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At least 379 records · Page 21

Solidification Using a Baffle in Sealed Ampoules (SUBSA)

Solidification Using a Baffle in Sealed Ampoules (SUBSA) will be the first materials science experiment conducted in the Microgravity Science Glovebox (MSG) Facility at the International Space Station (ISS) Alpha. The launch is schedule for May 31, 2002. Using the specially developed furnace, 10 Te and Zn-doped single crystals of InSb will be directionally solidified in microgravity. A key goal of the SUBSA investigation is to (i) clarify the origin of the melt motion in space laboratories and (ii) to reduce the magnitude of the melt motion to the point that it does not interfere with the transport phenomena. These goals will be accomplished through a special ampoule and furnace design. A disk-shaped baffle, positioned close to the freezing front, is used to reduce melt motion. Furthermore, the solidification will be visualized by using a transparent furnace, with a video camera, continuously sending images to the earth. This allows detection of bubbles and melt de-wetting that could cause surface tension driven convection. In preparation for the space experiments, 30 ground-based experiments were conducted. The results of ground based tests and numerical modeling will be presented. Based on numerical modeling, 12 mm 1D silica ampoules were selected. The small diameter ampoule favors closer placement of the baffle to the interface, without excessive radial segregation caused by forced convection while providing more damping of natural convection. The parts in the silica ampoule include 2 carbon springs made by Energy Science Laboratories, Inc., a pyrocarbon-coated graphite cylinder, pyrocarbon-coated graphite a baffle with the shaft and the InSb charge with the seed crystal grown by W.A. Bonner of Crystallod Inc.

Marin, C.↗

Vapor growth of GeTe single crystals in micro-gravity

The positive effects of micro-gravity on crystal growth and fundamental properties of the vapor transport reaction were established by analyzing the results of GeSe and GeTe vapor transport experiments performed on board Skylab. The analysis was based on a direct comparison of GeSe and GeTe crystals and of mass transport rate data obtained on earth and in space. For this purpose, a total of six transport experiments employing different concentrations of transport agent (GeI4) and two temperature gradients were performed during the Skylab 3 and 4 missions. Extensive ground-based studies demonstrated that the crystal morphology and the mass transport rates of the above systems are affected by the transport conditions, in particular by gravity-driven convection. The results demonstrate unambiguously a considerable improvement of the space crystals in terms of surface perfection, crystalline homogeneity and defect density. The observation of greater mass transport rates than expected in micro-gravity environment is of basic scientific and technological significance. This indicates that conventional transport models are incomplete and demonstrates that crystals of improved quality can be grown at reasonable rates by this technique in space. Results are of practical importance for the modification of crystal growth techniques on earth.

Wiedemeier, H.↗

Impurities in silicon solar cells

Metallic impurities, both singly and in combinations, affect the performance of silicon solar cells. Czochralski silicon web crystals were grown with controlled additions of secondary impurities. The primary electrical dopants were boron and phosphorus. The silicon test ingots were grown under controlled and carefully monitored conditions from high-purity charge and dopant material to minimize unintentional contamination. Following growth, each crystal was characterized by chemical, microstructural, electrical, and solar cell tests to provide a detailed and internally consistent description of the relationships between silicon impurity concentration and solar cell performance. Deep-level spectroscopy measurements were used to measure impurity concentrations at levels below the detectability of other techniques and to study thermally-induced changes in impurity activity. For the majority of contaminants, impurity-induced performance loss is due to a reduction of the base diffusion length. From these observations, a semi-empirical model which predicts cell performance as a function of metal impurity concentration was formulated. The model was then used successfully to predict the behavior of solar cells bearing as many as 11 different impurities.

