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Ar-Ar and I-Xe Ages of Caddo County and Thermal History of IAB Iron Meteorites

Inclusions in IAB iron meteorites include non-chondritic silicate and those with more primitive chondritic silicate composition. Coarse-grained gabbroic material rich in plagioclase and diopside occurs in the Caddo County IAB iron meteorite and represents a new type of chemically differentiated, extra-terrestrial, andesitic silicate. Other parts of Caddo contain mostly andesitic material. Caddo thus exhibits petrologic characteristics of parent body metamorphism of a chondrite-like parent and inhomogeneous segregation of melts. Proposed IAB formation models include parent body partial melting and fractional crystallization or incomplete differentiation due to internal heat sources, and impact/induced melting and mixing. Benedix et al. prefer a hybrid model whereby the IAB parent body largely melted, then underwent collisional breakup, partial mixing of phases, and reassembly. Most reported 129I- Xe-129 ages of IABs are greater than 4.56 Gyr and a few are greater than or = 4.567 Gyr. These oldest ages exceed the 4.567 Gyr Pb-Pb age of Ca, Al-rich inclusions in primitive meteorites,

Bogard, Donald D.↗

Software Testing and Verification in Climate Model Development

Over the past 30 years most climate models have grown from relatively simple representations of a few atmospheric processes to a complex multi-disciplinary system. Computer infrastructure over that period has gone from punch card mainframes to modem parallel clusters. Model implementations have become complex, brittle, and increasingly difficult to extend and maintain. Existing verification processes for model implementations rely almost exclusively upon some combination of detailed analysis of output from full climate simulations and system-level regression tests. In additional to being quite costly in terms of developer time and computing resources, these testing methodologies are limited in terms of the types of defects that can be detected, isolated and diagnosed. Mitigating these weaknesses of coarse-grained testing with finer-grained "unit" tests has been perceived as cumbersome and counter-productive. In the commercial software sector, recent advances in tools and methodology have led to a renaissance for systematic fine-grained testing. We discuss the availability of analogous tools for scientific software and examine benefits that similar testing methodologies could bring to climate modeling software. We describe the unique challenges faced when testing complex numerical algorithms and suggest techniques to minimize and/or eliminate the difficulties.

Clune, Thomas L.↗

Latitudinal variation of wind erosion of crater ejecta deposits on Mars

The characteristics of wind erosion as the dominant process involved in eroding crater ejecta deposits on Mars are studied. Present-day crater formation in mid to high latitudes involves impact into some thickness of aeolian debris, while impact in the equatorial zone is more likely to involve target materials consisting of coarse-grained aeolian lag deposits or even bedrock. Latitudinal variation dominates differences in ejecta emplacement mechanisms and probably differences in patterns of wind erosion of ejecta and surrounding intercrater materials. Escarpments develop as the deposits are eroded back toward crater rims. Erosion only takes places at escarpment edges where surface roughness may be low enough to allow particle entrainment. Preferential preservation of ejecta emplaced in thick debris may occur. An empirical model developed for wind erosion of ejecta deposits in nonmantled areas suggests that removal of ejecta materials on the average is exceedingly slow. Results suggest high differential aeolian erosion rates that are a function of both grain sizes and large-scale surface roughness.

Arvidson, R. E.↗

BioNet Digital Communications Framework

BioNet v2 is a peer-to-peer middleware that enables digital communication devices to talk to each other. It provides a software development framework, standardized application, network-transparent device integration services, a flexible messaging model, and network communications for distributed applications. BioNet is an implementation of the Constellation Program Command, Control, Communications and Information (C3I) Interoperability specification, given in CxP 70022-01. The system architecture provides the necessary infrastructure for the integration of heterogeneous wired and wireless sensing and control devices into a unified data system with a standardized application interface, providing plug-and-play operation for hardware and software systems. BioNet v2 features a naming schema for mobility and coarse-grained localization information, data normalization within a network-transparent device driver framework, enabling of network communications to non-IP devices, and fine-grained application control of data subscription band width usage. BioNet directly integrates Disruption Tolerant Networking (DTN) as a communications technology, enabling networked communications with assets that are only intermittently connected including orbiting relay satellites and planetary rover vehicles.

