composition of the overlying MO remains mafic. No further Bg segregation would be expected above ~2,500 km (i.e., 100–110 GPa) in a mafic MO, for a reasonable Bg grain size. If the MO were to be further depleted in Bg due to the “at equilibrium fractionation” mechanism described above (Figure 15), it would become even more mafic. At this point, it is difficult to imagine how such major mafic MO could have disappeared through dynamical processes, since seismic tomography does not provide evidence of such mantle reservoir today. Thus a pyrolite-type upper mantle seems difficult to form following this scenario. It makes the formation of a primary basal MO simultaneously with MO solidification quite unlikely.

**6. Conclusion**

Solidification within a deep convecting magma ocean (MO) was a key process in the formation of the Earth's interior (Ballmer, Lourenço, et al., 2017) and likely in the early mantle evolution for other planets: Mars (Elkins-Tanton et al., 2005), Mercury (Mouser et al., 2021) and the Moon (Dygert et al., 2017; Elkins-Tanton et al., 2011). This process is responsible for the separation of compatible elements that prefer the solid phase (e.g., Mg, Si) from incompatible elements which prefer the liquid phase (e.g., Al, Na, Fe). The solidification depth is governed by the geotherm and the melting curves. With density profiles of the melt and bridgmanite crystals crossing in the lower mantle, Caracas et al. (2019) suggested that crystal settling may occur toward neutral buoyancy depths. However, Both chemical composition and temperature contribute to the buoyancy of a crystal layer within a convecting reservoir. A low density contrast between crystals and melt would then paradoxically favor entrainment of crystals by the convective flow. Hence different scenarios may emerge: bottom-up solidification, or mid-mantle solidification making it possible to form a basal magma ocean.

In our study we have shown that the ability of the crystal fraction to sediment or to disperse within the domain is the result of a combination of the influence of the crystal size, the density difference between the crystals and the magma and the magma viscosity. We have shown that this ability is a function of the ratio of the convection over the buoyancy stress (expressed as the Sh dimensionless number). For a relevant range of parameters, we observe that the critical Sh_c values separating the suspension and sedimentation regimes can be lower than those values previously obtained from analog models (V. S. Solomatov et al., 1993). As a consequence, our results strengthen the idea that a suspension mechanism would be dominant over sedimentation during magma ocean solidification and, as a consequence, equilibrium crystallization would be favored compared to fractional crystallization.

In our models, we consider a particle size range ($10^{-4} - 10^{-3}$ m) and a density difference range between the magma and the particles ($10 - 100$ kg.m$^{-3}$), which are probably closer to the relevant MO conditions (see e.g., $\Delta\rho = -200$ to $200$ kg/m$^3$ in Figure 11) than the range of parameters proposed by Patočka et al. (2020) ($0.5 \times 10^{-3} - 10^{-2}$ m and $10 - 3,000$ kg.m$^{-3}$). Moreover, their models neglect a re-entrainment process by eliminating the particles that reach the bottom of the reservoir. Hence, it is not surprising that their models favor rapid crystal settling and fractional crystallization. Patočka et al. (2020) identified three settling regimes: “stone-like,” bi-linear and “dust-like” regimes depending on the ratio between the crystal's terminal velocity and the average vertical velocity of the flow. It appears that our models mostly fall into the “dust-like regime” where the terminal velocity of a particle is smaller than the average velocity within the convective reservoir. In the “dust-like” regime the particles from the models developed by Patočka et al. (2020) appear to be uniformly distributed in the reservoir in agreement with our models.

We also considered the density contrasts calculated from different end-members for the chemical composition of the early mantle by adding or subtracting up to 40% of bridgmanite (Bg) to a pyrolite mantle reference. Exploring the early mantle composition within such a range leads to a wide range of density differences between the molten and the solid phases. Hence the chemical composition also influences the ability of the crystals to cumulate at the bottom or in the middle of the magma ocean. Our models emphasize that (a) Bg grains are unlikely to segregate in a mantle of pyrolite composition, except in a shallow MO when the grain size may increase to 1 mm or more, (b) Bg grains are likely to segregate at the bottom of a MO enriched in SiO$_2$, compared to pyrolite, and (c) the formation of a basal MO simultaneously with mantle solidification is a possibility for mafic BSE compositions (although difficult to reconcile with the geochemical models of the Earth). We also note that a homogeneous bottom-up solidification of the MO is expected to produce a significant SiO$_2$ enrichment with increasing mantle depth in a primitive mantle (compatible with seismic observations) and a higher SiO$_2$ content in the BSE compared to pyrolite (compatible with geochemical models of the Earth).
While our study is a step toward a more realistic approach, several other processes not accounted here could be worth implementing in future models:

1. In our models we did not consider the time evolutions of the (a) crystal size, (b) the crystal fraction or (c) the density contrast during the chemical differentiation of the magma ocean. The kinetics of crystal nucleation and growth is difficult to constrain within a magma ocean environment. The crystal fraction evolves during the cooling of the magma ocean and will likely naturally increase as the temperature decreases. However, crystals may also reach higher temperature zones of the reservoir when entrained by convection which will lead to a decrease in the crystal fraction. Even if this complexity is not accounted for in our models, our parametric approach enable to anticipate between suspension or sedimentation regime for a given set of parameter values.

2. We have restricted our study to the crystal settling that may occur close to mechanical boundaries (CMB or solidified walls) where the velocity is lower than in the middle of the magma ocean (in “calm” conditions). Future models should explore parameters compatible with the center of the magma ocean (i.e., larger Rayleigh numbers). This would imply using much higher Reynolds numbers to correctly characterize the turbulent motion occurring from the scale of the crystal up to that of the whole magma ocean. In such a context, models would need to consider the inertial forces and turbulence equations.

3. Early in the Earth's evolution, the Moon was much closer to the Earth than today (Chen & Nimmo, 2016), which has generated huge tidal forces on both bodies. The Moon potentially started to re-accrete at a distance ranging from 5 to 15 Earth radii (today the distance is nearly 60 Earth radii). The tidal forcing induced by the presence of the Moon generates an oscillatory shear characterized by a maximum shear rate and a tidal frequency. Such an oscillatory shear may influence the convective flow within the magma ocean and the crystallization process (Ogilvie & Lesur, 2012). This effect would have varied in time during both the magma ocean solidification and as the Moon moved away from the Earth.

4. After the giant impact that probably induced the thickest magma ocean episode (Nakajima & Stevenson, 2015), the orbit parameters of the Earth were strongly affected and the Earth's spinning rate was probably much higher than today (Čuk & Stewart, 2012). While strong turbulence may favor suspension over sedimentation regimes, Julien et al. (1996) showed that accounting for Coriolis forces may lead to a reduction in the convective velocity and, as a consequence, favor sedimentation over suspension regimes. Strong turbulence in the presence of rotation is a complex process that is difficult to constrain in a solidifying magma ocean context in which solid and liquid phases co-exist (Fernando et al., 1991).

5. When crystallization of the magma ocean occurs close to a rigid layer, the relevant boundary conditions for crystal settling are closer to no-slip boundary conditions (Patočka et al., 2020) than to free-slip boundary conditions since the newly formed solid is much more viscous than the liquid. When considering non-interacting particles as in laboratory experiments (V. S. Solomatov et al., 1993) or free-slip boundary conditions as in our models, crystals cannot form solid bonds as observed in experiments on magmas (Lejeune & Richet, 1995). Because of the sintering effect, the bonds between crystals and the underlying bed can easily prevent re-entrainment and lead to a decrease in the efficiency of particle re-suspension.

These factors may affect the physics of convection and, hence, sedimentation and entrainment. If none of the current numerical models can simultaneously handle all of these complexities, the effects listed above should be accounted for in future developments of numerical models dedicated to crystal settling within a convective magma ocean. In any case, our study emphasizes the need to implement state of the art petrological and geochemical models within fluid dynamics models to better describe the early evolution of the Earth's mantle.

## Data Availability Statement

The data that support the findings of this study were obtained using the commercial software COMSOL Multi-physics (version 5.4). COMSOL Multiphysics is a simulation platform that provides fully coupled multiphysics and single-physics modeling capabilities. COMSOL Multiphysics (version 5.4) has been previously validated for two phase flow applications (Qaddah et al. (2019, 2020)). To compute our simulations we used the Heat Transfer (www.comsol.com/heat-transfer-module) and Computational Flow Dynamics (www.comsol.com/cfd-module) modules in addition to the main Multiphysics platform (www.comsol.com/comsol-multiphysics). All the parameters used in our simulation are listed and described in the manuscript. The open source software used for data visualization was Xmgrace (https://plasma-gate.weizmann.ac.il/Grace/). Data obtained can be downloaded from the following link: https://zenodo.org/record/7858690#.ZEZwxy0itAY.
*Code Availability:* The software used for this study is the commercial software COMSOL Multiphysics (version 5.4) previously validated for two phase flow applications (Qaddah et al. (2019, 2020)). User manual can be downloaded here: https://doc.comsol.com/5.4/doc/com.comsol.help.cfd/CFDModuleUsersGuide.pdf. A trial version of COMSOL Multiphysics may be requested (see www.comsol.com).

More details can be found on the following COMSOL webpages:

1. On the Foundations of the General Heat Transfer Equation: https://doc.comsol.com/6.1/docserver/#!/com.comsol.help.heat/heat_ug_theory.07.002.html.

2. Theory for Heat Transfer in Fluids: https://doc.comsol.com/6.1/docserver/#!/com.comsol.help.heat/heat_ug_theory.07.008.html.

3. The Euler Model Equations and in particular how incompressibility is handled: https://doc.comsol.com/6.1/docserver/#!/com.comsol.help.cfd/cfd_ugoppflow_multi.09.153.html.

4. The Boussinesq Approximation: https://doc.comsol.com/6.1/docserver/#!/com.comsol.help.cfd/cfd_ug_oppflow_noniso.07.20.html.

Acknowledgments

The authors thank Pierre Bonnand and Maylis Landeau for fruitful discussions. We thank Frances van Wyk de Vries for deep English proofread. We also thank the two anonymous reviewers for their constructive comments. This research received funding from French PNP program (INSU-CNRS) and the French Government Laboratory of Excellence initiative No. ANR-10-LABX-0006. This is contribution No. 598 of the ClerVolc program of the International Research Center for Disaster Sciences and Sustainable Development of the University of Clermont Auvergne.

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# 7 Évolution primitive du manteau : conséquences géologiques, pétrologiques et géochimiques

Les dernières étapes de solidification du manteau terrestre ont eu des conséquences ma-
jeures sur son évolution et sur sa structure interne telle que nous l'envisageons aujourd'hui.
Les étapes qui ont suivi la solidification du manteau ont ainsi gouverné la structuration chi-
mique de l'intérieur de la Terre, la mise en place de la tectonique des plaques et les phénomènes
de volcanisme à grande échelle qui se sont déroulés à l'Archéen.

Dans cette section, je présente des travaux résultant de collaborations avec des collègues pétrologues et/ou géochimistes auxquelles j'ai participé depuis mon arrivé au LMV. Je présente notamment l'influence qu'ont pu avoir les dernières étapes d'accrétion sur la composition chimique finale de la Terre, l'analyse d'une météorite qui pourrait être un reste de croute de planétésimal, les conséquences d'un solidus plus bas pour le matériel représentatif du manteau supérieur à l'Archéen ou encore l'origine des larges provinces volcaniques archéennes.

## 7.1 Érosion collisionnelle et rapport Mg/Si

Tôt dans l'histoire du Système Solaire, les collisions entre corps différenciés ont aussi af-
fecté la composition finale des planètes telluriques par destructions partielles des parties les
plus superficielles (Asphaug, 2010). Les chondrites à Enstatite sont considérées comme des
reliques du matériel primordial ayant formé la Terre (Javoy et al., 2010). Cependant, il existe
des différences significatives de composition chimique entre notre planète et cette classe de
 météorites qui restent à expliquer et notamment leur rapport Mg/Si. En nous appuyant sur des
 expériences en laboratoire (expériences de fusion jusqu'à 25 GPa) et sur des modélisations,
nous avons proposé pour la première fois un scénario complet qui rend compte de ces diffé-
rences : les collisions à répétition qui ont construit la Terre l'ont aussi amputée d'une fraction
de sa masse, faisant ainsi évoluer sa composition chimique (Boujibar et al., 2015). Une érosion
collisionnelle >15% de la masse de la Terre primitive permet de réconcilier les différences de
composition entre les chondrites à Enstatite et la Terre. À faibles pressions les premiers sili-
cates fondus sont enrichis en éléments incompatibles (Si, Al, Na) et appauvris en Mg. La perte
significative de la proto-croûte lors d'impacts répétés a permis une augmentation du rapport
Mg/Si jusqu'à sa valeur actuelle. Pour reproduire toutes les compositions en éléments majeurs
ainsi que certains mineurs, notre modèle implique une perte préférentielle en éléments volatils
lithophiles et une re-condensation des éléments réfractaires lithophiles après les impacts. Ce
travail a donné lieu à une publication dans la revue *Nature Communications* (Boujibar et al.,
2015).
<figure><img src="image_311.png" /></figure>

FIGURE 27 – Représentation schématique du fractionnement chimique par érosion collisionnelle. (a,b) Le chauffage primitif favorise une séparation rapide manteau-noyau suivie par le fractionnement chimique induit par cristallisation d'un océan magmatique profond (a) et/ou de zones partiellement fondues (b) qui permettent le transfert rapide de matériel fondu à la surface. Les 2 scénarios peuvent entraîner une stratification de la composition chimique et la formation d'une proto-croûte riche en SiO2. Les collisions répétées permettent une érosion de la proto-croûte enrichie en éléments incompatibles et d'une partie du manteau (c). Parmi la fraction de matériel volatilisée par impacts, la re-condensation des éléments réfractaires (d) est favorisée par rapport aux éléments volatils (D'après Boujibar et al. (2015)).

## 7.2 Fusion et formation d'une croûte sur un planétésimal

Les météorites sont les seules rescapées de l'histoire chaotique du Système Solaire et nous renseignent sur sa composition et son évolution. Des planétésimaux les plus anciens, seuls les noyaux métalliques formant leur centre nous sont parvenus sous la forme des météorites de fer. Il est beaucoup plus rare de trouver des échantillons provenant de leur surface. Ainsi, nous disposons de peu d'informations concernant la nature des planétésimaux qui ont formé les planètes actuelles. L'étude de la météorite NWA 8486, trouvée dans le désert du Sahara en 2014, met en évidence la composition d'un planétésimal formé durant les deux premiers millions d'années de l'histoire du Système Solaire. Ainsi, ce planétésimal présenterait à sa surface une croûte anorthositique, similaire à la croûte lunaire. La météorite Northwest Africa (NWA) 8486 représente donc un échantillon unique.

L'étude des minéraux de cette roche unique dans le cadre de la thèse de Paul Frossard a permis de préciser l'histoire du planétésimal sur lequel elle s'est formée (Frossard et al., 2019). Chose surprenante, les minéraux qui la composent ont de très fortes teneurs en europium et strontium. Ces deux éléments sont généralement concentrés dans des roches très particulières
<figure><img src="image_312.png" /></figure>

FIGURE 28 – Temps d'ascension des cristaux de plagioclase durant la phase tardive d'un océan magmatique. Ce temps est calculé pour une gamme de viscosités (0.1 à 10 Pa.s), de diamètres de cristaux (de 100 µm à 1 cm) et pour un contraste de densité $\Delta\rho = 50 \text{ kg/m}^3$ entre le cristal et la phase liquide. Le temps nécessaire à un cristal pour atteindre la surface de l'océan magmatique est représenté par une échelle de couleurs allant de 10 kyr (bleu) à 2 Myr (rouge). Cette figure montre que le temps de remontée du cristal est de quelques dizaines de milliers d'années dans les conditions de l'océan magmatique, sauf pour les petits cristaux d'environ 100 µm et les viscosités élevées de >10 Pa.s pour lesquels le temps de remontée est plus long (D'après Frossard et al. (2019)).

appelées anorthosites. Les anorthosites composent la majorité de la surface de la Lune. Depuis le retour des premiers échantillons lunaires associés aux missions Apollo, leur contexte de formation a été compris. Les anorthosites se seraient formées pendant le refroidissement de l'océan magmatique lunaire. La faible densité de ce minéral leur permet de flotter pour former une croûte en surface. Les échelles de temps nécessaire à la flottaison de ces minéraux sont essentiellement fonction de la viscosité du magma et de la taille des minéraux (Figure 28). Il est possible de produire les teneurs en europium et strontium dans cette météorite avec la fusion d'anorthosites lors d'un impact. Grâce à la forte production de chaleur par radioactivité dans les premiers millions d'années du Système Solaire, une grande partie des planétésimaux ont été partiellement fondus produisant un stade d'océan magmatique. Cette découverte montre que
les océans magmatiques sur les planétésimaux du Système Solaire interne ont pu former des roches similaires à celles présentes sur la Lune. La présence de telles croûtes sur des planétésimaux a pu influencer de manière significative la composition des planètes. Cette découverte a fait l'objet d'un article publié dans Geochemical Perspectives Letters (Frossard et al., 2019).

