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All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

An Assessment of Molten Metal Detachment Hazards During Electron Beam Welding in Space

The safety issue has been raised with regards to potential molten metal detachments from the weld pool and cold filler wire during electron beam welding in space. This investigation was undertaken to evaluate if molten metal could detach and come in contact with astronauts and burn through the fabric of the astronauts' Extravehicular Mobility Unit (EMU) during electron beam welding in space. Molten metal detachments from either the weld/cut substrate or weld wire could present harm to a astronaut if the detachment was to burn through the fabric of the EMU. Theoretical models were developed to predict the possibility and size of the molten metal detachment hazards during the electron beam welding exercises at Low Earth Orbit (LEO). The primary molten metal detachment concerns were those cases of molten metal separation from the metal surface due to metal cutting, weld pool splashing, entrainment and release of molten metal due to filler wire snap-out from the weld puddle, and molten metal accumulation and release from the end of the weld wire. Some possible ways of obtaining molten metal drop detachments would include an impulse force, or bump, to the weld sample, cut surface, or filler wire. Theoretical models were developed for these detachment concerns from principles of impact and kinetic energies, surface tension, drop geometry, surface energies, and particle dynamics. The surface tension represents the force opposing the liquid metal drop from detaching whereas the weight of the liquid metal droplet represents a force that is tending to detach the molten metal drop. Theoretical calculations have indicated that only a small amount of energy is required to detach a liquid metal drop; however, much of the energy of an impact is absorbed in the sample or weld plate before it reaches the metal drop on the cut edge or surface. The tendency for detachment is directly proportional to the weld pool radius and metal density and inversely proportional to the surface tension of the liquid metal. For a detachment the initial kinetic energy of the weld pool with respect to the plate has to exceed the energy to form the extra surface required for the detachment of the pool. The difficulty is in transferring the energy from the point of impact through the plate and sample to the cut edge. It is likely that not all of the kinetic energy is available for detaching the pool; some may be sequestered in weld pool oscillations. The coefficient of restitution for the collision will be lower than one if irreversible deformation, for example plastic flow deformation, takes place during the collision. Thus determining the amount of energy from an impact that actually reaches the molten metal droplet is critical. Various molten metal detachment scenarios were tested experimentally in an enclosed vacuum chamber using the Ukrainian Universal Hand Tool, an electron beam welder designed for space welding. The experimental testing was performed in a 4 ft. X 4 ft. vacuum chamber at Marshall Space Flight Center, evacuated to vacuum levels of at least 50 microTorr, and also some welding garment material was utilized to observe the effect of the molten metal detachments on the material. A "carillon" apparatus consisting of four pendulum hammer strikers, each weighing approximately 3.65 lbs, raised to predetermined specific heights was used to apply an impact force to the weld sample/plate during electron beam welding and cutting exercises. The strikers were released by switching on an electric motor to rotate a pin holding wires retaining the strikers at desired heights. The specimens were suspended so as to be free to respond to the blows with a sudden velocity increment. The specimens were mounted on a hinged plate for minimizing effective mass with the option to fasten it down so as to raise its effective mass closer to that anticipated for an actual space welding scenario. Measurements were made of the impact energy and the horizontal fling distances of the detached metal drops. It was not particularly easy to generate the detachments for this experiment. This document presents the details of the theoretical modeling effort and a summary of the experimental effort to measure molten metal drop detachments from terrestrial electron beam welding in the enclosed vacuum chamber. The results of the experimental effort have shown that molten metal detachments can occur from the sample/weld plate only if a sufficiently large impact force is applied to the weld plate. A "weld pool detachment parameter" was determined to indicate whether detachment would occur. Detachment can be either full or partial (dripping), Partial detachment means that the weld pool detached from one side of the liquid-solid boundary so as to leave a hole at the puddle site but remained attached over part of the liquid-solid boundary and dripped down the plate with no fully detached material detected. Full detachment, however, does not necessarily mean that the whole pool fully detached; in some cases only a smaller portion of the pool detached, the remainder dripping down the plate. The weld pool detachment parameter according to theory and according to the empirical data allows a determination of whether full detachments might occur. Theoretical calculations indicated titanium alloy would be the most difficult from which to detach molten metal droplets followed by stainless steel and then by aluminum. The experimental results were for the most part consistent with the theoretical analysis and predictions. The above theory is applicable to other situations as desired for assessing the potential for molten metal detachments.