Gifford, Kevin↗

Composition of Meridiani Hematite-rich Spherules: A Mass-Balance Mixing-Model Approach

One of the great surprises of the Mars Exploration Rovers (MER) mission is the discovery at Meridiani Planum that the surface hematite signature observed from orbit is attributable largely to a surface enrichment of hematite-rich spherules, thought to be concretions, that have weathered out of rocks similar to the underlying sulfate-rich rock formation [1]. A strong hematite signature has been observed by the Mini-TES [2] and by in-situ measurements of spherule-rich targets by the Mossbauer spectrometer (MB) [3] and the alpha-particle X-ray spectrometer (APXS) [4]. The Mini-TES derived spectrum of spherule-rich targets on the plains is consistent with nearly pure coarse-grained hematite, with perhaps as little as 5-10 areal % of other components [2]. The occurrence and abundance of the spherules as the bearer of the widespread hematite signature observed by MGS TES over much of Meridiani Planum is significant for global remote sensing, and their occurrence as concretions in the outcrop lithology is significant for the diagenetic history and role of water in the formation of the sedimentary rock formation [5].

jOLLIFF, b. l.↗

Li, Be, and B in minerals of a refractory-rich Allende inclusion

The abundances of Li, Be, and B and the isotopic ratios of Li and B have been measured by ion microprobe in melilite, pyroxene, anorthite, and spinel grains in a coarse-grained inclusion from the Allende meteorite. Based on the measurements, it is estimated that the bulk inclusion contains 200 ppb Li, 310 ppb Be, and 18 ppm B. The B is probably due to contamination. The Li-7/Li-6 ratios in spinels, pyroxene, and melilite are indistinguishable at the + or - 15% level and lie within the uncertainty (+ or - 15%) of the range of values reported for samples of the earth and meteorites. It has been determined that this inclusion contains an excess of Al-correlated Mg-26, implying that Al-26 was once present in it. The Li-Be-B effects for two solar-system proton-irradiation models which propose to account for Al-26 in Allende inclusions have been calculated. It is found that the predicted Li-Be-B abundances and isotopic ratios are grossly different from those observed in any solar-system materials.

Phinney, D.↗

Coarse-Grain Bandwidth Estimation Scheme for Large-Scale Network

A large-scale network that supports a large number of users can have an aggregate data rate of hundreds of Mbps at any time. High-fidelity simulation of a large-scale network might be too complicated and memory-intensive for typical commercial-off-the-shelf (COTS) tools. Unlike a large commercial wide-area-network (WAN) that shares diverse network resources among diverse users and has a complex topology that requires routing mechanism and flow control, the ground communication links of a space network operate under the assumption of a guaranteed dedicated bandwidth allocation between specific sparse endpoints in a star-like topology. This work solved the network design problem of estimating the bandwidths of a ground network architecture option that offer different service classes to meet the latency requirements of different user data types. In this work, a top-down analysis and simulation approach was created to size the bandwidths of a store-and-forward network for a given network topology, a mission traffic scenario, and a set of data types with different latency requirements. These techniques were used to estimate the WAN bandwidths of the ground links for different architecture options of the proposed Integrated Space Communication and Navigation (SCaN) Network. A new analytical approach, called the "leveling scheme," was developed to model the store-and-forward mechanism of the network data flow. The term "leveling" refers to the spreading of data across a longer time horizon without violating the corresponding latency requirement of the data type. Two versions of the leveling scheme were developed: 1. A straightforward version that simply spreads the data of each data type across the time horizon and doesn't take into account the interactions among data types within a pass, or between data types across overlapping passes at a network node, and is inherently sub-optimal. 2. Two-state Markov leveling scheme that takes into account the second order behavior of the store-and-forward mechanism, and the interactions among data types within a pass. The novelty of this approach lies in the modeling of the store-and-forward mechanism of each network node. The term store-and-forward refers to the data traffic regulation technique in which data is sent to an intermediate network node where they are temporarily stored and sent at a later time to the destination node or to another intermediate node. Store-and-forward can be applied to both space-based networks that have intermittent connectivity, and ground-based networks with deterministic connectivity. For groundbased networks, the store-and-forward mechanism is used to regulate the network data flow and link resource utilization such that the user data types can be delivered to their destination nodes without violating their respective latency requirements.