## 7.3 Fin de solidification et mise en place de la tectonique des plaques

Nous avons montré précédemment que les dernières étapes de solidification du manteau primitif se déroulaient au sein de fines couches plus ou moins profondes (voir section 6.2.2). La présence d'une couche fondue à faible profondeur pendant l'Hadéen et sa cristallisation finale autour de la limite Hadéen-Éoarchéen pourraient empêcher l'apparition de formations orogéniques élevées en raison de la compensation isostatique rapide de tout relief créé et du développement de failles tectoniques à grande échelle et zones de cisaillement (Monteux et al., 2020). L'absence de reliefs favoriserait à son tour une Terre où la majeure partie de sa surface serait recouverte d'eau peu profonde. Les failles majeures et les zones de cisaillement pourraient représenter des voies pour que l'eau liquide pénètre jusqu'aux niveaux inférieurs de la croûte provoquant ainsi une activité hydrothermale intense. En outre, cette couche très déformable à la profondeur de la croûte inférieure pourrait éventuellement isoler la croûte du manteau sous-jacent. Doglioni et al. (2011) ont proposé qu'une couche de fusion partielle stable entre l'asthénosphère et la lithosphère pourrait induire un découplage visqueux efficace entre les deux couches et expliquer la durée de vie des racines cratoniques. A l'Hadéen-Eoarchéen, le couplage visqueux entre le manteau et la croûte pourrait avoir induit le début du remaniement à grande échelle de la croûte hadéenne et la formation de blocs crustaux archéens stables. La persistance d'une couche partiellement fondue pourrait donc expliquer l'absence de fragments de croûte de l'Hadéen dans les archives géologiques et au début des archives géologiques de l'Archéen. Par conséquent, l'établissement d'un lien entre la chronologie des principaux événements de différenciation dans les archives géologiques et la cristallisation des dernières couches partiellement fondues pourrait aider à comprendre certains processus superficiels précoces.

Le passage de l'archéen au protérozoïque a mis fin à une période de grande instabilité à la surface de la Terre. Cette transition pourrait être liée à un changement de dynamique de l'intérieur de la Terre. Des expériences menées au LMV ont montré que le solidus du manteau supérieur était à une température plus basse que prévue pour une composition chondritique (Andrault et al., 2018). Selon cette étude, un tel solidus associé à un manteau plus chaud permettrait la présence d'une couche fondue profonde et persistante dans le manteau archéen. La solidification progressive de cette couche fondue aurait pu renforcer le couplage mécanique entre la lithosphère et l'asthénosphère. Un tel changement pourrait expliquer la transition d'une dynamique de surface dominée par un couvercle stagnant à une tectonique des plaques moderne avec des subductions profondes. L'intersection entre le solidus du manteau et un profil de température adiabatique avec une température potentielle correspondant à une fraction de $\phi_c \sim 40\%$ pourrait contraindre la profondeur du fond de la couche partiellement
fondue restante. Dans le cas de la solidification d'un manteau partiellement fondu depuis la frontière manteau-noyau vers la surface, la profondeur de la dernière couche partiellement fondue restante devrait donc être inférieure à 300 km comme proposé par Solomatov (2007). La cristallisation complète du manteau devrait se produire moins d'~1 Ga (Sleep et al., 2014) après la formation de l'océan magmatique lié à l'impact à l'origine du système Terre-Lune.

## 7.4 Origine des larges provinces volcaniques archéennes

Par le passé, des événements volcaniques majeurs ont induit des extinctions massives de la vie, la dislocation de continents et de grands soulèvements régionaux. Leur formation reste énigmatique car elle nécessite la fusion du manteau à des taux élevés et à grande profondeur. Pour sonder les propriétés du manteau partiellement fondu, des chercheurs ont réalisé des expériences à l'aide d'une presse à multi-enclumes couplée à des méthodes avancées de mesures in situ. Ils mettent en évidence l'importance d'une grande quantité de chaleur concentrée dans les profondeurs du manteau après la solidification d'un océan magmatique global. L'ascension de panaches mantelliques de régions profondes induit des anomalies thermiques de plusieurs centaines de degrés et la fusion du manteau dans les premiers 1000 km de profondeur. Ce mécanisme explique non seulement la composition chimique des laves anciennes, mais aussi l'évolution du volcanisme de point chaud au cours de l'histoire de la Terre. La composition des laves anciennes suggère la fusion du manteau à des profondeurs d'au moins 600-700 km et des taux de fusion entre 10 et 50%. Mais les conditions précises pour produire les différentes laves, par exemple les komatiites, restent mal contraintes. L'interprétation des compositions est d'autant plus difficile que les laves sont plus anciennes. Des études antérieures mettent en exergue la complexité des mécanismes de fusion à cause de la présence probable d'eau et de CO₂, et aussi à cause de l'évolution thermochimique des magmas lors de leur remonté vers la surface.

Dans le cadre de la thèse de Remy Pierru, nous avons fait une étude détaillée des conditions de pression et température nécessaires à la production des laves anciennes par la fusion du manteau de composition pyrolitique (Pierru et al., 2022). Grace à des méthodes originales de détection in situ de la fusion, nous avons pu synthétiser des échantillons avec des taux de fusion variés, pour une grande gamme de profondeurs dans le manteau, et de façon reproducible. Il apparaît que la nature des laves anciennes trouvées en surface est compatible avec la longue persistance d'un fort gradient de température dans le manteau profond. Ce type de gradient dit super-adiabatique est attendu après la solidification d'un océan magmatique profond. Avec l'établissement progressif des grands mouvements de convection dans le manteau qui caractérise la dynamique moderne de la Terre interne, de gros panaches mantelliques remontent vers la surface (Figure 29). Leur température élevée induit leur fusion progressive à de grandes profondeurs. Sur la base d'une modélisation géodynamique, nous montrons l'aplatissement progressif du profil super-adiabatique avec le refroidissement séculaire de la Terre. Cet effet est compatible avec la disparition progressive des laves anciennes générées à plus grandes profondeurs, sans pour autant empêcher les remontés de panaches profonds issus de
<figure><img src="image_313.png" /></figure>

FIGURE 29 – Diagramme de fusion du manteau : La chaleur accumulée dans le manteau profond après les épisodes d'océan magmatique induit la persistance d'un fort gradient de température. Dans ce cadre, un panache mantellique ascendant (ligne noire) est plusieurs centaines de degrés plus chaud que le manteau environnant. Ce type de panache fond partiellement lorsque sa température s'établie entre le solidus (bleu) et le liquidus (rouge) du manteau. Cela génère des magmas de compositions Komatiites, picrites et basaltes à plus de 700 km de profondeur et pour des taux de fusion atteignant jusqu'à 50%. À partir de Pierru et al. (2022).

la frontière noyau-manteau à l'origine de certaines îles océaniques.

Références personnelles

Boujibar, A., Andrault, D., Bolfan-Casanova, N., Bouhifd, M.A., **Monteux, J.**, 2015, Cosmochemical fractionation by collisional erosion during the Earth's accretion, *Nature Communications*, **6**:8295. **LIEN HAL**

Andrault D., Bolfan-Casanova N., Bouhifd A., Boujibar A., Garbarino G., Manthilake G., Mezouar M., **Monteux, J.**, Parisiades P., Pesce G., 2017, Toward a coherent model for the melting behavior of the deep Earth's mantle, *Physics of the Earth and Planetary Interiors* vol.265, p.67-81. **LIEN HAL**

Andrault D., Pesce G., Manthilake G., Monteux, J., Bolfan-Casanova N., Chantel J.,
Novella D., Guignot N., King A., Itié J.P., Hennet L., 2018, Deep and persistent melt layer in the Archaean mantle, Nature Geoscience. LIEN HAL

Frossard P., Boyet M., Bouvier A., Hammouda T., **Monteux, J.**, 2019, Evidence for anorthositic crust formed on an inner solar system planetesimal, Geochemical Perspectives Letters vol.11, p.28-32. LIEN HAL

Pierru R., Andrault D., Manthilake G., **Monteux, J.**, Devidal J.L., Guignot N., King A., Henry L. 2022, Deep mantle origin of large igneous provinces and komatiites, Sci. Adv. 8, eabo1036. LIEN HAL
ARTICLE

Received 13 Jun 2015 | Accepted 7 Aug 2015 | Published 23 Sep 2015

DOI: 10.1038/ncomms9295

OPEN

# Cosmochemical fractionation by collisional erosion during the Earth's accretion

Asmaa Boujibar<fnref n="1" />,†, Denis Andrault<fnref n="1" />, Nathalie Bolfan-Casanova<fnref n="1" />, Mohamed Ali Bouhifd<fnref n="1" /> & Julien Monteux<fnref n="1" />

Early in the Solar System's history, energetic collisions of differentiated bodies affected the final composition of the terrestrial planets through partial destruction. Enstatite chondrites (EC) are the best candidates to represent the primordial terrestrial precursors as they present the most similar isotopic compositions to Earth. Here we report that collisional erosion of >15% of the early Earth's mass can reconcile the remaining compositional differences between EC and the Earth. We base our demonstration on experimental melting of an EC composition at pressures between 1 bar and 25 GPa. At low pressures, the first silicate melts are highly enriched in incompatible elements Si, Al and Na, and depleted in Mg. Loss of proto-crusts through impacts raises the Earth's Mg/Si ratio to its present value. To match all major element compositions, our model implies preferential loss of volatile lithophile elements and re-condensation of refractory lithophile elements after the impacts.

<footnote n="1">¹Laboratoire Magmas et Volcans, Université Blaise Pascal, CNRS UMR-6524, 5 rue Kessler, 63000 Clermont-Ferrand, France. †Present address: Astromaterials Research and Exploration Science, NASA Johnson Space Center, 2101 NASA Parkway, Houston, Texas 77058, USA. Correspondence and requests for materials should be addressed to A.B. (email: asmaa.boujibar@nasa.gov).</footnote>
Large-scale melting occurred broadly in the first stages of planetary accretion¹. The impressive homogeneity of stable isotopic compositions of large bodies suggests extensive melting and formation of magma oceans¹. However, while large-scale melting can efficiently erase isotopic heterogeneities, low degrees of partial melting are a primary cause of chemical segregation. The possibility to form proto-crusts by low degrees of melting of chondritic material is evidenced by the discovery of felsic achondrites (GRA-06128/9; ref. 2). Early differentiation of planetary embryos was also recently suggested by a study that determined the initial content of the short-lived radionuclide ²⁶Al in angrites³. Therefore, early crusts could form by different processes, such as fractional crystallization of a magma ocean or the migration of silicate melts over networks of veins and dikes⁴. Despite the formation mechanism of these proto-crusts, their occurrence on accreting bodies should have played a major role in the final planetary composition, because energetic episodes of accretion have eroded the planetary surfaces⁵⁻⁸.

The chemical composition of the building blocks that accreted to form the Earth remains controversial. Our planet shows remarkable isotopic similarities with enstatite chondrites (EC), especially with those of the EH type⁹, for the elements whose isotopes do not fractionate during core segregation (O, Ca, N, Mo, Ru, Os, Cr, Ni, Ti and Sr). However, EC and the Earth present important chemical differences. First, EC are so reduced that their silicate phases are free of FeO, which differs from the present-day silicate mantle with 8 wt% FeO. This issue may eventually be solved by internal oxidation processes for some of the Fe metal⁹,¹⁰. A second issue is that EC show a Mg/Si weight ratio lower than 1 (~0.63; ref. 11), differing substantially from that of the Earth's upper mantle (~1.1; ref. 12). The Mg/Si ratio of bulk Earth (BE) could be slightly overestimated if the lowermost mantle is bridgmanitic (that is, perovskitic) rather than pyrolitic¹³. Furthermore, the Earth shows higher abundances of refractory lithophile elements (RLE) and lower concentrations of moderately volatile elements (as the alkali elements Li, Na, K and Rb) compared with EC and all other chondrites (Fig. 1).

In this study, we test whether collisional erosion of early crusts can explain the chemical divergence between the BE and EC. Based on experiments on the melting properties of synthetic EC at pressures between 1 bar and 25 GPa, we show that early

differentiated planetary bodies can develop silica- and alkali-enriched crusts. Loss of these crusts through impact erosion can ultimately increase the Mg/Si ratio of the planetary bodies to match the current Earth ratio. In addition, to further increase the budget in RLE and accurately reproduce the terrestrial concentrations of the major and minor elements, impact erosion must be accompanied with preferential loss of volatile lithophile elements and re-condensation of RLE.

## Results

**Partial melting of enstatite chondrites.** We experimentally investigated the composition of melts produced by low degrees of melting of synthetic EC powders, at low oxygen fugacity (3.6 to 1.8 log units below the iron/wustite buffer), at different pressure conditions expected for melt segregation in partially molten planetary embryos (see Methods section and Supplementary Fig. 1). Our pseudo-eutectic melts are all characterized by high concentrations of SiO₂, Al₂O₃ and Na₂O, and low MgO contents (Fig. 2). The change with pressure of the low-degree melt composition agrees with that previously reported at 1 bar (ref. 14). The most striking features are the increase of MgO (Fig. 2b) and decrease of SiO₂ (Fig. 2a) and Al₂O₃ (Fig. 2c) with pressure. The disappearance of clinopyroxene at 16 GPa and garnet at 24 GPa

<figure><img src="image_314.png" /></figure>

**Figure 2 | Chemical composition of pseudo-eutectic melts synthesized at high pressures.** We report the compositions of melts generated by partial melting of an EC-like mantle at pressures between 5 and 25 GPa (yellow squares). Our data set plots are in agreement with previous results performed at 1 bar (ref. 14) (dark circles). Whereas MgO content (a) increases with pressure in the silicate melts, the concentrations of SiO₂ (b) and Al₂O₃ (c) decrease. Sharp changes of the liquid compositions occur when the sample encounters phase transformations (shown with the grey arrows), in particular, with the disappearance of clinopyroxene (Cpx) at 15 GPa (vertical lines in d and f) and simultaneous disappearance of majorite (Maj) and appearance of bridgmanite (Bg, the MgSiO₃ perovskite; vertical grey areas in d–f) at 24 GPa.

<figure><img src="image_315.png" /></figure>

**Figure 1 | Major chemical differences between the chondrites and the bulk silicate Earth (BSE).** The abundances are normalized to Si and Cl chondrites¹¹,¹². From left to right, the lithophile elements are reported with decreasing their 50% condensation temperature. The depletion of volatile elements in the BSE results from the erosion of crusts enriched with incompatible elements and the subsequent loss of the most volatile elements.
(ref. 15) induces major CaO (Fig. 2d), Na₂O (Fig. 2e) and K₂O (Fig. 2f) enrichment of the liquid, respectively. Altogether, pseudo-eutectic liquids show compositions between rhyolitic and trachy-andesitic in the range of pressures investigated. In partially molten planetesimals, such melts should ascend relatively easily towards the planetary surface due to their low melt densities, even for low degrees of partial melting⁴. As the melts can re-equilibrate during their ascent to the surface, those produced at shallower depths are more likely to stay unaltered and produce proto-crusts enriched in incompatible elements. The most appropriate melts for the formation of proto-crusts should then be those produced at relatively low pressures and degrees of partial melting.

**Change of proto-Earth composition with collisional erosion.**

We now evaluate how collisional erosion of proto-crusts made of these pseudo-eutectic liquids would affect the chemical composition of an EH-type planetary embryo¹¹. First, we calculate the Mg/Si ratio of a planetary body after removal of pseudo-eutectic melts generated at average pressures of 1 bar to 25 GPa and compare it with the BE¹², with the hypothesis that ~7 wt% Si is present in the Earth's core⁹,¹⁶. By increasing the amount of crustal erosion, the Mg/Si ratio of the depleted EH planetoid increases towards the present-day BE ratio of ~0.9, owing to the high SiO₂ content of the melts (Fig. 3a). The lower the pressure of melt-solid equilibration, the higher the SiO₂ content in the melt, and therefore the crustal erosion should be the less extensive. The BE Mg/Si ratio can be achieved by accretion of EH chondrites and erosion of a crust of 15–18% of the planetary mass for solid-melt equilibrium at pressures below 10 GPa. This amount of crustal erosion is comparable to the loss of highly incompatible elements required to explain the mantle budget in volatile elements¹⁷, and is comparable to the amount of mass lost during hit and run simulations¹⁸. As the formation of such SiO₂-rich crust necessitates a low degree of partial melting

(at a level of 5–7%), removing proto-crust to a level of 15–18 wt% of the planetary mass requires repeated processes of proto-crust formation and collisional erosion. Repeated partial melting of the EH-type mantle would constantly produce an SiO₂-rich proto-crust, owing to the fixed pseudo-eutectic composition. The nature of planetary accretion itself provides the necessary energy to melt planetesimals and erode them or even disrupt them (see below). Simulations indicate that an accreting proto-planet should experience ~10⁵ collisions¹⁸.

