A 3D X-ray microtomography reevaluation of metal interconnectivity in a partially molten silicate matrix 

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From the nebula to the Asteroid Belt

Remnants of the early accreted small bodies of the Solar System are stored in the Asteroid Belt. The presence of such reservoir of primitive objects is not observed in other exoplanetary systems. Either the Solar System is an exception or there are observational biases due to a resolution that is not suffi cient. In any cases, the Asteroid Belt provides a unique laboratory to study the time-line of the evolution of planetesimals that accreted early. The present part aims at describing briefly the different steps of formation of our Solar System, from the gaseous nebula to the present planetary system with its anomalous Asteroid Belt.

Gravitational collapse of the protosolar nebula

The Universe is composed of a massive super structure made up of filaments surrounded by voids. These filaments are in turn composed of galaxy clusters and subsequently, galaxies. At a smaller scale, galaxies host planetary systems, i.e. stars and planets, and nebulae, i.e. gas clouds. A genetic link between planetary systems and nebulae has been proposed by Swedenborg (1734) who imagined that planetary systems could form from the gravitational collapse of a dense gas cloud. Observations of protoplanetary disks around young stellar objects indicate that most disks have a short lifetime of ¥ 6 Myr (Haisch, Jr. et al., 2001). Planetary accretion is likely to be main disk clearing process. However, the short timescale is likely to match only the formation of the giant planets (Boss and Goswami, 2006).
The protosun and protonebula formed from the gravitational collapse a dense cold molec-ular cloud Boss and Goswami (for a detailed review, see 2006, and references therein). Diffuse objects are stable and need to undergo a shock of some sort to collapse on themselves, e.g. the supernova of a neighboring star which may also bring short-lived radionuclides that will be incorporated in the first solids to condensate. Once the collapse initiated, the cloud is contracting on itself, starts to rotate, forms a disk perpendicular to the rotation axis and temperature rises. Due to a differential stress between the inner and outer regions of this disk, gas particles are slowed down, making them drift toward the center of the disk and forming the Sun. As the mass of the disk is reduced, the differential stress is less vigorous and the disk is able to cool. Density and temperature of a specific location will determine the chemical species that will be able to form. For a detailed review on the physics of nebular evolution, see Ciesla and Charnley (2006).

Primary accretion – Shaping the planetary embryos

Primary accretion defines the step in which meteorites parent bodies are formed, i.e. planetesimals. From a dynamical point of view, primary accretion of planetesimals can be subdivided into four steps (Nichols Jr, 2006): (1) gravitational collapse of gas and dusts, (2) formation of millimeter to centimeter sized grains from aggregation of small particles, (3) gravitational accretion of meter to kilometer sized objects and (4) collisions and impacts leading to planetary formation and evolution (e.g. differentiation, alteration). It is of note that the different steps do not have sharp limits and are likely to overlap between each other.

From the nebula to the Asteroid Belt 

As the protosolar disk cools down, elements are able to go from the gaseous state to the solid state, forming the first condensates with sizes on the order of the micrometer. These particles are subject to the dynamics of the gas causing them to collide and to coagulate thanks to Van der Waals forces. These first aggregates are porous and can easily dissipate the collisional energy, allowing them to reach centimeter to meter sizes (Cuzzi and Weiden-schilling, 2006; Russell et al., 2006). Then, these particles are large enough to escape the inward radial gas drag and will settle toward the midplane. Collision velocities between cen-timeter sized objects are too high to allow them to form aggregates and gravity forces are too low to bond them. Although counterintuitive, turbulence fosters accretion as it does not only have a global dispersing effect, but also concentrates the centimeter sized ones in some areas (Cuzzi and Weidenschilling, 2006). If particles density exceeds that of the gas, there can be local gravitational collapses that form small bodies with sizes larger than a meter and up to 10-100 km. Planetary embryos then form rapidly through runaway growth: the largest bodies have collisional cross sections increased due to their gravitational attraction, the largest one of a given region gains mass more rapidly than the next largest and dominates that region (Weidenschilling and Cuzzi, 2006). This process is repeated at different distances from the Sun, forming several embryos of the size of the Moon or Mars. Bodies of this size can no longer be shattered by collisions and will continue to evolve to form the terrestrial planets. In this context the presence of the Asteroid Belt of our Solar system can be questioned, it should have disappeared and be a part of the terrestrial planets.

