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The exoplanet field now abounds with new discoveries of planets and planetary systems. It is of great interest for the scientific community to understand the compositions and internal structures of these new planets outside our own solar system, and then infer their formation scenarios. In particular, the proper implementation of the equation-of-states of various matters into the calculation of internal structure is crucial. Thus, we have come up with this write-up that provides the detailed steps to turn an equation-of-state (EOS) into a mass-radius relation of exoplanets, and highlight the physics and chemistry involved in these calculations. It must be visualized!, Comment: For pedagogical purpose only (non-profit). Comments and suggestions welcome!

We explain the overall equilibrium-temperature-dependent trend in the exoplanet mass-radius diagram, using the escape mechanisms of hydrogen and relevant volatiles, and the chemical equilibrium calculation of molecular hydrogen (H$_2$) break-up into atomic hydrogen (H). We identify two Cosmic Hydrogen and Ice Loss Lines (CHILLs) in the mass-radius diagram. Gas disks are well known to disperse in ten million years. However, gas-rich planets may lose some or almost all gas on a much longer timescale. We thus hypothesize that most planets that are born out of a hydrogen-gas-dominated nebular disk begin by possessing a primordial H$_2$-envelope. This envelope is gradually lost due to escape processes caused by host-stellar radiation., Comment: (Version 3) Published in Icarus, Volume 414, 116033, 2024

Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune. A low occurrence rate of planets has been identified at around twice the size of Earth, known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass-radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations of state in the temperature-density graph and the entropy-pressure graph. We show that the radius valley can be explained by a compositional difference between smaller, predominantly rocky planets and larger planets that exhibit greater compositional diversity including cosmic ices (water, ammonia, methane) and gaseous envelopes. In particular, among the larger planets, when viewed from the perspective of planet equilibrium temperature, the hot ones are consistent with ice-dominated composition without significant gaseous envelopes, while the cold ones have more diverse compositions, including various amounts of gaseous envelopes., Comment: 30 pages, 15 figures

We discuss major challenges in modeling giant impacts between planetary bodies, focusing on the equations of state (EOS). During the giant impact stage of planet formation, rocky planets are melted and partially vaporized. However, most EOS models fail to reproduce experimental constraints on the thermodynamic properties of the major minerals over the required phase space. Here, we present an updated version of the widely-used ANEOS model that includes a user-defined heat capacity limit in the thermal free energy term. Our revised model for forsterite (Mg$_2$SiO$_4$), a common proxy for the mantles of rocky planets, provides a better fit to material data over most of the phase space of giant impacts. We discuss the limitations of this model and the Tillotson equation of state, a commonly used alternative model., Comment: M-ANEOS source code public release (https://github.com/isale-code/M-ANEOS); forsterite EOS public release (https://github.com/ststewart/aneos-forsterite-2019); manuscript accepted (no changes): Stewart, S., et al. (accepted). In J. Lane, T. Germann, and M. Armstrong (Eds.), 21st Biennial APS Conference on Shock Compression of Condensed Matter (SCCM19). AIP Publishing

The radii and orbital periods of 4000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. Yet an important question about the composition of planets ranging from 2 to 4 Earth radii still remains. They may either have a rocky core enveloped in a H2-He gaseous envelope (gas dwarfs) or contain a significant amount of multi-component, H2O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 Earth masses, if half-ice and half-rock by mass, have radii of 2.5 Earth radii, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2-4 Earth radii range requires a gas envelope of at most a few mass percentage points, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are water worlds., Comment: PNAS link: https://www.pnas.org/content/116/20/9723 Complete data and mass-radius tables are available at: https://www.cfa.harvard.edu/~lzeng/planetmodels.html