Hopkins, R. H.↗

Amorphous and Crystalline H20 Ice at Rhea's Inktomi Crater

We present the analysis of Cassini spectral data from spectral mapping of Saturnian icy moons Dione and Rhea, to investigate possible effects of impact crater formation on the relative abundances of crystalline and amorphous water ice in the moons' ice crusts. Both moons display morphologically young ray craters as well as older craters. Possible changes in ice properties due to crater formation are conjectured to be more visible in younger craters, and as such Rhea's well imaged ray crater Inktomi is analysed, as are older craters for comparison. We used data from Cassini's Visual and Infrared Mapping Spectrometer (VIMS). For each pixel in the VIMS maps, spectral data were extracted in the near-infrared range (1.75 micrometers less than lambda less than 2.45 micrometers). Analysis was begun by fitting a single Gaussian to the peak in absorption at 2.0 micrometers, which was then subtracted from the data, leaving residuals with a minimum on either side of the original 2.0-micrometers band. The spectra of the individual spatial pixels were then clustered by the differences between these minima, which are sensitive to changes in both ice grain size and crystallinity. This yielded preliminary maps which approximated the physical characteristics of the landscape and were used to identify candidates for further analysis. Spectra were then clustered by the properties of the 1.5-micrometers band, to divide the map into regions based on inferred grain size. For each region, the predicted differences in minima from the Gaussian residuals, over a range of crystallinities, were calculated based on the found grain sizes. This model was used to find the crystallinity of each pixel via grain size and characteristics of the residual function. Preliminary results show a greater degree of crystallization of young crater interiors, particularly in Rhea's ray crater Inktomi, where ice showed crystalline ice abundances between 33 percent and 61 percent. These patterns in ice crystallization are possibly attributable to increased heat generated during crater formation.

Saturn Satellites↗

A numerical and analytical study of nonlinear bifurcations associated with the morphological stability of two-dimensional single crystals

The nonlinear stability of a two-dimensional single crystal of pure material in an undercooled melt is studied both analytically and numerically. The quasi-steady state approximation is used for the thermal fields, and the effects of different solid and liquid thermal conductivities, isotropic interfacial growth kinetics, and isotropic surface tension are included. The bifurcation analysis is performed by calculating the instantaneous value of the fundamental component of the local normal growth speed for an interface perturbed by a single Fourier shape component. Numerically, the fundamental component of the interfacial growth speed is found by Fourier analysis of the solution to an integrodifferential equation obeyed at the interface. Analytically, an expansion technique is used to derive a solvability condition defining each of these bifurcation points. The analytical and numerical results are in very close agreement. Almost all of the bifurcations are subcritical, and the results are presented by giving values of the Landau coefficient as a function of the different dimensionless parameters used in the model.

Brush, L. N.↗

NASA Tech Briefs, October 2007

Topics covered include; Wirelessly Interrogated Position or Displacement Sensors; Ka-Band Radar Terminal Descent Sensor; Metal/Metal Oxide Differential Electrode pH Sensors; Improved Sensing Coils for SQUIDs; Inductive Linear-Position Sensor/Limit-Sensor Units; Hilbert-Curve Fractal Antenna With Radiation- Pattern Diversity; Single-Camera Panoramic-Imaging Systems; Interface Electronic Circuitry for an Electronic Tongue; Inexpensive Clock for Displaying Planetary or Sidereal Time; Efficient Switching Arrangement for (N + 1)/N Redundancy; Lightweight Reflectarray Antenna for 7.115 and 32 GHz; Opto-Electronic Oscillator Using Suppressed Phase Modulation; Alternative Controller for a Fiber-Optic Switch; Strong, Lightweight, Porous Materials; Nanowicks; Lightweight Thermal Protection System for Atmospheric Entry; Rapid and Quiet Drill; Hydrogen Peroxide Concentrator; MMIC Amplifiers for 90 to 130 GHz; Robot Would Climb Steep Terrain; Measuring Dynamic Transfer Functions of Cavitating Pumps; Advanced Resistive Exercise Device; Rapid Engineering of Three-Dimensional, Multicellular Tissues With Polymeric Scaffolds; Resonant Tunneling Spin Pump; Enhancing Spin Filters by Use of Bulk Inversion Asymmetry; Optical Magnetometer Incorporating Photonic Crystals; WGM-Resonator/Tapered-Waveguide White-Light Sensor Optics; Raman-Suppressing Coupling for Optical Parametric Oscillator; CO2-Reduction Primary Cell for Use on Venus; Cold Atom Source Containing Multiple Magneto- Optical Traps; POD Model Reconstruction for Gray-Box Fault Detection; System for Estimating Horizontal Velocity During Descent; Software Framework for Peer Data-Management Services; Autogen Version 2.0; Tracking-Data-Conversion Tool; NASA Enterprise Visual Analysis; Advanced Reference Counting Pointers for Better Performance; C Namelist Facility; and Efficient Mosaicking of Spitzer Space Telescope Images.

