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At least 127 records · Page 7

Understanding the Reactions Between Fe and Se Binary Diffusion Couples

Spurred by recent discoveries of high-temperature superconductivity in Fe-Se based materials, the magnetic, electronic, and catalytic properties of iron-chalcogenides have drawn significant attention. Furthermore, much remains to be understood about the sequence of phase formation in these systems. In this work, we shed light on this issue by preparing a series of binary Fe-Se ultrathin diffusion couples via designed thin film precursors and investigating their structural evolution as a function of composition and annealing temperature. Two previously unreported Fe-Se phases crystallized during the deposition process on a nominally room-temperature Si substrate in the 27-33% and 37-47% Fe (atomic percent) composition regimes. Both phases completely decompose after annealing to 200°C in a nitrogen glovebox. At higher temperatures, the sequence of phase formation is governed by Se loss in the annealing process, consistent with what would be expected from the phase diagram. Films rich in Fe (53-59% Fe) crystalized during deposition as β-FeSe (P4/nmm) with preferred c-axis orientation to the amorphous SiO 2 substrate surface, providing a means to non-epitaxial self-assembly of crystallographically aligned, iron-rich β-FeSe for future research. Our findings suggest the crystallization of binary Fe-Se compounds at room temperature via near diffusionless transformations should be a significant consideration in future attempts to prepare metastable ternary and higher order compounds containing Fe and Se.

36 MATERIALS SCIENCE↗

The Effects of Silicon and Niobium Concentration on the Solidification Behavior and Microstructure of Cast Monel Alloys

Cast Monel alloys are used in applications requiring a combination of good mechanical properties and excellent resistance to corrosion. Despite prevalent industrial use, relatively few studies have been conducted to investigate the relationships between composition, solidification behavior, and microstructure. Given that these alloys are used in the cast and welded conditions, these factors have a significant influence over the material properties. Here, in this work, microstructural characterization, electron probe microanalysis, X-ray diffraction, and differential scanning calorimetry were used to study how changes in Si and Nb concentrations affected the solidification path and microstructure of Monel alloys. It was found that increasing Nb concentration stabilized higher amounts of MC carbides and suppressed graphite formation during solidification. It was also found that the high nominal concentration and segregation of Si to the liquid led to the formation of Ni 31 Si 12 and other silicides via terminal eutectic reactions at the end of solidification. A pseudo-binary solidification diagram was constructed using experimental data and was applied to predict the mass fraction of solidified eutectic as a function of composition. The modeled microstructures were found to be in good agreement with experimentally measured phase fractions.

36 MATERIALS SCIENCE↗

Some possible filler alloys with low vapor pressures for refractory-metal brazing

A compilation of eutectics and melting-point minima for binary combinations of metals having vapor pressures below 10 to the minus 10th power torr at 1500 degrees K and .00005 torr at 2000 degree K is presented. These compositions and others near them on their phase diagrams are potential special brazing fillers for refractory metals. Some possible problems and advantages for fusion bonds of such mixtures are indicated. Evaluations of brazing fillers containing refractory metals are reported.

Morris, J. F.↗

Effect of a Nonplanar Melt-Solid Interface On Lateral Compositional Distribution During Unidirectional Solidification of a Binary Alloy with a Constant Growth Velocity V: Theory - Pt. 1

Infrared detected materials, such as Hg(1-x)Cd(x)Te, Hg(1-x)Zn(x)Te have energy gaps almost linearly proportional to their composition. Due to the wide separation of liquidus and solidus curves of their phase diagram, there are compositional segregation in both of the axial and radial directions of these crystals grown in the Bridgman system unidirectionally with constant growth rate. It is important to understand the mechanisms, which affect lateral segregation such that large radially uniform composition crystal can be produced. Following Coriel, etc's treatment, we have developed a theory to study the effect of a curved melt-solid interface shape on lateral composition distribution. The model is considered to be a cylindrical system with azimuthal symmetry and a curved melt-solid interface shape which can be expressed as a linear combination of a series of Bessell's functions. The results show that melt-solid interface shape has a dominant effect on the lateral composition distribution of these systems. For small values of beta, the solute concentration at the melt-solid interface scales linearly with interface shape with a proportional constant of the produce of beta and (1 -k), where beta = VR/D, with V as growth velocity, R as the sample radius, D as the diffusion constant and k as the distribution constant. A detailed theory will be presented. A computer code has been developed and simulations have been performed and compared with experimental results. These will be published in another paper.