Removal of proto-crust also affects the Al/Si, Ca/Si and Na/Si ratios (Fig. 3b and Supplementary Fig. 2). Interestingly, the misfits between Mg/Si, Al/Si, Ca/Si and Na/Si ratios in BE and in our model of EH-type planetoid depleted by crustal erosion show a clear correlation with the condensation temperatures of the elements of interest¹⁹ (Fig. 3b). Rather than being fortuitous, this trend can be understood in terms of differential re-condensation of the elements after collisional erosion. Our model implies that early differentiation of a planetary embryo forms a silica-rich crust (Fig. 4a,b) that is subsequently eroded and vaporized by energetic impacts (Fig. 4c). The eroded material is then chemically fractionated with a preferential condensation of the refractory elements relative to the volatiles (Fig. 4d). This explains the previously reported marked consequences on

**Figure 3 | Change by collisional erosion of the proto-planetary chemical composition.** (a) Change by collisional erosion of the planetary Mg/Si ratio by removal of a differentiated crust with a composition equivalent to that of pseudo-eutectic melts produced at pressures of 1 bar and 5, 10, 15, 20 and 25 GPa. Removal by collisional erosion from the model EH composition results in an increase of the Mg/Si ratio of the planetesimal. The grey area represents the Mg/Si ratio of the BE with 7 wt% Si dissolved into the core⁹,¹⁶. Erosion of a crust of >15% of the planet mass is required to reconcile the Mg/Si ratio of an EH-type planet with the present-day BE¹². (b) Correlation between residual misfits between BE and the EH proto-planet X/Si for X=Na, Ca and Al as a function of the 50% condensation temperature of the elements¹⁹. After the mass of eroded crust is adjusted to meet the Mg/Si ratios of BSE, there is a residual misfit for the abundances of other major elements (Supplementary Fig. 2). The correlation between BE enrichments and the condensation temperatures of the different elements suggests chemical fractionation during the processes of vaporization of the planetary surface, with re-condensation of the eroded material on the planetary surface (Fig. 4). (c) Degree of chemical fractionation required by our model, for different amounts of collisional erosion. Here we consider that the 15% of the crust (produced in the 0–5–GPa range) required to match the Mg/Si ratio of the BE and 16–40% of the planetary mantle are eroded by the impacts. For a total erosion of 31–45% of the planetary mass, for example, the actual Na/Si, Mg/Si, Ca/Si and Al/Si ratios of BE are reproduced when 100% of Al and Ca, 10% of Mg and 5% of Si are re-condensed on the planetary surface, which is in agreement with their condensation temperature. A negative value for Na denotes the fact that the residual mantle of our EH-type model (after collisional erosion) would still contain high Na contents compared with BE. In this case, additional Na volatilization from the residual mantle is required.

<figure><img src="image_316.png" /></figure>
<figure><img src="image_317.png" /><figcaption>**Figure 4** | Schematic model of chemical fractionation by collisional erosion. (a,b) Early heating leads to the rapid segregation of Fe-rich metal into the core. It is accompanied with the formation of a deep magma ocean¹ (a) and/or small-scale partial melting and formation of complex networks of veins and dikes⁴ (b) which allows fast transfer of melts to the surface⁴. Both can yield compositional stratification of the mantle and the formation of an SiO₂-rich proto-crust. (c) The repeated collisions induce erosion of the proto-crust enriched in incompatible elements, as well as part of the planetary mantle. (d) Within the fraction of material volatilized by meteoritic impacts, re-condensation of refractory elements is favoured compared with the volatile elements.</figcaption></figure>

the thermal history of Earth that could result from the loss of incompatible and refractory heat-producing elements, such as U and Th⁵,²⁰,²¹.

In fact, the Earth's budget in RLE can be reached by a number of different erosion and re-condensation models. The lowest amount of erosion (15–18 wt% of proto-crust to meet the right Mg/Si ratio) requires re-condensation of 100% of the refractory elements (Ca and Al) on the planetary surface (Fig. 3c). For higher amounts of planetary surface erosion (15–18 wt% proto-crust plus a mantle fraction), the models require less chemical fractionation during vaporization or re-condensation. For 40% mantle erosion, re-condensation of 84% of Al, 73% of Ca, 10% of Mg and 5% of Si is necessary (Fig. 3c and Table 1) to produce a planetary composition similar to Earth. Comparable fractionation of major elements with Ca- and Al-rich condensates depleted in Mg and Si was reported in the most primitive unequilibrated Semarkona ordinary chondrites (LL3.0; ref. 22). Also, such a degree of chemical fractionation during re-condensation may not be necessary if the composition of the parent body deviates from the EH chondrites (see below). Then, non-equilibrium processes, such as solar wind, could have favoured the loss of volatile elements from the gravitational field of the proto-planet. In addition, the volatile elements could have been partially atmophile due to hot planetary surfaces, which could have contributed to the volatile and refractory fractionation.

**The major sources of energy provided by planetary accretion.**

During planetesimal growth, the thermal state of a proto-planet depends on its initial heating caused by the decay of short-lived radionuclides such as ²⁶Al and ⁶⁰Fe (ref. 23), on its accretionary history and on how potential energy is dissipated during the iron/silicates segregation. Temperatures in excess of 2,000 K could have been reached within the first 2–3 million years after the formation of the first solids of the Solar System (calcium–aluminium-rich inclusions, CAI)²⁴. The early radioactive heating can therefore cause both segregation of a metal-rich core and silicate melting on planetary embryos that have quickly accreted (to attain a radius of 30 km within the first 3 million years; see Fig. 2 in Yoshino et al.²⁴). Kleine et al.²⁵ showed that high temperatures of early asteroids are in agreement with the young ages of iron meteorites, OC, CO and CR chondrites and the peak temperatures recorded by the same meteorites (see in ref. 25).

In addition to this radioactive heating, in the shallow parts of the impacted planet, impact heating (ΔT), superimposed to a sufficiently hot proto-planetary interior (with an initial

<figure><img src="image_318.png" /><figcaption>**Figure 5** | Shallow post-impact temperature as a function of the target radius R. Different pre-impact temperatures are illustrated (from T₀ = 500 to 2,000 K). We consider that (i) surface gravity is equal to g = 4/3 π G ρ R (G is the gravitational constant and ρ is the density of the target), (ii) kinetic energy of the impactor is controlled by the escape velocity of the impacted body (that is, v impacted = √(2gR)), (iii) the impactor and impacted body have the same densities, and (iv) only 30% of the incoming kinetic energy is converted into heat.</figcaption></figure>

temperature of T₀) can lead to temperatures (T = T₀ + ΔT) much larger than the vaporization temperature of silicates (~1,300 °C at 0.001 bar; see Fig. 5 above). This heating is localized in a spherical region called the isobaric core, just beneath the impact site (for example, ref. 26). By making the conservative assumptions that (i) kinetic energy of the impactor is controlled by the escape velocity of the impacted body, (ii) impactor and target body have the same densities and (iii) only 30% of the incoming kinetic energy is converted into heat, a simple energy balance indicates that ΔT (K) = 4.7 × 10⁻⁵ × R² (km) (refs 26,27).

Assuming that the impact occurs with the escape velocity of the impacted body is a conservative assumption in the sense that it is the minimum impact velocity; larger impact velocities can substantially increase the post-impact temperature below the surface. For instance, some episodes of hypervelocity impacts have probably played a major role during the accretion of the terrestrial planets. For example, a recent model suggests that Jupiter and Saturn have likely migrated inwards and then outwards early in the Solar System history²⁸, leading to strong resonance and high eccentricities of the planetesimals. As the resonance with Jupiter can significantly increase the impact
<table><caption>Table 1 | Resulting compositions with dual processes of collisional erosion and fractional re-condensation.</caption><thead><tr><th rowspan="2">Bulk Earth</th><th rowspan="2">Assumed core composition<sup>44</sup></th><th colspan="3">EH-like planet</th><th colspan="3">EH-like planet with adjusted core size</th></tr><tr><th>0% eroded mantle</th><th>25% eroded mantle</th><th>40% eroded mantle</th><th>0% eroded mantle</th><th>25% eroded mantle</th><th>40% eroded mantle</th></tr></thead><tbody><tr><td>Mg</td><td>15.6</td><td>13.8</td><td>12.8</td><td>10.8</td><td>15.9</td><td>15.8</td><td>15.6</td></tr><tr><td>Al</td><td>1.6</td><td>1.0</td><td>1.1</td><td>1.1</td><td>1.2</td><td>1.4</td><td>1.6</td></tr><tr><td>Si</td><td>16.6</td><td>15.0</td><td>13.7</td><td>11.5</td><td>17.2</td><td>16.9</td><td>16.6</td></tr><tr><td>Ca</td><td>1.7</td><td>1.1</td><td>1.2</td><td>1.2</td><td>1.3</td><td>1.5</td><td>1.7</td></tr><tr><td>Na</td><td>0.2</td><td>0.2</td><td>0.2</td><td>0.1</td><td>0.2</td><td>0.2</td><td>0.2</td></tr><tr><td>K</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>O</td><td>30.5</td><td>27.9</td><td>25.8</td><td>21.9</td><td>30.5</td><td>30.5</td><td>30.5</td></tr><tr><td>Fe</td><td>31.4</td><td>38.0</td><td>41.9</td><td>49.6</td><td>31.4</td><td>31.4</td><td>31.4</td></tr><tr><td>Co</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.1</td><td>0.1</td></tr><tr><td>Ni</td><td>1.6</td><td>2.3</td><td>2.5</td><td>3.0</td><td>1.6</td><td>1.6</td><td>1.6</td></tr><tr><td>S</td><td>0.6</td><td>0.6</td><td>0.6</td><td>0.7</td><td>0.6</td><td>0.6</td><td>0.6</td></tr></tbody></table>

We compare the actual bulk Earth composition (first column) (calculated based on bulk silicate Earth¹² composition and cosmochemical estimates of core composition⁴⁴ (second column)) with the EH-like Earth (third column) after erosion of (i) 15% of a crust composed of pseudo-eutectic melts produced at 0-5 GPa and (ii) 0-40% of its mantle. The erosion yields a significant depletion in the lithophile elements (Mg, Si, O, Na, Al and Ca) compared with the siderophile elements (Fe, Ni, Co and S). By adjusting the core size to the actual terrestrial core size (by fixing the concentrations of the siderophile elements to that of the Bulk Earth), the composition of our EH-like planetary model can reach values very close to that observed in the present-day Earth.

velocities²⁹, the kinetic energy, available during the impact processes on growing bodies, may have enhanced the vaporization and the excavation of their shallow material. This model, with marked migration of Jupiter and Saturn, is one suggested model of the dynamical evolution of the Solar System. Other models may not produce such high velocity collisions, but they would have a longer period during which frequent collisions could occur.

Vaporization following collisional erosion from large impacts is widely accepted³⁰. The abundance of impacts is supported by observations of the iron meteorites, which represent fragments of cores of differentiated bodies, which are now destroyed. These iron meteorite parent bodies are as old as the CAI, which are the oldest objects of the Solar System, that formed during the first million year after $T_0$ (ref. 31). Thus, collisional stripping operated in the very early stages of the formation of the Solar System.

## Discussion

Our experimental results show that surface erosion modifies more efficiently the planetary composition of smaller planetary bodies owing to lower internal pressures (Fig. 3a). This suggests a more efficient chemical fractionation early in the accretion history. As a matter of fact, silica- and alkali-rich compositions (andesitic to rhyolitic and trachyitic) have been observed in various asteroidal materials: bulk achondrites (GRA-06128/09), silicate enclaves in iron meteorites, glass inclusions or igneous clasts in aubrites, glass inclusions in the howardite, eucrite and diogenite meteorites, clasts in the ureilites. The oldest sampled materials of the Solar System with a granitic composition are only 5–30 Myr younger than the formation of the Solar System (see ref. 32 for a review). This indicates the formation of silicic crust nuclei very early in the inner Solar System.

A widespread Si isotopic dichotomy is observed between planetary/asteroidal bodies and the chondrites. There is a correlation between the enrichment in heavy Si (³⁰Si) with both (i) the depletion of the moderately volatile elements (K) and (ii) the depletion of Si relative to Mg for the Earth, the Moon, Vesta, Mars, the angrites (basaltic meteorites) parent body and the chondrites³³. As suggested by Pringle et al.³³, this correlation could be caused by early impact-induced evaporative loss, occurring as early as the formation of angrites, 2 Myr later than the formation of the oldest currently known objects of the Solar

System³⁴,³⁵ (Supplementary Note 1). Thus, the Si isotopic measurements fully support our model of early collisional erosion. It has also been proposed that energetic episodes of impacts can induce significant chemical fractionation of RLE in EL chondrites³⁶.

In contrast to the other planetary differentiation processes, such as core segregation or magma ocean crystallization, an early impact erosion affects the composition of both planetary bodies and the remaining unaccreted material, in a complementary way. Owing to a higher surface/volume ratio compared with the planetesimals, the chondritic material that was left over from the accretion may have preferentially reacted with gases produced by vaporization of the eroded crusts, which are enriched in SiO₂ and volatile lithophile elements. This can explain the enrichments in Na, S and Si observed at the edges of chondrules contained in carbonaceous and ordinary chondrites³⁷⁻³⁹. EC are the most alkali- and silica-rich chondrites¹¹,⁴⁰ (Fig. 1), but in contrast to the carbonaceous chondrites, this enrichment is global and not limited to chondrules (Supplementary Note 2). This is likely owing to the fact that EC have experienced important thermal metamorphism that usually erases the chemical gradients. Several studies have analysed the behaviour of alkali elements in chondrules in order to retrieve the conditions under which the chondrules form. The majority of these studies concluded that very high dust densities with high solid/gas ratios are required in the nebula to enrich the edges of chondrules in Na³⁷. This was previously attributed to aqueous alteration⁴¹. In light of our results, we propose that the destruction and vaporization of eroded proto-crusts can also contribute to this elevation of the dust/gas ratio of the nebula in the formation regions of chondrules.

The EH meteorites that are sampled today could have suffered an SiO₂ enrichment compared with their parent bodies, owing to interaction with crusts eroded from primordial planetesimals. This would have drifted their composition away from that of the Earth, compared with the original building blocks (Fig. 1). This common original material could have had a higher Mg/Si ratio and lower content in alkali elements than the EH chondrites. Consequently, our quantitative model of collisional erosion developed in this study (for example, Fig. 3) can be considered as the most extreme one, as less proto-crust erosion would be required to meet the actual BE chemical composition. Altogether, we show that collisional erosion could readily explain the major chemical divergences between the EH chondrites and Earth. It reinforces the model of the EH-like Earth⁹, nevertheless adding to
this model the idea that the common starting material could have been slightly depleted in SiO₂ and volatile lithophile elements in comparison with the EH chondrites.

**Methods**

**Preparation of starting materials.** The starting material was composed of 68 wt% silicate and 32 wt% metal with a chemical composition equivalent to the average composition of EC⁹ (Supplementary Table 1). While we are exclusively interested in the silicate properties, the presence of metals helps reproduce the EH-Earth conditions more precisely and buffer the oxygen fugacity. The silicate fraction was composed of ultra-pure oxides and carbonates (SiO₂, MgO, Al₂O₃, TiO₂, Cr₂O₃, MnO, Na₂CO₃, CaCO₃ and K₂CO₃) that were finely ground together, decarbonized and then dried overnight at 1,000 °C. The metal powders were composed of a fine mixture of ultra-pure Fe, Ni, Si, Mn, Co and/or FeS. All samples were S free, except for 5 wt% S in the metal of sample no. 104. Silicate and metal fractions were intimately mixed to obtain a homogeneous chondritic powder, that was kept constantly in a vacuum oven to avoid hydration.

**Details of the experimental conditions.** We conducted experiments at 5, 10, 20 and 25 GPa, with temperatures ranging from 1,380 to 1,900 °C using Kawai-type 1,000-t and 1,500-t multi-anvil presses. We heated the experiments to temperatures at or slightly above the solidus, that is, between 1,380 and 1,900 °C, for oxygen fugacities between -2.1 and -3.6 log units below the IW buffer (Supplementary Table 2). Assemblies were composed of Cr-doped MgO octahedra pressure media with edges of 18, 14 and 10 mm, coupled with tungsten carbide cubes with 11, 6 and 4 mm truncations, respectively. Pressure calibrations of both 1,000-t and 1,500-t presses were previously described⁴². The sample powder was loaded into a graphite capsule that was surrounded by MgO sleeves to prevent the sample pollution. High temperatures were achieved using an LaCrO₃ furnace and a ZrO₂ sleeve thermal insulator. Temperature was measured using a W₅Re/W₂₆Re thermocouple in experiment nos. 1,223 and 174, and estimated using the relation between temperature and electrical power for experiment nos. 1,216 and 104. Pressure and temperature uncertainties are estimated to be ~0.5 GPa and 100 °C, respectively.

To achieve homogeneous samples without relict of the starting powders, we first heated the samples above the liquidus temperature⁴³ for a couple of minutes. Temperature was then rapidly reduced (with a rate of 100 K in <20 s) to a temperature just above the reported solidus. The sample was then equilibrated between 30 min and 3 h. This procedure helps grain growth and allows segregation of relatively large pools of melt, which are usually difficult to collect with low degrees of partial melting⁴³.

**Chemical compositions of the coexisting phases.** The microstructure of recovered samples was observed using a scanning electron microscope (Supplementary Fig. 1). Phase relations and chemical compositions were determined using a CAMECA SX100 electron probe micro-analyser (Supplementary Table 1). We used an accelerating voltage of 15 kV, an electron beam defocused to 2–20 µm and a current of 15 nA, except for the chemical analyses of bridgmanites that were analysed with 2 nA. As standards, we used pure metals and silicates.

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## Acknowledgements

We thank B. Bourdon, M. Boyet, S. Charnoz, M. Javoy, E. Kaminski, R. Mishra, S. Keshav, D. Laporte, G. Libourel, H. Martin, Y. Marrocchi, M. Toplis, K. Righter and M. Zolensky for their fruitful discussions and various members of the Laboratoire Magmas et Volcans staff for essential help. This project received funds from INSU-CNRS, Université Blaise Pascal, Région Auvergne and the ANR 'Oxydeep' project. It is a LabEx Clervolc 170 contribution.

## Author contributions

A.B. conceived the study, conducted the experiments and acquired the data. A.B., D.A., N.B.-C. and J.M. modelled, interpreted and discussed the results. The manuscript was prepared by A.B., D.A., N.B.-C., M.A.B. and J.M.

## Additional information

**Supplementary Information** accompanies this paper at http://www.nature.com/naturecommunications

**Competing financial interests:** The authors declare no competing financial interests.

**Reprints and permission** information is available online at http://npg.nature.com/reprintsandpermissions/

**How to cite this article:** Boujibar, A. et al. Cosmochemical fractionation by collisional erosion during the Earth's accretion. *Nat. Commun.* 6:8295 doi: 10.1038/ncomms9295 (2015).