The Asteroid Belt and gas giants migrations

At this point, four features of the actual Solar System remain puzzling
1. At its position, Mars should have a size greater than a planetary embryo (i.e. similar to that of the Earth).
2. The asteroid belt lost most of its mass, but is still present. The processes that fostered its partial emptying remains uncertain.
3. Spectral signatures of asteroids show that dry (S-type asteroids) and hydrous (C-type asteroids) material were mixed, i.e. materials that formed at different places (above and beyond the snowline respectively).
4. The surface of the Moon exhibits a peak of cratering ¥ 700 Myr after planets accreted. This cataclysmic event is called the Late Heavy Bombardment (LHB) and remains misunderstood in the theory of planets formation.
Migrations of the gas giants provide a model that fits all these features (Tsiganis et al., 2005; Gomes et al., 2005; Morbidelli et al., 2005; Walsh et al., 2011, 2012). The idea that the gas giants may be able to migrate arose from the the observation of hot Jupiters (Mayor and Queloz, 1995), i.e. gaseous planets close to their star, while these bodies are likely to have formed beyond the snowline. The model of gas giants migration is based on two steps. (1) A first stage called the « Grand Tack model » in which Jupiter migrates inward due to gas-drag in the protonebula, and then outward due to a resonant motion with Saturn (Walsh et al., 2011, 2012). This inward-then- outward migration results in two important features: the scatter of material that accreted both inside and outside the snow-line, mixing dry and hydrous objects, and the truncation of the inner disk at 1 AU (Astronomical Unit), i.e. the Sun to Earth distance. Terrestrial planets formed in that truncated disk to reach their final sizes, except for Mars which formed out of this disk from the scarce planetary embryos that were ejected (Figure 1.1). Following the « Grand Tack model », these gas giants migration occurred early in the Solar System history, within its first million year (Figure 1.1). (2) Then, in a second step called the « Nice model », after a long quiescent period (¥ 700 Myr) an inward migration of Jupiter is caused by resonant motion with Saturn, while the latter, along with Uranus and Neptune, migrate outward (Figure 1.1), conducting to chaotic motions (Tsiganis et al., 2005; Gomes et al., 2005; Morbidelli et al., 2005). Uranus and Neptune are sent in the massive Kuiper belt, scattering it in all directions, included toward the inner regions. This event resulted in the delivery of the Late Heavy Bombardment (LHB) (Gomes et al., 2005) recorded on the surface of the Moon. Resonant motions between Jupiter and Saturn also ejected objects from the asteroid belt, reducing its mass by a factor of 10. This gas giants migration event is thought to be the last that reshaped the Solar System. It remains mainly unchanged for the 4 billion years to follow. Here the first stage, the « Grand Tack » is of prior interest as it shaped the Asteroid Belt and is responsible for the mixing of dry and hydrous materials.

Meteorites, messengers from the early Solar System

What remains from the early Solar System, besides the orbital data of the different objects are small bodies stored in the Asteroid Belt. These objects are early-formed rocks that recorded the diff erent events that shaped the Solar System as it is today. Most of these objects were not subject to complex geological history, they remained pristine, meaning that the primitive information they host was not erased. Meteorites thus provide complementary constraints on the early formation and evolution of the Solar System. Due some collision dynamics within the asteroid belt, small chunks of asteroids may be sent in all directions. Some of them may arrive on Earth. What falls on Earth is likely to be biased and not representative of the whole population of asteroids. Nonetheless, this biased sample of rocks is extremely diverse and complicated, and has not delivered all of its secrets yet.
Meteorites bring information about chemistry, timescales and timing of different processes. These data are used as constraints on the numerical simulations, and in turn the latters shed light on the history of some of these meteorites. Back and forth reasonings coupling data from natural samples, numerical models and laboratory experiments to reproduce the formation conditions of natural samples are needed to improve our understanding of the premises of the Solar System.
One of the basics of classification is to try to find characteristics that outline the differ-ences between different members of a population. In meteorites, this characteristic is the differentiation degree, i.e. how well silicate and metallic phases are separated. Differenti-ation is the process during which metal and silicates are separated to form a metallic core and a rocky mantle. Following this criteria of differentiation degree, three main families of meteorites arise (Figure 1.2), from the least differentiated and most primitive: chondrites in which metal and silicates are mixed together, to the most differentiated: achondrites which are constituted only of metal (iron meteorites) or of silicates (stony meteorites), indicating an efficient separation of both phases. The stony-iron meteorites are also considered as achon-drites, however the mixture of silicate and metal in these meteorites is considered to be the result of brecciation, except for pallasites; these objects will not be discussed in the following. The third family is embodied by the primitive achondrites, which constitute an intermediate between chondrites and achondrites, meaning that the differentiation process initiated but stopped before completion. These three families of meteorites are presented in the following, outlining the highlights they provide on the Solar System formation and differentiation.

