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The resolve survey atomic gas census and environmental influences on galaxy gas reservoirs

We present the H i mass inventory for the REsolved Spectroscopy Of a Local VolumE (RESOLVE) survey, a volume-limited, multi-wavelength census of >1500 z = 0 galaxies spanning diverse environments and complete in baryonic mass down to dwarfs of ∼10{sup 9} M{sub ⊙}. This first 21 cm data release provides robust detections or strong upper limits (1.4M {sub H i} < 5%–10% of stellar mass M {sub *}) for ∼94% of RESOLVE. We examine global atomic gas-to-stellar mass ratios (G/S) in relation to galaxy environment using several metrics: group dark matter halo mass M {sub h}, central/satellite designation, relative mass density of the cosmic web, and distance to the nearest massive group. We find that at fixed M {sub *}, satellites have decreasing G/S with increasing M {sub h} starting clearly at M {sub h} ∼ 10{sup 12} M{sub ⊙}, suggesting the presence of starvation and/or stripping mechanisms associated with halo gas heating in intermediate-mass groups. The analogous relationship for centrals is uncertain because halo abundance matching builds in relationships between central G/S, stellar mass, and halo mass, which depend on the integrated group property used as a proxy for halo mass (stellar or baryonic mass). On larger scales G/S trends are less sensitive to the abundance matching method. At fixed M {sub h} ≤ 10{sup 12} M{sub ⊙}, the fraction of gas-poor centrals increases with large-scale structure density. In overdense regions, we identify a rare population of gas-poor centrals in low-mass (M {sub h} < 10{sup 11.4} M{sub ⊙}) halos primarily located within ∼1.5× the virial radius of more massive (M {sub h} > 10{sup 12} M{sub ⊙}) halos, suggesting that gas stripping and/or starvation may be induced by interactions with larger halos or the surrounding cosmic web. We find that the detailed relationship between G/S and environment varies when we examine different subvolumes of RESOLVE independently, which we suggest may be a signature of assembly bias.

79 ASTRONOMY AND ASTROPHYSICS↗

The grism lens-amplified survey from space (glass). VII. The diversity of the distribution of star formation in cluster and field galaxies at 0.3 ≤ z ≤ 0.7

Exploiting the slitless spectroscopy taken as part of the Grism Lens-Amplified Survey from Space (GLASS), we present an extended analysis of the spatial distribution of star formation in 76 galaxies in 10 clusters at 0.3<z<0.7. We use 85 foreground and background galaxies in the same redshift range as a field sample. The samples are well matched in stellar mass (10{sup 8}−10{sup 11} M{sub ⊙}) and star formation rate (0.5–50 M{sub ⊙} yr{sup −1}). We visually classify galaxies in terms of broad band morphology, Hα morphology, and likely physical process acting on the galaxy. Most Hα emitters have a spiral morphology (41% ± 8% in clusters, 51% ± 8% in the field), followed by mergers/interactions (28% ± 8%, 31% ± 7%, respectively) and early-type galaxies (remarkably as high as 29% ± 8% in clusters and 15% ± 6% in the field). A diversity of Hα morphologies is detected, suggesting a diversity of physical processes. In clusters, 30% ± 8% of the galaxies present a regular morphology, mostly consistent with star formation diffused uniformly across the stellar population (mostly in the disk component, when present). The second most common morphology (28% ± 8%) is asymmetric/jellyfish, consistent with ram-pressure stripping or other non-gravitational processes in 18% ± 8% of the cases. Ram-pressure stripping appears significantly less prominent in the field (2% ± 2%), where the most common morphology/mechanism appears to be consistent with minor gas-rich mergers or clump accretion. This work demonstrates that while environment-specific mechanisms affect galaxy evolution at this redshift, they are diverse and their effects are subtle. A full understanding of this complexity requires larger samples and detailed and spatially resolved physical models.