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Invited Review

# Toward a coherent model for the melting behavior of the deep Earth's mantle

<figure><img src="image_322.png" /></figure>

CrossMark

D. Andrault<sup>a,*</sup>, N. Bolfan-Casanova<sup>a</sup>, M.A. Bouhifd<sup>a</sup>, A. Boujibar<sup>a</sup>, G. Garbarino<sup>b</sup>, G. Manthilake<sup>a</sup>, M. Mezouar<sup>b</sup>, J. Monteux<sup>a</sup>, P. Parisiades<sup>b</sup>, G. Pesce<sup>a</sup>

## ARTICLE INFO

**Article history:**

Received 13 May 2016

Received in revised form 20 January 2017

Accepted 13 February 2017

Available online 16 February 2017

## ABSTRACT

Knowledge of melting properties is critical to predict the nature and the fate of melts produced in the deep mantle. Early in the Earth's history, melting properties controlled the magma ocean crystallization, which potentially induced chemical segregation in distinct reservoirs. Today, partial melting most probably occurs in the lowermost mantle as well as at mid upper-mantle depths, which control important aspects of mantle dynamics, including some types of volcanism. Unfortunately, despite major experimental and theoretical efforts, major controversies remain about several aspects of mantle melting. For example, the liquidus of the mantle was reported (for peridotitic or chondritic-type composition) with a temperature difference of ~1000 K at high mantle depths. Also, the Fe partitioning coefficient ($D_{Fe}^{Bg/melt}$) between bridgmanite (Bg, the major lower mantle mineral) and a melt was reported between ~0.1 and ~0.5, for a mantle depth of ~2000 km. Until now, these uncertainties had prevented the construction of a coherent picture of the melting behavior of the deep mantle.

In this article, we perform a critical review of previous works and develop a coherent, semi-quantitative, model. We first address the melting curve of Bg with the help of original experimental measurements, which yields a constraint on the volume change upon melting ($\Delta V_m$). Secondly, we apply a basic thermodynamical approach to discuss the melting behavior of mineralogical assemblages made of fractions of Bg, $CaSiO_3$-perovskite and (Mg,Fe)O-ferropericlase. Our analysis yields quantitative constraints on the $SiO_2$-content in the pseudo-eutectic melt and the degree of partial melting (F) as a function of pressure, temperature and mantle composition; For examples, we find that F could be more than 40% at the solidus temperature, except if the presence of volatile elements induces incipient melting. We then discuss the melt buoyancy in a partial molten lower mantle as a function of pressure, F and $D_{Fe}^{Bg/melt}$. In the lower mantle, density inversions (i.e. sinking melts) appear to be restricted to low F values and highest mantle pressures.

The coherent melting model has direct geophysical implications: (i) in the early Earth, the magma ocean crystallization could not occur for a core temperature higher than ~5400 K at the core-mantle boundary (CMB). This temperature corresponds to the melting of pure Bg at 135 GPa. For a mantle composition more realistic than pure Bg, the right CMB temperature for magma ocean crystallization could have been as low as ~4400 K. (ii) There are converging arguments for the formation of a relatively homogeneous mantle after magma ocean crystallization. In particular, we predict the bulk crystallization of a relatively large mantle fraction, when the temperature becomes lower than the pseudo-eutectic temperature. Some chemical segregation could still be possible as a result of some Bg segregation in the lowermost mantle during the first stage of the magma ocean crystallization, and due to a much later descent of very low F, Fe-enriched, melts toward the CMB. (iii) The descent of such melts could still take place today. There formation should be related to incipient mantle melting due to the presence of volatile elements. Even though, these melts can only be denser than the mantle (at high mantle depths) if the controversial value of $D_{Fe}^{Bg/melt}$ is indeed as low as suggested by some experimental studies. This type of melts could contribute to produce ultra-low seismic velocity anomalies in the lowermost mantle.

© 2017 Elsevier B.V. All rights reserved.

<footnote><sup>a</sup>Laboratoire Magmas et Volcans, CNRS-OPGC-IRD, Université Clermont Auvergne, Clermont-Ferrand, France</footnote>

<footnote><sup>b</sup>European Synchrotron Radiation Facility, Grenoble, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: denis.andrault@univ-bpclermont.fr (D. Andrault).</footnote>
# Contents

<table><tbody><tr><td>1. Introduction</td><td>68</td></tr><tr><td>1.1. Melting in the early Earth's mantle</td><td>68</td></tr><tr><td>1.2. Evidences for mantle melting today.</td><td>68</td></tr><tr><td>2. Melting of pure bridgmanite</td><td>69</td></tr><tr><td>2.1. Important bridgmanite properties</td><td>69</td></tr><tr><td>2.2. Previous studies of bridgmanite melting.</td><td>70</td></tr><tr><td>2.3. Updated melting curve of bridgmanite</td><td>70</td></tr><tr><td>2.4. Volume of bridgmanite melting.</td><td>70</td></tr><tr><td>3. Melting diagrams for typical lower mantle materials</td><td>71</td></tr><tr><td>3.1. Experimental determination of the melting behavior.</td><td>71</td></tr><tr><td>3.2. Pseudo-eutectic type melting in the deep mantle?</td><td>72</td></tr><tr><td>3.3. Sequence of phase disappearance upon melting.</td><td>72</td></tr><tr><td>3.4. Liquidus temperatures and Bg-content in melts.</td><td>72</td></tr><tr><td>3.5. SiO<sub>2</sub> content in pseudo-eutectic melts.</td><td>74</td></tr><tr><td>3.6. Degree of partial melting at pseudo-eutectic temperatures.</td><td>74</td></tr><tr><td>4. Melt buoyancy in the deep mantle.</td><td>75</td></tr><tr><td>4.1. Major parameters controlling the melt buoyancy.</td><td>75</td></tr><tr><td>4.2. Volume of mantle melting</td><td>76</td></tr><tr><td>4.3. Liquid-solid Fe partitioning</td><td>77</td></tr><tr><td>4.4. Solid-liquid density contrast</td><td>77</td></tr><tr><td>5. Implications for crystallization of the magma ocean.</td><td>78</td></tr><tr><td>5.1. Dynamics of the magma ocean crystallization</td><td>78</td></tr><tr><td>5.2. Chemical similarities between the pseudo Eutectic-melt and peridotite</td><td>79</td></tr><tr><td>5.3. Maximum core temperature after magma ocean crystallization</td><td>79</td></tr><tr><td>Acknowledgments</td><td>79</td></tr><tr><td>Appendix A. Supplementary data</td><td>79</td></tr><tr><td>References</td><td>79</td></tr></tbody></table>

# 1. Introduction

## 1.1. Melting in the early Earth's mantle

Within the first 100 million years of the Earth's history, the giant Moon forming impact (MFI) melted the Earth almost entirely (Nakajima and Stevenson, 2015). The release of energy induced by the gravitational segregation of the impactor's core could have potentially heated the Earth's core by 3500–4000 degrees above the temperature reached prior to the giant impact (Herzberg et al., 2010; Rubie et al., 2015). It could have led to a core-mantle boundary (CMB) temperature of the order of 6000 K (Davies et al., 2015; Labrosse, 2015; Nakagawa and Tackley, 2010), well above the mantle solidus of ~4150 K (Andrault et al., 2011; Fiquet et al., 2010). Therefore, the MFI could have caused intensive melting of the mantle at all depths. However, geochemical evidences point out to large scale isotopic heterogeneities that seem to have survived the episode of MFI. For example, the excess in ¹⁸²W (produced by the decay of ¹⁸²Hf) measured in 2.7 Ga-old komatiites requires a large-scale magmatic differentiation during the first 30 Ma of the Solar system's history (Touboul et al., 2012). The difference in Xenon isotopic composition between MORBs and the Icelandic plume (Mukhopadhyay, 2012), also indicates two sources with distinct isotopic composition. Finally, geodynamical arguments suggest the presence of an unmixed and primordial material in the deep mantle (Davaille, 1999; Kellogg et al., 1999). Therefore, it is unlikely that primordial mantle temperatures exceeded the liquidus throughout the mantle.

A low viscosity of the magma-ocean is expected to induce vigorous and turbulent convective flow, favoring a homogeneous mixing. Heat flux at the magma ocean surface could have been as high as ~10⁶ W/m², which suggests a very fast crystallization, within ~10³ years after the MFI (Solomatov, 2007). Longer time scales for cooling are also possible, due to the possible formation of an opaque atmosphere at the Earth's surface preventing heat loss, or other geodynamical complications, such as physical or chemical

mantle layering, etc. (Lebrun et al., 2013; Sleep et al., 2014). On the other hand, petrological analyses of Archean and Proterozoic basalts preserved on the Earth's surface show primary magma compositions compatible with mantle potential temperatures of only 200–300 degrees higher than today (Herzberg et al., 2010). A similar temperature change is reported for Archean tonalite-tro ndhjemite-granodiorite associations of 4.0–2.5 Ga old (Martin and Moyen, 2002). Such a modest difference of mantle temperature compared to the present situation suggests a relatively rapid mantle cooling just after the MFI.

Finally, it has been suggested that a basal magma ocean (BMO) could have lasted in the lowermost mantle for very long times, billions of years, in correlation with an outer-core temperature significantly higher than the mantle solidus (e.g. Labrosse (2015)). This issue remains largely debated, however, because geodynamical models do not explain what could prevent such a hot core from rapid cooling (Monteux et al., 2016; Nakagawa and Tackley, 2010)).

## 1.2. Evidences for mantle melting today

In the upper mantle, seismic and magneto-telluric profiles present prominent anomalies, in particular at depths between 80 and 200 km (e.g. Romanowicz (1995)). Low velocity anomalies have also been reported atop the 410-km mantle discontinuity (Song et al., 2004; Tauzin et al., 2010). Low degree partial melting has often been advocated to explain these anomalies (Revenaugh and Sipkin, 1994), as thermochemical effects alone cannot explain the magnitude of geophysical anomalies. Possible mechanisms for mantle melting, however, are many. As for the temperature profile, anchor points of the geotherm are provided by phase transformations in major mantle minerals, typically olivine, the constituent responsible for the seismic discontinuities between 410 and 660 km depths. It yields a potential temperature (Tp) of ~1600 K, which corresponds to the extrapolation to the Earth's surface of the adiabatic temperature profile passing through these anchor points (Katsura et al., 2010). Such a mantle geotherm plots at
significantly lower temperatures compared to the melting curve of the peridotitic mantle determined experimentally (Zhang and Herzberg, 1994). Noticeable exceptions exist, for example at mantle ridges, where the adiabatic decompression leads to mantle melting in the asthenosphere. Mantle melting at higher depths implies either higher temperatures (such as for Oceanic Island Basalts (OIB)) or the presence of volatiles that depress the solidus (e.g. Hirschmann et al. 1999).

Temperatures in the lowermost mantle depart from the upper mantle geotherm as they are influenced by the hot core. A large decrease (>10%) of shear wave velocities is reported in the D"-layer sitting just above the CMB. Even if alternative interpretations are possible, such as a solid-state origin (e.g. Fe-enriched (Mg,Fe)O (Wicks et al., 2010)), it strongly suggests occurrence of partial melting (e.g. Herzberg et al. (2013), Rost et al. (2005))). Furthermore, the non-ubiquitous character of the seismic features in the D"-layer implies a CMB temperature lower than the mantle solidus. Otherwise, there would be a continuous melting line above the CMB. At the CMB pressure of 135 GPa, the solidus temperature of chondritic and peridotitic mantle was reported to be ~4150 K (Andrault et al., 2011; Fiquet et al., 2010). There, where seismic anomalies appear, mantle partial melting could occur for different reasons: (i) presence of volatile elements, such as in the study of (Nomura et al., 2014) where their pyrolitic composition included ~400 ppm H₂O, which lowered the solidus temperature to ~3570 K. However, we note that a high water content is unlikely in the lower mantle, due to the limited capability of lower mantle minerals to store water below the 660 km discontinuity (Bolfan-Casanova et al., 2003; Panero et al., 2015); (ii) presence of an excess of silica; The solidus temperature at the CMB of a mid-ocean ridge basalt, was reported to be 3800 (±150) K, thus significantly lower than for the melting of the average mantle (Andrault et al., 2014). Presence of basalt in the lowermost mantle is supported by seismic tomography imaging deep descent of slabs toward the CMB (e.g. (van der Hilst and Karason, 1999)); (iii) a very large amount of FeO could also lower the melting point of the mantle (Mao et al., 2005). Altogether, the non-ubiquitous seismic

features in the D"-layer could very well be correlated to the presence of volatiles, basalt and/or high FeO concentration, together with a CMB temperature of 4100 (±200) K (e.g. Andrault et al. (2016)),

## 2. Melting of pure bridgmanite

### 2.1. Important bridgmanite properties

MgO becomes extremely refractory with increasing pressure, with a melting point estimated at ~8000 K for a pressure of 135 GPa (Du and Lee, 2014). This contributes in making ferropericlase (Fp) the liquidus phase above 25 GPa, but only up to ~33 GPa, where Bg becomes the liquidus phase for mantle compositions (Ito et al., 2004). The melting curve of Bg dominates the topology of melting diagrams at high mantle depths. The role of Bg is further emphasized by a possible increase of Bg-content with increasing mantle depth, as the comparison between geophysical observations and experiments (e.g. Murakami et al. (2012), Samuel et al. (2005)) suggest a mantle (Mg+Fe)/Si ratio closer to unity.

Mantle Bg can adopt chemical compositions ranging from (Mg, Fe)SiO₃, produced after decomposition of olivine, to Al-bearing (Mg,Fe)SiO₃, after the high pressure transformation of majoritic garnet below the 660 km discontinuity. A higher compositional variability could also come from the intrinsic high compliance of the Bg crystal structure, which composition can be decomposed in a number of (theoretical) end-members (MgSiO₃, FeSiO₃, FeAlO₃, Al₂O₃, MgAlO₂.₅). It can adopt variable Mg/Si, Fe³⁺/ΣFe, Al/Fe ratios and Fe-content as a function of pressure, temperature, oxygen fugacity, and exchange with ferropericlase. (e.g. Boujibar et al. (2016), Lauterbach et al. (2000)). The Bg crystal chemistry can thus vary with mantle depth (Andrault et al., 2007) and also laterally if the mantle presents significant heterogeneities. We also remind that the transition pressure from majoritic garnet to Bg increases significantly with the Al-content: compared to pure MgSiO₃, an additional 3-4 GPa is required to produce Bg with ~10 wt% Al₂O₃ (Akaogi and Ito, 1999; Irifune et al., 1996).

<figure><img src="image_323.png" /><figcaption>**Fig. 1.** Melting curve of Bg inferred from different experimental and theoretical studies determined using LH-DAC for (Mg₀.₈₈Fe₀.₁₂SiO₃) (Zerr and Boehler, 1993), MgSiO₃ and Mg₃Al₂Si₃O₁₂ (Shen and Lazor, 1995), shock measurements for MgSiO₃ (Akins et al., 2004; Mosenfelder et al., 2009) and ab initio calculations for MgSiO₃ (e.g. de Koker and Stixrude (2009), Stixrude and Karki (2005)). We also include experimental reports of solidus and liquidus of peridotite (Fiquet et al., 2010), chondritic-type mantle (Andrault et al., 2011) and pyrolite with ~400 ppm H₂O (Nomura et al., 2014). Our new LH-DAC measurements performed from ~24 to ~135 GPa on a (Fe,Al)-rich Bg (red dots and blue guide for the eyes) plot in continuity with previous determinations of mantle melting performed at lower pressures using the large volume press (Blue dots, (Katsura and Ito, 1990; Presnall and Gasparik, 1990)).</figcaption></figure>
## 2.2. Previous studies of bridgmanite melting

In early experiments using laser-heating in the diamond anvil cell (LH-DAC), visual observations of the sample behavior were used as a major criterion to address the melting of Bg (Fig. 1). Two studies performed on MgSiO₃ and (Mg,Fe)SiO₃ compositions agree for a steep melting curve above the transition zone pressure, at ~24 GPa (Shen and Lazor, 1995; Zerr and Boehler, 1993). Comparison between the melting curves of MgSiO₃ and Mg₃Al₂Si₃O₁₂ evidences a significant melting temperature depletion, by ~300 K at 40 GPa, due to the presence of Al (Shen and Lazor, 1995). Early works were limited to 60–70 GPa, compared to the 135 GPa prevailing at the CMB. Concerning melting of MgSiO₃ in the upper mantle, we note an important curvature of the melting line typical of the lower-density polymorphs (Katsura and Ito, 1990; Presnall and Gasparik, 1990). It can be related to a rapid decrease of the volume of melting (ΔV_m) with increasing pressure and, thus, a relatively high melt compressibility.

Several theoretical works address the equation of state and the melting curve of Bg up to more than 135 GPa, using *ab initio* calculations (Fig. 1). The MgSiO₃ end-member is generally studied, because such calculations encounter difficulties in addressing the role of transition elements and point defects (such as Al³⁺, Fe³⁺, etc.). In all calculations, the initial slope of the melting curve (above ~24 GPa) is relatively steep. This points out to a relatively large volume of MgSiO₃-Bg melting, which is dominated by the ~10% volume change at the transition from majoritic garnet to Bg at 660 km-depth (Yu et al., 2011).