Wang, Jai-Ching↗

Effect of a Nonplanar Melt-Solid Interface on Lateral Compositional Distribution during Unidirectional Solidification of a Binary Alloy with a Constant Growth Velocity V: Theory - Part 1

Infrared detector materials, such as Hg(1-x)Cd(x)Te, Hg(1-x)Zn(x)Te have energy gaps almost linearly proportional to its composition. Due to the wide separation of liquidus and solidus curves of their phase diagram, there are compositional segregations in both of axial and radial directions of these crystals grown in the Bridgman system unidirectionally with constant growth rate. It is important to understand the mechanisms which affect lateral segregation such that large uniform radial composition crystal is possible. Following Coriell, etc's treatment, we have developed a theory to study the effect of a curved melt-solid interface shape on the lateral composition distribution. The system is considered to be cylindrical system with azimuthal symmetric with a curved melt-solid interface shape which can be expressed as a linear combination of a series of Bessell's functions. The results show that melt-solid interface shape has a dominate effect on lateral composition distribution of these systems. For small values of b, the solute concentration at the melt-solid interface scales linearly with interface shape with a proportional constant of the product of b and (1 - k), where b = VR/D, with V as growth velocity, R as sample radius, D as diffusion constant and k as distribution constant. A detailed theory will be presented. A computer code has been developed and simulations have been performed and compared with experimental results. These will be published in another paper.

Wang, Jai-Ching↗

Reduction of Phase Ambiguity in an Offset-QPSK Receiver

Proposed modifications of an offset-quadri-phase-shift keying (offset-QPSK) transmitter and receiver would reduce the amount of signal processing that must be done in the receiver to resolve the QPSK fourfold phase ambiguity. Resolution of the phase ambiguity is necessary in order to synchronize, with the received carrier signal, the signal generated by a local oscillator in a carrier-tracking loop in the receiver. Without resolution of the fourfold phase ambiguity, the loop could lock to any of four possible phase points, only one of which has the proper phase relationship with the carrier. The proposal applies, more specifically, to an offset-QPSK receiver that contains a carrier-tracking loop like that shown in Figure 1. This carrier-tracking loop does not resolve or reduce the phase ambiguity. A carrier-tracking loop of a different design optimized for the reception of offset QPSK could reduce the phase ambiguity from fourfold to twofold, but would be more complex. Alternatively, one could resolve the fourfold phase ambiguity by use of differential coding in the transmitter, at a cost of reduced power efficiency. The proposed modifications would make it possible to reduce the fourfold phase ambiguity to twofold, with no loss in power efficiency and only relatively simple additional signal-processing steps in the transmitter and receiver. The twofold phase ambiguity would then be resolved by use of a unique synchronization word, as is commonly done in binary phase-shift keying (BPSK). Although the mathematical and signal-processing principles underlying the modifications are too complex to explain in detail here, the modifications themselves would be relatively simple and are best described with the help of simple block diagrams (see Figure 2). In the transmitter, one would add a unit that would periodically invert bits going into the QPSK modulator; in the receiver, one would add a unit that would effect different but corresponding inversions of bits coming out of the QPSK demodulator. The net effect of all the inversions would be that depending on which lock point the carrier-tracking loop had selected, all the output bits would be either inverted or non-inverted together; hence, the ambiguity would be reduced from fourfold to twofold, as desired.

Berner, Jeff↗

Solidification cracking of refractory alloys: a computational and machine learning study to investigate composition-dependence for improved weldability and additive manufacturability

Large-batch numerical, CALculation of PHAse Diagrams (CALPHAD)-based solidification cracking calculations are performed and then analyzed with machine learning methods to generate models that relate chemistry of refractory alloys to cracking susceptibility. Kou’s solidification cracking index is used to study the refractory alloys including O, N, C binary mixtures with Mo, Ta, Nb, and W, the molybdenum-based TZM, Niobium-based C103, and Tantalum-based T111 and Ta-10 W, as well as hypothetical refractory ternary alloys. Findings strongly validate Kou’s Crack Susceptibility Index (CSI) against Varestraint test data for Nb- and Ta-based alloys, establishing CSI thresholds where refractory alloys with CSI < 15,000 K are likely weldable, CSI > 15,000 K are prone to cracking, and CSI > 25,000 K are likely unweldable (or unprintable). Furthermore, interstitial elements C, N, and O significantly increase crack susceptibility, with some existing material specifications coinciding with peak cracking susceptibility concentrations. Finally, machine learning-derived elemental potency factors enable rapid prediction of CSI from alloy chemistry for C103, TZM, Ta-10 W, and T-111 alloys. These results provide practical guidance for feedstock selection, powder reuse limits, and alloy specification amendments for welding and additive manufacturing applications.

