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At least 127 records · Page 7

Hot spots and active longitudes: Organization of solar activity as a probe of the interior

In order to investigate how solar activity is organized in longitude, major solar flares, large sunspot groups, and large scale photospheric magnetic field strengths were analyzed. The results of these analyses are reported. The following results are discussed: hot spots, initially recognized as areas of high concentration of major flares, are the preferred locations for the emergence of big sunspot groups; double hot spots appear in pairs that rotate at the same rate separated by about 180 deg in longitude, whereas, single hot spots have no such companions; the northern and southern hemispheres behave differently in organizing solar activity in longitude; the lifetime of hot spots range from one to several solar cycles; a hot spot is not always active throughout its lifetime, but goes through dormant periods; and hot spots with different rotational periods coexist in the same hemisphere during the same solar cycle.

Bai, Taeil↗

Flash Mixing on the White-Dwarf Cooling Curve: Understanding Hot Horizontal Branch Anomalies in NGC 2808

We present an ultraviolet color-magnitude diagram (CMD) spanning the hot horizontal branch (HB), blue straggler, and white dwarf populations of the globular cluster NGC 2808. These data, obtained with the Space Telescope Imaging Spectrograph (STIS), demonstrate that NGC 2808 harbors a significant population of hot subluminous HB stars, an anomaly only previously reported for the globular cluster omega Cen. Our theoretical modeling indicates that the location of these subluminous stars in the CMD, as well as the high temperature gap along the HB of NGC 2808, can be explained if these stars underwent a late helium-core flash while descending the white dwarf cooling curve. We show that the convective zone produced by such a late helium flash will penetrate into the hydrogen envelope, thereby mixing hydrogen into the hot helium-burning interior, where it is rapidly consumed. This phenomenon is analogous to the "born again" scenario for producing hydrogen-deficient stars following a late helium-shell flash. The flash mixing of the envelope greatly enhances the envelope helium and carbon abundances that, in turn, leads to a discontinuous increase in the HB effective temperatures. We argue that the hot HB gap is associated with this theoretically predicted dichotomy in the HB properties. Moreover, the changes in the emergent spectral energy distribution caused by these abundance changes are primarily responsible for explaining the hot subluminous HB stars. Although further evidence is needed to confirm that a late helium-core flash can account for the subluminous HB stars and the hot HB gap, we demonstrate that an understanding of these stars requires the use of appropriate theoretical models for their evolution, atmospheres, and spectra.

Brown, Thomas M.↗

Measurements of Aerosol, Ocean and Sky Properties at the HOT Site in the Central Pacific

Monthly cruises have been made to the HOT site (approximately 100 km north of Oahu) since October 1988. The goal of these cruises is to make hydrography, chemistry, and biology observations. Measurements are typically made at a near coastal station (Kahe) on the first day to test the equipment and to obtain coastal shallow water (approximately 1500 m) observations. The second and third days are spent at the HOT site. On the morning of the fourth day, measurements are made at the HOT site and noontime measurements are made at the Hale-Aloha station near the mooring before returning to port by early the next morning. The locations of the three stations are Kahe, HOT, and Hale-ALOHA buoy. The routine HOT measurements are available during the summer following the year of the observations. The 1998 measurements will therefore become available during the summer of 1999. The data sets can be obtained at the National Oceanographic Data Center (NODC) or from the HOT web site http://kahana.soest.hawaii.edu/hot/hot_jgofs.html.

Porter, John N.↗

Experimental Evaluation of Hot Films on Ceramic Substrates for Skin-Friction Measurement

An investigation has been performed on the use of low-thermal conductivity, ceramic substrates for hot films intended to measure skin friction. Hot films were deposited on two types of ceramic substrates. Four hot films used composite-ceramic substrates with subsurface thermocouples (TCs), and two hot films were deposited on thin Macor(R) substrates. All six sensors were tested side by side in the wall of the NASA Glenn Research Center 8-ft by 6-ft Supersonic Wind Tunnel (SWT). Data were obtained from zero flow to Mach 1.98 in air. Control measurements were made with three Preston tubes and two boundary-layer rakes. The tests were repeated at two different hot film power levels. All hot films and subsurface TCs functioned throughout the three days of testing. At zero flow, the films on the high-thermal conductivity Macor(R) substrates required approximately twice the power as those on the composite-ceramic substrates. Skin-friction results were consistent with the control measurements. Estimates of the conduction heat losses were made using the embedded TCs but were hampered by variability in coating thicknesses and TC locations.