Applying the survival function analysis to the planet radius distribution of the Kepler confirmed/candidate planets, we have identified two natural divisions of planet radius at 4 Earth radii and 10 Earth radii. These divisions place constraints on planet formation and interior structure model. The division at 4 Earth radii separates small exoplanets from large exoplanets above. When combined with the recently-discovered radius gap at 2 Earth radii, it supports the treatment of planets 2-4 Earth radii as a separate group, likely water worlds. For planets around solar-type FGK main-sequence stars, we argue that 2 Earth radii is the separation between water-poor and water-rich planets, and 4 Earth radii is the separation between gas-poor and gas-rich planets. We confirm that the slope of survival function in between 4 and 10 Earth radii to be shallower compared to either ends, indicating a relative paucity of planets in between 4-10 Earth radii, namely, the sub-Saturnian desert there. We name them transitional planets, as they form a bridge between the gas-poor small planets and gas giants. Accordingly, we propose the following classification scheme: (<2 Earth radii) rocky planets, (2-4 Earth radii) water worlds, (4-10 Earth radii) transitional planets, and (>10 Earth radii) gas giants., Comment: 19 pages, 8 figures, accepted for publication in MNRAS. arXiv admin note: text overlap with arXiv:1801.03993

The size distribution of exoplanets is a bimodal division into two groups: Rocky planet (<2 Earth radii) and water-rich planet (>2 Earth radii) with or without gaseous envelope., Comment: 2 pages, 4 figures, abstract publicly available since January 2017 (see https://www.hou.usra.edu/meetings/lpsc2017/pdf/1576.pdf) and presented at the 48th LPSC on March 23, 2017. Also See: http://adsabs.harvard.edu/abs/2017LPI....48.1576Z

The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High-energy, high-angular momentum giant impacts can create a post-impact structure that exceeds the corotation limit (CoRoL), which defines the hottest thermal state and angular momentum possible for a corotating body. In a typical super-CoRoL body, traditional definitions of mantle, atmosphere and disk are not appropriate, and the body forms a new type of planetary structure, named a synestia. Using simulations of cooling synestias combined with dynamic, thermodynamic and geochemical calculations, we show that satellite formation from a synestia can produce the main features of our Moon. We find that cooling drives mixing of the structure, and condensation generates moonlets that orbit within the synestia, surrounded by tens of bars of bulk silicate Earth (BSE) vapor. The moonlets and growing moon are heated by the vapor until the first major element (Si) begins to vaporize and buffer the temperature. Moonlets equilibrate with BSE vapor at the temperature of silicate vaporization and the pressure of the structure, establishing the lunar isotopic composition and pattern of moderately volatile elements. Eventually, the cooling synestia recedes within the lunar orbit, terminating the main stage of lunar accretion. Our model shifts the paradigm for lunar origin from specifying a certain impact scenario to achieving a Moon-forming synestia. Giant impacts that produce potential Moon-forming synestias were common at the end of terrestrial planet formation., Comment: Accepted for publication in Journal of Geophysical Research: Planets. Main text: 44 pages, 24 figures. Supplement: 16 pages, 5 figures, 3 tables

Applying survival function analysis to the planet orbital period (P) and semi-major axis (a) distribution from the Kepler sample, we find that all exoplanets are uniformly distributed in (ln a) or (ln P), with an average inner cut-off of 0.05 AU to the host star. More specifically, this inner cut-off is 0.04 AU for rocky worlds (1-2 Earth radii) and 0.08 AU for water worlds (2-4 Earth radii). Moreover, the transitional planets (4-10 Earth radii) and gas giants (>10 Earth radii) have a change of slope of survival function at 0.4 AU from -1 to -1/2, suggesting a different statistical distribution uniform in \Sqrt[a] inside 0.4 AU, compared to small exoplanets (<4 Earth radii). This difference in distribution is likely caused by the difference in planet migration mechanism, and susceptibility to host stellar irradiation, for gas-poor (<4 Earth radii) versus gas-rich (>4 Earth radii) planets. Armed with this knowledge and combined with the survival function analysis of planet size distribution, we can make precise estimates of planet occurrence rate and predict the TESS mission yield., Comment: 11 pages, 3 figures, under review with AJ, comments are very welcome and much appreciated!