Source record↗

Megaregolith insulation and the duration of cooling to isotopic closure within differential asteroids and the moon

Global cooling of the moon and large (R = 40-250 km) asterodis, was modeled, starting at or near the solidus. A crucial factor in determining the prevailing interval (Ic) of cooling between igenous crystallization and isotopic closure, for any given depth in the crust, is the extent to which the body is insulated by a regolith/megaregolith layer of porous, fragmental impact debris. Given plausible assumptions regarding the thicknesses of such layers on the moon and the eucrite parent asteroid (and regarding the radius of the eucrite asteroid), the results indicate that deep-crustal regions tend to remain above the Nd and Sr isotopic closure temperature for intervals that are long in comparison to the precision of modern Nd- and Sr-based age measurements, and in comparison to suggested chronologic scenarios of global differentiation. Ic intervals of as long as 100 my may be common among available samples of primordial, deep-crustal cumulates from both bodies. Chronologies for the gross solidification of the moon and the eucrite asteroid should allow for the possibility that any single age for a coarse-grained 'plutonic' or cumulate-textured rock might be many tens of millions of years younger than the igneous crystallization age.

Warren, Paul H.↗

Recent Results from a Laboratory Study of Charging Mechanisms in a Dusty Plasma

A laboratory investigation has been developed to experimentally study the interaction of micron sized particles with plasmas and electromagnetic radiation. The intent is to investigate under what conditions particles of various compositions and sizes become charged, or discharged, while exposed to an electron beam and UV radiation. This investigation uses a unique laboratory technique known as electrodynamic suspension of particles. Here, a single charged micron size particle is suspended in a quadrupole trap and then subjected to a controlled environment. In this paper, we will discuss recent results from this experiment in which different materials including polystyrene and aluminum oxide, and sizes ranging from 10 microns to 1 micron have been used to determine charge to mass ratios and then subjected to an electron beam and /or UV radiation. In each instance, the particle's charge as well as beam current flux and radiation intensity flux is measured. These results will be compared with initial results using salt crystals. It was found that a negatively charged salt crystal exposed for 30 minutes to a 500 eV electron beam with primary electron beam current of -3.06 x 10(exp -5) picoamps yielded a secondary electron current of 3.23 x 10(exp -5) picoamps. Additionally, the particle was observed to be steadily losing charge over this time interval. By studying the microphysics of one particle, a better understanding of theoretical models and other laboratory results associated with particle charging mechanisms can be achieved.

Venturini, Catherine C.↗

Energy landscape in Ni-Co-Cr and related alloys

Among multi-principal element alloys, the NiCoCr middle-entropy alloy has an outstanding combination of strength and ductility at both low and elevated temperatures. Equiatomic NiCoCr is a single-phase alloy with the face centered cubic (fcc) crystal structure. A low stacking fault energy in the fcc matrix is a cause of a relatively low creep in this alloy. The hexagonal close-packed (hcp) structure differs from the fcc by a stacking of atomic layers. The energy difference between the hcp and fcc structures is known to correlate with the stacking fault energy in the fcc phase. We compute formation and relative structural energies versus composition in the Ni-Co-Cr ternary and related quaternary systems, discuss possibilities of compositional adjustments, and compare theoretical predictions with experiment. We acknowledge funding by NASA’s Aeronautics Research Mission Directorate (ARMD) via Transformational Tools and Technologies (TTT) Project.

Multiscale↗

Basalt generation at the Apollo 12 site. Part 1: New data, classification, and re-evaluation