Fragomeni, James M.↗
NASA NTRS2018

Levitation Experiments on ISS: Science and Applications

Levitation experiments on the International Space Station (ISS) are ongoing. The European Space Agency (ESA) Materials Science Laboratory Electromagnetic Levitator (MSL-EML) has been in operation since 2015. US investigators are on several of the European Topical Teams and have been heavily involved with the experiments since 2009. The experiments include magneto-hydrodynamic (MHD) modeling of macro-convection, the effects of convection on microstructure, investigation of metallic glass formation, and much more. Recently NASA selected four proposals to the MaterialsLab NASA Research Announcement (NRA) for experiments on the Japan Aerospace eXploration Agency (JAXA) Electrostatic Levitation Furnace (ELF), which was launched to the ISS in 2015. It is estimated that the four US investigators will have flight experiments on ELF within the next few years. The experiments range from a novel method to measure interfacial tension to investigations of thermophysical properties of metals, metal oxides, and non-linear optical materials. Using the MSL-EML and ELF, US investigators are studying a wide range of NASA exploration-relevant materials. Levitation experiments enable exploration in many ways. For example, high quality thermophysical properties of high-temperature materials are critical to develop accurate models of casting, welding, and metal additive manufacturing, which could lead to more efficient and more reliable production of metallic parts for exploration, commercial, and industrial applications. High-quality thermophysical properties could also lead to the development of functional oxide glass and optical materials. In many cases, the accuracy of available property data is the limiting factor in the predictive capabilities of the models. Many thermophysical properties can be measured in a levitator on Earth, but with convective contamination. This contamination plays a significant role in the formation of the intermediate phases. In particular, nucleation and viscosity measurements demand quiescent conditions that can only be attained in microgravity-based levitation systems. A brief overview of the ongoing and planned levitation experiments on the ISS will be presented, followed by the exploration-relevance.

SanSoucie, Michael P.↗
NASA NTRS1986

Theoretical analysis of the electrical aspects of the basic electro-impulse problem in aircraft de-icing applications

A summary of modeling the electrical system aspects of a coil and metal target configuration resembling a practical electro-impulse deicing (EIDI) installation, and a simple circuit for providing energy to the coil, was presented. The model was developed in sufficient theoretical detail to allow the generation of computer algorithms for the current in the coil, the magnetic induction on both surfaces of the target, the force between the coil and target, and the impulse delivered to the target. These algorithms were applied to a specific prototype EIDI test system for which the current, magnetic fields near the target surfaces, and impulse were previously measured.

Henderson, R. A.↗
NASA NTRS2014

Multiphysics Modeling of an Annular Linear Induction Pump With Applications to Space Nuclear Power Systems

An annular linear induction pump (ALIP) that could be used for circulating liquid-metal coolant in a fission surface power reactor system is modeled in the present work using the computational COMSOL Multiphysics package. The pump is modeled using a two-dimensional, axisymmetric geometry and solved under conditions similar to those used during experimental pump testing. Real, nonlinear, temperature-dependent material properties can be incorporated into the model for both the electrically-conducting working fluid in the pump (NaK-78) and structural components of the pump. The intricate three-phase coil configuration of the pump is implemented in the model to produce an axially-traveling magnetic wave that is qualitatively similar to the measured magnetic wave. The model qualitatively captures the expected feature of a peak in efficiency as a function of flow rate.

Kilbane, J.↗
NASA NTRS1989

Optical evidence for the metallization of Xenon at 132(5) GPa

Xe has been compressed in a diamond-anvil cell to approximately 200 GPa. The metallization of Xe by band-gap closure was investigated by obtaining optical data in both the metallic and insulating states. In the metallic state, the pressure dependence of the plasma frequency was determined from absorption data fitted with a free-electron model. In the insulating state, the pressure dependence of the band gap was determined from absorption data fitted with an indirect-band-gap model. The optical data indicate that the insulator-to-metal transition in Xe occurs at 132(5) GPa.