Noffz, Gregory K.↗

Advances in Hot-Structure Development

The National Aeronautics and Space Administration has actively participated in the development of hot structures technology for application to hypersonic flight systems. Hot structures have been developed for vehicles including the X-43A, X-37, and the Space Shuttle. These trans-atmospheric and atmospheric entry flight systems that incorporate hot-structures technology are lighter weight and require less maintenance than those that incorporate parasitic, thermal-protection materials that attach to warm or cool substructure. The development of hot structures requires a thorough understanding of material performance in an extreme environment, boundary conditions and load interactions, structural joint performance, and thermal and mechanical performance of integrated structural systems that operate at temperatures ranging from 1500 C to 3000 C, depending on the application. This paper will present recent advances in the development of hot structures, including development of environmentally durable, high temperature leading edges and control surfaces, integrated thermal protection systems, and repair technologies. The X-43A Mach-10 vehicle utilized carbon/carbon (C/C) leading edges on the nose, horizontal control surface, and vertical tail. The nose and vertical and horizontal tail leading edges were fabricated out of a 3:1 biased, high thermal conductivity C/C. The leading edges were coated with a three-layer coating comprised of a SiC conversion of the C/C, followed by a CVD layer of SiC, followed by a thin CVD layer of HfC. Work has also been performed on the development of an integrated structure and was focused on both hot and warm (insulated) structures and integrated fuselage/tank/TPS systems. The objective was to develop integrated multifunctional airframe structures that eliminate fragile external thermal-protection systems and incorporate the insulating function within the structure. The approach taken to achieve this goal was to develop candidate hypersonic airframe concepts, including structural arrangement, load paths, thermal-structural wall design, thermal accommodation features, and integration of major components, optimize thermalstructural configurations, and validate concepts through a building block test program and generate data to improve and validate analytical and design tools.

Rivers, H. Kevin↗

The Hottest Horizontal-Branch Stars in Omega Centauri: Late Hot Flasher vs. Helium Enrichment

UV observations of some massive globular clusters uncovered a significant population of very hot stars below the hot end of the horizontal branch (HB), the so-called blue hook stars. This feature might be explained either by the late hot flasher scenario here stars experience the helium flash while on the white dwarf cooling curve or by the helium-rich sub-population recently postulated to exist in some clusters. Spectroscopic analyses of blue hook stars in omega Cen and NGC 2808 support the late hot flasher scenario, but the stars contain much less helium than expected and the predicted C, N enrichment could not be verified from existing data. We want to determine effective temperatures, surface gravities and abundances of He, C, N in blue hook and canonical extreme horizontal branch (EHB) star candidates. Moderately high resolution spectra of stars at the hot end of the blue horizontal branch in the globular cluster omega Cen were analysed for atmospheric parameters (T(sub eff), log g) and abundances using LTE and Non-LTE model atmospheres. In the temperature range 30,000 K to 50,000 K we find that 37% of our stars are helium-poor (log nHe/nH less than -2), 49% have solar helium abundance within a factor of 3 (-1.5 less than or equal to log nHe/nH less than or equal to -0.5) and 14% are helium rich (log nHe/nH greater than -0.4). We also find carbon enrichment in step with helium enrichment, with a maximum carbon enrichment of 3% by mass. At least 30% of the hottest HB stars in omega Centauri show helium abundances well above the predictions from the helium enrichment scenario (Y = 0.42 corresponding to log nHe/nH approximately equal to -0.74). In addition the most helium-rich stars show strong carbon enrichment as predicted by the late hot flasher scenario. We conclude that the helium-rich HB stars in omega Cen cannot be explained solely by the helium-enrichment scenario invoked to explain the blue main sequence.

