Kamacite sulfurization in the solar nebula

Abstract— The kinetics and mechanisms of kamacite sulfurization were studied experimentally at temperatures and H₂S/H₂ ratios relevant to the solar nebula. Pieces of the Canyon Diablo meteorite were heated at 558 K, 613 K, and 643 K in 50 parts per million by volume (ppmv) H₂S-H₂ gas mixtures for up to one month. Optical microscopy and x-ray diffraction analyses show that the morphology and crystal orientation of the resulting sulfide layers vary with both time and temperature. Electron microprobe analyses reveal three distinct phases in the reaction products: monosulfide solid solution (mss), (Fe, Ni, Co)_1-xS, pentlandite (Fe, Ni, Co)_9-xS₈, and a P-rich phase. The bulk composition of the remnant metal was not significantly changed by sulfurization. Kamacite sulfurization at 558 K followed parabolic kinetics for the entire duration of the experiments. Sulfide layers that formed at 613 K grew linearly with time, while those that formed at 643 K initially grew linearly with time then switched to parabolic kinetics upon reaching a critical thickness. The experimental results suggest that a variety of thermodynamic, kinetic, and physical processes control the final composition and morphology of the sulfide layers. We combine morphological, x-ray diffraction, electron microprobe, and kinetic data to produce a comprehensive model of sulfide formation in the solar nebula. Then, we present a set of criteria to assist in the identification of solar nebula condensate sulfides in primitive meteorites.     

Grain motions in the solar nebula

Isotopic analyses of meteorites suggest the possibility that some interaction between supernova ejecta and grains occurred in the solar nebula. In particular, the dynamics of grain motions in the solar nebula can explain the observed mixing of nucleosynthetic components. The effect of a shock wave on the motions of grains are examined. A steady-state, plane shock propagating into a uniform region of gas and dust grains is followed by a zone of gas/grain slip, in which the grains are accelerated by drag forces from the pre-shock to the post-shock gas velocity, i.e. reducing the relative velocity between the gas and grains to zero. On the basis of these calculations, it is estimated that if grains carried the isotopic anomalies investigated by Lee, Papanastassoiu, and Wasserburg (1978), then those grains could be no bigger than 2×10^–4 cm in size. A scenario is suggested in which the sluggishness of grains provides a natural way to concentrate and mix the nucleosynthetic components carried by grains in the ejecta and in the solar nebula.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Accumulation of planetesimals in the solar nebula

Characteristic time scales relevant to the accumulation of planetesimals in a gaseous nebula are examined and the accumulation toward the planets is simulated by numerically solving a growth equation for a mass distribution function. The eccentricity and inclination of planetesimals are assumed to be determined by a balance between excitation due to mutual gravitational scattering and dissipation due to gas drag. Two kinds of mass motion in the radial direction, i.e., diffusion due to mutual scattering and inward flow due to gas drag, are both taken into account. The diffusion is shown to be effective in later stages with a result of accelerating the accumulation. As to the coalescent collision cross section, the usual formula for a binary encounter in a free space is used but the effect of tidal disruption which increases substantially the cross section is taken into account. Numerical results show that the gravitational enhancement factor (i.e., the so-called “Safronov number”), contained in the cross section formula, always takes a value of the order of unity but the accumulation proceeds relatively rapidly owing to the effects of radial diffusion and tidal disruption. That is, a proto-Earth, a proto-Jupiter, and a proto-Saturn with masses of 1×10²⁷ g are formed in 5×10⁶, 1×10⁷, and 1.6×10⁸ years, respectively. Also, a tentative numerical computation for the Neptune formation shows that a proto-Neptune with the same mass requires a long accumulation time, 4.6×10⁹ years. Finally, the other effects which are expected to reduce the above growth times further are discussed.     

Numerical models of the primitive solar nebula

Numerical models have been constructed to represent probable conditions in the primitive solar nebula. A two solar mass fragment of a collapsing interstellar gas cloud has been represented by a uniformly rotating sphere. Two cases have been considered: one in which the internal density of the sphere is uniform and the other in which the density falls linearly from a central value to zero at the surface (the uniform and linear models). These assumptions served to define the distribution of angular momentum per unit mass with mass fraction. The spheres were flattened into disks, and models of the disks were found in which there was a force balance in the radial and vertical directions, subject to certain approximations, and with everywhere the assigned values of angular momentum per unit mass. The radial pressure gradient of the gas was included in the force balance. The energy transport in the vertical direction involved convection and radiative equilibrium; the principal contributors to opacity at lower temperatures were metallic iron grains and ice. The models contained two convection zones, an inner one due to the dissociation of hydrogen molecules, and an outer one in which there was a high opacity due to metallic iron grains. The characteristic semithickness of the disks ranged from about 0.1 astronomical units near the center to about one astronomical unit near the exterior. Characteristic angular momentum transport times and radiation lifetimes for these models of the initial solar nebula were estimated. Both types of characteristic lifetime were as short as a few years near the inner part of the models, and became about 10⁴ years or longer at distances greater than ten astronomical units.     