Cheung, Kar-Ming↗

Troctolite 76535 - A study in the preservation of early isotopic records

The lunar rock considered in the present investigation is a coarse-grained troctolite granulite containing about 58(vol)% plagioclase, 37% olivine, 4% pyroxene, and less than 1% accessory phases with a texture which indicates formation as a cumulate at depths between 10 and 30 km followed by an extended period of slow cooling. A description is presented of noble gas studies of separated minerals from 76535. The quantity of fission xenon from the in situ decay of Pu-244 provides further evidence for different, mineral-specific, isotopic closure times. The presented data shows that 76535 loses its surface-correlated xenon component upon disaggregation. No other xenon component is lost. The presence of solar gases in 76535 would seem to argue in favor of the external acquisition of the parentless extinct isotope effects and consequently favor 'thermal diffusion' and 'adsorption' over local redistribution models.

Caffee, M.↗

Development of Standardized Lunar Regolith Simulant Materials

Lunar exploration requires scientific and engineering studies using standardized testing procedures that ultimately support flight certification of technologies and hardware. It is necessary to anticipate the range of source materials and environmental constraints that are expected on the Moon and Mars, and to evaluate in-situ resource utilization (ISRU) coupled with testing and development. We describe here the development of standardized lunar regolith simulant (SLRS) materials that are traceable inter-laboratory standards for testing and technology development. These SLRS materials must simulate the lunar regolith in terms of physical, chemical, and mineralogical properties. A summary of these issues is contained in the 2005 Workshop on Lunar Regolith Simulant Materials [l]. Lunar mare basalt simulants MLS-1 and JSC-1 were developed in the late 1980s. MLS-1 approximates an Apollo 11 high-Ti basalt, and was produced by milling of a holocrystalline, coarse-grained intrusive gabbro (Fig. 1). JSC-1 approximates an Apollo 14 basalt with a relatively low-Ti content, and was obtained from a glassy volcanic ash (Fig. 2). Supplies of MLS-1 and JSC-1 have been exhausted and these materials are no longer available. No highland anorthosite simulant was previously developed. Upcoming lunar polar missions thus require the identification, assessment, and development of both mare and highland simulants. A lunar regolith simulant is manufactured from terrestrial components for the purpose of simulating the physical and chemical properties of the lunar regolith. Significant challenges exist in the identification of appropriate terrestrial source materials. Lunar materials formed under comparatively reducing conditions in the absence of water, and were modified by meteorite impact events. Terrestrial materials formed under more oxidizing conditions with significantly greater access to water, and were modified by a wide range of weathering processes. The composition space of lunar materials can be modeled by mixing programs utilizing a low-Ti basalt, ilmenite, KREEP component, high-Ca anorthosite, and meteoritic components. This approach has been used for genetic studies of lunar samples via chemical and modal analysis. A reduced composition space may be appropriate for simulant development, but it is necessary to determine the controlling properties that affect the physical, chemical and mineralogical components of the simulant.