Applying the survival function analysis to the planet radius distribution of the Kepler exoplanet candidates, we have identified two natural divisions of planet radius at 4 Earth radii and 10 Earth radii. These divisions place constraints on planet formation and interior structure model. The division at 4 Earth radii separates small exoplanets from large exoplanets above. When combined with the recently-discovered radius gap at 2 Earth radii, it supports the treatment of planets 2-4 Earth radii as a separate group, likely water worlds. Thus, for planets around solar-type FGK main-sequence stars, we argue that 2 Earth radii is the separation between water-poor and water-rich planets, and 4 Earth radii is the separation between gas-poor and gas-rich planets. We confirm that the slope of survival function in between 4 and 10 Earth radii to be shallower compared to either ends, indicating a relative paucity of planets in between 4-10 Earth radii, namely, the sub-Saturnian desert there. We name them transitional planets, as they form a bridge between the gas-poor small planets and gas giants. Accordingly, we propose the following classification scheme: (<2 Earth radii) rocky planets, (2-4 Earth radii) water worlds, (4-10 Earth radii) transitional planets, and (>10 Earth radii) gas giants., Comment: 10 pages, 2 figures, under review with MNRAS, comments are very welcome and much appreciated!

Exoplanets smaller than Neptune are numerous, but the nature of the planet populations in the 1-4 Earth radii range remains a mystery. The complete Kepler sample of Q1-Q17 exoplanet candidates shows a radius gap at ~ 2 Earth radii, as reported by us in January 2017 in LPSC conference abstract #1576 (Zeng et al. 2017). A careful analysis of Kepler host stars spectroscopy by the CKS survey allowed Fulton et al. (2017) in March 2017 to unambiguously show this radius gap. The cause of this gap is still under discussion (Ginzburg et al. 2017; Lehmer & Catling 2017; Owen & Wu 2017). Here we add to our original analysis the dependence of the radius gap on host star type., Comment: 2pages, 1 figure, RNAAS 2017

In the past few years, the number of confirmed planets has grown above 2000. It is clear that they represent a diversity of structures not seen in our own solar system. In addition to very detailed interior modeling, it is valuable to have a simple analytical framework for describing planetary structures. Variational principle is a fundamental principle in physics, entailing that a physical system follows the trajectory which minimizes its action. It is alternative to the differential equation formulation of a physical system. Applying this principle to planetary interior can beautifully summarize the set of differential equations into one, which provides us some insight into the problem. From it, a universal mass-radius relation, an estimate of error propagation from equation of state to mass-radius relation, and a form of virial theorem applicable to planetary interiors are derived., Comment: accepted by ApJ

This work aims at exploring the scaling relations among rocky exoplanets. With the assumption of internal gravity increasing linearly in the core, and staying constant in the mantle, and tested against numerical simulations, a simple model is constructed, applicable to rocky exoplanets of core mass fraction (CMF) $\in 0.1\sim0.4$ and mass $\in 0.1 \sim 10 M_{\oplus}$. Various scaling relations are derived: (1) core radius fraction $\rm CRF \approx \sqrt{CMF}$, (2) Typical interior pressure $P_{\text{typical}} \sim g_{\rm{s}}^2$ (surface gravity squared), (3) core formation energy $E_{\rm diff} \sim \frac{1}{10} E_{\rm grav}$ (the total gravitational energy), (4) effective heat capacity of the mantle $C_{\rm p}\approx \left( \frac{M_{\rm{p}}}{M_{\oplus}} \right) \cdot 7 \cdot 10^{27}$ J K$^{-1}$, and (5) the moment of inertia $I\approx \frac{1}{3} \cdot M_{\rm{p}} \cdot R_{\rm{p}}^2$. These scaling relations, though approximate, are handy for quick use owing to their simplicity and lucidity, and provide insights into the interior structures of rocky exoplanets. As examples, this model is applied to several planets including Earth, GJ 1132b, Kepler-93b, and Kepler-20b, and made comparison with the numerical method., Comment: accepted by ApJ