Models of the formation of the solar nebula

Models of the collapse of a protostellar cloud and the formation of the solar nebula reveal that the size of the nebula produced will be the larger of $\text{R}{}_{\mathrm{<mtext>CF</mtext>}}\text{≡ J}{}^2\text{/k}{}^2\text{GM}{}^3\text{and}\text{R}{}_{\mathrm{<mtext>V</mtext>}}\text{≡ (GMv/2c}{}_{\mathrm{<mtext>c</mtext>}}{}^3\text{)}\text{1}\text{2}$ (where J, M, and c_s are the total angular momentum, total mass, and sound speed of the protosetellar material; G is the gravitational constant; k is a number of order unity; and v is the effective viscosity in the nebula). From this result it can be deduced that low-mass nebulas are produced if P ≡ (R_V/R_CF)² ? 1; “massive” nebulas result if P ? 1. Gravitational instabilities are expected to be important for the evolution of P ? 1 nebulas. The value of J distinguishes most current models of the solar nebula, since P ∝ J^?4. Analytic expressions for the surface density, nebular mass flux, and photospheric temperature distributions during the formation stage are presented for some simple models that illustrate the general properties of growing protostellar disks. It does not yet seem possible to rule out either P ? 1 or P < 1 for the solar nebula, but observed or possible heterogeneities in composition and angular-momentum orientation favor P < 1 models.     

Secular resonances in the primitive solar nebula

We present here a very simple model that could explain the relatively high eccentricities and inclinations observed in the minor planet belt. This model is based upon the sweeping of the secular resonances ₆ and ₁₆ through the belt due to the gravitational effect of the dissipation of a primitive solar nebula. The sweeping of the ₁₆ secular resonance (responsible for the high inclinations) is very sensitive to the density profile of the nebula. For the model to work we need a density profile proportional to ^–k with between 1.0 and 1.5.     

Accumulation processes in the primitive solar nebula

Particle accumulation processes are discussed for a variety of physical environments, ranging from the collapse phase of an interstellar cloud to the different parts of the models of the primitive solar nebula constructed by Cameron and Pine. Because of turbulence in the collapsing interstellar gas, it is concluded that interstellar grains accumulate into bodies with radii of a few tens of centimeters before the outer parts of the solar nebula are formed. These bodies can descend quite rapidly through the gas toward midplane of the nebula, and accumulation to planetary size can occur in a few thousand years. Substantial modifications of these processes take place in the outer convection zone of the solar nebula, but again it is concluded that bodies in that zone can grow to planetary size in a few thousand years.From the discussion of the interstellar collapse phase it is concluded that the angular momentum of the primitive solar nebula was predominantly of random turbulent origin, and that it is plausible that the primitive solar nebula should have possessed satellite nebulae in highly elliptical orbits. It is proposed that the comets were formed in these satellite nebulae.A number of other detailed conclusions are drawn from the analysis. It is shown to be plausible that an iron-rich planet should be formed in the inner part of the outer nebular convection zone. Discussions are given of the processes of planetary gas accretion, the formation of satellites, the T Tauri solar wind, and the dissipation of excess condensed material after the nebular gases have been removed by the T Tauri solar wind. It is shown that the present radial distances of the planets (but not Bode's Law) should be predicted reasonably well by a solar nebula model intermediate between the uniform and linear cases of Cameron and Pine.     

The effects of self-gravity on the solar nebula

We study the distribution and transport of angular momentum in a self-gravitating accretion disk formed during the collapse of a rotating gas cloud. Using the surface density for the low-viscosity models and minimum-mass models presented by Cassen and Summers, Poisson's equation is solved explicitly to determine the effects of self-gravitation of the protostellar disk. Analytic expressions for the angular momentum of the central star and other relevant quantities of interest during the formation stage are presented.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.On leave from the City College of the City University of New York, U.S.A.     