Carpenter, P.↗

NASA Tech Briefs, October 2013

Topics include: A Short-Range Distance Sensor with Exceptional Linearity; Miniature Trace Gas Detector Based on Microfabricated Optical Resonators; Commercial Non-Dispersive Infrared Spectroscopy Sensors for Sub-Ambient Carbon Dioxide Detection; Fast, Large-Area, Wide-Bandgap UV Photodetector for Cherenkov Light Detection; Mission Data System Java Edition Version 7; Adaptive Distributed Environment for Procedure Training (ADEPT); LEGEND, a LEO-to-GEO Environment Debris Model; Electronics/Computers; Millimeter-Wave Localizers for Aircraft-to-Aircraft Approach Navigation; Impedance Discontinuity Reduction Between High-Speed Differential Connectors and PCB Interfaces; SpaceCube Version 1.5; High-Pressure Lightweight Thrusters; Non-Magnetic, Tough, Corrosion- and Wear-Resistant Knives From Bulk Metallic Glasses and Composites; Ambient Dried Aerogels; Applications for Gradient Metal Alloys Fabricated Using Additive Manufacturing; Passivation of Flexible YBCO Superconducting Current Lead With Amorphous SiO2 Layer; Propellant-Flow-Actuated Rocket Engine Igniter; Lightweight Liquid Helium Dewar for High-Altitude Balloon Payloads; Method to Increase Performance of Foil Bearings Through Passive Thermal Management; Unibody Composite Pressurized Structure; JWST Integrated Science Instrument Module Alignment Optimization Tool; Radar Range Sidelobe Reduction Using Adaptive Pulse Compression Technique; Digitally Calibrated TR Modules Enabling Real-Time Beamforming SweepSAR Architectures; Electro-Optic Time-to-Space Converter for Optical Detector Jitter Mitigation; Partially Transparent Petaled Mask/Occulter for Visible-Range Spectrum; Educational NASA Computational and Scientific Studies (enCOMPASS); Coarse-Grain Bandwidth Estimation Scheme for Large-Scale Network; Detection of Moving Targets Using Soliton Resonance Effect; High-Efficiency Nested Hall Thrusters for Robotic Solar System Exploration; High-Voltage Clock Driver for Photon-Counting CCD Characterization; Development of the Code RITRACKS; and Enabling Microliquid Chromatography by Microbead Packing of Microchannels.

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.↗

HTMT-class Latency Tolerant Parallel Architecture for Petaflops Scale Computation

Computational Aero Sciences and other numeric intensive computation disciplines demand computing throughputs substantially greater than the Teraflops scale systems only now becoming available. The related fields of fluids, structures, thermal, combustion, and dynamic controls are among the interdisciplinary areas that in combination with sufficient resolution and advanced adaptive techniques may force performance requirements towards Petaflops. This will be especially true for compute intensive models such as Navier-Stokes are or when such system models are only part of a larger design optimization computation involving many design points. Yet recent experience with conventional MPP configurations comprising commodity processing and memory components has shown that larger scale frequently results in higher programming difficulty and lower system efficiency. While important advances in system software and algorithms techniques have had some impact on efficiency and programmability for certain classes of problems, in general it is unlikely that software alone will resolve the challenges to higher scalability. As in the past, future generations of high-end computers may require a combination of hardware architecture and system software advances to enable efficient operation at a Petaflops level. The NASA led HTMT project has engaged the talents of a broad interdisciplinary team to develop a new strategy in high-end system architecture to deliver petaflops scale computing in the 2004/5 timeframe. The Hybrid-Technology, MultiThreaded parallel computer architecture incorporates several advanced technologies in combination with an innovative dynamic adaptive scheduling mechanism to provide unprecedented performance and efficiency within practical constraints of cost, complexity, and power consumption. The emerging superconductor Rapid Single Flux Quantum electronics can operate at 100 GHz (the record is 770 GHz) and one percent of the power required by convention semiconductor logic. Wave Division Multiplexing optical communications can approach a peak per fiber bandwidth of 1 Tbps and the new Data Vortex network topology employing this technology can connect tens of thousands of ports providing a bi-section bandwidth on the order of a Petabyte per second with latencies well below 100 nanoseconds, even under heavy loads. Processor-in-Memory (PIM) technology combines logic and memory on the same chip exposing the internal bandwidth of the memory row buffers at low latency. And holographic storage photorefractive storage technologies provide high-density memory with access a thousand times faster than conventional disk technologies. Together these technologies enable a new class of shared memory system architecture with a peak performance in the range of a Petaflops but size and power requirements comparable to today's largest Teraflops scale systems. To achieve high-sustained performance, HTMT combines an advanced multithreading processor architecture with a memory-driven coarse-grained latency management strategy called "percolation", yielding high efficiency while reducing the much of the parallel programming burden. This paper will present the basic system architecture characteristics made possible through this series of advanced technologies and then give a detailed description of the new percolation approach to runtime latency management.

Sterling, Thomas↗

The effect of solute additions on the steady-state creep behavior of dispersion-strengthened aluminum.

