUS disciplines together with a demonstration example of the final risk-informed safety margin analysis is published in a separate paper. LOTUS is meant to provide the methodology framework into which the user can plug his established tools and codes. With the CD-A, the plant owner/operator will characterize his core design with the tools he has. He will then integrate his tools/methods into the LOTUS framework for the downstream safety analysis. For the current CD-A demonstration, the tools used are the already coupled codes PHISICS and RELAP5-3D, while cross section generation is done using the Studsvik lattice code HELIOS-2.

97 MATHEMATICS AND COMPUTING↗

Coupling, lifetimes, and “strong coupling” maps for single molecules at plasmonic interfaces

The interaction between excited states of a molecule and excited states of a metal nanostructure (e.g., plasmons) leads to hybrid states with modified optical properties. When plasmon resonance is swept through molecular transition frequency, an avoided crossing may be observed, which is often regarded as a signature of strong coupling between plasmons and molecules. Such strong coupling is expected to be realized when 2|$\langle$U$\rangle$|/ℏΓ > 1, where $\langle$U$\rangle$ and Γ are the molecule–plasmon coupling and the spectral width of the optical transition, respectively. Because both $\langle$U$\rangle$ and Γ strongly increase with decreasing distance between a molecule and a plasmonic structure, it is not obvious that this condition can be satisfied for any molecule–metal surface distance. Here, in this work, we investigate the behavior of $\langle$U$\rangle$ and Γ for several geometries. Surprisingly, we find that if the only contributions to Γ are lifetime broadenings associated with the radiative and nonradiative relaxation of a single molecular vibronic transition, including effects on molecular radiative and nonradiative lifetimes induced by the metal, the criterion 2|$\langle$U$\rangle$|/ℏΓ > 1 is easily satisfied by many configurations irrespective of the metal–molecule distance. This implies that the Rabi splitting can be observed in such structures if other sources of broadening are suppressed. Additionally, when the molecule–metal surface distance is varied keeping all other molecular and metal parameters constant, this behavior is mitigated due to the spectral shift associated with the same molecule–plasmon interaction, making the observation of Rabi splitting more challenging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Shock-driven kinetic and diffusive mix in high-Z pusher ICF designs

Revolver and Double Shell Inertial Confinement Fusion capsule designs hope to achieve a robust volumetric thermonuclear burn via the use of a high-Z pusher shell filled with a cryogenic D–T fuel. Unfortunately, mix of the pusher material into the fuel (gas) may adversely impact the burn performance. Hydrodynamic instability of the metal/gas interface as the mix source is an obvious concern, but 1D effects may also be detrimental. Such effects include plasma diffusion at material interfaces, which has been the subject of numerous theoretical, computational, and experimental investigations. However, other 1D mix mechanisms may exist, which have yet to be thoroughly explored. In particular, plasma kinetic effects may drive the mix when a shock breaks out of the metal/gas interface. Using the state-of-the-art, hybrid (kinetic-ion/fluid electron), multi-ion Vlasov–Fokker–Planck code, iFP, we show herein that shock-driven kinetic effects can reconfigure the interface and the interfacial width subsequently grows diffusively. Finally, we consider any implications for high-Z pusher designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of H + Exchange and Surface Impurities on Bulk and Interfacial Electrochemistry of Garnet Solid Electrolytes