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Chondrites, primitive meteorites

Chondrites are among the most primitive objects of the Solar System. They have a particular texture with three main components: Calcium-Aluminum rich Inclusions (CAIs), chondrules and a fine-grained matrix. These components are likely to have formed indepen-dently in the protoplanetary disk and recorded the physico-chemical properties of the disk at the location and time of their formation. Hence, they represent the almighty truth for nebular evolution models. Depending on the proportion of each component, bulk chemistry and oxygen isotope signature, different categories of chondrites are defined: carbonaceous, ordinary and enstatite. In a first time, information hosted in each component of chondrites are investigates, then interest is taken to the whole rock to understand why these components that formed in different conditions are aggregated together.

Chondritic components and condensation sequences

To understand the formation of meteorites during the cooling of the protoplanetary disk, the condensation sequences can be addressed (Davis and Richter, 2013). This sequence shows that the first condensates, over the range 1800 to 1400 K, are refractory minerals hosting mainly calcium, aluminum and some magnesium (Figure 1.3, inset). These phases corre-spond to the CAIs, which are refractory inclusions composed of calcium and aluminum rich minerals, such as hibonite (CaAl12O19), perovskite (CaTiO3 ), spinel (MgAl2O4) and anor-thite (CaMgSi2O6). The high temperature required to form these inclusions along with the absence of volatile elements suggest that CAIs are likely to be the first condensates that formed in the early Solar System. Dating of these refractory inclusion with lead isotopic sys-tem makes these objects the oldest of the Solar System with absolute ages of 4567.18 ± 0.5 Myr (Amelin et al., 2002) or 4568.2 ± 0.3 Myr (Bouvier and Wadhwa, 2010). CAIs formation age is considered as the event dating the beginning of the solid Solar System.
Upon decreasing temperature, condensation sequences show the condensation of metallic phases and less refractory silicates (olivine (Mg,Fe)2 SiO4, pyroxene (Ca,Mg,Fe)2Si2 O6 and feldspar (K,Na)AlSi3O8 or CaAl2Si2 O8, Figure 1.3), forming chondrules (spherical objects with millimeter to centimeter sizes) and the fine-grained matrix. Metallic phases mostly occur under the form of Fe-Ni alloy and / or troilite FeS. Their presence can be easily ex-plained with the condensation sequences (Figure 1.3), although sulfur condensates later and at lower temperature than iron due to its volatility. The presence of troilite in chondrules can then be understood in the framework of the different models that often assume the recy-cling and mixing of different materials (Zanda, 2004; Connolly and Jones, 2016). Secondary alteration processes may have changed the oxidation degree of the metallic phases, allowing the formation of iron oxides (e.g. magnetite in CI chondrites, King et al., 2015).
The exact formation process of chondrules is still unresolved, many different models exist which will not be developed here (for more information, see Zanda, 2004; Connolly and Jones, 2016, and references therein). Some characteristics are common between the different models: the spherical shape of chondrules indicate that they formed partially or entirely molten and the presence of silicate glass indicate that they were cooled on extremely short timescales. Due to the presence of relict chondrules included in others, multiple formation episodes must have taken place, recycling the previously formed material. The fine-grained matrix of chondrites is volatile-rich. The presence of interstellar organic compounds argues that temperature did not exceed 700 K since their formation (Chambers, 2006). These materials must have been formed in a cold region. Chondrites correspond then to a mixture of materials accreted at different heliocentric distance. The successive migrations of the gas giant planets are most likely responsible for mixing such different materials.