79 ASTRONOMY AND ASTROPHYSICS↗

Periodic Accretion-powered Flares from Colliding EMRIs as TDE Imposters

When a main-sequence star undergoes Roche lobe overflow onto a supermassive black hole (SMBH) in a circular extreme mass ratio inspiral (EMRI), a phase of steady mass transfer ensues. Over millions of years, the binary evolves to a period minimum before reversing course and migrating outward as a brown dwarf. Because the time interval between consecutive EMRIs is comparable to the mass-transfer timescale, the semimajor axes of two consecutive mass-transferring EMRIs will cross on a radial scale of less than a few au. We show that such EMRI crossing events are inevitably accompanied by a series of mildly relativistic, grazing physical collisions between the stars. Each collision strips a small quantity of mass, primarily from the more massive star, which generally increases their radial separation to set up the next collision after a delay of decades to centuries (or longer) set by further gravitational radiation. Depending on the mass of the SMBH, this interaction can result in N{sub c}∼1--10{sup 4} gas production events of mass ∼M{sub ⊙}/N{sub c}, thus powering a quasi-periodic sequence of SMBH accretion-powered flares over a total duration of thousands of years or longer. Although the EMRI rate is 2–3 orders of magnitude lower than the rate of tidal disruption events (TDEs), the ability of a single interacting EMRI pair to produce a large number of luminous flares—and to make more judicious use of the available stellar fuel—could make their observed rate competitive with the TDE rate, enabling them to masquerade as “TDE imposters.” Gas produced by EMRI collisions is easier to circularize than the highly eccentric debris streams produced in TDEs. We predict flares with bolometric luminosities that decay both as power laws shallower than t{sup −5/3} and as decaying exponentials in time. Viscous spreading of the gaseous disks produced by the accumulation of previous mass-stripping events will place a substantial mass of gas on radial scales ≳10--100 au at the time of a given flare, providing a possible explanation for the “reprocessing blanket” required to explain the unexpectedly high optical luminosities of some candidate TDE flares.

79 ASTRONOMY AND ASTROPHYSICS↗

The Infall of the Virgo Elliptical Galaxy M60 toward M87 and the Gaseous Structures Produced by Kelvin–Helmholtz Instabilities

We present Chandra observations of hot gas structures, which are characteristic of gas-stripping during infall, in the Virgo cluster elliptical galaxy M60 (NGC4649) located 1 Mpc east of M87. Chandra X-ray images at 0.5–2 keV show a sharp leading edge in the surface brightness that is 12.4 ± 0.1 kpc north and west of the galaxy center in the direction of M87 and characteristic of a merger cold front due to M60's motion through the Virgo ICM. We measured a temperature of 1.00 ± 0.02 keV for an abundance of 0.5 Z{sub ⊙} inside the edge and 1.37{sub −0.19}{sup +0.35} keV for an abundance of 0.1 Z{sub ⊙} in the Virgo ICM free stream region. We find that the observed jump in surface brightness yields a density ratio n{sub in}/n{sub out}=6.44{sub −0.67}{sup +1.04} between gas inside the edge and in the cluster free stream region. If the edge is a cold front due solely to the infall of M60 in the direction of M87, we find a pressure ratio of 4.7{sub −1.4}{sup +1.7} and Mach number of 1.7{sub −0.3}{sup +0.3}. For 1.37 keV Virgo gas, we find a total infall velocity for M60 of v{sub M60}=1030±180 km s{sup −1}. We calculate the motion in the plane of the sky to be v{sub tran}=1012{sub −192}{sup +183} km s{sup −1}, implying an inclination angle of ξ=11{sub −3}{sup +3}°. Surface brightness profiles also show the presence of a faint, diffuse gaseous tail. We identify filamentary gaseous wing structures caused by the galaxy’s motion through the ICM. The structure and dimensions of these wings are consistent with simulations of Kelvin–Helmholtz instabilities, as expected if the gas-stripping is close to inviscid.

79 ASTRONOMY AND ASTROPHYSICS↗

LoTSS Jellyfish Galaxies. IV. Enhanced Star Formation on the Leading Half of Cluster Galaxies and Gas Compression in IC3949

