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DOE OSTI2025

Characterization of Fuel-to-Coolant Heat Transfer During Reactivity-Initiated Accidents Using Tightly Coupled Thermal Hydraulics and Fuel Thermomechanics

The reactivity-initiated accident (RIA) is a complex scenario with several tightly interacting physical phenomena. Accurately predicting fuel behavior during these transients is difficult due to limitations in the modeling of fuel-to-coolant heat transfer. Common approaches to simulate RIAs involve standalone calculations using either a fuel performance code or a thermal-hydraulic code. The complex interdependencies of thermal-hydraulic and fuel mechanical behavior suggest that a tight coupling between these codes may provide more accurate predictions of fuel-to-coolant heat transfer and cladding mechanical response. Here, RELAP5-3D and BISON are coupled in this paper to simulate RIAs, and a sensitivity analysis is performed to rank key thermal properties and two-phase heat transfer parameters relevant for fuel-to-coolant heat transfer and cladding failure mechanisms in UO 2 –Zircaloy-4 systems. Gas gap conductance, film boiling heat transfer uncertainty, pulse width, fuel-specific heat capacity, and cladding-specific heat capacity were identified as important parameters. Variations in figures of merit resulting from changes to pulse width and the material thermal properties indicate that time-dependent heat transfer rates are significant for safety-relevant mechanical parameters due to the time dependence of cladding ductility and pellet-cladding mechanical interaction loading. The results suggest that the thermal-hydraulic factors have a nonnegligible influence on the thermomechanical solution and vice versa. Tight coupling of both sets of physics is recommended to improve prediction of fuel behavior during RIAs. Highlights include the following: 1. The RELAP5-3D thermal-hydraulic code and the BISON fuel performance code are tightly coupled for simulation of RIA transients with energy depositions at the Zircaloy-4 cladding failure threshold. 2. Departure from nucleate boiling occurred for all simulated cases. Due to the ductility of fresh fuel, substantial ballooning occurred in most cases. 3. Gas gap conductance, fuel-specific heat capacity, cladding-specific heat capacity, transient pulse width, and film boiling heat transfer were the dominant thermal factors impacting the safety figures of merit at energy depositions.

Critical Heat Flux (CHF)↗

DOE OSTI2026

Atomically Resolved Acoustic Dynamics Coupled with Magnetic Order in a Van der Waals Antiferromagnet

Magnetoelastic coupling in van der Waals (vdW) magnetic materials enables a unique interplay between the spin and lattice degrees of freedom. Characterizing the elastic responses with atomic and femtosecond resolution across the magnetic transition is essential for guiding the design of magnetically tunable actuators and strain-mediated spintronic devices. Here, ultrafast X-ray diffraction employed at a free-electron laser reveals that the atomic displacements, wave vectors, and dispersion relations of acoustic phonon modes in a vdW antiferromagnet FePS3 are coupled with the magnetic order, by tracking both in-plane and out-of-plane Bragg peaks upon optical excitation across the Néel temperature (TN). One transverse mode shows that a quasi-out-of-plane atomic displacement undergoes a significant directional change across TN. Its quasi-in-plane wave vector is derived by comparing the measured sound velocity and the first-principles calculations. The other transverse mode is an interlayer shear acoustic mode whose amplitude is strongly enhanced in the antiferromagnetic phase, exhibiting eight times stronger amplitude than the longitudinal acoustic mode below TN. The atomically resolved characterization of acoustic phonon dynamics that couple with magnetic ordering opens opportunities for harnessing unique magnetoelastic coupling in vdW magnets on ultrafast timescales.

coherent acoustic phonons↗

DOE OSTI2025

A Monte-Carlo method for Coulomb collisions in moderately coupled plasmas

Here, we introduce a new approach for coupling cumulative and single-scattering distributions, extending Monte Carlo methods for Coulomb collisions in weakly coupled plasmas into the moderately coupled regime. Using time steps typical of cumulative-scattering methods, we show that this approach not only recovers leading-order corrections proportional to the inverse Coulomb logarithm but also solves the full Boltzmann collision integral. A key feature of the method is its simplicity: it can be integrated into cumulative-scattering methods for weakly coupled plasmas with only ~ 10 additional lines of code.