Moehler, S.↗

Metagenomic Study of Iron Homeostasis in Iron Depositing Hot Spring Cyanobacterial Community

Introduction: It is not clear how an iron-rich thermal hydrosphere could be hospitable to cyanobacteria, since reduced iron appears to stimulate oxidative stress in all domains of life and particularly in oxygenic phototrophs. Therefore, metagenomic study of cyanobacterial community in iron-depositing hot springs may help elucidate how oxygenic prokaryotes can withstand the extremely high concentrations of reactive oxygen species (ROS) produced by interaction between environmental Fe2+ and O2. Method: Anchor proteins from various species of cyanobacteria and some anoxygenic phototrophs were selected on the basis of their hypothetical role in Fe homeostasis and the suppression of oxidative stress and were BLASTed against the metagenomes of iron-depositing Chocolate Pots and freshwater Mushroom hot springs. Results: BLASTing proteins hypothesized to be involved in Fe homeostasis against the microbiomes from the two springs revealed that iron-depositing hot spring has a greater abundance of defensive proteins such as bacterioferritin comigratory protein (Bcp) and DNA-binding Ferritin like protein (Dps) than a fresh-water hot spring. One may speculate that the abundance of Bcp and Dps in an iron-depositing hot spring is connected to the need to suppress oxidative stress in bacteria inhabiting environments with high Fe2+ concnetration. In both springs, Bcp and Dps are concentrated within the cyanobacterial fractions of the microbial community (regardless of abundance). Fe3+ siderophore transport (from the transport system permease protein query) may be less essential to the microbial community of CP because of the high [Fe]. Conclusion: Further research is needed to confirm that these proteins are unique to photoautotrophs such as those living in iron-depositing hot spring.

Brown, I.↗

Hot-Fire Test Results of Liquid Oxygen/RP-2 Multi-Element Oxidizer-Rich Preburners

As part of the Combustion Stability Tool Development project funded by the Air Force Space and Missile Systems Center, the NASA Marshall Space Flight Center was contracted to assemble and hot-fire test a multi-element integrated test article demonstrating combustion characteristics of an oxygen/hydrocarbon propellant oxidizer-rich staged-combustion engine thrust chamber. Such a test article simulates flow through the main injectors of oxygen/kerosene oxidizer-rich staged combustion engines such as the Russian RD-180 or NK-33 engines, or future U.S.-built engine systems such as the Aerojet-Rocketdyne AR-1 engine or the Hydrocarbon Boost program demonstration engine. To supply the oxidizer-rich combustion products to the main injector of the integrated test article, existing subscale preburner injectors from a previous NASA-funded oxidizer-rich staged combustion engine development program were utilized. For the integrated test article, existing and newly designed and fabricated inter-connecting hot gas duct hardware were used to supply the oxidizer-rich combustion products to the oxidizer circuit of the main injector of the thrust chamber. However, before one of the preburners was used in the integrated test article, it was first hot-fire tested at length to prove it could provide the hot exhaust gas mean temperature, thermal uniformity and combustion stability necessary to perform in the integrated test article experiment. This paper presents results from hot-fire testing of several preburner injectors in a representative combustion chamber with a sonic throat. Hydraulic, combustion performance, exhaust gas thermal uniformity, and combustion stability data are presented. Results from combustion stability modeling of these test results are described in a companion paper at this JANNAF conference, while hot-fire test results of the preburner injector in the integrated test article are described in another companion paper.

Protz, C. S.↗

Hot-Fire Test Results of an Oxygen/RP-2 Multi-Element Oxidizer-Rich Staged-Combustion Integrated Test Article