Further considerations on contracting solar nebula

Prentice (1978a) in his modern Laplacian theory of the origin of the solar system has established the scenario of the formation of the solar system on the basis of the usual laws of conservation of mass and angular momentum and the concept of supersonic turbulent convection that he has developed. In this, he finds the ratio of the orbital radii of successively disposed gaseous rings to be a constant - 1.69. This serves to provide a physical understanding of the Titius-Bode law of planetary distances. In an attempt to understand the law in an alternative way, Rawal (1984) starts with the concept of Roche limit. He assumes that during the collapse of the solar nebula, the halts at various radii are brought about by the supersonic turbulent convection developed by Prentice and arrives at the relation: R _p= Ra^p, where R _pare the radii of the solar nebula at various halts during the collapse, R the radius of the present Sun and a = 1.442. a is referred here as the Roche constant. In this context, it is shown here that Kepler's third law of planetary system assumes the form: T _p = T ₀(a^3/2)^p, where T _p are the orbital periods at the radii R _p, T ₀ - 0.1216d - 3 h, and a the Roche constant. We are inclined to interpret T ₀' to be the rotation period of the Sun at the time of its formation when it attained the present radius. It is also shown that the oribital periods T _pcorresponding to the radii R _psubmit themselves to the Laplace's resonance relation.     

The identification of early condensates from the solar nebula

Calcium-aluminum-rich chondrules which are highly deficient in alkalis were extracted from the carbonaceous chondrite Allende and yield a range of compositions with the lowest measured isotopic composition of $\text{(}{}^{87}\text{Sr}\text{/}{}^{86}\text{Sr}\text{)}{}_{\mathrm{<mtext>ALL</mtext>}}\text{= 0.69877±0.00002}$ and identify this material as the earliest known condensate from the solar nebula. Other chondrules suggest the possible presence of even more primitive Sr in this meteorite. This result also shows that some chondritic material formed very near the earliest part of the condensation sequence. Using alkali-deficient planetary objects (Moon, basaltic achondrites, Angra dos Reis, Allende), the Sr data indicate a time interval for condensation of 10 m.y. (from ALL to BABI) if condensation occurred in a solar Rb/Sr environment. A variety of alkali-rich olivine chondrules and CaAl-rich aggregates from Allende fail to determine an isochron and indicate that the element distribution in this meteorite was disturbed later than 3.6ae, possibly recently, in a cometary nucleus. This disturbance requires that the determination of initial ⁸⁷Sr/⁸⁶Sr be done on essentially Rb-free phases. Strontium data from equilibrated chondrites and from an iron meteorite establish an interval for metamorphism or differentiation in protoplanetary objects which followed the condensation process by ≈80 mm.y. The chronology for condensation and early planetary evolution obtained for Sr is in disagreement with the ¹²⁹I chronology but can be brought into agreement, if it is assumed that the high temperature iodine containing phases have not been affected by the metamorphic events determined by Sr.     

Experimental studies of magnetite formation in the solar nebula

Abstract— Oxidation of Fe metal and Gibeon meteorite metal to magnetite via the net reaction 3 Fe (metal) + 4 H₂O (gas) = Fe₃O₄ (magnetite) + 4 H₂ (gas) was experimentally studied at ambient atmospheric pressure at 91–442 °C in H₂ and H₂-He gas mixtures with H₂/H₂O molar ratios of ～4–41. The magnetite produced was identified by x-ray diffraction. Electron microprobe analyses showed 3.3 wt% NiO and 0.24 wt% CoO (presumably as NiFe₂O₄ and CoFe₂O₄) in magnetite formed from Gibeon metal. The NiO and CoO concentrations are higher than expected from equilibrium between metal and oxide under the experimental conditions. Elevated NiO contents in magnetite were also observed by metallurgists during initial stages of oxidation of Fe-Ni alloys. The rate constants for magnetite formation were calculated from the weight gain data using a constant surface area model and the Jander, Ginstling-Brounshtein, and Valensi-Carter models for powder reactions. Magnetite formation followed parabolic (i.e., diffusion-controlled) kinetics. The rate constants and apparent activation energies for Fe metal and Gibeon metal are: These rate constants are significantly smaller than the parabolic rate constants for FeS growth on Fe metal in H₂S-H₂ gas mixtures containing 1000 or 10 000 ppmv H₂S (Lauretta et al., 1996a). The experimental data for Fe and Gibeon metal are used to model the reaction time of Fe alloy grains in the solar nebula as a function of grain size and temperature. The reaction times for 0.1–1 μm radius metal grains are generally within estimated lifetimes of the solar nebula (0.1–10 Ma). However, the calculated reaction times are probably lower limits, and further study of magnetite formation at larger H₂/H₂O ratios, at lower temperatures and pressures, and as a function of metal alloy composition is needed for further modeling of nebular magnetite formation.     