Goettel, Kenneth A.↗
NASA NTRS1974

External field effects on solidification - Macroscopic and microscopic models

Comparison of theoretical effects of magnetic and gravitational fields on melts of metals and semiconductors provides two kinds of insight into space processing materials problems. First, the task of comparing effects of the two fields yields mathematical models which may be used to estimate material properties and responses to processing under various field conditions. Then, by using these models, microgravity effects can be inferred from magnetic field data already obtained in laboratories on earth. Magnetohydrodynamics (static and oscillating fields) and the Free Volume Model are used to study macroscopic effects, and Sekerka's interface stability theory is used to show how external fields can affect microsegregation. It is demonstrated that the mathematical formalism is essentially the same for describing macroscopic effects of both microgravity and magnetic fields.

Miller, R. I.↗
NASA NTRS1995

Non-LTE line-blanketed model atmospheres of hot stars. 1: Hybrid complete linearization/accelerated lambda iteration method

A new munerical method for computing non-Local Thermodynamic Equilibrium (non-LTE) model stellar atmospheres is presented. The method, called the hybird complete linearization/accelerated lambda iretation (CL/ALI) method, combines advantages of both its constituents. Its rate of convergence is virtually as high as for the standard CL method, while the computer time per iteration is almost as low as for the standard ALI method. The method is formulated as the standard complete lineariation, the only difference being that the radiation intensity at selected frequency points is not explicity linearized; instead, it is treated by means of the ALI approach. The scheme offers a wide spectrum of options, ranging from the full CL to the full ALI method. We deonstrate that the method works optimally if the majority of frequency points are treated in the ALI mode, while the radiation intensity at a few (typically two to 30) frequency points is explicity linearized. We show how this method can be applied to calculate metal line-blanketed non-LTE model atmospheres, by using the idea of 'superlevels' and 'superlines' introduced originally by Anderson (1989). We calculate several illustrative models taking into accont several tens of thosands of lines of Fe III to Fe IV and show that the hybrid CL/ALI method provides a robust method for calculating non-LTE line-blanketed model atmospheres for a wide range of stellar parameters. The results for individual stellar types will be presented in subsequent papers in this series.

Hubeny, I.↗
NASA NTRS1985

Transient Analysis of a Magnetic Heat Pump

An experimental heat pump that uses a rare earth element as the refrigerant is modeled using NASTRAN. The refrigerant is a ferromagnetic metal whose temperature rises when a magnetic field is applied and falls when the magnetic field is removed. The heat pump is used as a refrigerator to remove heat from a reservoir and discharge it through a heat exchanger. In the NASTRAN model the components modeled are represented by one-dimensional ROD elements. Heat flow in the solids and fluid are analyzed. The problem is mildly nonlinear since the heat capacity of the refrigerant is temperature-dependent. One simulation run consists of a series of transient analyses, each representing one stroke of the heat pump. An auxiliary program was written that uses the results of one NASTRAN analysis to generate data for the next NASTRAN analysis.

Schroeder, E. A.↗
NASA NTRS1995

Derived parameters for NGC 6791 from high-metallicity isochrones

We have computed 8, 10, and 12 Gyr isochrones and physically consistent models of zero-age red horizontal branch stars for stellar masses between 0.55 and 1.3 solar mass, all at (fe/H) = +0.15. Comparison to the NGC 6791 BVI photometry of Kaluzny & Udalski (1992) and Montgomery et al. (1994) yields an age of 10.0 +/- 0.5 Gyr at an apparent distance modulus 13.49 less than (m-M)(sub V) less than 13.70. The color offsets required to fit the isochrones, combined with the spectroscopic results of Friel & Janes (1993), imply that the foreground reddening to NGC 6791 lies in the range 0.24 greater than E(B -V) greater than 0.19 with +0.27 less than (Fe/H) less than + 0.44. These results are derived using a technique by which we predict color shifts and apply these to the isochrones to simulate progressively higher metallicities. The zero-age horizontal branch model suggest that the red horizontal branch stars of NGC 6791 have masses approximately less than 0.7 solar mass. The masses are similar to those found for M67 red horizontal branch stars by Tripicco et al. (1993) and for globular cluster red horizontal branch stars, even though the M67 progenitors are approximately 0.2 solar-mass more massive, while the progenitors of globular cluster horizontal branch stars are similarly less massive. This suggests the presence of a mechanism, not strongly dependent on metallicity, which reduces stellar envelopes on the zero-age horizontal branch to a given mass rather than by a given amount.