With Mapping Nearby Galaxies at APO integral field spectroscopy, we present a resolved analysis of star formation for 29 jellyfish galaxies in nearby clusters, identified from radio continuum imaging taken by the Low Frequency Array. Simulations predict enhanced star formation on the "leading half" (LH) of galaxies undergoing ram pressure stripping, and in this work we report observational evidence for this elevated star formation. The dividing line (through the galaxy center) that maximizes this star formation enhancement is systematically tied to the observed direction of the ram-pressure-stripped tail, suggesting a physical connection between ram pressure and this star formation enhancement. We also present a case study on the distribution of molecular gas in one jellyfish galaxy from our sample, IC3949, using Atacama Large Millimeter/submillimeter Array CO J = 1 – 0, HCN J = 1 – 0, and HCO + J = 1 – 0 observations from the ALMA MaNGA Quenching and Star Formation Survey. The H2 depletion time (as traced by CO) in IC3949 ranges from ~1 Gyr in the outskirts of the molecular gas disk to ~11 Gyr near the galaxy center. IC3949 shows a clear region of enhanced star formation on the LH of the galaxy where the average depletion time is ~2.7 Gyr, in line with the median value for the galaxy on the whole. Dense gas tracers, HCN and HCO + , are only detected at the galaxy center and on the LH of IC3949. Our results favor a scenario in which ram pressure compresses the interstellar medium, promoting the formation of molecular gas that in turn fuels a localized increase of star formation.

79 ASTRONOMY AND ASTROPHYSICS↗

M32 analogs? A population of massive ultra-compact dwarf and compact elliptical galaxies in intermediate-redshift clusters

We report the discovery of relatively massive, M32-like ultra compact dwarf (UCD) and compact elliptical (CE) galaxy candidates in 0.2<z<0.6 massive galaxy clusters imaged by the Cluster Lensing And Supernova survey with Hubble (CLASH) survey. Examining the nearly unresolved objects in the survey, we identify a sample of compact objects concentrated around the cluster central galaxies with colors similar to cluster red sequence galaxies. Their colors and magnitudes suggest stellar masses around 10{sup 9}M{sub ⊙}. More than half of these galaxies have half-light radii smaller than 200 pc, falling into the category of massive UCDs and CEs, with properties similar to M32. The properties are consistent with a tidal stripping origin, but we cannot rule out the possibility that they are early-formed compact objects trapped in massive dark matter halos. The 17 CLASH clusters studied in this work on average contain 2.7 of these objects in their central 0.3 Mpc and 0.6 in their central 50 kpc. Our study demonstrates the possibility of statistically characterizing UCDs/CEs with a large set of uniform imaging survey data.

79 ASTRONOMY AND ASTROPHYSICS↗

Formation of Black Hole X-Ray Binaries with Non-degenerate Donors in Globular Clusters

In this Letter, we propose a formation channel for low-mass X-ray binaries with black hole accretors and non-degenerate donors via grazing tidal encounters with subgiants. We estimate that in a typically dense globular cluster with a core density of 10{sup 5} stars pc{sup −3}, the formation rates are about one binary per Gyr per 50–100 retained black holes. The donors—stripped subgiants—will be strongly underluminous when compared to subgiant or giant branch stars of the same colors. The products of tidal stripping are underluminous by at least one magnitude for several hundred million years when compared to normal stars of the same color, and differ from underluminous red stars that could be produced by non-catastrophic mass transfer in an ordinary binary. The dynamically formed binaries become quiescent LMXBs, with lifetimes of about a Gyr. The expected number of X-ray binaries is one per 50–200 retained black holes, while the expected number of strongly underluminous subsubgiant is about half this. The presence of strongly underluminous stars in a GC may be indicative of the presence of black holes.

79 ASTRONOMY AND ASTROPHYSICS↗

On the Magnetic Protection of the Atmosphere of Proxima Centauri b

The discovery of exoplanets orbiting red dwarfs, such as Proxima Centauri b, has led to questions of their habitability and capacity to retain liquid surface water. While Proxima b is in a “temperate orbit,” i.e., an Earth at that location would not freeze or boil its oceans, its proximity to a parent star with quite high magnetic activity is likely to influence its atmospheric evolution and habitability. Planetary magnetic fields can prevent direct stripping away of the planetary atmosphere by the stellar wind, but ion escape can still occur at the magnetic poles. This process, the polar wind, is well known to occur at Earth and may have contributed to the habitability of Earth’s early atmosphere. The polar wind is highly variable and sensitive to both ionizing radiation and geomagnetic activity. The higher ionizing radiation levels of M dwarfs at habitable zone distances are expected to increase the polar wind by orders of magnitude and, instead of helping create a habitable atmosphere, may strip away enough volatiles to render the planet inhospitable. Here, we compute the ionospheric outflow of an Earth-twin subject to the enhanced stellar EUV flux of Proxima b, and the effect on atmospheric escape timescales. We show that an Earth-like planet would not survive the escape of its atmosphere at that location, and therefore the pathway to habitability for Proxima b requires a very different atmospheric history than that of Earth.