36 MATERIALS SCIENCE↗

The effect of phosphorus on the formation of the Widmanstaetten pattern in iron meteorites.

Use of a combination of a revised Fe-Ni-P phase diagram and laboratory cooling experiments on Fe-Ni-P alloys to determine the effect of P on the formation of the Widmanstaetten pattern. From the phase diagram results, two reaction paths were found for the formation of kamacite (1) gamma (taenite) yields alpha (kamacite) + gamma (taenite) and (2) gamma yields gamma + Ph /phosphide, (FeNi)3P/ yields alpha + gamma + Ph. The reaction path gamma yields alpha + gamma is preferred at low P contents, while at higher P contents and at Ni contents greater than 7.0 wt.%, the reaction path gamma yields gamma + Ph yields alpha + gamma + Ph controls the formation of kamacite. Above 7 wt.% Ni, the effect of P on the equilibrium nucleation temperature of kamacite is quite small, less than about plus or minus 30 C with respect to the Fe-Ni binary diagram. The addition of P (greater than 0.1 wt.%) to meteorites promotes nucleation of kamacite at higher temperatures and effectively lowers the amount of undercooling necessary to nucleate kamacite homogeneously. Ni has just the opposite effect, decreasing the temperature of nucleation and increasing the amount of undercooling. It is concluded that significant amounts of undercooling, 50 to 100 C, are necessary for the nucleation of the Widmanstaetten structure in meteorites, and that chemical equilibrium is maintained in the various phases of slowly cooled iron meteorites to 650 C and probably to 600 C.

Goldstein, J. I.↗

Optical Studies of model binary miscibility gap system

In order to develop a better understanding of separation processes in binary miscibility gap metal alloys, model transparent fluid systems were studied. The system selected was diethylene glycol-ethyl salicylate which has convenient working temperatures (288 to 350 K), low toxicity, and is relatively easy to purify. The system is well characterized with respect to its phase diagram, density, surface and interfacial tensions, viscosity and other pertinent physical properties. Studies of migration of the dispersed phase in a thermal gradient were performed using conventional photomicroscopy. Velocities of the droplets of the dispersed phase were measured and compared to calculated rates which included both Stokes and thermal components. A holographic microscopy system was used to study growth, coalescence, and particle motions. Sequential holograms allowed determination of particle size distribution changes with respect to time and temperature. Holographic microscopy is capable of recording particle densities up to 10 to the 7th power particles/cu cm and is able to resolve particles of the order of 2 to 3 microns in diameter throughout the entire volume of the test cell. The reconstructed hologram produces a wavefront that is identical to the original wavefront as it existed when the hologram was made. The reconstructed wavefront is analyzed using a variety of conventional optical methods.

Lacy, L. L.↗

A new interpretation of luminous blue stars

A major revision of current theoretical ideas about the brightest blue stars must be made if Carson's (1976) radiative opacities are adopted in stellar models. Unlike earlier opacities, these exhibit a large 'bump' due to CNO ionization, which leads to very strong central condensation, convective instability, and pulsational instability in hot diffuse stellar envelopes. Despite a number of theoretical uncertainties, the new picture of the structure of very luminous stars is reasonably successful in accounting for a variety of previously unexplained observations. The stellar models for the phase of core hydrogen burning predict large radii and rather cool effective temperatures for O stars and a spreading out of the main-sequence band in the H-R diagram toward luminous cool supergiants for masses higher than about 20 solar masses. In massive X-ray binary systems, circular orbits and supergiant-like visual companions are expected to be quite common. Long-period variability is predicted to exist for massive blue supergiants of luminosity class Ia. The models for helium stars predict large radii and rather cool effective temperatures for Wolf-Rayet stars, as well as multimodal pulsational instability and, possibly, surface turbulence for these stars.