Dorman, Ben↗
NASA NTRSDate not supplied

A Transmission Electron Microscopy Study of a Refractory Metal Grain from a Calcium-Aluminum-Rich Inclusion in the Leoville CV3 Chondrite

Introduction: Calcium-aluminum-rich inclusions (CAIs) are an important component of chondritic meteorites. They can contain materials that are thermodynamically predicted and isotopically age dated to be among the first-formed solids in our solar system [1-5]. Observed in some CAIs are micron to sub-micron sized inclusions rich in Fe, Ni, and high-Z elements such as Pt, Os, Ir and W, in the form of refractory metal nuggets (RMNs), fremdlinges, and ‘nugget like objects’ (NLOs) [1,6]. Refractory siderophile elements such as Os, Ir and Ru are thermodynamically predicted to condense at temperatures well in excess of the major CAI phases such as melilite, perovskite, spinel and hibonite [2,7-9]. These refractory metal inclusions in CAIs can therefore serve as probes into the thermodynamic landscape of the early solar protoplanetary disk. Here we report on a refractory grain identified in a CAI of the Leoville CV3 chondrite. This work is part of an ongoing effort to gain insight into the thermochemistry of the early solar system through systematic analyses of the structure and chemistry of various components in CAIs [10-13]. Sample and Analytical Techniques: A fluffy type A CAI (Fig. 1A) was identified in a section of the Leoville, CV3 chondrite (Center for Meteorite Studies, Arizona State University collection, #821_C_3) using a JOEL-JXA 8530F electron microprobe at Arizona State University. Backscattered electron (BSE) imaging and energy-dispersive X-ray spectroscopy (EDS) were used to identify refractory metal grains in the CAI using a Thermo Fisher (formerly FEI) Helios NanoLab 660 G3 focused-ion-beam scanning-electron microscope (FIBSEM) located at the Kuiper Materials Imaging and Characterization Facility (KMICF) at the Lunar and Planetary Laboratory, University of Arizona. The FIB is equipped with an EDAX EDS system. We selected one of the larger (micron-sized) refractory metal grains, designated as ‘Spud’ (Fig. 1B) for further analysis. ‘Spud’ was extracted and thinned to electron transparency (<100 nm) using the FIB-SEM located in KMICF, following methods described by [14- 15]. The FIB section was analyzed using a 200 keV Hitachi HF5000 scanning transmission electron microscope (S/TEM) located at KMICF. The HF5000 is equipped with cold-field emission gun, 3rd-order spherical aberration corrector for STEM imaging, and an Oxford Instruments X-Max N 100 TLE energydispersive spectroscopy (EDS) system with dual 100 mm2 windowless silicon-drift detectors (Ω = 2.0 sr). Selected-area electron-diffraction (SAED) patterns were acquired to aid in determination of crystallinity and phase. Results: The mineralogy, texture, and morphology of the CAI are consistent with that of a fluffy type A (FTA) CAI [16]. BSE imaging at high magnifications revealed grains with high contrast, indicative of compositions rich in elements of higher atomic number relative to surrounding material. These high-Z grains have sizes that range from ∼250 nm to 4 µm. EDS analyses confirm that the bright grains are metal-rich inclusions. A minor fraction of the grains are composed of only Fe and Ni, but the majority (∼60%) of the identified inclusions also contained various refractory siderophiles including Os, Ru, Zr, Ir and Mo. EDS analysis on the FIB-SEM of Spud shows that it contains Fe, Ni, Mo and Ru. High-angle annular dark-field (HAAFD) imaging and EDS mapping in the TEM (Fig. 2) show that Spud