Based on the propagation of shock waves, MgSiO₃ melting was identified at 5000–5500 K for a pressure above 100 GPa (Akins et al., 2004; Mosenfelder et al., 2009). It was suggested that the volume of Bg melting becomes very small at pressures typical of the lowermost mantle (Mosenfelder et al., 2009; Petitgirard et al., 2015). From 1 bar to ~24 GPa, there is also a clear decrease of the melting slope of MgSiO₃ with increasing pressure (Katsura and Ito, 1990; Presnall and Gasparik, 1990). It can be related to a rapid decrease of the volume of melting (ΔV_m) with increasing pressure associated to a relatively high melt compressibility.

## 2.3. Updated melting curve of bridgmanite

In this article, we report original measurements of the melting curve of a (Fe,Al)-bearing Bg phase with Fe/(Mg + Fe) = 0.12 and Al/Fe = 0.9. We acknowledge that this composition corresponds to relatively high Al and Fe contents compared to the expected composition for natural Bg. Experiments were performed using LH-DAC coupled with *in situ* X-ray diffraction on the ID-27 beamline (ESRF, France). All experimental methods are detailed in Supplementary Materials. At relatively low pressures, the melting curve of this Bg appears significantly more flat than those reported for pure MgSiO₃ (Fig. 1). This observation tends to confirm a significant effect of Al on the melting slope, as reported previously between Al-free and Al-bearing starting materials (Shen and Lazor, 1995). We also find that the discontinuous increase of the melting curve slope, related to the majorite to Bg phase transition, is not observed at ~24 GPa, but instead at ~30–35 GPa for this (Fe, Al)-bearing composition. This behavior can be logically related to extension to higher pressures of the garnet stability field in the presence of Al, as described in previous works for Fe-free starting materials (Akaogi and Ito, 1999; Irifune et al., 1996). The relatively lower melting temperature of (Fe,Al)-bearing Bg in the 25–35 GPa pressure range, compared to pure-MgSiO₃ and, most importantly, to other lower mantle minerals such as MgO, explains why Bg is not the liquidus phase in this pressure range for typical mantle compositions (Ito et al., 2004).

At higher pressures, the slope of the (Fe,Al)-bearing Bg melting curve remains fairly constant up to the CMB pressure of 135 GPa, which contrasts with the flattening reported for MgSiO₃. This makes the different available results to converge to a temperature of 5100–5500 K for the melting of Bg at the CMB. We remind that the melting curve of MgSiO₃-Bg should always plot at higher temperature than that of the (Fe,Al)-bearing composition, due to the incompatible character of Fe and Al. Thus, our experimental determination of the (Fe,Al)-bearing Bg melting curve implies that the melting temperature of MgSiO₃-Bg at very high mantle pressures was underestimated by a couple hundred degrees in some previous studies (de Koker and Stixrude, 2009; Mosenfelder et al., 2009). Thus, for further discussions, we will choose as a reference the higher melting curve of MgSiO₃ Bg as determined from *ab initio* calculations (Stixrude and Karki, 2005). It can be modeled using a modified Simon and Glatzel equation [T = T₀ (P/a + 1)¹/²] with parameters T₀ = 91 K, a = 0.00125 GPa and c = 2.83 (Simon and Glatzel, 1929).

We note that the liquidus temperature profile reported previously for peridotite (Fiquet et al., 2010) appears superimposed with the melting curve of MgSiO₃-Bg derived from *ab initio* calculations and shock experiments (Fig. 1). This is unexpected because (i) the more complex chemical composition of the peridotitic Bg phase, compared to MgSiO₃, and (ii) additional Fp and CaSiO₃-perovskite (CaPv) phases should both lower the peridotite liquidus below the melting temperature of pure MgSiO₃. In their study, (Fiquet et al., 2010) observed large crystals of Bg at the center of the heated spot, where the melting behavior was monitored using *in situ* X-ray diffraction. Chemical composition of Bg grains measured at different locations on a sample synthesized at ~61 GPa show Fe/(Mg + Fe) and Al/Si ratios of ~2.5% and ~8%, respectively. It is possible that their reported measurements of the peridotite liquidus correspond in fact to the melting curve of these large Bg grains.

## 2.4. Volume of bridgmanite melting

The dT/dP slope of the Bg melting curve is directly related to the volume (ΔV_m) and entropy (ΔS_m) of Bg melting through the classical Clapeyron relation dT/dP = ΔV_m/ΔS_m. ΔS_m was reported to be 42.2 J/mol K for MgSiO₃ at room pressure, based on calorimetric measurements (Stebbins et al., 1984). For melting of MgSiO₃ in the stability field of Bg, *ab initio* simulations suggest a ΔS_m value 1.5 times higher (Stixrude et al., 2009). Assuming then a constant ΔS_m value of 63.3 J/mol K for melting of (Fe,Al)-bearing Bg at all lower mantle conditions, we now calculate ΔV_m values from the Clapeyron slopes of the different melting curves available for Bg (Fig. 2a). For the (Fe,Al)-bearing composition, we observe a progressive decrease of ΔV_m/V_Bg varying from 13% at low pressures for some *ab initio* calculations (Stixrude et al., 2009) or even 19% for a shock-wave study (Mosenfelder et al., 2009), to 3–4% at pressures of 135 GPa. The flatter ΔV_m found for the (Fe,Al)-bearing implied by our results is due to a more linear melting curve measured from 30 to 35 GPa to 135 GPa, compared to pure MgSiO₃ (Fig. 1). We also show recent measurements of the MgSiO₃-glass density performed in the DAC at 300 K up to the CMB pressure (Petitgirard et al., 2015). The ΔV_m/V_Bg recalculated from the later study is significantly lower than all other calculations at high pressures, which should translate into a very flat melting curve. Based on the shadowed region in Fig. 2a, we define a most probable range of ΔV_m/V_Bg values decreasing from 11(±2)% to 4(±1)% when pressure is increased from 24 to 140 GPa, respectively.
<figure><img src="image_324.png" /><figcaption>**Fig. 2.** (a) Normalized volume of melting (ΔV<sub>m</sub>/V<sub>Bg</sub>, where ΔV<sub>m</sub> = V<sub>melt</sub> – V<sub>Solid</sub> and V<sub>Bg</sub> is volume of Bridgmanite) derived from the melting curve of Bg (Fig. 1) with various (Mg,Fe)(Si,Al)O<sub>3</sub> compositions We also report the value of 18% measured for pure MgSiO<sub>3</sub> at 1 bar (Lange, 1997) and ΔV<sub>m</sub>/V<sub>Bg</sub> recalculated from density measurements of MgSiO<sub>3</sub>-glass in a DAC (Petitgirard et al., 2015). Shadowed pink region is the most probable range of mantle ΔV<sub>m</sub>/V<sub>Bg</sub> values. (b) ΔV<sub>m</sub> derived from the solidus and/or liquidus profiles of the A-chondritic (Andrault et al., 2011) and F-peridotitic (Fiquet et al., 2010) models of mantle melting. Calculation of ΔV<sub>m</sub>/V<sub>Bg</sub> along solidus and liquidus profiles using the Clapeyron relation assume an ideal mixing model to estimate the melt entropy (see paragraph 4.2).</figcaption></figure>

We also calculated ΔV<sub>m</sub> at pressures below 24 GPa using ΔS<sub>m</sub> = 42.2 J/mol K (Stebbins et al., 1984) and using the Clapeyron of melting curves measured in large volume press (LVP) experiments. We note that the final interpretation of ΔV<sub>m</sub> can be complicated by the occurrence of four different MgSiO<sub>3</sub> polymorphs between 1 bar and 24 GPa (Presnall, 1995). In particular, the Clapeyron slope of majorite melting remains largely uncertain, due to a limited pressure range available. For this reason, we modeled the MgSiO<sub>3</sub> melting line using a 2nd degree polynomial regression across the whole pressure range from 0 to 24 GPa. The calculated ΔV<sub>m</sub>/V<sub>Bg</sub> decreases strongly with increasing pressure converging to 1% at ~24 GPa (Fig. 2a). It makes a volume change of ~8% at the majorite to Bg transition for the (Fe,Al)-bearing composition of our study, or ~10% in average for the most probable range of ΔV<sub>m</sub>/V<sub>Bg</sub> that we have defined above, both values agreeing well with the ~10% suggested previously for MgSiO<sub>3</sub> (Yu et al., 2011).

**3. Melting diagrams for typical lower mantle materials**

**3.1. *Experimental determination of the melting behavior***

Studying experimentally phase relations in a partially molten
geological material under P-T conditions of the Earth's interior
remains a challenging task. The use of LVP facilitates largely the
chemical analysis of coexisting phases in recovered samples, com-
pared to LH-DAC. For example, melting behavior of fertile peri-
dotite and CI chondritic mantle were documented up to ~35 GPa
(Ito et al., 2004). It was demonstrated that the liquidus phase

changes from Fp to Bg at about 33 GPa, a situation that was con-
firmed later by LH-DAC experiments (Andrault et al., 2011;
Fiquet et al., 2010). However, LVP samples (and a fortiori LH-DAC
samples) synthesized at lower mantle conditions always encounter
relatively large temperature gradients, which yields heterogeneous
microstructure and chemical zoning. In such cases, the sequence of
phase disappearance from solidus to liquidus temperatures is usu-
ally retrieved from the position of phases relative to the tempera-
ture gradient. Still, this procedure prevents the precise
determination of the equilibrium solid-liquid partition coefficients.

When coupled with *in situ* X-ray diffraction, LH-DAC is well su-
ted to determine melting curves of various geological materials,
because the available temperature range extends up to more than
6000 K (Suppl. Fig. 1). Melting criteria are generally based on the
disappearance of diffraction peaks and phase(s), which corre-
sponds in fact to the determination of a pseudo-eutectic tempera-
ture (PET). Recently, pseudo-eutectic melting of peridotite (Fiquet
et al., 2010), chondritic-mantle (Andrault et al., 2011) and pyrolite
(Nomura et al., 2014) was reported at substantially different tem-
peratures. Disagreements cannot be reconciled based on the mod-
erate compositional variations between starting materials, among
which the major difference lies in the Bg/(Bg + CaPv + Fp) ratio
from 0.59, 0.63 and 0.75 for peridotite, pyrolite and chondritic
mantle, respectively. Studies using peridotitic (F-peridotitic model)
and chondritic (A-chondritic model) starting materials show simi-
lar solidus evolution as a function of pressure, pointing out to a PET
of 4150 ± 150 K at the CMB. The lower value reported in the study
using pyrolite could be due to a more precise determination of the
solidus, thanks to the use of 3D X-ray tomography, but more likely
because of the presence in their sample of 400 ppm H₂O that triggers melting (Nomura et al., 2014).

## 3.2. Pseudo-eutectic type melting in the deep mantle?

The melting diagram between the three lower mantle phases (Bg, CaPv and Fp) presents an eutectic behavior (e.g. de Koker et al. (2013), Liebske et al. (2005), Liebske and Frost (2012)), which implies (i) a PET and (ii) a melt composition at the PET located within the ternary diagram. The PET and the melt composition should be independent of the Bg, CaPv and Fp molar fractions in the bulk material, as long as the chemical compositions of these three phases do not vary significantly. A major issue for geological materials is that the onset of melting (the solidus) can possibly occur at a temperature lower than the PET. In such a case, a melt appears without disappearance of a phase from the mineral assemblage. This can happen when the solubility limit of an incompatible element is overpassed at a given condition of pressure and temperature. This behavior has not been reported yet for any mantle compositions under the P-T conditions typical of the lower mantle. In contrast, available LH-DAC experiments report disappearance of one phase at the onset of melting. Also, chemical analyses of melts obtained after partial melting of peridotite at ~24 GPa show compositions close to the starting material (e.g. with a relatively lower MgO/SiO₂ ratio (Tronnes and Frost, 2002)), which is incompatible with incipient mantle melting.

Above the solidus temperature, partition coefficients between Bg or CaPv and the melt ($D^{\text{solid/melt}}$) were investigated experimentally for many elements. Except for a very few of them (such as Li and Ba), $D^{\text{solid/melt}}$ values are found to lie above $3 \times 10^{-1}$, which corresponds to a moderately incompatible behavior (Corgne et al., 2005). These results suggests that the minor elements may

not reach their solubility limit and, therefore, melting would not occur below the PET.

Of course, volatiles such as H₂O (but also CO₂) are well known to depress the solidus and potentially favor incipient mantle melting. We note, however, that (i) carbonate phases may be relatively refractory in the lower mantle (Thomson et al., 2014) and (ii) a high water content in the lower mantle is unlikely, due to limited capability of the lower mantle minerals to store water below the 660 km discontinuity (Bolfan-Casanova et al., 2003). Thus, even if water has an effect on the solidus, water may not be actually present. In summary, experimental evidences strongly suggest a moderate temperature difference between solidus and PET, if any.

## 3.3. Sequence of phase disappearance upon melting

In the ternary diagram between Bg, CaPv and Fp, the difference in composition between the bulk mantle composition and the melt defines the sequence of phase disappearance upon melting. For example, melting of peridotite would likely induce a melting sequence from CaPv (at solidus), Bg to Fp (at liquidus), if the PE-melt would present significantly higher CaSiO₃-content and lower (Mg,Fe)O-content, compared to peridotite. Thus, the ternary diagram can be divided into six different regions where the melting sequence should be different, depending on the PE-melt composition (Fig. 3).

Composition of melts relevant to deep mantle partial melting were reported after experiments performed at 24.5 GPa using LVP (Tronnes and Frost, 2002) and 80 GPa using LH-DAC (Tateno et al., 2014). Despite the fact that these melts may differ from PE-melts, if experimental temperatures have been higher than PET, they provide precious anchors for melt compositions in the ternary diagram. Composition of these two melts (corresponding to 24.5 and 80 GPa) plot on each side of the Fp/Bg ratio of 0.37, which corresponds to the peridotite composition. This observation is compatible with a third experimental anchor point where the liquidus phase has changed from Fp to Bg at about ~33 GPa for a fertile peridotite (Ito et al., 2004). Thus, the melt composition evolves toward higher (Mg,Fe)O-contents with increasing pressure.

Another important observation is the melt composition at 80 GPa, which presents a CaPv/Fp ratio very close to the peridotitic value of 0.15. It suggests that both phases, CaPv and Fp, disappear almost simultaneously at the PET upon partial melting of peridotite in the deep lower mantle. In this work, we make the assumption that CaPv and Fp disappear simultaneously at the PET at lower mantle pressures. This assumption is not severe. If Fp would disappear first, negligible amount of CaPv would remain. Indeed, the total amount of CaPv is below ~6 mol% for compositions relevant to the deep mantle. In the case CaPv would disappear first, higher Fp content could theoretically remain after melting at the PET. Indeed, Fp is found at a level of 19, 32 or 35 mol%, for chondritic, pyroitic or peridotitic compositions, respectively. However, the molar volume of Fp is twice less than those of Bg and CaPv. Also, it is likely that the melt dissolves a significant part of Fp at the PET (Tateno et al., 2014; Tronnes and Frost, 2002), which should yield to a relatively low Fp-content in the residual solid.

## 3.4. Liquidus temperatures and Bg-content in melts

The melting behavior can be modeled at various mantle pressures (for example 40 GPa, 80 GPa and 135 GPa) using (pseudo) binary phase diagrams, where one end-member is Bg, the liquidus phase, and the other is the sum of all the other chemical components (Fig. 4). We prefer to use Fe-free Bg as an end-member, instead of (Fe,Al)-bearing Bg, due to the preferential partition of Fe to the melt (this matter is discussed later in the article). Still,

<figure><img src="image_325.png" /><figcaption>**Fig. 3.** Ternary diagram between Bg, Fp and CaPv, the three major phases in the lower mantle. Due to its eutectic shape, melt compositions should always plot within this diagram. The Red dot and lines correspond to the peridotitic composition and its associated Fp/Bg, CaPv/Bg and CaPv/Fp ratios. Blue dots are melt compositions determined experimentally (Ito et al., 2004; Tateno et al., 2014; Tronnes and Frost, 2002). The blue arrow shows the change in melt composition with pressure. In each colored region of the ternary diagram, the expected sequence of phase disappearance upon melting are reported inside circles: 1, 2 and 3 are solidus, intermediate and liquidus phases, respectively.</figcaption></figure>
<figure><img src="image_326.png" /><figcaption>**Fig. 4.** Binary melting diagram at 40, 80 and 135 GPa between Fe-free Bg and the sum of all other chemical components. Anchor points for the binary melting diagram are the melting temperature of the mantle relevant Bg (Stixrude and Karki, 2005), see Fig. 1) and the A-chondritic solidus and liquidus temperatures (Andrault et al., 2011). We also report previous estimates of MgSiO₃-content in PE-melt (de Koker et al., 2013; Liebske and Frost, 2012; Tateno et al., 2014).</figcaption></figure>

we consider an Al-bearing Bg end-member, because the Al-behavior upon partial melting remains poorly constrained. Compositional axis of such binary diagram is thus the molar fraction of Fe-free Bg. Melts include Fp, CaPv, (virtual) FeSiO₃-Bg and a fraction of Fe-free Bg end-members. Peridotitic and chondritic mantle, as well as our (Fe,Al)-bearing Bg composition plot at 59, 75 and 88 mol% of Fe-free Bg, respectively. For the PET, the A-chondritic model indicate “solidus” temperatures of 2690, 3340 and 4130 K at pressures of 40, 80 and 135 GPa, respectively (Andrault et al., 2011). For the Fe-free Bg end-member, we use *ab initio* calculations for MgSiO₃-Bg (Stixrude and Karki, 2005), as discussed above. Two LH-DAC studies report liquidus temperatures of A-chondritic and F-peridotitic models (Andrault et al., 2011; Fiquet et al., 2010). Finally, the independent reports of the Bg-content in melts (i) measured after partial melting of pyrolite (Tateno et al., 2014) and (ii) calculated in the MgSiO₃-MgO system (de Koker et al., 2013; Liebske and Frost, 2012) are also shown. We note that the two later studies did not included the CaPv component, which could numerically yield an overestimation of the Bg-content in the melt.