New data are reported from five previously unanalyzed Apollo 12 mare basalts that are incorporated into an evaluation of previous petrogenetic models and classification schemes for these basalts. This paper proposes a classification for Apollo 12 mare basalts on the basis of whole-rock Mg# (molar 100*(Mg/(Mg+Fe))) and Rb/Sr ratio (analyzed by isotope dilution), whereby the ilmenite, olivine, and pigeonite basalt groups are readily distinguished from each other. Scrutiny of the Apollo 12 feldspathic 'suite' demonstrates that two of the three basalts previously assigned to this group (12031, 12038, 12072) can be reclassified: 12031 is a plagioclase-rich pigeonite basalt; and 12072 is an olivine basalt. Only basalt 12038 stands out as a unique sample to the Apollo 12 site, but whether this represents a single sample from another flow at the Apollo 12 site or is exotic to this site is equivocal. The question of whether the olivine and pigeonite basalt suites are co-magmatic is addressed by incompatible trace-element chemistry: the trends defined by these two suites when Co/Sm and Sm/Eu ratios are plotted against Rb/Sr ratio demonstrate that these two basaltic types cannot be co-magmatic. Crystal fractionation/accumulation paths have been calculated and show that neither the pigeonite, olivine, or ilmenite basalts are related by this process. Each suite requires a distinct and separate source region. This study also examines sample heterogeneity and the degree to which whole-rock analyses are representative, which is critical when petrogenetic interpretation is undertaken. Sample heterogeneity has been investigated petrographically (inhomogeneous mineral distribution) with consideration of duplicate analyses, and whether a specific sample (using average data) plots consistently upon a fractionation trend when a number of different compostional parameters are considered. Using these criteria, four basalts have been identified where reported analyses are not representative of the whole-rock composition: 12005, an ilmenite basalt; 12006 and 12036, olivine basalts; and 12031 previously classified as a feldspathic basalt, but reclassified as part of the pigeonite suite.

Neal, Clive R.↗

Influence of gravity-free solidification on microsegregation

Single crystalline germanium has been grown for the first time in space aboard Skylab Mission No. 2. The crystal growth experiment, designed to characterize the influence of gravity-free solidification on microsegregation of a semiconductor material, contained three crystals. One was doped with Ga; the second with Sb; and the third with B. Portions of the germanium crystals were remelted and subsequently resolidified at 5 microns per second under controlled conditions by the gradient freeze technique. Detailed spreading resistance measurements made on the Ga doped Ge crystals indicate that microsegregation in space is reduced by two to five-fold in the bulk and eight-fold near the surface, while macrosegregation in space is reduced by six-fold in the bulk. The effective segregation coefficient for Ga in Ge was analyzed extensively and was found to be larger for space solidification. This has the implication that the solute boundary layer at the growth interface in space is correspondingly thinner. The solidification interface is significantly smoother and is found to be initially convex toward the melt in space. A convective mixing model has been advanced to explain the absence of gravity on convective mixing and solute segregation during solidification.

Yue, J. T.↗

Flux creep in Bi2Sr2CaCu2O8(sub +x) single crystals

The results of a magnetic study on a Bi2Sr2CaCu2O(8+x) single crystal are reported. Low field susceptibility (dc and ac), magnetization cycles and time dependent measurements were performed. With increasing the temperature the irreversible regime of the magnetization cycles is rapidly restricted to low fields, showing that the critical current J(sub c) becomes strongly field dependent well below T(sub c). At 2.4 K the critical current in zero field, determined from the remanent magnetization by using the Bean formula for the critical state, is J(sub c) = 2 10(exp 5) A/sq cm. The temperature dependence of J(sub c) is satisfactorily described by the phenomenological law J(sub c) = J(sub c) (0) (1 - T/T(sub c) (sup n), with n = 8. The time decay of the zero field cooled magnetization and of the remanent magnetization was studied at different temperatures for different magnetic fields. The time decay was found to be logarithmic in both cases, at least at low temperatures. At T = 4.2 K for a field of 10 kOe applied parallel to the c axis, the average pinning energy, determined by using the flux creep model, is U(sub o) = 0.010 eV.

Agostinelli, E.↗

Evaluation of a New Cloud Droplet Activation Parameterization wtih in Situ Data from CRYSTAL-FACE and CSTRIPE

The accuracy of the 2003 prognostic, physically based aerosol activation parameterization of A. Nenes and J. H. Seinfeld (NS) with modification introduced by C. Fountoukis and A. Nenes in 2005 (modified NS) is evaluated against extensive microphysical data sets collected on board the Center for Interdisciplinary Remotely Piloted Aircraft Studies (CIRPAS) Twin Otter aircraft for cumuliform and stratiform clouds of marine and continental origin. The cumuliform cloud data were collected during NASA's Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE, Key West, Florida, July 2002), while the stratiform cloud data were gathered during Coastal Stratocumulus Imposed Perturbation Experiment (CSTRIPE, Monterey, California, July 2003). In situ data sets of aerosol size distribution, chemical composition, and updraft velocities are used as input for the NS parameterization, and the evaluation is carried out by comparing predicted cloud droplet number concentrations (CDNC) with observations. This is the first known study in which a prognostic cloud droplet activation parameterization has been evaluated against a wide range of observations. On average, predicted droplet concentration in adiabatic regions is within -20% of observations at the base of cumuliform clouds and -30% of observations at different altitudes throughout the stratiform clouds, all within experimental uncertainty. Furthermore, CDNC is well parameterized using either a single mean updraft velocity w or by weighting droplet nucleation rates with a Gaussian probability density function of w. This study suggests that for nonprecipitating warm clouds of variable microphysics, aerosol composition, and size distribution the modified NS parameterization can accurately predict cloud droplet activation and can be successfully implemented for describing the aerosol activation process in global climate models.