occurs in melilite (Ca1.9Al1.99Si1.06O7). Spud contains a subhedral to anhedral morphology and is compositionally heterogenous (polyphasic, Fig. 2). Local spatial correlation occurs among Fe, Ni, and Pt, and also among Os, Ru, and Mo. SAED patterns show that the Fe-Ni-Pt, Fe-Os-Mo-Ru and Fe-Pt regions are crystalline. Discussion: CAIs can contain various types of inclusions rich in Fe, Ni and refractory siderophiles such as Os, Ru, W and Pt [1]. RMNs are micron-sized, single phase alloy grains and can contain Os, Ir, Ru and Rh [1,7,17]. NLOs are also micron-sized inclusions, but contain two phases, a refractory metal, and an oxide [6]. Fremdlinge are the largest of such inclusions (tens of microns in size) and are complex aggregates of Fe-Ni alloy, silicates, oxides, and sulfides [1,17]. While the size of Spud matches previous descriptions of RMNs and NLOs, Spud is neither a single-phase alloy like RMNs, nor does it contain one metal phase and one oxide like NLOs. Spud does not match the above described categories of refractory metal inclusions. The presence of refractory siderophiles such as Mo, Os, Ru, and Pt suggests a high-temperature origin. Thermodynamic modelling by [7] indicates condensation temperatures of 1917 K, 1693 K, 1613 K and 1415 K for Os, Mo, Ru and Pt respectively. These models also show that following the initial condensation of a refractory metal, alloying of solutes such as Fe, Ni and W, occurs in levels proportional to their partial pressures in the surrounding gas. Such alloying occurs at temperatures above the condensation temperatures of common CAI phases such as melilite (1529 K), perovskite (1441 K), spinel (197 K) and forsterite (1354 K) [2]. The polyphasic nature of Spud could be the result of such high-temperature alloying, possibly shortly after the condensation of Mo and Ru at 1693 K and 1613 K respectively. That Spud occurs as an inclusion is consistent with it having formed prior to and at temperature above that of its host melilite in this FTA CAI, which is qualitatively consistent with such prior thermodynamic modeling. Further, the polyphasic nature of Spud is similar to refractory grains from a FTA CAI in the Northwest Africa (NWA) 8323, CV3 chondrite [11-13]. These data suggest that such refractory metal grains could have been widespread in the inner and early solar protoplanetary disk and represent some of the earliest formed solids to have condensed. Acknowledgments: Research and instrumentation supported by NASA grants #NNX12AL47G, #NNX15AJ22G and #80NSSC19K0509, and NSF grants #1531243 and #0619599. Fig 2. STEM data on ‘Spud’. HAADF Image (Top) False-color EDS Maps (Bottom) References: [1] MacPherson G. J. (2014) T. of Geochem. Vol I: Met. And Cosmochem. Processes, 139-179. [2] Lodders K. (2003) ApJ, 591, 1220-1247. [3] Ebel D. S. (2006) Met. & the Early S. Sys. II., 253- 277. [4] Amelin Y. (2002) Science, 297, 1678-1683. [5] Connelly J.N. et.al. (2012) Science, 338, 651-655. [6] Schwander D. et al. (2015) GCA, 18, 70-87. [7] Palme H. and Wlotzka F. (1976) EPSL, 33, 45-60. [8] Berg T. et al. (2009) ApJ, 702, 172-176. [9] Liffman K. et al. (2021) Icarus, 221, 89-105. [10] Zega T.J. et al. (2021) PSJ, 2, 115. [11] Ramprasad T. et al. (2020) LPSC LI, Abstract #2472. [12] Ramprasad T. et al. (2021) Microscopy & Microanalysis, S1, 2792-2794. [13] Ramprasad T. et al. (2021) 84th MetSoc, Abstract #6123. [14] Zega T.J. et al. (2007) MAPS, 42, 1373-1386. [15] Ramprasad T. et al. (2022) MAPS, in revision. [16] Grossman L. (1975), GCA, 39, 433-454. [17] El Goresy A. et al. (1978) LPSC IX, Abstract#1100