79 ASTRONOMY AND ASTROPHYSICS↗

On the general theory of thin airfoils for nonuniform motion

General thin-airfoil theory for a compressible fluid is formulated as boundary problem for the velocity potential, without recourse to the theory of vortex motion. On the basis of this formulation the integral equation of lifting-surface theory for an incompressible fluid is derived with the chordwise component of the fluid velocity at the airfoil as the function to be determined. It is shown how by integration by parts this integral equation can be transformed into the Biot-Savart theorem. A clarification is gained regarding the use of principal value definitions for the integral which occur. The integral equation of lifting-surface theory is used a s the starting point for the establishment of a theory for the nonstationary airfoil which is a generalization of lifting-line theory for the stationary airfoil and which might be called "lifting-strip" theory. Explicit expressions are given for section lift and section moment in terms of the circulation function, which for any given wing deflection is to be determined from an integral equation which is of the type of the equation of lifting-line theory. The results obtained are for airfoils of uniform chord. They can be extended to tapered airfoils. One of the main uses of the results should be that they furnish a practical means for the analysis of the aerodynamic span effect in the problem of wing flutter. The range of applicability of "lifting-strip" theory is the same as that of lifting-line theory so that its results may be applied to airfoils with aspect ratios as low as three.

BIBLIOGRAPHY-WINGS↗

Study on reduction and back extraction of Pu(IV) by urea derivatives in nitric acid conditions

The reduction kinetics of Pu(IV) by hydroxyl-semicarbazide (HSC), hydroxyurea (HU) and di-hydroxyurea (DHU) in nitric acid solutions were investigated separately with adequate kinetic equations. In addition, counter-current cascade experiments were conducted for Pu split from U in nitric acid media using three kinds of reductant, respectively. The results show that urea derivatives as a kind of novel salt-free reductant can reduce Pu(IV) to Pu(III) rapidly in the nitric acid solutions. The stripping experimental results showed that Pu(IV) in the organic phase can be stripped rapidly to the aqueous phase by the urea derivatives, and the separation factors of plutonium /uranium can reach more than 10{sup 4}. This indicates that urea derivatives is a kind of promising salt-free agent for uranium/plutonium separation. In addition, the complexing effect of HSC with Np(IV) was revealed, and Np(IV) can be back-extracted by HSC with a separation factor of about 20.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A micro hot test of the Chalmers-GANEX extraction system on used nuclear fuel

In the present study, a 'micro hot test' has been performed using the Chalmers-GANEX (Group Actinide Extraction) system for partitioning of used nuclear fuel. The test included a pre-extraction step using N,N-di-2- ethylhexyl-butyramide (DEHBA) in n-octanol to remove the bulk part of the uranium. This pre-extraction was followed by a group extraction of actinides using the mixture of TBP and CyMe{sub 4}-BTBP in cyclohexanone as suggested in the Chalmers-GANEX process, and a three stage stripping of the extracted actinides. Distribution ratios for the extractions and stripping were determined based on a combination of γ- and α-spectrometry, as well as ICP-MS measurements. Successful extraction of uranium, plutonium and the minor actinides neptunium, americium and curium was achieved. However, measurements also indicated that co-extraction of europium occurs to some extent during the separation. These results were expected based on previous experiments using trace concentrations of actinides and lanthanides. Since this test was only performed in one stage with respect to the group actinide extraction, it is expected that multi stage tests will give even better results. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Continuous back extraction operation by a single liquid-liquid centrifugal extractor