Meskhidze, Nicholas↗

Computational Icing Analysis on NASA’s SIDRM Geometry to Investigate Collection Efficiency

Computational icing analysis results were compared to experimental icing tunnel data including aerothermal (e.g. dry air) and supercooled water droplet rime-ice conditions from tests conducted in early 2022 at the NASA Icing Research Tunnel (IRT). The Simulated Intercompressor Duct Research Model (SIDRM) test article was used in this study, and its geometry represents the inter-compressor duct region of a turbofan engine. The test article’s purpose is to study the physics of supercooled water icing and ice crystal icing. This study compared three different icing codes: FENSAP-ICE (Eulerian approach), LEWICE3D (Lagrangian approach), and GlennICE (Lagrangian approach). All three icing codes were conducted on SIDRM’s complex body flow-field and compared to different experimental supercooled water rime runs. The test article instrumentation (pressure taps, thermocouples, etc.) and 3D laser scans of final ice shapes were used to compare against the different icing code simulations. The overall objectives are to understand how the icing codes handle capturing collection efficiency on the complex test article’s unheated surfaces. In the aerothermal cases, pressure tap readings matched the CFD results, but dry air CFD underpredicted thermocouple readings. Collection efficiency results from all three icing codes matched well together on the main body leading edge, main body slope, and the strut leading edges. All three icing codes underpredicted the final ice shape using a single-shot constant ice density approach, with more difficulty coming from the strut leading edge ice shape due to the swept wing like flow field. NASA’s overall goal for this effort is to develop computational icing tools to assist in the design and certification of engines for flight in icing conditions.

Supercooled icing, SIDRM, aerodynamics, computatio↗

A Flexible Parameterization for Shortwave Optical Properties of Ice Crystals

A parameterization is presented that provides extinction cross section sigma (sub e), single-scattering albedo omega, and asymmetry parameter (g) of ice crystals for any combination of volume, projected area, aspect ratio, and crystal distortion at any wavelength in the shortwave. Similar to previous parameterizations, the scheme makes use of geometric optics approximations and the observation that optical properties of complex, aggregated ice crystals can be well approximated by those of single hexagonal crystals with varying size, aspect ratio, and distortion levels. In the standard geometric optics implementation used here, sigma (sub e) is always twice the particle projected area. It is shown that omega is largely determined by the newly defined absorption size parameter and the particle aspect ratio. These dependences are parameterized using a combination of exponential, lognormal, and polynomial functions. The variation of (g) with aspect ratio and crystal distortion is parameterized for one reference wavelength using a combination of several polynomials. The dependences of g on refractive index and omega are investigated and factors are determined to scale the parameterized (g) to provide values appropriate for other wavelengths. The parameterization scheme consists of only 88 coefficients. The scheme is tested for a large variety of hexagonal crystals in several wavelength bands from 0.2 to 4 micron, revealing absolute differences with reference calculations of omega and (g) that are both generally below 0.015. Over a large variety of cloud conditions, the resulting root-mean-squared differences with reference calculations of cloud reflectance, transmittance, and absorptance are 1.4%, 1.1%, and 3.4%, respectively. Some practical applications of the parameterization in atmospheric models are highlighted.

parameterization↗

The Shergottite Age Paradox and the Relative Probabilities of Ejecting Martian Meteorites of Differing Ages