T. Ramprasad↗
NASA NTRS2010

RCC Plug Repair Thermal Tools for Shuttle Mission Support

A thermal math model for the Space Shuttle Reinforced Carbon-Carbon (RCC) Plug Repair was developed to increase the confidence in the repair entry performance and provide a real-time mission support tool. The thermal response of the plug cover plate, local RCC, and metallic attach hardware can be assessed with this model for any location on the wing leading edge. The geometry and spatial location of the thermal mesh also matches the structural mesh which allows for the direct mapping of temperature loads and computation of the thermoelastic stresses. The thermal model was correlated to a full scale plug repair radiant test. To utilize the thermal model for flight analyses, accurate predictions of protuberance heating were required. Wind tunnel testing was performed at CUBRC to characterize the heat flux in both the radial and angular directions. Due to the complexity of the implementation of the protuberance heating, an intermediate program was developed to output the heating per nodal location for all OML surfaces in SINDA format. Three Design Reference Cases (DRC) were evaluated with the correlated plug thermal math model to bound the environments which the plug repair would potentially be used.

Rodriguez, Alvaro C.↗
NASA NTRS1969

Self-consistent many-electron theory of electron work functions and surface potential characteristics for selected metals

Electron work functions, surface potentials, and electron number density distributions and electric fields in the surface region of 26 metals were calculated from first principles within the free electron model. Calculation proceeded from an expression of the total energy as a functional of the electron number density, including exchange and correlation energies, as well as a first inhomogeneity term. The self-consistent solution was obtained via a variational procedure. Surface barriers were due principally to many-body effects; dipole barriers were small only for some alkali metals, becoming quite large for the transition metals. Surface energies were inadequately described by this model, which neglects atomistic effects. Reasonable results were obtained for electron work functions and surface potential characteristics, maximum electron densities varying by a factor of over 60.

Smith, J. R.↗
NASA NTRS1975

Developments in convective heat transfer models featuring seamless and selected detail surfaces, employing electroless plating

Several model/instrument concepts employing electroless metallic skin were considered for improvement of surface condition, accuracy, and cost of contoured-geometry convective heat transfer models. A plated semi-infinite slab approach was chosen for development and evaluation in a hypersonic wind tunnel. The plated slab model consists of an epoxy casting containing fine constantan wires accurately placed at specified surface locations. An electroless alloy was deposited on the plastic surface that provides a hard, uniformly thick, seamless skin. The chosen alloy forms a high-output thermocouple junction with each exposed constantan wire, providing means of determining heat transfer during tunnel testing of the model. A selective electroless plating procedure was used to deposit scaled heatshield tiles on the lower surface of a 0.0175-scale shuttle orbiter model. Twenty-five percent of the tiles were randomly selected and plated to a height of 0.001-inch. The purpose was to assess the heating effects of surface roughness simulating misalignment of tiles that may occur during manufacture of the spacecraft.

Stalmach, C. J., Jr.↗
NASA NTRS1980

The role of P2O5 in silicate melts

Phase equilibria data in the systems SiO2-P2O5, P2O5-M(x)O(y), and P2O5-M(x)O(y)-SiO2 are employed in conjunction with chromatographic and spectral data to investigate the role of P2O5 in silicate melts. P2O5 depolymerizes pure SiO2 melts by entering the network as a four-fold coordinated cation, but polymerizes melts in which an additional metal cation other than silicon is present. In this complex system P2O5 acts to increase phase separation by further enrichment of the high charge density cations Ti, Fe, Mg, Mn, Ca, in the ferrobasaltic liquid. The dual behavior of P2O5 is explained in a model which requires complexing of phosphate anions and metal cations in the melt. This interaction destroys Si-O-M-O-Si bonds polymerizing the melt. The higher concentration of Si-O-M-O-Si bond complexes in immiscible ferrobasaltic liquids relative to their conjugate immiscible granite liquids explains the partitioning of P2O5 into the ferrobasaltic liquid.

Ryerson, F. J.↗
NASA NTRS1999

[Observations in the Outer Galaxy of Metal Abundances]

This project involved observations of far-infrared (FIR) fine-structure lines of [S III] (19,33 microns), [O III] (52,99 microns), and [N III] (57 microns) in the outer Galaxy (galactocentric radius R = 11-18 kpc), in order to study the variation of metal abundances with radius in the Galaxy. The metal abundance gradient is a fundamental input into models of galaxy evolution, and greatly constrains theories of galaxy evolution, stellar structure and evolution, and star formation. In addition, we observed the [C III (158 microns) and [O I] (63 microns) lines in these same regions to study molecular cloud structure in the low metallicity outer Galaxy. These observations were carried out over two weeks in August 1995 aboard the Kuiper Airborne Observatory, which was stationed at Hickam AFB at the time. Two Harvey Mudd students worked with me planning the observations and accompanied me on the flights. These students, and two other Harvey Mudd students, worked with me during the remaining time of the grant period analyzing these data and preparing them for publication These data have formed the basis for two journal articles in a professional astronomical journal. The first off these articles has been published (Rudolph et al. 1997, "Far-Infrared Abundance Measurements in the Outer Galaxy", The Astrophysical Journal, 489, 94-101). The second article is in preparation (Rudolph et al. 1999, "The Abundance Gradient in the Galaxy", in preparation for The Astrophysical Journal).

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