Boltzmann collision integral↗

DOE OSTI2025

Differential Ligation Alters Electronic State and Coupling Signals of Iron-Sulfur Clusters in Flavin-Based Electron Bifurcation

Flavin-based electron bifurcation (FBEB) is employed by microorganisms for controlling pools of redox equivalents by reversibly splitting electron pairs into high- and low-energy levels from an initial midpoint potential. Our ability to harness this phenomenon is crucial for biocatalytic design which is limited by our understanding of energy coupling in the bifurcation system. In Pyrococcus furiosus, FBEB is carried out by the NADH-dependent ferredoxin:NADP+-oxidoreductase (NfnSL), coupling the uphill reduction of ferredoxin in NfnL to the downhill reduction of NAD+ in NfnS from oxidation of NADPH. Flanking the bifurcating flavin are two site-differentiated iron-sulfur clusters; the nearest is a glutamate-ligated [4Fe-4S] cluster in NfnL. Recent biochemical experiments substituting the native glutamate with cysteine led to loss of coupling between the uphill and downhill pathways, in contrast to the tight thermodynamic coupling in the native system. To understand how this decoupling is biochemically manifested by the cysteine-substituted [4Fe-4S] in NfnL, we employed electron paramagnetic resonance (EPR) spectroscopy to identify changes in electronic architecture and square wave voltammetry (SWV) to probe thermodynamic shifts produced by the substitution. We observed notable g-value shifts in the EPR for the cysteine-substituted iron-sulfur cluster in addition to significant downward shifts in the redox potential, as well as the disappearance of several low-field signals observed in the native NfnSL complex. These results suggest the site-differentiated glutamate residue facilitates higher spin states in the [4Fesingle bond4S] cluster to bridge energetic gaps in electron transfer to the bifurcating flavin in the native complex, preventing unwanted short-circuiting seen in the cysteine-substituted complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Comparison of methods for the NMR measurement of motionally averaged dipolar couplings

Motionally averaged dipolar couplings are an important tool for understanding the complex dynamics of catalysts, polymers, and biomolecules. While there is a plethora of solid-state NMR pulse sequences available for their measurement, in can be difficult to gauge the methods’ strengths and weaknesses. In particular, there has not been a comprehensive comparison of their performance in natural abundance samples, where 1H homonuclear dipolar couplings are important and the use of large MAS rotors may be required for sensitivity reasons. In this work, we directly compared some of the more common methods for measuring C–H dipolar couplings in natural abundance samples using L-alanine (L-Ala) and the N-formyl-L-methionyl-L-leucyl-L-phenylalanine (fMLF) tripeptide as model systems. Here, we evaluated their performance in terms of accuracy, resolution, sensitivity, and ease of implementation. We found that, despite the presence of 1H homonuclear dipolar interactions, all methods, with the exception of REDOR, were able to yield the reasonable dipolar coupling strengths for both mobile and static moieties. Of these methods, PDLF provides the most convenient workflow and precision at the expense of low sensitivity. In low-sensitivity cases, MAS-PISEMA and DIPSHIFT appear to be the better options.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Constraints on the Higgs boson self-coupling from the combination of single and double Higgs boson production in proton-proton collisions at $\sqrt{s} = 13$ TeV