Laser Ablation ICP-MS (LA-ICP-MS) has been widely accepted as a microanalytical technique for in-situ trace (ppb) elemental analysis on the micron scale in a variety of geologic materials. LA-ICP-MS (single or multi-collector) provides both elemental and isotopic measurements critical for a wide range of geological research by generating a fine grained aerosol (nm scale) during the laser ablation event and delivering that aerosol to the ICP ion source of the mass spectrometer via an inert carrier gas. LA-ICP-MS, however, suffers from limitations in analyzing high ionization potential elements as well as elements subject to atmospheric and argon based interferences. LA-ICP-MS also has limitations in analyzing major elements due to detector saturation. An alternative laser ablation technique, Laser Induced Breakdown Spectroscopy (LIBS), employs an optical spectrometer integrated into the laser ablation system that analyzes the laser induced plasma at the sample surface across the entire optical spectrum for emission lines of every element in the periodic table. Elements that are difficult or impossible to measure with LA-ICP-MS are now possible to analyze with LIBS down to low ppm levels with CCD and/or ICCD detection. We introduce a new laser based technique, “Tandem LA-LIBS”, that combines LA for ICP-MS and LIBS into one integrated laser ablation system. This system has the effect of expanding the elemental coverage and the dynamic range of the laser ablation experiment as measurements from ppb to % level matrix elements can now be analyzed in a single ablation experiment. We present both femtosecond and nanosecond Tandem LA-LIBS quantitative and qualitative data on wide range of geological materials for those elements that are difficult or impossible by traditional LA-ICP-MS techniques such as F, H, O, N, C, S, halogens, etc. We also demonstrate that the simultaneous measurement of trace, minor and major elements are now possible in a single laser ablation experiment with Tandem LA-LIBS technology.

The utility of the Hf-182 (bar-tau ==13 x 10(exp 6) yr) -W-182 chronometer for early solar system processes is now well established. At the 2002 LPSC meeting we first reported new Hf-W data for chondritic meteorites showing that some crucial data as well as interpretations of Lee and Halliday for chondrites were incorrect. Our results were confirmed by reports of two other groups. This new data imply a much-shorter timescale for the early Solar System evolution and the formation of the Earth s core more consistent with the original conclusions of Harper and Jacobsen. Thus, the chondritic Hf-W evolution is now well established as beginning with epsilon(sub W)(0) = -3.45 +/- 0.25 at the time of origin of the solar system and evolving to -2.2 by 20 Myr and -1.9 +/- 0.20 at present. However, there are a number of iron meteorite data that suggest the existence of initial W lower than those measured for chondrites. If the low epsilon(sub W)(0) of -4 to -5 are correct then we face an embarrassing dilemma of differentiated iron meteorites being older than the primitive chondrites, or we would have to conclude that there is an additional pre-history of 5-10 Myr in primitive chondritic meteorites prior to the closure of the Hf-182 - W-182 system. Such a prolonged early time does not seem reasonable to us. We have therefore initiated a study to resolve this issue.

Leya et al. (2000) showed that neutron capture on Ta-181 results in a production rate of Ta-182 (decays with a half-life of 114 days to W-182) sufficiently high to cause significant shifts in W-182 abundances considering the neutron fluences due to the cosmic ray cascade that were known to occur near the lunar surface. Leya et al. concluded that this cosmogenic production of W-182 may explain the large positive epsilon(sub W-182) values that Lee et al. (1997) had reported in some lunar samples rather than being produced from decay of now extinct Hf-182 (bar tau = 13 x 10(exp 6) yr). If the large range in epsilon(sub W-182) of lunar samples (0 to +11 in whole rock samples) was due to decay of now extinct Hf-182, it would require a very early time of formation and differentiation of the lunar crust-mantle system (with high Hf/W ratios) during the earliest stages of Earth s accretion. This result was both surprising and difficult to understand. The ability to explain these results by a more plausible mechanism is therefore very attractive. In a recent report Lee et al. (2002) showed that there were excesses of W-182 and that epsilon(sub W-182) was correlated with the Ta/W ratios in the mineral phases of individual lunar rock samples. This is in accord with W-182 variations in lunar samples being produced by cosmic-ray induced neutron capture on Ta-182.

Evidence for early differentiation of the earth's mantle is presented based on measurements of Nd-143/Nd-144 and Nd-142/Nd-144 ratios in an approximately 3.8 Gyr-old supracrustal rock from Isua, West Greenland. Coupled (Sm-146,147)-(Nd-142,143) systematics suggest that the fractionation of Sm/Nd took place 4.44-4.54 Gyr ago, due to extraction of a light rare earth element-enriched primordial crust.