As part of the Combustion Stability Tool Development project funded by the Air Force Space and Missile Systems Center, the NASA Marshall Space Flight Center was contracted to assemble and hot-fire test a multi-element integrated test article demonstrating combustion characteristics of an oxygen/hydrocarbon propellant oxidizer-rich staged-combustion engine thrust chamber. Such a test article simulates flow through the main injectors of oxygen/kerosene oxidizer-rich staged combustion engines such as the Russian RD-180 or NK-33 engines, or future U.S.-built engine systems such as the Aerojet-Rocketdyne AR-1 engine or the Hydrocarbon Boost program demonstration engine. For the thrust chamber assembly of the test article, several configurations of new main injectors, using relatively conventional gas-centered swirl coaxial injector elements, were designed and fabricated. The design and fabrication of these main injectors are described in a companion paper at this JANNAF meeting. New ablative combustion chambers were fabricated based on hardware previously used at NASA for testing at similar size and pressure. An existing oxygen/RP-1 oxidizer-rich subscale preburner injector from a previous NASA-funded program, along with existing and new inter-connecting hot gas duct hardware, were used to supply the oxidizer-rich combustion products to the oxidizer circuit of the main injector of the thrust chamber. Results from independent hot-fire tests of the preburner injector in a combustion chamber with a sonic throat are described in companion papers at this JANNAF conference. The resulting integrated test article - which includes the preburner, inter-connecting hot gas duct, main injector, and ablative combustion chamber - was assembled at Test Stand 116 at the East Test Area of the NASA Marshall Space Flight Center. The test article was well instrumented with static and dynamic pressure, temperature, and acceleration sensors to allow the collected data to be used for combustion analysis model development. Hot-fire testing was conducted with main combustion chamber pressures ranging from 1400 to 2100 psia, and main combustion chamber mixture ratios ranging from 2.4 to 2.9. Different levels of fuel film cooling injected from the injector face were examined ranging from none to about 12% of the total fuel flow. This paper presents the hot-fire test results of the integrated test article. Combustion performance, stability, thermal, and compatibility characteristics of both the preburner and the thrust chamber are described. Another companion paper at this JANNAF meeting includes additional and more detailed test data regarding the combustion dynamics and stability characteristics.

Hulka, J. R.↗

FAUST I. The hot corino at the heart of the prototypical Class I protostar L1551 IRS5

The study of hot corinos in solar-like protostars has been so far mostly limited to the Class 0 phase, hampering our understanding of their origin and evolution. In addition, recent evidence suggests that planet formation starts already during Class I phase, which therefore represents a crucial step in the future planetary system chemical composition. Hence, the study of hot corinos in Class I protostars has become of paramount importance. Here, we report the discovery of a hot corino towards the prototypical Class I protostar L1551 IRS5, obtained within the ALMA (Atacama Large Millimeter/submillimeter Array) Large Program FAUST (Fifty AU STudy of the chemistry in the disc/envelope system of solar-like protostars). We detected several lines from methanol and its isotopologues (13CH3OH and CH2DOH), methyl formate, and ethanol. Lines are bright towards the north component of the IRS5 binary system, and a possible second hot corino may be associated with the south component. The methanol lines' non-LTE analysis constrains the gas temperature (∼100 K), density (≥1.5 × 10^8 per cu.cm), and emitting size (∼10 au in radius). All CH3OH and 13CH3OH lines are optically thick, preventing a reliable measure of the deuteration. The methyl formate and ethanol relative abundances are compatible with those measured in Class 0 hot corinos. Thus, based on this work, little chemical evolution from Class 0 to I hot corinos occurs.

astrochemistry, stars: formation, ISM: molecules↗

A Noble-Transition Alloy Excels at Hot-Carrier Generation in the Near Infrared

Above-equilibrium “hot”-carrier generation in metals is a promising route to convert photons into electrical charge for efficient near-infrared optoelectronics. However, metals that offer both hot-carrier generation in the near-infrared and sufficient carrier lifetimes remain elusive. Alloys can offer emergent properties and new design strategies compared to pure metals. In this work, it is shown that a noble-transition alloy, Au x Pd 1-x , outperforms its constituent metals concerning generation and lifetime of hot carriers when excited in the near-infrared. At optical fiber wavelengths (e.g., 1550 nm), Au 50 Pd 50 provides a 20-fold increase in the number of ≈0.8 eV hot holes, compared to Au, and a threefold increase in the carrier lifetime, compared to Pd. The discovery that noble-transition alloys can excel at hot-carrier generation reveals a new material platform for near-infrared optoelectronic devices.

36 MATERIALS SCIENCE↗

Evidence of hot carrier extraction in metal halide perovskite solar cells

The presence of hot carriers is presented in the operational properties of an (FA,Cs)Pb(I, Br, Cl) 3 solar cell at ambient temperatures and under practical solar concentration. Albeit, in a device architecture that is not suitably designed as a functional hot carrier solar cell. At 100 K, clear evidence of hot carriers is observed in both the high energy tail of the photoluminescence spectra and from the appearance of a nonequilibrium photocurrent at higher fluence in light J–V measurements. At room temperature, however, the presence of hot carriers in the emission at elevated laser fluence is shown to compete with a gradual red shift in the PL peak energy as photoinduced halide segregation begins to occur at higher lattice temperature. The effects of thermionic emission of hot carriers and the presence of a nonequilibrium carrier distribution are also shown to be distinct from simple lattice heating. In conclusion, this results in large unsaturated photocurrents at high powers as the Fermi distribution exceeds that of the heterointerface controlling carrier transport and rectification.