The Higgs boson (H) trilinear self-coupling, λ 3 , is constrained via its measured properties and limits on the HH pair production using the proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV . The combination of event categories enriched in single-H and HH events is used to measure κ λ , defined as the value of λ 3 normalized to its standard model prediction, while simultaneously constraining the Higgs boson couplings to fermions and vector bosons. Values of κ λ outside the interval -1.2 < κ λ < 7.5 are excluded at 2σ confidence level, which is compatible with the expected range of -2.0 < κ λ < 7.7 under the assumption that all other Higgs boson couplings are equal to their standard model predicted values. Relaxing the assumption on the Higgs couplings to fermions and vector bosons the observed (expected) κ λ interval is constrained to be within -1.4 < κ λ < 7.8 (-2.3 < κ λ < 7.8) at 2σ confidence level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Large Hyperfine Coupling Arising from Pseudo- 2 S Ground States in a Series of Lutetium(II) Metallocene Complexes

The synthesis of molecules with strong coupling between electronic and nuclear spins represents an important challenge in molecular quantum information science. Here, we report the synthesis and characterization of the divalent lutetium metallocene complexes Lu(Cp Me 5 )(Cp iPr 5 ) (Cp Me 5 = pentamethylcyclopentadienyl; Cp iPr 5 = pentaisopropylcyclopentadienyl), Lu(Cp iPr 4 Et ) 2 (Cp iPr 4 Et = ethyltetraisopropylcyclopentadienyl), and Lu(Cp iPr 4 ) 2 (Cp iPr 4 = tetraisopropylcyclopentadienyl). The molecular structures of these complexes, as determined through singlecrystal X-ray diffraction, feature a common bent sandwich geometry, with average Cp–Lu–Cp angles ranging from 159.9° to 152.6°. Analysis of continuous-wave electron paramagnetic resonance (EPR) spectra for the complexes reveals nearly isotropic g tensors with only a slight deviation from that of a free electron. Moreover, an extremely large splitting of the eight-line spectra indicates the presence of strong hyperfine coupling, and simulations provide isotropic hyperfine coupling constants of A iso = 4.38, 4.30, and 4.17 GHz across the series, where the value of A iso is found to decrease as the Cp–Lu–Cp angle becomes more acute. Notably, these values are the largest yet observed for any lanthanide complex. Moreover, EPR and computational analysis show that the large values of A iso stem from large s-orbital character up to 41.2% in the corresponding singly occupied molecular orbitals. To our knowledge, this degree of s-character in a molecular orbital is the largest yet reported for an open-shell isolable complex. These results outline a general strategy toward the isolation of paramagnetic molecules with strong hyperfine coupling and highly isotropic doublet electronic ground states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Development, Application, and Mechanistic Interrogation of a Dual Ni Catalysis Approach to Photoredox-Based C(sp 3 )–C(sp 3 ) Cross-Coupling

The installation of alkyl substituents such as methyl groups is a crucial tactic for the synthesis and diversification of medicinal compounds with improved pharmacological profiles. However, strategies that leverage methyl radical for C(sp 3 ) methylation remain underdeveloped due to the challenge of obtaining cross-selectivity between fleeting aliphatic radicals and alkyl electrophiles. Here, we report the development, application, and interrogation of a conceptually novel mechanistic framework for C(sp 3 )–Me bond formation using two distinct Ni catalysts capable of cross-coupling sterically and electronically diverse alkyl halides (chlorides and bromides) with methyl radical generated photocatalytically from benzaldehyde dimethyl acetal. Furthermore, by modifying the alkyl substituents on the acetal coupling partner, we demonstrate cross-couplings beyond methylation to access an array of 1°–1° and 1°–2° alkyl–alkyl bonds. Experimental and computational mechanistic studies provide support for cooperativity between an in situ-generated (bpy)Ni I (X) catalyst that facilitates XAT and inner-sphere C–C bond formation and a (Tp*)Ni II (acac) cocatalyst that captures methyl radical and engages in concurrent outer-sphere S H 2 coupling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Boundary-Layer-Coupled and Decoupled Clouds in Global Storm-Resolving Models: Comparisons With the ARM Observations