Stothers, R.↗

Is Betelgeuse the Outcome of a Past Merger?

We explore the possibility that the star α Orionis (Betelgeuse) is the outcome of a merger that occurred in a low-mass-ratio (q= $\mathcal{M}$ 2 /$\mathcal{M}$ 1 = 0.07–0.25) binary system some time in the past hundreds of thousands of years. To that goal, we present a simple analytical model to approximate the perturbed internal structure of a post-merger object following the coalescence of a secondary in the mass range 1–4 M ⊙ into the envelope of a 15–17 M ⊙ primary. We then compute the long-term evolution of post-merger objects for a grid of initial conditions and make predictions about their surface properties for evolutionary stages that are consistent with the observed location of Betelgeuse in the Hertzsprung–Russell diagram. We find that if a merger occurred after the end of the primary’s main-sequence phase, while it was expanding toward becoming a red supergiant star and typically with radius ∼200–300 R ⊙ , then its envelope is spun up to values that remain in a range consistent with Betelgeuse observations for thousands of years of evolution. We argue that the best scenario that can explain both the fast rotation of Betelgeuse and its observed large space velocity is one where a binary was dynamically ejected by its parent cluster a few million years ago and then subsequently merged. An alternative scenario in which the progenitor of Betelgeuse was spun up by accretion in a binary and released by the supernova explosion of the companion requires a finely tuned set of conditions but cannot be ruled out.

79 ASTRONOMY AND ASTROPHYSICS↗

Metastable formation and disordering kinetics of body-centered orthorhombic CrNi 2 laths in a Cr-Ni binary alloy

Chromium (Cr) alloys combine low density with high-temperature strength but suffer from brittleness and rapid softening. Body-centered orthorhombic (BCO) CrNi 2 laths have been shown to improve Cr-alloy high-temperature strength retention, yet their thermal stability and transformation behavior remain unclear. CrNi 2 conventionally forms through long-range ordering from a face-centered cubic (FCC) phase. Using multiscale microscopy and neutron diffraction, we show that CrNi 2 instead nucleates from a body-centered cubic (BCC) matrix, in a binary Cr 85 Ni 15 alloy. Despite aging above the equilibrium ordering temperature, CrNi 2 persists for ∼220 h at 760 °C before fully disordering, indicating sluggish transformation kinetics. The formation and decomposition follow differing transformation pathways (BCC → CrNi 2 → FCC), revealing kinetic asymmetry not captured by equilibrium Cr-Ni phase diagrams. In conclusion, these findings redefine the transformation behavior of CrNi 2 , establish its metastable kinetic window, and suggest alloying strategies to stabilize CrNi 2 for precipitation strengthening of high-temperature Cr-alloys.

CrNi2 transformation kinetics↗

Physical State and Distribution of Materials at the Surface of Pluto from New Horizons LEISA Imaging Spectrometer