The effect of solute additions on the steady-state creep behavior of coarse-grained dispersion-strengthened aluminum alloys was studied. Recrystallized dispersion-strengthened solid solutions were found to have stress and temperature sensitivities quite unlike those observed in single-phase solid solutions having the same composition and grain size. The addition of magnesium or copper to the matrix of a recrystallized dispersion-strengthened aluminum causes a decrease in the steady-state creep rate which is much smaller than that caused by similar amounts of solute in single-phase solid solutions. All alloys exhibited essentially a 4.0 power stress exponent in agreement with the model of Ansell and Weertman. The activation energy for steady-state creep in dispersion-strengthened Al-Mg alloys, as well as the stress dependence, was in agreement with the physical model of dislocation climb over the dispersed particles.

Reynolds, G. H.↗

Lunar highland rock types: Their implications for impact-induced fractionation

Lunar rocks may be classified into three major groups: (1) coarse-grained igneous rocks, (2) fine-grained igneous rocks, and (3) breccias. Group 1 is interpreted as primitive lunar crustal rocks that display various degrees of crushing and/or annealing. Group 2 is interpreted as volcanic rocks. Group 3 is interpreted as resulting from impacts on the lunar surface and is subdivided on the basis of matrix textures into fragmental breccias, crystalline breccias that have been annealed, and crystalline breccias with igneous matrices. A synthesis of the data concerning lunar highlands polymict breccias compels the prediction that the breccias should have homogeneous matrices from rock to rock within regions of the highlands of limited size where impact mixing has been efficient and extensive. But the returned breccias, even from one landing site, display a wide range in composition. This incompatibility between prediction and observation is a paradox that may be resolved by a process that acts after impact mixing to cause a differentiation of the breccia compositions. Partial melting of the local average crustal composition (as modeled by the average soil composition for each site) and separation of melt and residue in ejecta and/or fall-back blankets are compatible with the reviewed data and may resolve the paradox.

Phinney, W. C.↗

The petrology of the Apollo 12 ilmenite basalt suite

Mineral chemistry data and petrographic interpretations as well as fractionation modeling determined independently indicate that the bulk chemical variations in the ilmenite suite can be reconciled with differentiation within a single cooling unit. Olivine porphyritic basalts, medium-grained basalts with evolved compositions, and coarse-grained olivine cumulates are found in the suite. It is suggested that most of the chemical variation within the suite could result from fractionation of olivine equivalent to the composition of phenocrysts in vitrophyre 12008 which serves well as a parental magma for the other textural-chemical variants. The relative cooling rate sequence within all three textural-chemical subgroups was determined, and systematic correlations between the degree of olivine addition or subtraction and the relative cooling rate is indicated.

Dungan, M. A.↗

Metal with anomalously low Ni and Ge concentrations in the Allan Hills A77081 winonaite

The Ge content of metal in the Allan Hills A77081 winonaite was determined by high-sensitivity electron microprobe analysis. By optimizing analytical conditions for Ge determination, a detection limit of about 75 ppm could be achieved. In A77081 some small kamacite grains contain less Ni and Ge and more Co than coarse-grained metal. These small grains are always associated with sulfide, raising the possibility that anomalous metal is related to eutectic melting. However, when published partition coefficients for Ni and Ge in the Fe-Ni-S system are used to model fractionation of these elements during eutectic melting, one finds that secondary metal should be enriched in Ni and depleted in Ge. Thus, the positive Ni-Ge correlation found in this study is the opposite of the expected trend. No explanation for this discrepancy has yet been found. Nonetheless, the existence of anomalous metal is an indication that A77081, and probably other winonaites as well, have undergone some fractionation. This supports the notion that the high-temperature history of winonaites is related to the formation of IAB iron meteorites, whose silicate inclusions are very similar to winonaites.