At each selected mantle pressure, we draw lines from the melting temperature of the Bg end-member, through the liquidus temperature of the A-chondritic model, toward the PET (Fig. 4). These lines provide estimates of liquidus temperatures as a function of the bulk mantle composition. In addition, intersections between these lines and PET provide estimates of the Bg-content in PE-melts, as a function of pressure. Uncertainties arise from (i) controversial reports of the Bg melting temperature as a function

of pressure (Fig. 1) and (ii) unknown curvature of the liquidus profile in these diagrams. Consequently, we colored in pink regions where the presence of liquidus is the most probable. We excluded from colored regions PE-melts with a fraction of Fe-free Bg higher than peridotite, because it would be contradictory with Bg becoming the liquidus phase above ~33 GPa (Ito et al., 2004). We note that our method is not appropriate to pressures lower than ~33 GPa, when Bg is not the liquidus phase.

Based on the width of the regions of confidence, liquidus temperatures appears to be constrained within ±150 K at all mantle pressure, temperature and compositions. An uncertainty to which we should add a similar value associated to the experimental error in the determination of PET and Bg melting temperature. On the other hand, uncertainty in Bg-content in PE-melt and along liquidus lines is about ±5%. The Bg-content in the PE-melt appears almost independent of lower mantle pressure at a value of 55 (±5) mol%. With increasing temperature above PET, the Bg-content in melt should logically increase until it reaches the bulk mantle composition. Altogether, these binary melting diagrams can be numerically constrained by three parameters: (i) a constant Bg-content of 55(±5) mol% in PE-melt, and two modified Simon and Glatzel (SG) equations $[T(P) = T_0 (P/a+1)^{1/c}]$ with parameters (ii) $T_0 = 2045$ K, $a = 92$ GPa and $c = 1.3$ for the PET (Andrault et al., 2011) and (iii) $T_0 = 91$ K, $a = 0.00125$ GPa and $c = 2.83$ for the Bg end-member (Stixrude and Karki, 2005). Then, liquidus temperatures between PE-melt and Bg can be defined as a function of pressure and mantle composition using:
<figure><img src="image_327.png" /><figcaption>Fig. 5. Pressure change of the SiO₂-content in pseudo-eutectic melt. Horizontal dotted lines are X(SiO₂) typical of olivine, peridotite, pyrolite and chondritic-mantle. The red line is derived from the Bg melting curve (Stixrude and Karki, 2005) associated with the thermodynamical treatment elaborated for the discussion of Fig. 4. Dashed lines represent previous calculations (de Koker et al., 2013; Liebske and Frost, 2012) or the experimental determination (Tateno et al., 2014) of X(SiO₂) in melts. The shaded gray area corresponds to the most likely X(SiO₂) of lower mantle melts.</figcaption></figure>

$$T_{\text{Mantle}}^{\text{Liq}}(P, X_{\text{Bg}}^{\text{Mantle}}) = \text{SG}(\text{Bg}) - [(\text{SG}(\text{Bg}) - \text{SG}(\text{PEM})) \\ \times (1 - X_{\text{Bg}}^{\text{Mantle}})/(1 - X_{\text{Bg}}^{\text{PEM}})]$$

where SG(PEM) and SG(Bg) are PE-melt and Bg melting temperatures, respectively, calculated at a target mantle pressure (P) using SG equations. X<sub>Bg</sub><sup>PEM</sup> and X<sub>Bg</sub><sup>Mantle</sup> are Bg mole fractions in the PE-melt (fixed at 55 mol%) and the bulk mantle, respectively.

For a peridotitic mantle composition, binary phase diagrams suggest a difference of less than 300 K between PET and liquidus at all lower mantle pressures. This is in very good agreement with the value of 250 K proposed based on a thermodynamic melting model (Liebske and Frost, 2012). The difference between the PET and the liquidus increases for larger fractions of Bg in the bulk material, and in a primitive chondritic mantle it can reach up to 500 degrees. This confirms the wide range of mantle depths where partial melting should have occurred in the framework of an early magma ocean (e.g. Kojitani and Akaogi (1997), Miller et al. (1991)).

### 3.5. SiO₂ content in pseudo-eutectic melts

Another parameter controlling the melt properties is its SiO₂-content (X(SiO₂)). It can be derived directly from Fig. 4, by converting the amount of Fe-free Bg in the melt into its SiO₂ contribution. Based on our primary assumption that Fp and CaPv dissolve concomitantly in the melt at the PET, the SiO₂-content of the CaPv component is also added to the melt composition. This calculation can be performed for all types of melt along liquidii, as long as pressure is above ~33 GPa. Still, we only discuss here the composition of PE-melts. We actually translate into X(SiO₂) the regions of confidence defined above for Bg-contents in PE-melts (Fig. 5). Independent values of X(SiO₂) in lower mantle melts were reported previously based on ab initio calculations (de Koker et al., 2013), thermodynamic modeling of LVP experiments (Liebske and Frost, 2012) and chemical analyses of LH-DAC samples (Nomura et al., 2011; Tateno et al., 2014). At about ~33 GPa, the change of liquidus phase from Fp to Bg reported upon peridotite melting suggests that X(SiO₂) in the melt crosses the peridotitic value of 38.3% (Ito et al., 2004).

The melt X(SiO₂) likely remains significantly lower than 0.40 at higher pressures in the lower mantle, because Bg was broadly reported to be at the liquidus for pyrolite (Nomura et al., 2014) and peridotite (Fiquet et al., 2010). The fact that two models (de Koker et al., 2013; Liebske and Frost, 2012) propose higher X(SiO₂) could be related to calculations restricted to the MgSiO₃-MgO system. The difference between the simple MgO-SiO₂ system and the mantle-relevant compositions suggests that Ca and Fe should enter the melt preferentially as CaO and FeO, rather than CaSiO₃ and FeSiO₃, thus lowering X(SiO₂). Such behavior translates into a significantly stronger incompatible character of Ca and Fe, compared to Mg and Si (Liebske et al., 2005), which is already well known for low-pressure melting. The range of possible melt X(SiO₂) appears to extend between the peridotite and a previous work performed on LH-DAC samples (Tateno et al., 2014). It corresponds to an almost fixed X(SiO₂) value of 37.0% (±1.5%). This most probable range of X(SiO₂) plots in good continuity with data reported at lower pressure based on LVP experiments (Ito et al., 2004; Tronnes and Frost, 2002). In summary, deep PE-melts appear to adopt a composition only slightly enriched in Fp compared to peridotite, if any.

### 3.6. Degree of partial melting at pseudo-eutectic temperatures

We can now calculate the expected degree of partial melting (F) at the PET for peridotitic, pyrolitic and chondritic mantle compositions, based on our estimation of deep-mantle melt compositions (Figs. 4 and 5). F (in vol%) at PET can be estimated using the molar volumes for Bg, Fp and CaPv (The equations of state defining the effect of pressure and temperature on volumes are described below). Logically, the calculated F value at PET varies with the difference in composition between the PE-melt and the bulk material. The closest the mantle composition is from the melt, the highest F value is expected at the PET. Calculated ranges of possible F values at PET appear to be more than 83, 74 and 46 vol%, for peridotitic, pyrolitic and chondritic mantle compositions, respectively (Fig. 6).

We note that a similar conclusion was reached previously (e.g. Herzberg and Zhang (1998)) based on the residual harzburgite signature of most komatiites with Cretaceous and late-Archaean
<figure><img src="image_328.png" /><figcaption>**Fig. 6.** Degrees of mantle partial melting (vol%) expected at pseudo-eutectic temperature (PET) in the lower mantle under the assumptions that CaPv and Fp phases disappear jointly upon melting. Degrees of partial melting are calculated for typical chondritic, pyrolitic and peridotitic mantle compositions, based on the possible range of PE-melt composition refined in Fig. 5. T-14 stands for Tateno et al. (2014).</figcaption></figure>

ages, which can be interpreted to have formed by about 25–60% anhydrous melting of mantle peridotite in hot plumes.

The melting relations discussed above have implications for our understanding of the melting in the deep mantle today. For example, in the ultra-low velocity zones (ULVZ) just above the CMB, the high F values determined for PET in this study imply that the ULVZ cannot correspond to partial melting of the average mantle, because the degree of partial melting in the ULVZ as inferred by seismology is much lower than the minimum value of 46% calculated for a chondritic-type mantle. A lower F-value could be achieved (i) for a locally high concentration in volatile elements, which would favor incipient mantle melting below the PET or (ii) for another type of geological material, such as subducted basalts (Andrault et al., 2014).

# 4. Melt buoyancy in the deep mantle

## 4.1. Major parameters controlling the melt buoyancy

Dynamical behavior of a partially molten mantle is largely affected by the density contrast between the melt and the solid fractions ($\Delta\rho_{m-s} = (\rho_m - \rho_s)/\rho_s$). While melt buoyancy plays a major role in chemical segregation and planetary differentiation, the fact that its sign is positive or negative produces two different geodynamical situations. Melt buoyancy can also vary with mantle depth, due to (i) a possible change of the melt composition and (ii) different PVT equations of state for the melt and the mantle residue. In the present-day mantle, ascent, or descent, of some melts could contribute to surface volcanism, or accumulation of melts in the lowermost mantle, respectively. In a crystallizing magma ocean, it is classically accepted that crystals would settle, compact and reject the melt toward the Earth's surface (Boukare et al., 2015; Solomatov, 2007). However, this question became much debated after it was proposed that an early basal magma ocean could be produced by dense melts stored above the CMB (Labrosse et al., 2007; Nomura et al., 2011). Solid-liquid density inversions are not unusual. Many years ago, it was already proposed that basaltic and komatiitic magmas would become denser than olivine and garnet at depths of 245–500 km (Agee, 1998).

<figure><img src="image_329.png" /><figcaption>**Fig. 7.** Relative buoyancy between mantle melts of various compositions and (i) the (Mg,Fe)SiO₃ Bg with Fe-contents of 0, 10, or 20% (blue lines) and (ii) the lower mantle at pressures of 65 and 135 GPa (red lines). Along each blue or red lines, the melt and the given solid phase (Bg or lower mantle) have the same density. Higher SiO₂-content or lower Fe/(Mg + Fe) ratio, compared to a given line, yield melts buoyant compared to the solid phase considered. The gray region corresponds to the likely SiO₂-content in PET-melts in the mantle (see Fig. 5). SiO₂-content values for chondritic and peridotitic mantle are also reported. This Figure is modified from (Funamori and Sato, 2010).</figcaption></figure>

Major parameters controlling the buoyancy of deep-mantle melts are (i) changes in atomic packing between solid and liquid phases, which most generally produces a positive volume of melting ($\Delta V_m$), (ii) Fe partition coefficient between the solid residue and the melt ($D_{\text{Fe}}^{\text{Bg/melt}}$), because Fe is the heaviest major element, and (iii) MgO/SiO₂ ratio in the melt, because SiO₂-based atomic packing presents a relatively high bulk modulus. We chose to use $D_{\text{Fe}}^{\text{Bg/melt}}$ ($D = X_{\text{Fe}}^{\text{Bg}}/X_{\text{Fe}}^{\text{melt}}$, with X being the molar fraction), rather than
the distribution coefficient $K_{\text{Fe}}^{\text{Bg/melt}}$ ($K = (X_{\text{Fe}}/X_{\text{Mg}})^{\text{Bg}}/(X_{\text{Fe}}/X_{\text{Mg}})^{\text{melt}}$), because $X_{\text{Mg}}^{\text{melt}}$ can vary with pressure, temperature and bulk com-
position independently from $X_{\text{Fe}}^{\text{melt}}$. Nothing prevents $X_{\text{Mg}}^{\text{melt}}$ and $X_{\text{Fe}}^{\text{melt}}$ to vary in a correlated way, which would contradict the
proper definition of K.

Concerning the volume difference between solids and melts, both phases undergo (i) volume changes upon P and T according to their respective equation of state and (ii) a number of structural transformations with increasing mantle depth. In the solid state, equation of states of major mantle minerals are relatively well con-
strained (e.g. (Matas et al., 2007)). Structural transformations in the melt are much more progressive than in the solid, but can still contribute to a net increase of the melt density with increasing mantle depths. Due to the disordered and time-dependent nature of the melt structure, each structural entity has a finite lifetime. And when pressure is applied, structural entities can progressively evolve. In polymerized liquids, polyhedral chains can bend, eventu-
ally break and recompose differently (Stolper and Ahrens, 1987; Wang et al., 2014). All major cations progressively change their coordination shell (Bajgain et al., 2015) to allow compaction of the oxygen sub-lattice (Zeidler et al., 2014). The major change is probably Si, which progressively changes coordination number from fourfold to sixfold between ~20 and ~40 GPa (Benmore et al., 2010; Guillot and Sator, 2007; Sanloup et al., 2013; Sato and Funamori, 2010). These progressive transformations yield a room pressure bulk modulus significantly lower for the melt than for the crystalline counterpart. However, the pressure derivative of the bulk modulus is generally much higher, due to the progressive loss of some compaction mechanisms, after major voids have dis-
appeared from the melt structure at moderate pressures.

At shallow mantle depths, while the melt structure has already undergone significant compaction, major mantle minerals, in par-
ticular olivine, have not yet transformed to a denser polymorph. For this reason, there could be a neutral melt buoyancy, or even a positive $\Delta\rho_{m-s}$ (i.e. a sinking melt), at mantle depths just above the 410 km discontinuity (Matsukage et al., 2005; Sakamaki et al., 2006). It could produce a kind of density trap, where melts produced above and below would accumulate and remain gravita-
tionally stable in this mantle region (e.g. Lee et al. (2010)). At lower mantle pressures, a previous study tentatively addresses $\Delta\rho_{m-s}$ for a number of melt and solid compositions (Fig. 7; (Funamori and Sato, 2010), see also (Thomas et al., 2012)). Reporting in this dia-
gram our estimates of $X(\text{SiO}_2)$ in PE-melt retrieved from Fig. 5 nar-
rows down the range of possible silica contents between ~35.2 and ~38.3 mol%. We note that the $\text{SiO}_2$-content in the melt should increase with increasing temperature above the PET, because the PE-melt is relatively depleted in $\text{SiO}_2$ compared to the mantle com-
position. Ultimately, the melt and the bulk mantle become similar at the liquidus temperature, when the solid residue disappears completely. Altogether, the rather limited range of possible $\text{SiO}_2$-content in mantle melts points out to the fact that the less constrained parameters needed to address melt buoyancy at mantle depths are $\Delta V_m$, the volume of melting, and $D_{\text{Fe}}^{\text{Bg/melt}}$, the Fe solid-liquid partitioning.

## 4.2. Volume of mantle melting

While the $\Delta V_m$ corresponding to the melting of a pure phase, such as Bg, can be estimated based on its melting curve (Fig. 2a), the volume of melting becomes more difficult to address in the case of the partial melting of the mantle between its solidus and liquidus. In addition, the equation of state of the melt changes sig-
nificantly with its composition (de Koker et al., 2013; Thomas and Asimow, 2013). For example, $\text{Mg}_2\text{SiO}_4$-liquid becomes denser than lower mantle phases at pressures above ~40 GPa, while $\text{MgSiO}_3$-liquid remains buoyant at all mantle pressures (Thomas

and Asimow, 2013). Thus, assuming a simplified melt composition, such as MgSiO₃, may not be much relevant for discussing the buoyancy of natural melts in the deep mantle. A more realistic exercise is to estimate the real density difference between the solid residue and a melt of relevant composition in the Bg-CaPv-Fp system. The solid residue can be a simple phase (Bg, or Fp below ~33 GPa), or a typical mantle composition (e.g. pyrolite), which would be relevant to model melt buoyancy in the context of an early crystallizing magma ocean (high F), or partial melting in the present-day lower mantle (low F), respectively. The melt composition at various P and T can be derived from the melting diagrams (Fig. 4).

In Fig. 2b, we intend to use the slopes of solidus and liquidus reported for mantle melting from LH-DAC experiments (Andrault et al., 2011; Fiquet et al., 2010) to retrieve thermodynamical information relevant to melts. We compare the solidus, or liquidus, profile to a Clapeyron slope which would record melting of the first fraction of solid mantle, or the last fraction of Bg, respectively. At the solidus temperature, the entropy of melting ($\Delta S_m$) can be estimated from the sum of melting entropies of each phase present in the melt, plus a mixing entropy. We used $\Delta S_m^i$ values of 63.3, 63.3 and 13.0 J/mol K for the melting entropy of Bg (Stixrude et al., 2009), CaPv (similar to Bg) and Fp, respectively. We note that the room pressure value of $\Delta S_m^{\text{MgO}}$ was reported to be significantly larger than that of Fp, at ~35 J/mol K, however, it decreases rapidly with increasing pressure to 25 GPa (Vocadlo and Price, 1996). Composition of the PE-melt is considered to be 60% Bg, 30% Fp and 10% CaPv, in agreement with Figs. 3 and 4. However, changing the phase contents does not affect greatly the calculated $\Delta S_m$ value of ~55 J/mol K. At the liquidus temperature, we assume that the $\Delta S_m$ of the bulk rock is similar to that of Bg, neglecting the fact that the melt in which last grains of Bg get dissolved has a composition slightly different from Bg. Based on these assumptions, we calculate volumes of melting at solidus and liquidus, using the Clapeyron equation (Fig. 2b).