14 SOLAR ENERGY↗

Machine learning assisted bayesian inference of mix and hot-spot conditions in NIF implosions

Experiments on the National Ignition Facility (NIF) have provided clear evidence of ablator material mixing into the Hot-Spot, leading to degraded performance. However, inferring the amount of mix and Hot-Spot conditions from typical experimental observations (e.g. x-ray spectra and images) is highly challenging. Here, we have developed an analysis method that utilizes machine learning assisted Bayesian inference to find the probability distributions of the Hot-Spot and mix conditions. This approach uses a neural network, trained on an idealized 2-dimensional representation of the Hot-Spot and mix distribution, and Bayesian inference to find the statistical distributions of Hot-Spot conditions that provide a match with observations. We have tested this method with synthetic data from simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Microstructure refinement of hot deformed Dy-free NdFeB magnets through a novel cold sintering approach by pressure-assisted spark plasma sintering

Anisotropic fine-grained Dy-free NdFeB high-performance magnets were produced using a novel cold sintering approach by pressure-assisted spark plasma sintering (SPS). The NdFeB nanocrystalline ribbon powders were subjected to cold sintering below 450 °C using pressure-assisted SPS, followed by hot deformation at 710 °C and 810 °C via SPS. Results indicate that cold sintering below 450 °C effectively restricts grain growth in the NdFeB magnets, yielding sub-100 nm scale grains across both fine-grained regions and most coarse-grained regions. The refined grain structure achieved through cold sintering allows for a lower hot deformation temperature as compared with the magnet by conventional sintering, as finer grains allow easier deformation and grain sliding/rotation. This process produces a highly fine-grained and anisotropic microstructure to achieve high magnetic performance (i.e., high intrinsic coercivity, remanence, and maximum energy product) in the magnets. The cold sintering (at 350 °C) and lower hot deformation temperatures required (e.g., 710 °C) help control grain coarsening and limit grain size that is commensurate with the size of a single magnetic domain of the Nd 2 Fe 14 B magnetic matrix phase, resulting in high intrinsic coercivity (H ci =11.4 kOe). Furthermore, the reduced hot deformation temperature mitigates the formation of coarse grain bands, leading to improved magnetic properties, specifically an increased remanence (B r = 14.3 kGs) and a high maximum energy product ((BH) max = 48 MGOe). In conclusion, cold sintered hot deformed NdFeB magnet also shows good thermal stability with reversible temperature coefficient α(B r )= -0.097 %/K and α(H ci )= -0.616 %/K at elevated temperatures up to 400 K.

Cold Sintering↗

Plasmon-Induced Hot-Carrier Excited-State Dynamics in Plasmonic Semiconductor Nanocrystals

The variance of carrier relaxation pathways for WO 3–x plasmonic semiconductor nanocrystals (PSNCs) is monitored by transient absorption spectroscopy following excitation of the localized surface plasmon resonance (LSPR) versus the optical band gap (E g,opt ). Excitation of the LSPR leads to efficient hot carrier population above the Fermi level in WO 3–x via Landau damping, in analogy to noble metal LSPR relaxation mechanisms. Hot carrier depopulation occurs on the femtosecond timescale, observed as the concomitant recovery of an LSPR bleach with the appearance of discrete interband and intraband photoinduced absorption features. Further, by comparison, the direct excitation of E g,opt results in trion recombination at donor–acceptor sites within the WO 3–x NC, consistent with exciton decay dynamics observed for typical wide-band-gap semiconductor NCs. From the analysis of pump power dependency data, a hot-carrier electron–phonon coupling constant of 1.47 × 10 11 J K –1 s –1 cm –3 is extracted. The direct comparison of the decay dynamics following E g,opt versus LSPR excitation confirms that the observed plasmon in trioctylphosphine oxide passivated, spherical WO 3–x is a resonance state in which hot carriers are generated only from excitation on resonance with the LSPR frequency. This study on WO 3–x PSNCs provides a toolset that can be used to evaluate the role of hot carriers following LSPR excitation of n-type, plasmonic transparent conducting oxide NCs, where enhancement of photocatalysis, photovoltaic performance, and optical enhancement has been reported.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anisotropic Hot Spot Formation at a Grain Boundary in Shock-Compressed TATB High Explosive Crystal