The very early history of the Earth has been one of the great enduring puzzles in the history of geology. We report evidence which clearly can be described as a vestige of a beginning, because the evidence that we report cannot be interpreted in any other way except as a geochemical signal of processes active in the very early history of the Earth. The evidence itself is a very small anomaly in the abundance of SM-146. The primary aims of this study were to: (1) verify the existence of the 'lost continents' of the Hadean era; and (2) determine their mean age.

High-precision Sr isotopic data were obtained on carbonate samples from the Neoproterozoic Shaler Group, Victoria Island (Canada). Results indicate that, between ca. 790 and 850 Ma, the Sr-87/Sr-86 ratio of seawater varied betweeen 0.70676 and 0.70561, with the minimum value at about 830 Ma. A curve of the Sr-87/Sr-86 seawater ratio vs. age showed that the new data substantially improve the existing isotopic record of Sr in seawater for the period 790-850 Ma. The Sr isotopic system data were coupled with data for the Nd isotopic system to model changes in the seafloor spreading rates (hydrothermal flux) and the continental erosion for the period 500-900 Ma. Results indicate that hydrothermal flux reached a maximum value at ca. 830 Ma, while a maximum in erosion rate occurred at ca. 570 Ma. These peaks are considered to be related to the developments in the Pan-African and related orogenic events.

Precambrian Sr isotope stratigraphy was investigated by determining variations in Sr-87/Sr-86 ratios in the Upper Proterozoic carbonate succession from Svalbard and East Greenland. Data from this study were combined with those from literature to construct a curve of Sr-87/Sr-86 versus time for Upper Proterozoic seawater. The curve for the Upper Riphean-Vandian showed that the isotopic composition of Sr in seawater was low (Delta Sr-87 of about -500) between 900 and 650 Ma but rose rapidly to about +30 by 600 Ma (this range of long-term variation exceeds the total Phanerozoic variation). The very low values of Delta Sr-87 inferred for the Riphean require that, for this time, the submarine hydrothermal water flux was a large fraction of the Sr input to the oceans, while the rise in Delta Sr-87 in the Upper Proterozoic seawater reflects both a change in the ratio of hydrothermal and continental fluxes of Sr to the oceans, and a change in the isotopic composition of Sr from continental sources.

A Sm-Nd isotopic study on samples from the Fiskenaesset Anorthosite Complex in West Greenland was conducted to estimate the age of crystallization of the complex. A five-point isochron, including data for whole-rock samples of anorthosite, metagabbro, metaperidotite, and separates of calcic plagioclase and mafic matrix from a coarse megacrystic leucogabbro, corresponds to an age of 2.86 + or - 0.05 Ga, with initial sigma(Nd) of +2.9 + or - 0.4. This implies a relatively short time interval, on the order of 70 Ma, during which anorthosite formation, tonalite emplacement, and high-grade metamorphism took place.

The Sm-Nd isotopic data on clastic and chemical sediments are used with the present-day age distribution of continental crustal rocks to estimate the rates of crustal accretion, growth and recycling throughout earth's history. A new method for interpreting Nd model ages on both chemical and clastic sediments is proposed. A general relationship is derived between the mean crustal residence time of material recycled from the crust to the mantle (i.e., sediments), the mean age of the crust, and the crustal growth and recycling rates. This relationship takes into account the fact that the age distribution of material in the continental crust is generally different from the age distribution of material recycled into the mantle. The episodic nature of the present-day age distribution in crustal rocks results in similar episodicity in the accretion and recycling rates. The results suggest that by about 3.8 Ga ago, about 40 percent of the present continental volume was present. Recycling rates were extremely high 3-4 Ga ago and declined rapidly to an insignificant value of about 0.1 cu km/a during most of the Phanerozoic. The Nd model age pattern on sediments suggests a fairly high rate of growth during the Phanerozoic.

To characterize the input to the oceans of rare earth elements (REE) in the dissolved and the suspended loads of rivers, the REE concentrations were measured in samples of Amazon, Indus, Mississippi, Murray-Darling, and Ohio rivers and in samples of smaller rivers that had more distinct drainage basin lithology and water chemistry. It was found that, in the suspended loads of small rivers, the REE pattern was dependent on drainage basin geology, whereas the suspended loads in major rivers had relatively uniform REE patterns and were heavy-REE depleted relative to the North American Shale composite (NASC). The dissolved loads in the five major rivers had marked relative heavy-REE enrichments, relative to the NASC and the suspended material, with the (La/Yb)N ratio of about 0.4 (as compared with the ratio of about 1.9 in suspended loads).