For the A-chondritic model, the values of $\Delta V_m/V_{\text{Bg}}$ at the solidus and at the liquidus appear almost independent of mantle pressure, at values of 4(±1)% and 6(±1)%, respectively. The $\Delta V_m/V_{\text{Bg}}$ at the solidus of the F-peridotitic model plots at similar values, however, due to a larger curvature in the melting curve, its associated $\Delta V_m/V_{\text{Bg}}$ varies more with pressure. We note that if we would have included a supplementary non-ideal mixing contribution to $\Delta S_m$ (de Koker et al., 2013), the $\Delta V_m/V_{\text{Bg}}$ values would have been ~0.5% higher. Altogether, the different trends available suggest

<figure><img src="image_330.png" /><figcaption>**Fig. 8.** Change in Fe partitioning ($D_{\text{Fe}}^{\text{Bg/melt}}$) between the Bg and a coexisting melt. Starting materials for LH-DAC experiments were olivine (blue, (Nomura et al., 2011)), chondritic-type mantle (green, (Andrault et al., 2012)) and peridotite (red, (Tateno et al., 2014)). Open circles correspond to previous multi-anvil experiments (Boujibar et al., 2016; Ito et al., 2004; Tronnes and Frost, 2002). The red arrow corresponds to the range of $D_{\text{Fe}}^{\text{Bg/melt}}$ measured in a same study at varying F values.</figcaption></figure>
<figure><img src="image_331.png" /><figcaption>**Fig. 9.** A possible, schematic, melting diagram between MgSiO₃ and FeSiO₃ in the lower mantle. We plot FeO + SiO₂ as the Fe-bearing end-member because FeSiO₃-Bg is unstable, except maybe at very high pressures. Vertical purple dashed lines are compositions of coexisting Bg and melt. Strong curvatures of solidus and liquidus lines can yield a decrease of D<sup>Bg/melt</sup><sub>Fe</sub> with increasing temperature between the eutectic and the liquidus temperature, in agreement with a previous study (Boujibar et al., 2016).</figcaption></figure>

(i) a small variation of the volume of melting with temperature increasing from the solidus to the liquidus and (ii) a small decrease with pressure from ~6% to ~4% from 30 to 130 GPa, respectively. This significantly positive value of ΔV<sub>m</sub>/V<sub>Bg</sub> should contribute to a positive melt buoyancy for all types of melts.

### 4.3. Liquid-solid Fe partitioning

Based on LVP experiments performed up to ~35 GPa, Fe is recognized as an incompatible element, with a concentration ~1.5 to ~3 times higher in the melt compared to the solid mantle (e.g. Ito et al. (2004), Liebske et al. (2005)). For samples recovered from LH-DAC experiments, Fe was reported to become extremely incompatible with the Bg structure at pressures above ~70 GPa, with a Fe concentration more than 10 times higher in the melt, compared to Bg (Nomura et al., 2011) (Fig. 8). Such an enrichment of iron in melts (associated to a very low Fe-concentration in the residual Bg) favors their higher density relative to the solid residue, facilitating their sinking towards the CMB. In this previous study, olivine was used as a starting material and the absence of Al could have favored a relatively low D<sup>Bg/melt</sup><sub>Fe</sub> value (Wood and Rubie, 1996). Still, another study performed on an Al-bearing peridotitic composition using the same experimental methodology confirms the very low Fe-content in the residual Bg (Tateno et al., 2014). We note that the Al partition coefficient between Bg and melt (D<sup>Bg/melt</sup><sub>Al</sub>) was also reported to decrease significantly from 1.8 to 0.64 with increasing pressure from 34 to 88 GPa in the same study. On the other hand, much higher D<sup>Bg/melt</sup><sub>Fe</sub> values of 0.5–0.6 were reported for a chondritic-mantle starting material using in situ X-ray fluorescence spectroscopy (Andrault et al., 2012). These last results favor denser Bg grains and buoyant melts. The controversy cannot arise from slight compositional differences between starting materials, especially between peridotitic and chondritic mantle compositions used in Tateno et al. (2014) and Andrault et al. (2012), respectively. It should be related to differences in experimental and/or analytical techniques.

A recent study addresses the value of D<sup>Bg/melt</sup><sub>Fe</sub> as a function of F, the degree of partial melting, based on LVP experiments performed at ~25 GPa (Boujibar et al., 2016). D<sup>Bg/melt</sup><sub>Fe</sub> was found to vary from ~1 to a constant value of ~0.3, for F values below ~5 wt% or above 10 wt%, respectively. It suggests a D<sup>Bg/melt</sup><sub>Fe</sub> negatively correlated

with temperature between the solidus and the liquidus, in agreement with a typical binary melting diagram (Fig. 9). Thus, controversial results between previous LH-DAC experiments could arise from different heating conditions. Experiments reporting very low D<sup>Bg/melt</sup><sub>Fe</sub> values were performed using a very thin insulating material (hardly detectable using X-ray diffraction). A clear advantage is to facilitate the recovery of relatively thick samples, which can be cut after the experiment in order to obtain relatively large and homogeneous sample regions for chemical analyses using the electron microprobe. However, such experimental procedure implies strong axial temperature gradient between the two diamonds. The center part of the recovered samples is likely experience relatively high temperatures, potentially close to the liquidus (high F possibly inducing low D<sup>Bg/melt</sup><sub>Fe</sub>, Fig. 9). Alternatively, experiments reporting higher D<sup>Bg/melt</sup><sub>Fe</sub> values used very thin samples well embedded in the insulating material (producing major diffraction peaks). While this type of loading minimizes axial temperature gradients in the sample, it makes the sample recovery much more difficult. In a previous study, X-ray diffraction was used to monitor carefully the onset of melting at the solidus temperature (Andrault et al., 2011) (low F possibly inducing high D<sup>Bg/melt</sup><sub>Fe</sub>). Differences in heating procedure and thus in melting temperature between previous works could have induce significantly different values of D<sup>Bg/melt</sup><sub>Fe</sub>. We note that the Fe behavior could be complicated by other factors: (i) the role of Al, which is not well constrained at high pressures; Due to the strong Al-Fe coupling in the Bg structure, an Al-depletion from the Bg structure would contribute to lower D<sup>Bg/melt</sup><sub>Fe</sub>; (ii) the variable Fe<sup>2+</sup> and Fe<sup>3+</sup> fractions, because each one could partition differently between Bg and the melt, etc. A full quantitative model of D<sup>Bg/melt</sup><sub>Fe</sub> at lower mantle conditions requires additional experimental and theoretical studies.

### 4.4. Solid-liquid density contrast

The Δρ<sub>m-s</sub> can be evaluated based on the density of both phases. In the following calculations, we consider a bulk mantle of pyrolitic composition with a bulk Fe/(Mg + Fe) ratio (Fe#) of 0.1. We adjust the Fe-contents in the solid and the melt in order to reproduce the bulk mantle Fe-content, for various values of D<sup>Bg/melt</sup><sub>Fe</sub>, which remains an adjustable parameter in the calculation. For coexisting solid and melt compositions, we first calculate the densities in the solid state, before we apply a correction to the melt density of 6% to 4% for pressures between 30 and 130 GPa, respectively, to take into account the volume of melting (Fig. 2). Composition of the solid can correspond either to (i) pure Bg, as expected for the residual solid from solidus to liquidus temperatures in our pseudo-binary melting diagrams (Fig. 4), or to (ii) the mineral assemblage typical of pyrolite, which would correspond to the mantle composition in case of incipient melting. On the other hand, composition of the melt is approximated by a mixture of 55% Bg, 6.2% CaPv and 38.8% Fp, which represents well the PE-melt at all lower mantle pressures (Fig. 4). We neglect the P-T dependence of melt composition, because the X(SiO₂) value of the PET (i) does not vary significantly with pressure and (ii) is not very different from the bulk pyrolitic mantle. Densities at high P and T of the solid and the melt are calculated based on their respective molar fractions of the following five different end-members: Al-bearing MgSiO₃, FeSiO₃, MgO, FeO, CaPv, using the PVT equation of state of each of them. We used the Mie-Grüneisen formalism with an auto-coherent set of elastic parameters (Matas et al., 2007).

For the solid-liquid density contrast, two end-member situations arise:

(A) During the first stages of magma ocean crystallization, F values are expected to be large (Fig. 10). They could range between ~0.6 and 1, which corresponds to temperatures
<figure><img src="image_332.png" /><figcaption>**Fig. 10.** Density contrast for various couples of coexisting melt and Bg, in the context of a crystallizing magma ocean (F higher than 0.4). All values are normalized to the density of a same Bg having an Fe# of 5% (red). Negative values correspond to buoyant melt. We report relative densities of Bg with Fe# of 1% (green), fully molten pyrolite (yellow) and partial melts calculated for F values from 0.9 to 0.4. We perform the calculation for $D_{\text{Fe}}^{\text{Bg}/\text{melt}}$ values of 0.1 (blue area, corresponding to Nomura et al. (2011), Tateno et al. (2014)) and 0.5 (brown area, corresponding to Andrault et al. (2012)).</figcaption></figure>

<figure><img src="image_333.png" /><figcaption>**Fig. 11.** Domains of positive or negative melt buoyancy for varying degrees of mantle partial melting and various possible values of the solid-liquid Fe partition coefficient. We report boundaries between "sink" and "float" domains at pressures of 30, 50, 90 and 130 GPa. The pink shaded region corresponds to a density contrast within 0.5%. Horizontal orange shaded regions correspond to ranges of $D_{\text{Fe}}^{\text{Bg}/\text{melt}}$ reported around 0.1 (T-14 & N-11; (Nomura et al., 2011; Tateno et al., 2014)) and 0.5 (A-12; (Andrault et al., 2012)) at high mantle depths (Fig. 8).</figcaption></figure>

between the PET and the liquidus (Fig. 6). The situation corresponds to a variable fraction of Bg grains entrained in a major amount of melt. Close to the liquidus (F ~ 1), Fe# in Bg could vary from ~0.05 to ~0.01, depending on the controversial values of $D_{\text{Fe}}^{\text{Bg}/\text{Melt}}$ from 0.5 to 0.1, respectively, because the Fe# in the melt is ~0.1, similar to the bulk mantle. Using the procedure described above, we calculate $\Delta\rho_{m-s}$ between coexisting Bg and pyrolitic melt along melting curves and obtain mostly negative values, meaning relatively denser Bg grains (Fig. 10). The value of $\Delta\rho_{m-s}$ increases with pressure, due to a smaller volume of fusion at higher pressures but remains negative at all pressures from 30 to 135 GPa. $\Delta\rho_{m-s}$ also increases with decreasing the melt fraction, because the melt Fe# increases faster than the solid Fe#. We find no solid-melt density crossover for

$D_{\text{Fe}}^{\text{Bg}/\text{Melt}} = 0.5$, at least for F values higher than 0.4. For $D_{\text{Fe}}^{\text{Bg}/\text{Melt}} = 0.1$, Bg can become less dense than the melt for F values below ~0.7 in the lower mantle.

(B) At the latest stages of magma ocean crystallization, as well as in the context of partial melting in the present-day lower mantle, the situation corresponds to a minor amount of melt trapped in the solid mantle. This situation corresponds to incipient mantle melting below the PET (low F) made possible due to the presence of volatile elements. The solid phase can be Bg or pyrolite, depending on the melting degree, F. Here, we report $\Delta\rho_{m-s}$ values corresponding to a solid phase made of pure Bg, however, results are not very different for pyrolite. Due to the lack of constraints, we assume a melt with $X(\text{SiO}_2)$ equal to that of the PE-melt. Under these assumptions, the major change in melt composition with decreasing F is a higher Fe#. Calculations show that a denser melt, compared to a bridgmanitic mantle, is favored for (i) lower $D_{\text{Fe}}^{\text{Bg}/\text{Melt}}$, (ii) lower F and (iii) higher pressures (Fig. 11). There is a significant range of parameters, for values of F below 0.7 and $D_{\text{Fe}}^{\text{Bg}/\text{Melt}}$ below 0.45, where melts could sink in the solid mantle toward the CMB. Still, we remind here that the possible increase of $D_{\text{Fe}}^{\text{Bg}/\text{Melt}}$ at low F values (Boujibar et al., 2016) would favor buoyant melts.

# 5. Implications for crystallization of the magma ocean

## 5.1. Dynamics of the magma ocean crystallization

The crystallization of the early magma ocean is the primary mechanism invoked to produce a chemical stratification of the mantle (Boyet and Carlson, 2005; Caro et al., 2005). Concerning the mantle depth at which the crystallization began, our model suggests a mantle liquidus increasing smoothly with pressure up to the CMB pressure of 135 GPa (i.e. the A-chondritic model in Fig. 1). Thus, the adiabatic temperature profile of the cooling magma ocean, which also presents a relatively constant slope, would likely cross the liquidus starting from the CMB upwards (e.g. Fig. 7a in (Thomas and Asimow, 2013)). Magma ocean solidification should therefore occur from bottom up. Talking about the magma ocean solidification, we note that major changes in
the dynamics of the magma ocean should occur at F values lower than ~40%, the critical melt fraction when the mantle becomes more viscous (Abe, 1997), rather than when the adiabatic profile crosses the liquidus or the solidus (Monteux et al., 2016).

It has been proposed that Bg grains could settle in the magma ocean, inducing rejection of melts toward the Earth's surface (Boukare et al., 2015; Solomatov, 2007). Our calculations confirm a Bg denser than the coexisting melt at F values higher than 0.7 (Fig. 11). Still, the effective gravitational segregation of Bg grains in a crystallizing magma ocean is not obvious. Highly turbulent flows have certainly dominated in the molten mantle. Δρ<sub>m-s</sub> may not have been be sufficiently high to counterbalance mixing forces, especially in the lowermost mantle where Δρ<sub>m-s</sub> decreases. This could have prevented major chemical segregation until late stages of the magma ocean crystallization. On the other hand, while an abrupt change in rheological behavior at F ~ 40% should disable turbulent mixing flows, it should also slow down chemical segregation by inhibiting the atomic diffusion. Thus, the two side-effects of crystallization, turbulent flow followed by high mantle viscosity, are not in favor of large scale chemical heterogeneities early in the crystallizing Earth's mantle.

Following the assumption that Bg grains have efficiently segregated from the crystallizing magma ocean, the melt composition should drift toward higher Fe#, because Fe enters preferentially into the melt (e.g. Boukare et al. (2015)) and also to a slightly higher SiO₂-content (due to the composition of the PET melt, Fig. 5). Increasing the Fe# in melt favors higher Δρ<sub>m-s</sub> and sinking melts. This effect could have contributed to produce an early BMO (Labrosse et al., 2007) and/or overturns (Elkins-Tanton, 2008). However, our melting model suggests that the Fe-enrichment of the melt could remain moderate. If we consider the most extreme case of (i) full gravitational segregation of the crystallizing Bg grains, (ii) a D<sub>Fe</sub><sup>Sol/lig</sup> value close to 0 and (iii) a bulk fractional crystallization of 60% (thus F = 0.4), we find that the melt would reach Fe# of ~0.25 (for a bulk pyroitic mantle with Fe# of ~0.1). For a more reasonable sets of parameters, a high degree of Fe-enrichment can only occur at the very final stages of the magma ocean crystallization.

## 5.2. Chemical similarities between the pseudo Eutectic-melt and peridotite

Major consequences arise from the very high F values found at the PET (Fig. 6). Brutal solidification of the magma ocean could occur when the degree of partial melting becomes lower than 83% (for peridotite), 74% (for pyrolite) or 56% (for chondritic mantle) at a given mantle depth. Such F values are significantly higher than the threshold value of 40% necessary to produce a relatively viscous mantle (Abe, 1997). Therefore, final mantle crystallization could be achieved at the same time as the mantle became viscous. It would disable chemical segregation by melt gravitation in a mushy mantle and favor instead a homogeneous mantle after bulk magma ocean crystallization. Mantle overturn would also be unlikely, because the magma ocean would crystallize before a too significant Fe-enrichment of the melt.

Our model shows that the peridotite composition is close to the PE-melt at high pressure (Figs. 3–6). This compositional similarity was already discussed a long time ago (e.g. Zhang and Herzberg (1994)). This situation could result from a large scale chemical differentiation during magma ocean crystallization, where the upper part of the mantle would correspond to the last melt that solidified, and the residual solid, Bg, would be concentrated in the deep mantle. A floating layer of peridotitic melt of several hundred kilometers thickness (possibly even more than 1000 km) would have crystallized as a bulk, in agreement with our high F values at the PET. A highly bridgmanitic deep lower mantle would agree with

previous studies (Matas et al., 2007; Murakami et al., 2012; Samuel et al., 2005).

Today, presence of volatile elements could induce incipient partial melting in the deep mantle. The melt could be denser than the mantle and sink, in the case the value of D<sub>Fe</sub><sup>Bg/melt</sup> would indeed be as low as 0.4, as suggested by some previous studies (Nomura et al., 2011; Tateno et al., 2014). Sinking melts could produce the ULVZ in the lowermost mantle, independently from the temperature prevailing in the lowermost mantle early in Earth's history. This scenario contrasts with another one suggesting that the ULVZ are the relic of an ancient BMO (Labrosse et al., 2007).