The first ten million years in the solar nebula

Abstract— The ²⁶Al/²⁷Al ratio in a large number of calcium-aluminum inclusions (CAIs) is a rather uniform 5 × 10^?5, whereas in chondrules the ratio is either undetectable or has a much lower value; the simplest interpretation of this is that there was an interval of a few million years between the times that these two meteoritic constituents formed stable solids. The present investigation was undertaken as an exploration of the physics of the processes in the solar nebula during and after the accumulation of the Sun. Understanding the time scales of events in this nebular model, to see if this would cast light on this apparent CAI to chondrule time interval, was the major motivation for the exploration. There were four stages in the history of the solar nebula; in stage 1, a fragment of an interstellar molecular cloud collapsed to form the Sun and solar nebula; in stage 2, the nebula was in approximate steady state balance between infall from the cloud and accretion onto the Sun and was in its FU Orionis accumulation stage; in stage 3, the Sun had been mainly accumulated and there was a slow residual mass flow into the Sun while it was in its classical T Tauri stage; and in stage 4, the nebula had finished accreting material onto the Sun (now a weak-lined T Tauri star) and was in a static condition with no significant dissipation or motions, other than removal at the inner edge due to the T Tauri solar wind and photoevaporation beyond 9 astronomical units (AU). It is found that the energy source keeping the nebula warm during stages 3 and 4 is recombination of ionized H in the ionized bipolar jets and the T Tauri coronal expansion solar wind. The parameters of the heating model were adjusted to locate the ice sublimation line at 5.2 AU. In this work, a nebular model is used with a surface density of 4.25 × 10³ gm/cm² at 1 AU and a variation with radial distance as the inverse first power. Under normal conditions in the nebula, there is a negative pressure gradient that provides partial radial support for the gas, which thus circles the Sun more slowly than large solid objects do. Large objects undergo a slow inward spiral due to the gas drag; very small objects move essentially with the gas but have a slow inward drift; and intermediate objects (e.g., 1 m) have a fairly large inward drift velocity that traverses the full radial extent of the nebula in considerably less than the CAI to chondrule time interval. Such objects are thus lost unless they can grow rapidly to larger sizes. Near the inner edge (bow) of the nebula during stage 4, the pressure gradient becomes positive, creating a narrow zone of zero gas drag toward which solids drift from both directions, facilitating planetesimal formation in the inner solar nebula. Recent theoretical and experimental results on sticking probabilities of solids show that icy surfaces have the best sticking properties, but icy interstellar grains can only stick together when subjected to impact velocities of less than 2000 cm/sec. However, if the solid objects are very underdense, then a collision leads to interpenetration and many points at which the small constituent grains can adhere to one another, and thus coagulation becomes possible for such underdense objects. Simulations were made of such coagulation in the outer solar nebula, and it was found that the central plane of the nebula quickly becomes filled with meter-sized and larger bodies that rapidly accumulated near the top of the nebula and rapidly descended; in a few thousand years this quickly leads to gravitational instabilities that can form planetesimals. These processes led to the rapid formation of Jupiter in the nebula (and the slightly less rapid formation of the other giant planets). The early formation of Jupiter opens an annular gap in the nebula, and thus a second region is created in the nebula with zero gas drag. It is concluded that CAIs were formed at the end of stage 2 of the nebula history and moved out into the nebula for long-term storage, and that most chondrules were formed by magnetic reconnection flares in the bow region of the nebula during stage 4, several million years later. Carbonaceous meteorites should be formed on the far side of the Jovian gap, with the chondrules being heated by flares on the early Jupiter irradiating materials in the nearby zone of zero gas drag, and they should have essentially the same ²⁶Al ages as the CAIs (this will be very hard to confirm owing to scarcity of Al mineral phases in these chondrules).     

26Al and the partial ionization of the solar nebula

Calculation of the ionization state and consequent magnetic Reynolds number for the solar nebula shows that the presence of²⁶Al will result in strong coupling of the gas to magnetic fields. In the absence of²⁶Al,⁴⁰K will still result in substantial ionization, but the degree of magnetic coupling is much more model dependent.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.also Department of Astronomy.     

A tidal theory for the origin of the solar nebula

There are two angular momentum (AM) problems associated with the formation of stars in general and the solar system in particular. The first is how to dispose of the AM possessed by turbulent protostellar clouds. Two-dimensional calculations of the gravitational infall of rotating gas clouds by several authors now indicate that stars are formed in groups or clusters rather than as single entities. Added evidence comes from observation of probable regions of star formation and young clusters, plus the fact that most stars are presently members of binaries or other multiples. Thus the first problem is solved by postulating the fragmentation of massive clouds with most of the AM ending up in the relative orbits. These clusters are notoriously unstable and evolve with the ejection of single stars like the Sun.The second problem is the uneven distribution of AM with mass in the solar system. It turns out that the collapse time for the majority of the infalling material is comparable to the time necessary for significant dynamical interaction of the protostellar fragment with its neighbors. It is found here through calculations utilizing very simplified numerical models that the last few tens of percent of infalling material can easily have sufficient AM transferred to it by the tidal action of passing protostars to form a solar nebula and ensure alignment of the solar spin. The most important parameter is the degree of central condensation: fragments without several tenthsM in a central core tend to be torn apart by encounters, or at least stimulated into binary fission. A stabilizing central mass maintains its identity and acquires a rotating envelope of material.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Properties of the solar nebula and the origin of the moon