Secondary high explosives (HEs) exhibit rich microstructure that promotes the formation of hot spots responsible for detonation initiation, but the role of microstructural interfaces remains poorly quantified. To this end, we develop extensions for the generalized crystal-cutting method (GCCM) to prepare molecular dynamics (MD) simulation cells containing grain boundaries (GBs) and other crystal–crystal interfaces with prescribed tilt and twist orientations. Using the GCCM, we perform MD simulations of shock interactions with a GB between the (001) and (100) crystal facets in the secondary HE TATB (1,3,5-triamino-2,4,6-trinitrobenzene). Our MD simulations reveal a strong directional dependence to the formation of a hot spot at the GB interface. In particular, transmission of the shock from the (001) grain to the (100) grain yields a hot spot in the (100) grain at the GB interface, whereas no hot spot is produced when an equivalent shock transits the GB in the opposite direction. We trace the origin of this GB anisotropy to three dominant factors: (1) the intrinsic differences in shock-deformation mechanisms and wave structures for the bulk (100) and (001) grains, which leads to distinct geometries and mechanical impedances upon shock arrival to the GB depending on which grains are donor or acceptor for the transmitted shock; (2) the different time intervals separating the initial shock rise and the formation of steady wave structures in the respective donor–acceptor configurations; and (3) the differences in time scales required to re-establish local thermal equilibrium. Interfacial hot spots form when these factors combine to impede development of a steady two-wave structure and instead induce a localized, pseudosingly shocked region that undergoes a higher rate of work production (resulting in a higher temperature) compared to when the steady two-wave structure develops further from the interface. The extensions to the GCCM approach presented here are anticipated to facilitate a wide range of MD studies that focus on understanding the role of crystal–crystal interfaces in molecular materials.

organic↗

Plasmonic Hot-Carrier Generation and Catalysis in Ti 3 C 2 O 2 from Real-Time TDDFT Simulations

Photoinduced hot electrons are central to plasmon-driven catalysis. Atomically thin Ti 3 C 2 O 2 , with high carrier density and broad optical absorption, offers a promising platform for plasmon-driven reactions. However, comprehensive investigations of its plasmon resonance, hot-carrier generation, and plasmonic catalytic performance remain limited. In this work, real-time time-dependent density functional theory (rt-TDDFT) was employed to study Ti 3 C 2 O 2 ’s plasmon excitation and hot-carrier generation from nonradiative plasmon damping. The temporal evolution of the dipole moment reveals plasmon resonance in Ti 3 C 2 O 2 , followed by strong plasmon damping that redistributes the stored energy to generate hot carriers. Ti 3 C 2 O 2 with low oxygen vacancy concentration (O v -Ti 3 C 2 O 2 ) exhibits plasmonic behavior resembling the pristine surface, and the plasmon-generated hot electrons can markedly reduce the dissociation barrier of CO 2 at the oxygen vacancy. These findings provide fundamental insights into the plasmonic properties of Ti 3 C 2 O 2 and how they drive its catalytic performance in surface reactions, which is valuable for advancing plasmon-driven catalysis.

CO2 reduction↗

Highly Efficient Plasmon Induced Hot-Electron Transfer at Ag/TiO 2 Interface

Plasmon induced hot carrier transfer is a promising novel approach for solar energy conversion, but its practical application is often hindered by its low efficiency. This work demonstrates an unprecedented quantum efficiency of plasmonic hot-electron transfer of up to 53 ± 2% from 1.7 nm silver nanoparticles to anatase nanoporous TiOsub>2 films at 400 nm excitation. This efficient hot-electron transfer consists of contributions of both hot electrons generated by plasmon decay through exciting Ag intraband transitions and Ag-to-TiO 2 interfacial charge-transfer transitions. The efficiencies of both pathways increase at smaller Ag particle sizes from 5.9 to 1.7 nm, suggesting that decreasing particle sizes is a promising way toward efficient plasmonic hot-carrier extraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