From Earth based observations Pluto is known to be the host of N2, CH4 and CO ices and also a dark red material. Very limited spatial distribution information is available from rotational visible and near-infrared spectral curves obtained from hemispheric measurements. In July 2015 the New Horizons spacecraft reached Pluto and its satellite system and recorded a large set of data. The LEISA spectro-imager of the RALPH instruments are dedicated to the study of the composition and physical state of the materials composing the surface. In this paper we report a study of the distribution and physical state of the ices and non-ice materials on Pluto's illuminated surface and their mode and degree of mixing. Principal Component analysis as well as various specific spectral indicators and correlation plots are used on the first set of 2 high resolution spectro-images from the LEISA instrument covering the whole illuminated face of Pluto at the time of the New Horizons encounter. Qualitative distribution maps have been obtained for the 4 main condensed molecules, N2, CH4, CO, H2O as well as for the visible-dark red material. Based on specific spectral indicators, using either the strength or the position of absorption bands, these 4 molecules are found to indicate the presence of 3 different types of ices: N2-rich:CH4:CO ices, CH4-rich(:CO:N2?) ices and H2O ice. The mixing lines between these ices and with the dark red material are studied using scatter plots between the various spectral indicators. CH4 is mixed at the molecular level with N2, most probably also with CO, thus forming a ternary molecular mixture that follows its phase diagram with low solubility limits. The occurrence of a N2-rich - CH4-rich ices mixing line associated with a progressive decrease of the CO/CH4 ratio tells us that a fractionation sublimation sequence transforms one type of ice to the other forming either a N2-rich - CH4-rich binary mixture at the surface or an upper CH4-rich ice crust that may hide the N2-rich ice below. The strong CH4-rich - H2O mixing line witnesses the subsequent sublimation of the CH4-rich ice lag left behind by the N2:CO sublimation (N spring-summer), or a direct condensation of CH4 ice on the cold H2O ice (S autumn). The weak mixing line between CH4-containing ices and the dark red material and the very sharp spatial transitions between these ices and this non-volatile material are probably due to thermal incompatibility. Finally the occurrence of a H2O ice - red material mixing line advocates for a spatial mixing of the red material covering H2O ice, with possibly a small amount intimately mixed in water ice. From this analysis of the different materials distribution and their relative mixing lines, H2O ice appears to be the substratum on which other ices condense or non-volatile organic material is deposited from the atmosphere. N2-rich ices seem to evolve to CH4-dominated ices, possibly still containing traces of CO and N2, as N2 and CO sublimate away. The spatial distribution of these materials is very complex. The high spatial definition of all these composition maps, as well as those at even higher resolution that will be soon available, will allow us to compare them with Pluto's geologic features observed by LORRI panchromatic and MVIC multispectral imagers to better understand the geophysical processes in action at the surface of this astonishingly active frozen world.

Schmitt, B.↗

Determination of Systems Suitable for Study as Monotectic Binary Metallic Alloy Solidification Models

Succinonitrile-water and diethylene glycol-ethyl salicylate are two transparent systems which have been studied as monotectic binary metallic alloy solidification models. Being transparent, these systems allow for the direct observations of phase transformations and solidification reactions. The objective was to develop a screening technique to find systems of interest and then experimentally measure those systems. The succinonitrile-water system was used to check the procedures. To simulate the phase diagram of the system, two computer programs which determine solid-liquid and liquid-liquid equilibria were obtained. These programs use the UNIFAC method to determine activity coefficients and together with several other programs were used to predict the phase diagram. An experimental apparatus was developed and the succinonitrile-water phase diagram measured. The diagram was compared to both the simulation and literature data. Substantial differences were found in the comparisons which serve to demonstrate the need for this procedure.

Smith, J. E., Jr.↗

Unusual electronic transport in (1 - x )Cu 2 Se-( x )CuInSe 2 hierarchical composites

The ability to control the relative density of electronic point defects as well as their energy distribution in semiconductors could afford a systematic modulation of their electronic, optical, and optoelectronic properties. Using a model binary hybrid system Cu 2 Se–CuInSe 2 , we have investigated the correlation between phase composition, microstructure, and electronic transport behavior in the synthesized composites. We found that both Cu 2 Se and CuInSe 2 phases coexist at multiple length scales, ranging from sub-ten nanometer to several micrometers, leading to the formation of a hybrid hierarchical microstructure. Astonishingly, the electronic phase diagram of the (1 - x)Cu 2 Se–(x)CuInSe 2 (15% ≤ x ≤ 100%) hierarchical composites remarkably deviates from the trend normally expected for composites between a heavily doped semiconductor (Cu 2 Se) and a poorly conducting phase (CuInSe 2 ). A sudden 3-fold increase in the electrical conductivity and carrier concentration along with a marginal increase in the carrier mobility is observed for composites at the vicinity of equimolar composition (48% ≤ x ≤ 52%). The carrier concentration increases from ~1.5 × 10 20 cm -3 for the composites with x ≤ 45% to 5.0 × 10 20 cm -3 for x = 50%, and remains constant at 4.5 × 10 20 cm -3 with x value in the range of 52% < x ≤ 90%, then quickly drops to 8 × 10 18 cm -3 for pristine CuInSe 2 phase (x = 100%). The atypical electronic behavior was rationalized in the light of the formation of an inter-band (IB) within the band gap, which arises from the hybridization of native electronic point defects from both Cu 2 Se and CuInSe 2 phases in the resulting hierarchical composites. The result points to a new strategy to modulate the electronic structure of semiconductor composites to maximize interaction and coupling between two fundamentally contrasting properties enabling access to electronic hybrid systems with potential applications as interactive and stimuli-responsive multifunctional materials.