Chondrites as whole rocks

The different compounds building chondrites formed in different regions, at different times and different temperatures. However, they ended together up forming the same material. Relative dating (Pb-Pb and Al-Mg isotopic systems) of chondrules indicate formation ages ranging from 0 to 4 Myr after CAIs (Amelin and Krot, 2007; Villeneuve et al., 2009), with a peak between 1.5 and 3 Myr (Villeneuve et al., 2009). A continuum formation between CAIs and chondrules most likely exist, but CAIs must have survived during all the chondrule for-mation time before being accreted along with them (detailed information on these processes can be found in Weidenschilling and Cuzzi, 2006; Chambers, 2006). An extended accretion process over time best explains the different compositions and textures of the different chon-drite classes. Absolute ages of chondrites parent bodies accretion range from 1.8 Myr to 3.6 Myr after CAIs (Sugiura and Fujiya, 2014).
Mixing CAIs, chondrules and matrix in different proportions and in different conditions gives a whole zoology of chondrites which can be distributed into three classes: carbona-ceous, ordinary and enstatite. Carbonaceous chondrites have relatively high matrix abun-dances, from 35 up to >99 vol% (Weisberg et al., 2006), and host a significant amount of carbonaceous matter. Ordinary chondrites are mainly composed of millimeter sized chon-drules, from 60 to 80 vol%, low matrix amount (up to 15 vol%) and scarce CAIs (<1 vol%) (Weisberg et al., 2006). They are classified following their metallicity into H chondrites (high metallicity), L chondrites (low metallicity) and LL chondrites (very low metallicity). Finally, enstatite chondrites have similar volume proportions of CAIs, chondrules and matrix than ordinary chondrites but are defined by a very low oxygen fugacity. Indeed, silicates are mostly magnesian and iron is almost entirely in the metallic state and is found forming alloys with silicon (Weisberg et al., 2006). Enstatite chondrite chondrules are mainly formed by enstatite (MgSiO3). Due to the extreme reducing conditions, sulfide phases are composed of unusual species (e.g. calcium sulfides, magnesium sulfides or even chromium sulfides).

Achondrites

Achondrites are the result of differentiation processes. It depicts a family of meteorites that lost their chondritic texture and have different compositions than chondrites. As a result, most achondrites are either composed of silicates without metal (stony meteorites), or metal without silicates (iron meteorites). However, some of them are still a mixture of metal and silicates (stony-iron meteorites such as pallasites and mesosiderites), but with a refractory mineralogy and a different distribution of metal: it seems gathered and forming a network in opposition to chondrites in which it is finely spread. All these meteorites sample different regions of a differentiated planetesimal. Stony meteorites are representative of the crust or mantle of the body, while iron meteorites sample the core. Pallasites are thought to be representative of the core-mantle boundary, explaining the mixture of iron with refractory minerals. Starting from a chondritic material, differentiation requires heating and melting of the body to allow metal-silicate separation. Achondrites are representative of the final state differentiation. Igneous processes that occurred erased all information about incipient differentiation and nebular processes. Instead, these meteorites recorded the last event before they were ejected from their parent body, i.e. cooling and core or mantle/crust crystallization.

Table of contents :

1 State of the art 
1.1 From the nebula to the Asteroid Belt
1.2 Meteorites, messengers from the early Solar System
1.3 General approach on interconnection thresholds and dihedral angles in twophases systems
1.4 Metal-silicate differentiation and small bodies evolution
1.5 Thesis outline
2 Methods 
2.1 Description of the experimental system
2.2 Experimental setups
2.3 Analytical techniques
2.4 MELTS thermodynamic modeling
3 Metal segregation in planetesimals: Constraints from experimentally determine interfacial energies 
3.1 Introduction
3.2 Experimental setup
3.3 Dihedral angle measurement
3.4 Determination of interfacial energies and consequences on phase relations
3.5 Metal-silicate differentiation in early accreted planetesimals
3.6 Conclusion
4 A 3D X-ray microtomography reevaluation of metal interconnectivity in a partially molten silicate matrix 
4.1 Introduction
4.2 Experimental setup
4.3 Results
4.4 Discussion
4.5 Conclusion
5 Magma oceans in early-accreted small bodies and Pallasite formation 
5.1 Introduction
5.2 Magma ocean modeling
5.3 Equilibrium magma ocean
5.4 Implications for differentiation
5.5 Conclusion
6 A petrographic analysis of primitive achondrites 
6.1 Introduction
6.2 Methods
6.3 Petrographic features
6.4 Thermometry and calculation of oxygen fugacity
6.5 Formation conditions of primitive achondrites
6.6 Conclusion
7 Conclusions et perspectives 
8 Conclusions and future prospects

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