The accurate representation of interactions between clouds and planetary boundary layer (PBL) is a persistent challenge in climate models, critical for simulating surface energy budget. The emergence of kilometer-grid-scale global storm resolving models (GSRMs) offers the potential for enhanced details of PBL processes in these complex interactions. This study evaluates the representation of PBL-coupled and decoupled clouds in nine GSRM simulations against extensive ground-based observations by the Department of Energy Atmospheric Radiation Measurement (ARM) program, across six sites encompassing diverse regimes such as marine and continental environments in tropics and midlatitude. By differentiating coupling based on the relative positions between cloud bases and PBL tops, our analysis focuses on the simulation of PBL height, cloud frequency, position and vertical extent. The GSRMs generally exhibit commendable agreements with observed cloud structures and PBL diurnal cycles across different ARM sites. In contrast to the relatively consistent representation of decoupled clouds, discrepancies exist between the simulated and the observed coupled clouds, particularly in areas of intense convection, for example, over tropical rainforests and mountainous regions. These biases are probably associated with the models' tendency to underestimate the boundary layer humidity and the frequency of coupled clouds within different ranges of PBL heights. This study underscores the importance for continuous improvements in the representation of boundary layer and convection within these global kilometer-grid-scale models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

General framework for quantifying dissipation pathways in open quantum systems. III. Off-diagonal subsystem–bath couplings

This paper extends the previously reported theory of dissipation pathways [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111 (2024)] to incorporate off-diagonal subsystem–bath coupling, which is often required to model molecular systems where the environment directly influences transitions and couplings between subsystem states. We systematically derive master equations for both population transfer and dissipation into individual bath components, for which we also rigorously prove energy conservation and detailed balance. The approach is based on second-order perturbation theory with respect to the subsystem–bath couplings, whose form is not limited to any specific model. The accuracy of the developed method is tested by applying it to diverse model Hamiltonians involving linearly coupled harmonic oscillator baths and comparing the outcomes against the hierarchical equations of motion (HEOM) method. Overall, our method accurately quantifies the contributions of specific bath components to the overall dissipation while significantly reducing the computational cost compared to numerically exact methods such as HEOM, thus offering a path to examine how vibronic interactions steer non-adiabatic processes in realistic chemical systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Design and Study of Inductively Coupled Plasma Chamber Components Using the SupRISE Test Device at DIII-D

The DIII-D National Fusion Facility aims to increase the auxiliary heating power for the tokamak by upgrading the Neutral Beam Injection (NBI) system. In collaboration with North Carolina State University, the conventional ‘arc and filament’ NBI ion sources will be converted to inductively coupled plasma (ICP) sources which utilize radio frequency (RF) coupling to maximize reliability for high power operation. In support of this initiative, a full scale test device (SupRISE, Superior Radiofrequency Ion Source Experiment) is currently under construction at the DIII-D Facility. In preparation for the construction of a full scale prototype that can be installed on the DIII-D NBI system, experiments on SupRISE will be conducted to determine the optimal RF frequency for high power coupling, Faraday shield slit configuration, and ICP chamber length. SupRISE is comprised of an approximately 30 x 70 cm quartz dielectric vessel with an internal Faraday shield enclosed in a secondary vacuum chamber to ensure structural stability of the dielectric. Actively cooled front and back plates are designed to reduce the thermal stresses on the plasma facing components and mate with the existing accelerator used by the NBI system at DIII-D. 50 kW of RF power will be coupled to the plasma through the quartz over a variable frequency range of 4-8 MHz to sustain a plasma density of ∼ 10 18 m −3 for a 10 s ON, 210 s OFF duty cycle. Various modelling efforts have been employed to simulate the thermal and stress profiles over the primary components of the SupRISE device as well as the inductance behavior of the RF antenna. These simulation results and the final design for SupRISE will be presented. An additional reduced-scale predecessor ICP source (called RISE) has been used to develop a predictive match model that will be applied to frequency optimization studies on SupRISE. Furthermore, the outcomes of this research and complementary efforts at North Carolina State University are essential for the incorporation of ICP NBI positive ion sources at the DIII-D facility.