36 MATERIALS SCIENCE↗

High Variability in Vela X-1: Giant Flares and Off States

Aims. We investigate the spectral and temporal behavior of the high mass X-ray binary Vela X-1 during a phase of high activity, with special focus on the observed giant flares and off states. Methods. INTEGRAL observed Vela X-1 in a long almost uninterrupted observation for two weeks in 2003 Nov/Dec. The data were analyzed with OSA 7.0 and FTOOLS 6.2. We derive the pulse period, light curves, spectra, hardness ratios, hardness intensity diagrams, and study the eclipse. Results. In addition to an already high activity level, Vela X-1 exhibited several very intense flares, the brightest ones reaching a maximum intensity of more than 5 Crab in the 20-40 keV band and several off states where the source is no longer detected by INTEGRAL. We determine the pulse period to be 283.5320 +/- 0.0002 s which is stable throughout the whole observation. Analyzing the eclipses resulted in an improvement of the ephemeris. Spectral analysis of the flares shows that there seem to be two types of flares: relatively brief flares which can be extremely intense, and show spectral softening, contrary to high intensity states which are longer and show no softening. Conclusions. Both flares and off states are interpreted as being due to a strongly structured wind of the optical companion. When Vela X-1 encounters a cavity with strongly reduced density, the flux will drop triggering the onset of the propeller effect which inhibits further accretion, thus giving rise to off states. The required drop of the density of the material to trigger the propeller effect in Vela X-1 is of the same order as predicted by theoretical papers on the densities in the OB star winds. The same structured wind can give rise to the giant flares when Vela X-1 encounters a dense blob in the wind.

Kreykenbohm, Ingo↗

Ultraviolet Spectropolarimetry Conservative and Nonconservative Mass Transfer in OB Interacting Binaries

The current consensus is that at least half of the OB stars are formed in binary or multiple star systems. The evolution of OB stars is greatly influenced by whether the stars begin as close binaries, and the evolution of the binary systems depend on whether the mass transfer is conservative or nonconservative. FUV/NUV spectropolarimetry is poised to answer the latter question. This paper discusses how the Polstar spectropolarimetry mission can characterize the degree of nonconservative mass transfer that occurs at various stages of binary evolution, from the initial mass reversal to the late Algol phase, and quantify its amount. The proposed instrument combines spectroscopic and polarimetric capabilities, where the spectroscopy can resolve Doppler shifts in UV resonance lines with 10 km/s precision, and polarimetry can resolve linear polarization with 10 −3 precision or better. The spectroscopy will identify absorption by mass streams and other plasmas seen in projection against the stellar disk as a function of orbital phase, as well as scattering from extended splash structures, including jets. The polarimetry tracks the light coming from material not seen against the stellar disk, allowing the geometry of the scattering to be tracked, resolving ambiguities left by the spectroscopy and light-curve information. For example, nonconservative mass streams ejected in the polar direction will produce polarization of the opposite sign from conservative transfer accreting in the orbital plane. Time domain coverage over a range of phases of the binary orbit are well supported by the Polstar observing strategy. Special attention will be given to the epochs of enhanced systemic mass loss that have been identified from IUE observations (pre-mass reversal and tangential gas stream impact). We show how the history of systemic mass and angular momentum loss/gain episodes can be inferred via ensemble evolution through the r–q diagram. Combining the above elements will significantly improve our understanding of the mass transfer process and the amount of mass that can escape from the system, an important channel for changing the final mass and ultimate supernova of a large number of massive stars found in binaries at close enough separation to undergo interaction.

Geraldine J. Peters↗

Inclination and orbital-phase-dependent resonance line-profile calculations applied to cataclysmic variable winds

The implications of IUE resonance-line profiles of novalike variables and dwarf novae in outburst for theoretical models in which these objects are formed in constant-ionization stellar winds are investigated theoretically, with a focus on the 1549-A line of C IV. The model proposed by Drew (1986) is extended and refined to account for arbitrary inclinations of the large opaque continuum-emitting disk and the presence of a dark binary companion; the data and results are presented in extensive diagrams and graphs and characterized in detail. Findings reported include a wind C(3+) number density an order of magnitude or more greater than the density of Si(3+) and N(4+) and wind mass-loss rates greater than about 10 to the -10th solar mass/yr.

Drew, J. E.↗