The apparent paradox that the majority of impacts yielding Martian meteorites appear to have taken place on only a few percent of the Martian surface can be resolved if all the shergottites were ejected in a single event rather than in multiple events as expected from variations in their cosmic ray exposure and crystallization ages. If the shergottite-ejection event is assigned to one of three craters in the vicinity of Olympus Mons that were previously identified as candidate source craters for the SNC (Shergottites, Nakhlites, Chassigny) meteorites, and the nakhlite event to another candidate crater in the vicinity of Ceraunius Tholus, the implied ages of the surrounding terranes agree well with crater density ages. EN,en for high cratering rates (minimum ages), the likely origin of the shergottites is in the Tharsis region, and the paradox of too many meteorites from too little terrane remains for multiple shergottite-ejection events. However, for high cratering rates it is possible to consider sources for the nakhlltes which are away from the Tharsis region. The meteorite-yielding impacts may have been widely dispersed with sources of the young SNC meteorites in the northern plains, and the source of the ancient orthopyroxenite, ALH84001, in the ancient southern uplands. Oblique-impact craters can be identified with the sources of the nakhlites and the orthopyroxenite,, respectively, in the nominal cratering rate model, and with the shergottites and orthopyroxenite, respectively, in the high cratering rate model. Thus, oblique impacts deserve renewed attention as an ejection mechanism for Martian meteorites.

Borg, L. E.↗

Beyond Melting: Amorphous Bonding for Joining and Consolidation

Crystallization may be the hidden constraint in thermoplastic composite manufacturing. It requires tightly controlled cooling, induces residual stresses through shrinkage, and introduces path-dependent behavior that complicates predictive modeling yet remains essential for structural performance. This work asks: can bonding be achieved without relying on melt-driven crystallization? To address this, thin (5–20 μm) polyetherimide (PEI) interlayers are pre-healed to slow-cooled polyaryletherketone (PAEK) in two contexts. The first, Thermabond®, is sub-melt joining of low melt-PAEK laminates. Results show that bond quality is governed primarily by processing (i.e., adequate healing and film handling) rather than modest changes in interlayer thickness. This concept is then extended to laminate-scale manufacturing through an architecture known as OATMEAL (Out-of-autoclave Amorphous/semicrystalline Thermoplastic Material for Energy-efficient Aerospace-grade Laminates). PEI is healed to carbon fiber reinforced polyetheretherketone (PEEK) at the prepreg and excess PEI is then ablated from the surface. Crystallinity is developed off-line during prepreg fabrication, while subsequent consolidation occurs below the melt temperature to preserve it. Cross-ply warpage experiments show that, contrary to intuition, repeated amorphous interfaces reduce global curvature by lowering the effective stress lock-in temperature and eliminating crystallization shrinkage from the lamina response. Correspondingly, laminate behavior is accurately predicted using classical laminate theory (CLT) with a single effective stress-free temperature, whereas conventional CF/PEEK requires accounting for crystallization-driven effects. By decoupling interfacial healing from crystallization, OATMEAL enables sub-melt consolidation, reduces energy consumption by up to 75%, and increases manufacturing throughput by fivefold. These results demonstrate that amorphous bonding is not only a joining strategy, but a pathway to more predictable and scalable thermoplastic composite manufacturing.

solidification↗

Secondary arm coarsening and microsegregation in superalloy PWA-1480 single crystals: Effect of low gravity

Single crystal specimens of nickel base superalloy PWA-1480 were directionally solidified on ground and during low gravity (20 sec) and high gravity (90 sec) parabolic maneuver of KC-135 aircraft. Thermal profiles were measured during solidification by two in-situ thermocouples positioned along the sample length. The samples were quenched during either high or low gravity cycles so as to freeze the structures of the mushy zone developing under different gravity levels. Microsegregation was measured by examining the solutal profiles on several transverse cross-sections across primary dendrites along their length in the quenched mushy zone. Effect of gravity level on secondary arm coarsening kinetics and microsegregation have been investigated. The results indicate that there is no appreciable difference in the microsegregation and coarsening kinetics behavior in the specimens grown under high or low gravity. This suggests that short duration changes in gravity/levels (0.02 to 1.7 g) do not influence convection in the interdendritic region. Examination of the role of natural convection, in the melt near the primary dendrite tips, on secondary arm spacings requires low gravity periods longer than presently available on KC-135. Secondary arm coarsening kinetics show a reasonable fit with the predictions from a simple analytical model proposed by Kirkwood for a binary alloy.

Vijayakumar, M.↗