DIII-D↗

DOE OSTI2024

Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry

A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group–subgroup chains is presented. The canonical U(4) > U(3) > U(2) > U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4) coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single U(4) > SU S (2) Ⓧ SU T (2) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N) . It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).

Cross-Coupling Reaction↗

DOE OSTI2024

HYDRODYNAMIC TESTING OF ZIRCALOY TO STEEL HUB COUPLINGS FOR USE IN ADVANCED TEST REACTOR I-LOOP TUBE

The ATR I-positions' isolation from the flux trap region provides an opportunity for a test facility that could create conditions representative of commercial light water reactors. Such a facility requires piping couplings and joints that withstand extreme thermal and pressure cycling. Also, transitioning from steel to zircaloy piping inside the reactor vessel allows the neutronic properties of zircaloy to be leveraged while using cost-effective stainless steel outside of the core. Grayloc-style hub couplings will act as transition points between stainless steel piping and zircaloy piping inside the reactor vessel. These couplings have not been sufficiently tested for leakage where there is a transition between materials. This transition is a concern because the thermal expansion coefficients of the materials differ. Seal integrity between the two components may be greatly affected by thermal expansion at the connection. Thus, the effect of thermal cycling must be assessed. Thermal and pressure cycling and hydrodynamic testing will be conducted to verify seal integrity of the steel to zircaloy hub coupling when subjected to ATR conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Electrocatalytic CN Coupling: Advances in Urea Synthesis and Opportunities for Alternative Products

Urea is an essential fertilizer produced through the industrial synthesis of ammonia (NH 3 ) via the Haber–Bosch process, which contributes ≈1.2% of global annual CO 2 emissions. Electrocatalytic urea synthesis under ambient conditions via CN coupling from CO 2 and nitrogen species such as nitrate (NO 3 − ), nitrite (NO 2 − ), nitric oxide (NO), and nitrogen gas (N 2 ) has gained interest as a more sustainable route. However, challenges remain due to the unclear reaction pathways for urea formation, competing reactions, and the complexity of the resulting product matrix. This review highlights recent advances in catalyst design, urea quantification, and intermediate identification in the CN coupling reaction for electrocatalytic urea synthesis. Furthermore, this review explores future prospects for industrial CN coupling, considering potential nitrogen and carbon sources and examining alternative CN coupling products, such as amides and amines.

Chemistry↗

DOE OSTI2024

Coupled model for liquid lithium plasma facing components

Numerical analysis provides the design choice and operating window of liquid metal Plasma Facing Components (PFC) concepts. Coupled analysis of boundary plasma together with the surrounding boundary structures is required. Here, to achieve this goal, PPPL is developing a comprehensive multi-physics model for modeling of PFCs in fusion devices. The model includes the fluid-kinetic code SOLPS-ITER and the flow and heat transfer code CFX from ANSYS. SOLPS-ITER was augmented with a liquid metal boundary condition algorithm, allowing direct two-way coupling of the plasma analysis with the two-dimensional analytical slab flow model which includes heat convection in the liquid metal PFC. The target heat flux resulting from this coupled analysis is used as a boundary condition for detailed 3D Computational Fluid Dynamics (CFD) Magneto Hydro Dynamics (MHD) and heat transfer analysis. A new formulation of MHD equations is introduced in the numerical procedure ensuring current conservation of the discretized equations. Results of the 3D analysis are used for final validation of the coupled model. A PFC design where a porous wall is used to stabilize the liquid metal surface, while MHD drive is used to push the liquid metal flow inside the PFC, will be investigated in the regimes where vapor shielding is created for enhanced volumetric plasma heat dissipation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Alkali Metal Control of Triplet-Mediated C–H Activation in Iron-Mediated Coupling of Dinitrogen and Benzene