Kracher, Alfred↗

The Divnoe meteorite: Petrology, chemistry, oxygen isotopes and origin

The Divnoe meteorite is an olivine-rich primitive achondrite with subchondritic chemistry and mineralogy. It has a granoblastic, coarse-grained, olivine groundmass (CGL: coarse-grained lithology) with relatively large pyroxene-plagioclase poiklitic patches (PP) and small fine-grained domains of an opaque-rich lithology (ORL). Both PP and ORL are inhomogeneously distributed and display reaction boundaries with the groundmass. Major silicates, olivine Fa(20-28) and orthopyroxyene Fs(20-28 Wo(0.5-2.5), display systematic differences in composition between CGL and ORL as well as a complicated pattern of variations within CGL. Accessory plagioclase has low K content and displays regular igneous zoning with core compositions An(40-45) and rims An(32-37). The bulk chemical composition of Divnoe is similar to that of olivine-rich primitive achondrites, except for a depletion of incompatible elements and minor enrichment of refractory siderophiles. Oxygen isotope compositions for whole-rock and separated minerals from Divnoe fall in a narrow range, with mean delta O-18 = +4.91, delta O-17 = +2.24, and Delta O-17 = -0.26 +/- 0.11. The isotopic composition is not within the range of any previously recognized group but is very close to that of the brachinites. To understand the origin of Divnoe lithologies, partial melting and crystallization were modelled using starting compositions equal to that of Divnoe and some chondritic meteorites. It was found that the Divnoe composition could be derived from a chondritic source region by approximately 20 wt% partial melting at Ta approximately 1300 C and log(fO2) = IW-1.8, followed by approximtely 60 wt% crystallization of the partial melt formed, and removal of the still-liquid portion of the partial melt. Removal of the last partial melt resulted in depletion of the Divnoe plagioclase in Na and K. In this scenario, CGL represents the residue of partial melting, and PP is a portion of the partial melt that crystallized in situ. The ORL was formed during the final stages of partial melting by reaction between gaseous sulfur and residual olivine in the source region. A prominent feature of Divnoe is fine micron-scale chemical variations within olivine grains, related to lamellar structures the olivines display. The origin of these structures is not known.

Petaev, M. I.↗

Detection of Crystalline Hematite Mineralization on Mars by the Thermal Emission Spectrometer: Evidence for Near-surface Water

The Thermal Emission Spectrometer (TES) instrument on the Mars Global Surveyor (MGS) mission has discovered a remarkable accumulation of crystalline hematite ((alpha-Fe2O3) that covers an area with very sharp boundaries approximately 350 by 350-750 km in size centered near 2 S latitude between 0 and 5 W longitude (Sinus Meridiani). Crystalline hematite is uniquely identified by the presence of fundamental vibrational absorption features centered near 300, 450, and >525/cm, and by the absence of silicate fundamentals in the 1000/cm region. Spectral features resulting from atmospheric CO2, dust, and water ice were removed using a radiative transfer model. The spectral properties unique to Sinus Meridiani were emphasized by removing the average spectrum of the surrounding region. The depth and shape of the hematite fundamental bands show that the hematite is crystalline and relatively coarse grained (>5-10 micron). Diameters up to and greater than 100s of micrometers are permitted within the instrumental noise and natural variability of hematite spectra. Hematite particles <5-10 micron in diameter (either as an unpacked or hard-packed powders) fail to match the TES spectra. The spectrally-derived areal abundance of hematite varies with particle size from approximately 10% for particles >30 micron in diameter to 40-60% for unpacked 10 micron powders. The hematite in Sinus Meridiani is thus distinct from the fine-grained (diameter <5-10 micron), red, crystalline hematite considered, on the basis of visible, near-IR data, to be a minor spectral component in Martian bright regions like Olympus-Amazonis. Sinus Meridiani hematite is closely associated with a smooth, layered, friable surface that is interpreted to be sedimentary in origin. This material may be the uppermost surface in the region, indicating that it could be a late-stage sedimentary unit, or it could be a layered portion of the heavily cratered plains units. We consider five possible mechanisms for the formation of coarse-grained, crystalline hematite. These processes fall into two classes depending on whether they require a significant amount of near-surface water: (1) chemical precipitation that includes origin by (a) precipitation from oxygenated, Fe-rich water (iron formations), (b) hydrothermal extraction and crystal growth.

Christensen, P. R.↗