We have developed a small, high-performance liquid-liquid countercurrent centrifugal extractor for the nuclear fuel cycle. The single extractor allows extraction with many multiple theoretical stages due to the formation of Taylor vortices. We have previously demonstrated multistage extraction for a forward extraction system. In this study, we have applied the centrifugal extractor to a continuous back extraction system with di(2-ethylhexyl)phosphoric acid. We examined the performance of our concept of the centrifugal extractor by varying the rotational speeds of the inner rotor and the nitric acid concentration in the stripping solution. The dispersion behavior, flow characteristics were determined and the back extraction performance was examined for a single chemical species and for multiple species. Complete back extraction by continuous process was achieved and it showed the possibility to minimize the volume and nitric acid concentration of the stripping solution. Our centrifugal extractors may provide a more effective separation system than the conventional separation process that uses many continuously connected extractors. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Dissolution of metal oxides and separation of uranium from lanthanides and actinides in supercritical carbon dioxide

This paper investigates the feasibility of extracting and separating uranium from lanthanides and other actinides by using supercritical fluid carbon dioxide (sc-CO{sub 2}) as a solvent modified with tri-n-butylphosphate (TBP) for the development of a counter current stripping technique, which would be a more efficient and environmentally benign technology for spent nuclear fuel reprocessing compared to traditional solvent extraction. Several actinides (U, Pu, and Np) and europium were extracted in sc-CO{sub 2} modified with TBP over a range of nitric acid concentrations and then the actinides were exposed to reducing and complexing agents to suppress their extractability. According to this study, uranium/europium and uranium/plutonium extraction and separation in sc-CO{sub 2} modified with TBP is successful at nitric acid concentrations of less than 6 M and at nitric acid concentrations of less than 3 M with acetohydroxamic acid or oxalic acid, respectively. A scheme for recycling uranium from spent nuclear fuel by using sc-CO{sub 2} and counter current stripping columns is presented. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Radio-Frequency Rapid Thermal Processing Enabling Spatial Phase Transformation and Nanocrystallization of Soft Magnetic Amorphous Alloys

Thermal processing of soft magnetic amorphous and nanocrystalline alloys is explored under the influence of radio-frequency induction-heating techniques. Direct induction-heating concepts based on longitudinal and transverse flux heating are examined and the details of electromagnetic fields interaction with metallic strips are discussed by analytical calculations as well as finite element analysis. Initial experimental results confirming spatial control of phase transformations and nanocrystallization within a single strip of Finemet Fe-based amorphous ribbons are reported. Here, the degree to which primary and secondary crystallization temperature are achieved depends on the spacing between the ribbon relative to the induction coil as well as the coil design and configuration. For transverse coil configurations, the local temperature and therefore microstructural evolution is different across the lateral dimension of processed ribbons, with reduced gap sizes producing enhanced peak temperatures and larger temperature distributions with greater spatial variation in microstructure. In addition, indirect susceptor-based induction heating under tension is performed and the impact of microstructure is demonstrated. Herein, potential for exploiting spatially optimized phase transformations is illustrated through electromagnetic field–assisted processing in a scalable manufacturing process with amorphous and nanocrystalline soft magnetic alloys.

36 MATERIALS SCIENCE↗

Overcoming Anode Instability in Solid‐State Batteries through Control of the Lithium Metal Microstructure

Abstract Enabling the lithium metal anode (LMA) in solid‐state batteries (SSBs) is the key to developing high energy density battery technologies. However, maintaining a stable electrode–electrolyte interface presents a critical challenge to high cycling rate and prolonged cycle life. One such issue is the interfacial pore formation in LMA during stripping. To overcome this, either higher stack pressure or binary lithium alloy anodes are used. Herein, it is shown that fine‐grained ( d = 20 µm) polycrystalline LMA can avoid pore formation by exploiting the microstructural dependence of the creep rates. In a symmetric cell set‐up, i.e., LiǀLi 6.25 Al 0.25 La 3 Zr 2 O 12 (LLZO)ǀLi, fine‐grained LMA achieves > 11.0 mAh cm −2 compared to ≈ 3.6 mAh cm −2 for coarse‐grained LMA ( d = 295 µm) at 0.1 mA cm −2 and at moderate stress of 2.0 MPa. Smaller diffusion lengths (≈ 20 µm) and higher diffusivity pathway along dislocations ( D d ≈ 10 −7 cm 2 s −1 ), generated during cell fabrication, result in enhanced viscoplastic deformation in fine‐grained polycrystalline LMA. The electrochemical performances corroborate well with estimated creep rates. Thus, microstructural control of LMA can significantly reduce the required stack pressure during stripping. These results are particularly relevant for “anode‐free” SSBs wherein both the microstructure and the mechanical state of the lithium are critical parameters.