Direct coupling of N 2 with abundant feedstocks like benzene to form N-containing organic compounds is a promising strategy for N 2 fixation pathways. The challenge of coupling N 2 activation and C–H bond oxidative addition was recently solved by introducing a reversible benzene C–H bond activation process mediated by a low-valent Fe(0) complex, which gave an organometallic product that could couple with partially reduced N 2 . Interestingly, the energetics of the C–H oxidative addition/reductive elimination step depends on the choice of alkali metal. However, the reason why the alkali metal influences the C–H bond activation remained elusive. In this work, we present a comprehensive study on this Fe(0)-mediated reversible C–H activation. Through density functional theory combined with high-level coupled cluster calculations, we discovered that the intermediate-spin triplet (S = 1) controls the energy of the transition state for C–H cleavage, while the high-spin quintet (S = 2) controls the position of the equilibrium. Na + drives the equilibrium toward oxidative addition due to an electrostatic effect, while K + and Rb + are dominated by a steric effect that favors the iron(0) species. The key role played by nonbonding interactions in the Fe-mediated C–H activation provides a conceptual model for alkali control over organometallic transformations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Complex-Valued Intermolecular Coupling Enables Directional Exciton Transport in Excitonic Circuits

Molecular systems capable of directing the flow of excitons are key to the development and optimization of optoelectronic materials. The transport of excitons across multiple molecules is governed by an intermolecular electronic coupling network. In this article, we consider the effects of complex-valued intermolecular electronic coupling on exciton transport. Here, we present a molecular motif capable of generating complex-valued coupling under excitation with circularly polarized light. We use theoretical modeling and simulation to illustrate how complex coupling can be leveraged to drive the rotational flux of excitons in cyclic molecular networks and direct the exciton population in branched molecular networks.

chromophores↗

DOE OSTI2025

Redox Couples Control Band Bending, Photovoltage, and Quasi-Fermi Levels in Tungsten Oxide (WO 3 ) Photoanodes

Tungsten oxide (WO 3 ) is a well-known photoanode and photocatalyst for photoelectrochemical (PEC) water oxidation. Because the compound has a deep valence band, it can facilitate the oxygen evolution reaction without added cocatalysts, and it can drive the oxidation of species with much higher electrochemical potentials, including the conversion of water to hydrogen peroxide, sulfate to persulfate, and iodate to meta-periodate. Here, we use the liquid vibrating Kelvin probe surface photovoltage (liquid VK-SPV) technique in combination with open circuit potential (OCP) and photoelectrochemical (PEC) scans to assess the possibility of reaching such oxidizing potentials in aqueous electrolytes and at open circuit. Here, this is done by mapping the quasi-Fermi levels of electrons and holes at the interfaces as a function of the light intensity. Nanostructured WO 3 photoelectrodes for this purpose were fabricated by thermal annealing of a tungstic acid solution on fluorine-doped tin oxide. Electrochemical measurements are conducted at open circuit and 400 nm LED light illumination in electrolytes containing fast (O 2 /H 2 O 2 ), slow (O 2 /H 2 O), and very oxidizing (NaIO 4 /NaIO 3 ) redox couples. Photovoltage values scale with the light intensity and with the built-in potential for each redox couple and reach values up to 0.61 V under 20 mW cm –2 illumination for the NaIO 4 electrolyte. This shows that the photoelectrodes behave like Schottky-type diodes whose maximum possible energy output is determined mainly by the built-in voltage of each junction. For slow redox couples, the quasi-Fermi level of the holes increases with light intensity due to hole accumulation at the WO 3 –liquid interface. For example, for the O 2 /H 2 O electrolyte, interfacial hole accumulation and removal occur on the 90–300 s time scale. For the fast hole acceptor H 2 O 2 , on the other hand, the quasi-Fermi level of the photoholes is pinned to the electrochemical potential of the O 2 /H 2 O 2 couple. This limits the energy conversion efficiency of the electrode. Overall, these results reveal the influence of charge transfer thermodynamics and kinetics on the photovoltage of WO 3 . Furthermore, the work further establishes VK-SPV as a contactless method to observe the photovoltage, carrier dynamics, and quasi-Fermi levels of semiconductor-liquid junctions.

Electrodes↗