Contact loss and current constriction pose significant challenges at the Li metal interface of solid-state batteries. For garnet-structured Li 7 La 3 Zr 2 O 12 (LLZO), these effects are amplified by Li + /H + exchange and surface contamination reactions, which lead to conductivity losses and poor Li wetting. In this study, we utilize a variety of surface treatment processes across 37 cells to selectively induce proton exchange and contamination reactions in LLZO. The resulting bulk and surface chemistry is systematically characterized and correlated to changes in electrochemical properties. Additionally, we combine impedance analysis and finite element method modeling to deconvolute sources of impedance contributions at the Li metal interface. Specifically, we show that constriction impedance at the Li metal interface arises not solely from voids, but also from ionically-resistive surface contaminants. Further, these findings emphasize the connection between ionic conductivity and constriction, demonstrating that micron-scale ionically-resistive components increase constriction even with identical contact geometries. Finally, we leverage our comprehensive dataset to highlight unstable overpotential growth as a failure mechanism, additionally showing that the phase of a cell’s impedance is a sensitive indicator for the onset of interfacial instability. Overall, this study clarifies the impacts of proton exchange and surface contamination on electrochemical properties at the Li|solid electrolyte interface and elucidates insights that are generalizable to other solid-state battery systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Signatures of a spin-active interface and a locally enhanced Zeeman field in a superconductor-chiral material heterostructure

A localized Zeeman field, intensified at heterostructure interfaces, could play a crucial role in a broad area including spintronics and unconventional superconductors. Conventionally, the generation of a local Zeeman field is achieved through magnetic exchange coupling with a magnetic material. However, magnetic elements often introduce defects, which could weaken or destroy superconductivity. Alternatively, the coupling between a superconductor with strong spin-orbit coupling and a nonmagnetic chiral material could serve as a promising approach to generate a spin-active interface. Here, we leverage an interface superconductor, namely, induced superconductivity in noble metal surface states, to probe the spin-active interface. Our results unveil an enhanced interface Zeeman field, which selectively closes the surface superconducting gap while preserving the bulk superconducting pairing. The chiral material, i.e., trigonal tellurium, also induces Andreev bound states (ABS) exhibiting spin polarization. The field dependence of ABS manifests a substantially enhanced interface Landég-factor (g eff ~ 12), thereby corroborating the enhanced interface Zeeman energy.

Science & Technology - Other Topics↗

Tetracene Functionalized Si(111) Achieves Enhanced Solar-to-Chemical Energy Conversion via Molecular Acceptor States

The properties of semiconductor|liquid interfaces play a critical role in determining the efficiency of solar-to-hydrogen (STH) conversion. Here, we investigate how molecular functionalization of Si(111) and Si(111)|TiO 2 surfaces impacts photoelectrochemical (PEC) hydrogen production efficiency. We find that functionalization of ∼3% of the atop sites of Si(111) with either 9-anthracene (Anth) or 5-tetracene (Tet), with the remaining sites passivated by methyl groups, provides substrates with high electronic quality and low surface oxide densities, as determined by X-ray photoelectron spectroscopy (XPS) measurements. Surface photovoltage (SPV) spectroscopy shows that surfaces modified with Anth or Tet exhibit an increased photovoltage, with Tet-functionalized surfaces yielding an additional 192 meV relative to methyl-terminated Si(111), indicating improved charge separation for Si-Tet. Further improvement in onset potential was achieved by replacing a nitrogen-containing TiO 2 atomic layer deposition (ALD) precursor (TDMAT) with a precursor lacking nitrogen (TTIP), which eliminates the parasitic defect band in the TiO 2 overlayer (p-Si(111)-Tet|TTIP-TiO 2 |Pt: V OC = +0.283 ± 0.041 V vs RHE). Density functional theory (DFT) analysis demonstrates that compared with Anth-modified Si(111), the Tet-modified surface exhibits more hybridized Si(111)-Tet states closer to the silicon band edges. Mercury contact current–voltage (I–V, dark) measurements quantified the relative interfacial density of states of Si-Tet, Si-Anth and Si-Me surfaces─revealing that the interfacial state density was highest for Si-Tet. This suggests that such hybridized interfaces serve to capture better photoexcited charge, which enables facile electron transfer to molecular acceptors in solution. Altogether, the data indicate that beneficial hybrid molecular LUMO surface states interacting with the Si conduction band edge results in improved hydrogen evolution (HER) performance for p-Si devices.

Group theory↗