The isotopic composition of Nd is reported for eight banded iron formations (BIFs) ranging in age from 0.65 to 3.4 Ga. The data suggest a trend of increasingly positive epsilon(Nd) values with age which is interpreted to reflect isotopic variations in Precambrian seawater. The Urucum (0.65 Ga) and the Gunflint (1.9 Ga) BIFs yield negative epsilon(Nd) values between -6 and 0. The remaining BIFs, with ages of 1.84 to 3.4 Ga, have predominantly positive values between -1 and +4. The Nd isotopic signature of BIFs changes from a principally continental source to a dominantly depleted mantle source from the present into the Archean.

A report on REE concentrations within the estuary of the Great Whale River in northwest Quebec and in Hudson Bay is given, showing concentrations which are less than those predicted by conservative mixing of seawater and river water, indicating removal of REE from solution. REE removal is rapid, occurring primarily at salinities less than 2 percent and ranges from about 70 percent for light REE to no more than 40 percent for heavy REE. At low salinity, Fe removal is essentially complete. The shape of Fe and REE vs. salinity profiles is not consistent with a simple model of destabilization and coagulation of Fe and REE-bearing colloidal material. A linear relationship between the activity of free ion REE(3+) and pH is consistent with a simple ion-exchange model for REE removal. Surface and subsurface samples of Hudson Bay seawater show high REE and La/Yb concentrations relative to average seawater, with the subsurface sample having a Nd concentration of 100 pmol/kg and an epsilon(Nd) of -29.3; characteristics consistent with river inputs of Hudson Bay. This indicates that rivers draining the Canadian Shield are a major source of nonradiogenic Nd and REE to the Atlantic Ocean.

The aim, within the bounds of the Early Crustal Genesis Project, was the isotopic and chemical study of selected early crustal meta-sedimentary rocks. Western Australia was chosen as the first field area to examine, as the Yilgarn and Pilbara Blocks comprise one of the largest and most varied Precambrian terranes. Furthermore, the Western Gneiss Terrane (on the western flank of the Yilgarn Block) and the Pilbara Block are both non-greenstone in character; these types of terrane were relatively neglected, but are of great significance in the understanding of early crustal meta-sediments. The meta-sediments of aluminous or peraluminous character, commonly also enriched in Mg and/or Fe relative to the more common pelitic meta-sediments, and at many locations, deficient in one or more of the elements Ca, N, and K, were initially chosen.

Sm-Nd and Rb-Sr isotopic data on suspended material from rivers draining a variety of rock types and ages are presented. The bulk load of rivers and their source rocks are compared in terms of their isotopic characteristics and model ages. The Nd and Sr isotope systematics of the upper crust exposed to weathering are obtained along with the Nd model age distribution of the North American continental surface. The average Sm-Nd and Rb-Sr isotopic parameters for the upper continental crust today are refined.

A detailed Sm-Nd and Rb-Sr isotopic study of the Isua clastic metasediments has been performed in the context of recently established stratigraphy for the Isua section. Samples from the sequence B are investigated for the first time. A clear correlation between lithology and isotopic characteristics is pointed out. The results indicate the existence of at least three distinct components for each of the distinct sequences A and B. It is suggested that some of these components may be derived from continental crustal sources that predate the time of depositon of these sediments by as much as about 0.4 b.y. A large pre-3.8 Ga continental crust is also inferred by the data.

A detailed Nd isotopic study of the large and well-dated Hamersley and Michipicoten banded iron formations (BIFs) has been conducted. The Hamersley BIFs (Lake Superior type) are located in the Pilbara craton of Western Australia and the Michipicoten BIFs (Algoma type) are located in the northeastern corner of Lake Superior in Ontario, Canada. Their initial epsilon(Nd) values are variable and in the range of 0 to +4. The Fe/Nd ratio in present-day hydrothermal waters and BIFs are both 100,000, suggesting that the source of much of the Fe in BIFs (and Archean seawater) was hydrothermal water circulating through Archean midocean ridge systems.