The basic geochemical model of the structure of the Moon proposed by Anderson, in which the Moon is formed by differentiation of the calcium, aluminium, titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this Moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the Moon slightly inside the orbit of Mercury. Some condensed metallic iron is likely to enter the Moon in this position, and since the Moon is assembled at a very high temperature, it is likely to have been fully molten, so that the iron can remove the iridium from the silicate material and carry it down to form a small core. Interactions between the Moon and Mercury lead to the present rather eccentric Mercury orbit and to a much more eccentric orbit for the Moon, reaching past the orbit of the Earth, establishing conditions which are necessary for capture of the Moon by the Earth. In this orbit the Moon, no longer fully molten, will sweep up additional material containing iron oxide. This history accounts in principle for the two major ways in which the bulk composition of the Moon differs from that of the Allende inclusions.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

Homogeneous distribution of Fe isotopes in the early solar nebula

To examine the iron (Fe) isotopic heterogeneities of CI and ordinary chondrites, we have analyzed several large chips (approximately 1 g) from three CI chondrites and three ordinary chondrites (LL5, L5, and H5). The Fe isotope compositions of five different samples of Orgueil, one from Ivuna and one from Alais (CI chondrites), are highly homogeneous. This new dataset provides a δ⁵⁶Fe average of 0.02 ± 0.04‰ (2SE, n = 7), which represents the best available value for the Fe isotopic composition of CI chondrites and probably the best estimate of the bulk solar system. We conclude that the homogeneity of CI chondrites reflects the initial Fe isotopic homogeneity of the well‐mixed solar nebula. In contrast, larger (up to 0.26‰ in δ⁵⁶Fe) isotopic variations have been found between separate approximately 1 g pieces of the same ordinary chondrite sample. The Fe isotope heterogeneities in ordinary chondrites appear to be controlled by the abundances of chondritic components, specifically chondrules, whose Fe isotope compositions have been fractionated by evaporation and recondensation during multiple heating events.     

Evolution of grains in a turbulent solar nebula

In accretion disk models of the solar nebula, turbulence is driven by convective instability. This mechanism requires high opacity, which must be provided by solid grains. Evolution of the grain size distribution in a turbulent disk is computed numerically, using realistic collisional outcomes and strengths of grain aggregates, rather than an arbitrary “sticking efficiency.” The presence of turbulence greatly increases the rate of grain collisions; the coagulation rate is initially much greater than in a nonturbulent disk. Aggregates quickly reach sizes ～0.1–1 cm, but erosion and breakup in collisions prevent growth of larger bodies for plausible aggregate impact strengths. These aggregates are too small to settle to the plane of the disk, and planetesimal formation is impossible as long as the turbulence persists. However, the opacity of the disk is reduced by aggregate formation; some combinations of opacity law and surface density produce an optically thin disk, cutting off turbulent convection. The disk may experience alternating periods of turbulence and quiescence, as grains are depleted by coagulation and replenished by infall from the presolar cloud. Planetesimals can form only during the quiescent intervals; it is argued that such episodes were rare during the lifetime of the accretion disk.     

Models of particle layers in the midplane of the solar nebula

In the absence of global turbulence, solid particles in the solar nebula tend to settle into a thin layer in the central plane. Shear between this layer and pressure-supported gas produces localized turbulence in the midplane; the thickness of the particle layer is determined by balance between settling and turbulent diffusion. A numerical model is described, which allows computation of the vertical structure of a layer of particles of arbitrary size, with self-consistent distributions of particle density, turbulent velocity, and radial fluxes of particles and gas. Effects of varying particle size and the abundances of solids and gas are evaluated. If the surface density of solids is increased by an order of magnitude over nominal solar abundance, the peak density within a layer of small particles can approach the critical value needed for gravitational instability. However, depletion of the nebular gas is much less effective for raising the density of such a layer to the critical value, due to decreased coupling of particles to the gas as the density of the gas decreases. The variation of radial particle flux with surface density of the particle layer is not consistent with secular instability of the layer driven by gas drag.