25 ENERGY STORAGE↗

Dendrite–Free Potassium Metal Anodes in a Carbonate Electrolyte

Potassium (K) metal anodes suffer from a challenging problem of dendrite growth. In this study, it is demonstrated that a tailored current collector will stabilize the metal plating–stripping behavior even with a conventional KPF 6 –carbonate electrolyte. A 3D copper current collector is functionalized with partially reduced graphene oxide to create a potassiophilic surface, the electrode being denoted as rGO@3D–Cu. Potassiophilic versus potassiophobic experiments demonstrate that molten K fully wets rGO@3D–Cu after 6 s, but does not wet unfunctionalized 3D–Cu. Electrochemically, a unique synergy is achieved that is driven by interfacial tension and geometry: the adherent rGO underlayer promotes 2D layer–by–layer (Frank–van der Merwe) metal film growth at early stages of plating, while the tortuous 3D–Cu electrode reduces the current density and geometrically frustrates dendrites. The rGO@3D–Cu symmetric cells and half–cells achieve state–of–the–art plating and stripping performance. Here, the symmetric rGO@3D–Cu cells exhibit stable cycling at 0.1–2 mA cm –2 , while baseline Cu prematurely fails when the current reaches 0.5 mA cm –2 . The half–cells cells of rGO@3D–Cu (no K reservoir) are stable at 0.5 mA cm –2 for 10 000 min (100 cycles), and at 1 mA cm –2 for 5000 min. The baseline 3D–Cu, planar rGO@Cu, and planar Cu foil fails after 5110, 3012, and 1410 min, respectively.

25 ENERGY STORAGE↗

Multifunctional Separator Allows Stable Cycling of Potassium Metal Anodes and of Potassium Metal Batteries

Here, this is the first report of a multifunctional separator for potassium-metal batteries (KMBs). Here, double-coated tape-cast microscale AlF 3 on polypropylene (AlF 3 @PP) yields state-of-the-art electrochemical performance: symmetric cells are stable after 1000 cycles (2000 h) at 0.5 mA cm –2 and 0.5 mAh cm –2 , with 0.042 V overpotential. Stability is maintained at 5.0 mA cm –2 for 600 cycles (240 h), with 0.138 V overpotential. Postcycled plated surface is dendrite-free, while stripped surface contains smooth solid electrolyte interphase (SEI). Conventional PP cells fail rapidly, with dendrites at plating, and “dead metal” and SEI clumps at stripping. Potassium hexacyanoferrate(III) cathode KMBs with AlF 3 @PP display enhanced capacity retention (91% at 100 cycles vs 58%). AlF 3 partially reacts with K to form an artificial SEI containing KF, AlF 3 , and Al 2 O 3 phases. The AlF 3 @PP promotes complete electrolyte wetting and enhances uptake, improves ion conductivity, and increases ion transference number. The higher of K + transference number is ascribed to the strong interaction between AlF 3 and FSI – anions, as revealed through 19 F NMR. The enhancement in wetting and performance is general, being demonstrated with ester- and ether-based solvents, with K-, Na-, or Li- salts, and with different commercial separators. In full batteries, AlF 3 prevents Fe crossover and cycling-induced cathode pulverization.

NMB↗

Accurate Determination of Coulombic Efficiency for Lithium Metal Anodes and Lithium Metal Batteries

Lithium (Li) metal is an ideal anode material for high energy density batteries. However, its low Coulombic efficiency (CE) and formation of dendrites during the plating and stripping processes has hindered its applications in rechargeable Li metal batteries. The accurate measurement of Li CE is a critical factor to predict the cycle life of Li metal batteries, but the measurement of Li CE is affected by various factors that often leads to conflicting values reported in the literature. Here, we investigate various factors that affect the measurement of Li CE and propose a more accurate method of determining Li CE. It was also found that the capacity used for cycling greatly affects the stabilization cycles and the average CE. A higher cycling capacity leads to a shorter number of stabilization cycles and higher average CE. With a proper high-concentration ether-based electrolyte, Li metal can be cycled with a high average CE of 99.5 % for over 100 cycles at a high capacity of 6 mAh cm-2 suitable for practical applications.

Adams, Brian D.↗