## 5.3. Maximum core temperature after magma ocean crystallization

After the Moon forming giant impact, the Earth has been largely molten. Subsequent cooling of the magma ocean could have been relatively fast, within 100 ky (Abe, 1997; Monteux et al., 2016; Solomatov, 2007). It was proposed that a BMO could have persisted in the lowermost mantle for a much longer time, due to a large amount of heat stored in the core (Labrosse et al., 2007). Still, the early temperature of the CMB (a good proxy for the core temperature), as well as the lifetime of the BMO remain highly debated. To keep a hot BMO thermally stable, there must be a layer of solid material just above it producing an efficient thermal blanketing between the molten BMO in contact with the hot core and the solid mantle. This solid shell would hamper escape of the core heat. This solid material could only be Bg, the liquidus phase in the deep mantle. Consequently, the Bg melting point of ~5400 K at a pressure of 135 GPa (Fig. 1) corresponds formally to the highest possible CMB temperature after crystallization of the magma ocean. It is ~1300 K above the current CMB temperature.

However, a temperature of ~5400 K represents an improbable upper limit for the early CMB temperature. The reason is that the physical contact between the BMO and the overlaying Bg layer can react chemically. The further away from Bg is the chemical composition of the BMO, the lower should be the equilibrium temperature, in agreement with binary phase diagrams (Fig. 4). Therefore, the more likely the CMB temperature after magma ocean crystallization could correspond to the first occurrence of a more viscous mantle at the CMB (Monteux et al., 2016). This temperature is estimated to ~4400 K, only ~300 K higher than the CMB temperature today (Andrault et al., 2016).

## Acknowledgments

This work has been supported by the ANR contract "OxyDeep". This research was financed by the French Government Laboratory of Excellence initiative no. ANR-10-LABX-0006, the Région Auvergne and the European Regional Development Fund. This is Laboratory of Excellence ClerVolc contribution number 242.

## Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.pepi.2017.02.009.

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# Deep and persistent melt layer in the Archaean mantle

Denis Andrault<sup>1*</sup>, Giacomo Pesce<sup>1,4</sup>, Geeth Manthilake<sup>1</sup>, Julien Monteux<sup>1</sup>, Nathalie Bolfan-Casanova<sup>1</sup>, Julien Chantel<sup>1</sup>, Davide Novella<sup>1</sup>, Nicolas Guignot<sup>2</sup>, Andrew King<sup>2</sup>, Jean-Paul Itié<sup>2</sup> and Louis Hennet<sup>1,3</sup>

The transition from the Archaean to the Proterozoic ended a period of great instability at the Earth's surface. The origin of this transition could be a change in the dynamic regime of the Earth's interior. Here we use laboratory experiments to investigate the solidus of samples representative of the Archaean upper mantle. Our two complementary in situ measurements of the melting curve reveal a solidus that is 200-250 K lower than previously reported at depths higher than about 100 km. Such a lower solidus temperature makes partial melting today easier than previously thought, particularly in the presence of volatiles (H₂O and CO₂). A lower solidus could also account for the early high production of melts such as komatiites. For an Archaean mantle that was 200-300 K hotter than today, significant melting is expected at depths from 100-150 km to more than 400 km. Thus, a persistent layer of melt may have existed in the Archaean upper mantle. This shell of molten material may have progressively disappeared because of secular cooling of the mantle. Crystallization would have increased the upper mantle viscosity and could have enhanced mechanical coupling between the lithosphere and the asthenosphere. Such a change might explain the transition from surface dynamics dominated by a stagnant lid on the early Earth to modern-like plate tectonics with deep slab subduction.

Melting is a first-order phase transformation that has drastic consequences for various geophysically observable material properties, such as seismic-wave velocities and electrical conductivity (EC). As geological materials are chemically complex, they generally melt partially over a wide range of temperatures between their solidus and liquidus. In the early stages of the Earth's formation, extensive melting occurred down to great mantle depths, with the formation of a magma ocean, through the combination of radiogenic heating, impact-induced heating during accretionary events and gravitational energy release during core-mantle separation<fnref n="1" />. Partial melting can still occur today in the mantle, but at limited degrees of partial melting (F) and in specific regions. It occurs close to the Earth's surface when hot mantle materials undergo decompression, as at mid-ocean ridges. Also, seismic, magnetotelluric and electrical anomalies suggest the presence of melts at mantle depths between 80 and 200 km (ref. ²), just atop the 410 km mantle discontinuity³ and above the core-mantle boundary⁴. In these regions, thermochemical heterogeneities alone cannot explain the magnitude of anomalies.

Careful experiments are needed to address properly the evolution of the mantle solidus with pressure. Ideally, one should determine the onset of melting in the presence of the right amount of volatiles, such as CO₂ and H₂O, which unfortunately remains uncertain⁵ and could vary from one geological setting to another. Generally, the dry solidus is used as a reference to which is added the role of volatiles⁶. The dry-solidus profile currently accepted for the upper mantle is derived from a few studies performed on KLB-1 peridotite⁷⁻⁹, garnet peridotite¹⁰, Allende meteorite¹¹ and the CMAS (CaO, MgO, Al₂O₃ and SiO₂) composition¹². All these studies report melting temperatures significantly higher than the present-day temperature profile¹³ (Supplementary Fig. 1). All previous studies used the so-called 'quench method' based on the analyses of recovered samples. This

method is not well adapted to detect the onset of melting, which can correspond to *F* values smaller than 1 wt% in natural samples¹⁴.

In this study, we determined the mantle solidus temperature using two independent in situ techniques, EC and X-ray diffraction, at pressures and temperatures up to 28 GPa and 2,300 K, in a multi-anvil apparatus.

## Determination of the mantle solidus

Using EC, we first observed dehydration of the cell assembly, followed by crystallization of the glass starting material at a temperature below 1,573 K (Supplementary Fig. 5a). A complete sample dehydration and crystallization is evidenced by a perfect reproducibility of the sample conductivity when performing various cycles of cooling and heating. Full crystallization in this temperature range is also evidenced by analyses of the microstructure of quenched samples. On further heating, we observed a sudden increase of the slope in the EC profile, above a threshold temperature of 1,815–1,865 K (Fig. 1, Supplementary Fig. 5b and Supplementary Table 2). This can be interpreted as that just above the solidus temperature, *F* is very low in the sample and the melt wets only some specific grain surfaces, and not others, because the surface energy depends on its crystallographic orientation. With increasing temperature, the melt interconnection between the two electrodes improves. The melt progressively becomes the dominant conductive phase, with an ionic conduction mechanism¹⁵. Previous studies on partial melting report precisely the same behaviour in the evolution of sample conductivity with temperature¹⁶⁻¹⁸.

Using X-ray diffraction, we first monitored the sample crystallization at temperatures from 1,200 K to 1,600 K (Supplementary Fig. 6), until the diffraction pattern remained independent of time. At this point, the set of diffractions peaks corresponded well with the expected mineralogy (Supplementary Fig. 7). We observed

<footnote n="1">¹Université Clermont Auvergne, CNRS, IRD, OPGC, Laboratoire Magmas et Volcans, Clermont-Ferrand, France. ²Synchrotron SOLEIL, Gif-sur-Yvette, France. ³Conditions Extrêmes et Matériaux: Haute Température et Irradiation, CNRS, Orléans, France. Present address: ⁴School of Geosciences, The University of Edinburgh, Edinburgh, UK. *e-mail: denis.andrault@uca.fr</footnote>
<figure><img src="image_334.png" /></figure>

**Fig. 1 | EC results.** The sample EC was measured at increasing temperatures for a nominal pressure of 5 GPa after various pre-heating cycles. The clear change in slope at 1,700 K indicates a change in the conductivity mechanism at the onset of sample melting. A further increase of temperature induces a better interconnection of the melt between the electrodes, before ionic conduction in the interconnected melt becomes largely dominant (additional details are reported in Supplementary Fig. 5).

olivine and its high-pressure polymorphs, and majoritic garnet and pyroxenes were also visible for pressures below ~14 GPa. At sub-solidus conditions, the relative peak intensities were very compatible with those theoretically expected based on atomic topologies, which hence revealed an equilibrated microstructure. No significant changes were observed on further heating until the sample behaviour changed abruptly: all the diffraction peaks from the sample suddenly underwent major changes of their intensities with time. Large intensity variations could be seen in real time on diffraction profiles recorded by the Ge detector (Supplementary Fig. 8). Such instability denotes a fast grain rotation in the X-ray beam. We estimate that a grain rotation of less than 1° is enough to stop the diffraction signal of a grain previously oriented in ideal Bragg conditions. Decreasing the sample temperature by 10–20 K stopped entirely the rapid variation in peak intensities. Thus, this sudden change above a critical temperature is not compatible with a continuous increase with temperature of grain-growth rate. Instead, the observed fast grain rotation can be related to the presence of a thin film of melt at the grain boundary. The melt induces a discontinuous increase in the rate of atomic diffusion, which possibly favours growth of some surfaces of the grains at the expense of others. A similar technique was used previously to determine the solidus of basalt in a laser-heated diamond anvil cell¹⁹.

Some experimental charges were quenched at temperatures just below or just above the onset of melting to probe the textural evolution using a scanning electron microscope (SEM). Under subsolidus conditions, the starting material appears well recrystallized into grains of several microns with polygonal shape (Fig. 2). A good textural equilibrium is evidenced by sharp grain-boundary angles, often close to 120°, and linear grain boundaries in between junctions²⁰. Based on chemical maps, the mineralogical content at 5 GPa, for example, is an intimate mixture of olivine, clinopyroxene, orthopyroxene and garnet. No remaining traces of the glass starting material were observed. Above the solidus, we could observe some melt after an extensive search using the SEM. The melt occurs in the shape of very thin films along grain boundaries and nanometre-size pockets at triple junctions, as typically observed in partially molten systems²¹,²². Due to the short duration of the experiments, the microstructure may not correspond to full equilibrium. However,

<figure><img src="image_335.png" /></figure>

**Fig. 2 | Images of recovered samples.** a,b, Using the field-emission gun electron microscope, microphotographs were acquired on samples recovered after heating just above (a) and just below (b) the solidus temperature. In both cases, the pressure was 5 GPa. For a temperature above the solidus, very thin films and nanometre-size pockets of melt are clearly visible (pink arrows). c, The polygonal shape of grains is typical of good textural equilibrium. d, The sample mineralogy was refined from chemical map. Ol, olivine; Cpx, clinopyroxene; Gt, garnet; Opx, orthopyroxene.

one can estimate the degree of partial melting to less than 1%, based on the fraction of sample surface covered by the melt (the most-shiny regions). The melt composition could not be determined accurately because of chemical interferences with the composition of surrounding minerals.

Based on the new mantle solidus and using $T_0 = 1,373$ K at room pressure²³, we calculated an equation of melting using the Simon and Glatzel (SG)²⁴ equation [$T_m(P) = T_0(P/a + 1)^{1/c}$]. In this equation, *a* and *c* are adjustable parameters and *P* is pressure (Supplementary Table 3). A similar SG equation can model the dry liquidus reported in previous studies performed on KLB-1 peridotite⁸,²⁵. The change in chemical composition, for example, between KLB peridotite and the chondritic-type mantle used in this study could induce significant differences in the solidus and liquidus temperatures²³. However, the data set on the melting properties of the mantle-relevant compositions at mantle depths higher than 100–150 km remains insufficient to discuss these potential differences, which are therefore included in the uncertainties.

## Comparison with previous melting studies

Although our data set is consistent with previous studies below 3–4 GPa (our study is not more precise than previous works at low pressures), it shows a mantle solidus lower than those previously reported for higher pressures (Fig. 3). The difference is, on average, 250 K for mantle depths greater than 200 km. The only study in close agreement with ours is that performed on an Allende-meteorite type composition, which included sulfur in the starting material¹¹. The reason for the discrepancy with other studies can be manifold:

(1) Some previous studies used compositions that were too simplistic to represent properly the mantle state, for example, the CMAS composition used in Litasov and Ohtani¹². For such a composition, the onset of melting may only occur when the pseudo-eutectic temperature is reached. In our study, the starting material contains Fe, Ti, Cr and Na in addition to the
<figure><img src="image_336.png" /><figcaption>**Fig. 3** | The new solidus temperature profile. The onset of the melting of a chondritic-type mantle composition was determined up to 28 GPa using EC (red squares) and X-ray diffraction (green squares). The new solidus is compared with previous studies performed using the quench method on the peridotitic mantle<sup>7-10</sup> or the simplified CMAS<sup>12</sup> composition. The new solidus plots significantly lower at pressures above 4–5 GPa.</figcaption></figure>

CMAS basis. It was shown that such compositional changes can yield a difference of solidus temperature of a couple 100 K (refs 7,23).

(2) The major melting criterion used in previous studies is the observation of molten regions in recovered samples. The formation of melt pockets can be difficult to detect at the lowest *F* values. Previous studies dedicated to this matter have established special techniques to detect the onset of melting<sup>14,26</sup>. However, the SEM images published in previous works correspond to an extremely high *F*, with a large fraction of the sample fully molten<sup>9,12,25</sup>. In contrast, our two in situ techniques are very sensitive to detect the onset of melting (Methods). In a previous study, the transmission electron microscope was used to differentiate grains that were solid at high temperature from secondary grains that rapidly recrystallized at the grain interfaces on quenching<sup>7</sup>. Some of the reported experiments show the absence of melt at temperatures higher than our new solidus temperatures, which we can only try to explain by the next point.

(3) Previous studies used mixtures of oxide powders with typical grain sizes on the order of micrometres. The heterogeneous grain composition does not favour the occurrence of nanoscale regions with the chemical composition of the solidus melt. Significant atomic diffusion is needed, over a distance typical of the grain size, to induce melting at the solidus temperature. The mean atomic path is estimated to be less than 10 nm per minute in the solid state at 2,000 K (ref. 27). Therefore, kinetic effects, which were not taken into account in previous studies, can largely inhibit the melting of a mixture of oxides at the solidus temperature. In contrast, we used a glass with an ideal chemical homogeneity at the atomic scale. Chemical interactions are much facilitated, even though the glass eventually recrystallized in nanograins above the glass-liquid transition temperature, as observed in our study.

Only a few studies report the value of *F* at temperatures between the solidus and the liquidus at upper mantle conditions and these studies do not agree well with each other (Supplementary Fig. 9). The disagreement could come from differences in the chemical composition between the starting materials (peridotite<sup>8</sup>, garnet-peridotite<sup>10</sup>

or CMAS<sup>12</sup>) or to a difficult control of *P*–*T* conditions during the melting experiments. A theoretical study dedicated to the melting behaviour at relatively low pressure shows that the melt productivity can be highly variable with pressure, temperature and chemical composition<sup>28</sup>. In particular, the nature and the concentration of incompatible elements (Na and K) and *a fortiori* of volatile elements (H, C and S) can help to maintain relatively low *F* values over a significant temperature range above the solidus. Therefore, although the two in situ techniques used in this study are well suited to determine the solidus (because they can detect a small amount of melt), the variation of *F* with temperature between the solidus and the liquidus remains uncertain. This matter requires additional experimental studies.

## Partial melting in the mantle today

We now compare our solidus profile with geotherms reported for the first 700 km mantle depths (Supplementary Fig. 1). First, we remember that the shallow temperature profile depends on the type of geological setting: the younger is the crust, the steeper is the thermal gradient close to the Earth's surface. Nevertheless, all the geotherms meet a mean adiabatic temperature gradient at mantle depths greater than ~250 km (ref. 13). At the present-day, the surface potential temperature (*T*<sub>p</sub>) is reported from ~1,600 K to a maximum of 1,750 K (ref. 29). Both oceanic and continental lithosphere geotherms<sup>30</sup> currently plot at lower temperatures than the solidus, in agreement with a mantle state that is essentially solid. In that sense, our new measurements confirm that the possible occurrence of partial melting in specific regions of the upper mantle, suggested by geophysical measurements<sup>3,22</sup>, should be dominated by the role of volatiles (H<sub>2</sub>O and CO<sub>2</sub>). Still, the lower solidus temperature makes upper-mantle partial melting easier than previously thought.

## Partial melting in the Archaean mantle

Studies of non-arc basalts of Archaean and Proterozoic ages have revealed that the mantle *T*<sub>p</sub> was significantly higher, by 50–100 K or more, compared with the present-day maximum *T*<sub>p</sub> of ~1,750 K (refs 31–33). Komatiitic lavas, which are generated from hotter mantle plumes, also point to a significantly hotter mantle temperature in the past. The shallow temperature profile was also different during the Archaean. The internal heat production was twice to four times that of today<sup>34</sup>, which favours a steeper temperature profile in the lithosphere. Other effects instead favour a thicker lithosphere: (1) the early Earth initially operated in a regime dominated by a stagnant lid, with only episodic subduction of ageing plates<sup>35</sup> and (2) the transport of heat to the surface could have been dominated by intense volcanism, which plays a heat-pipe role<sup>36</sup>. Altogether, it was modelled that the early temperature profile in the shallow mantle could have lain in between the steeper oceanic and milder continental profiles<sup>37</sup> (Fig. 4 and Supplementary Fig. 1).

According to our results, an increase in the *T*<sub>p</sub> of the ambient mantle above 1,800–1,850 K should generate a partially molten layer within the upper mantle (Fig. 4). Comparable slopes between the mantle solidus and the adiabatic gradient at depths greater than 200–250 km make *T*<sub>p</sub> ≈ 1,900 K a maximum value before intensive melting occurs in the entire upper mantle. It is actually possible that the value of *T*<sub>p</sub> = 1,900 K was reached just after crystallization of the early magma ocean; a higher *T*<sub>p</sub> would be associated with high *F* values, which implies a low viscosity that favours a rapid mantle cooling<sup>38</sup>. Our discussion does not include the role of volatile elements (H<sub>2</sub>O and CO<sub>2</sub>), because their concentrations in the early mantle remain poorly constrained. Their presence is expected to decrease the mantle solidus and favour mantle melting, possibly at *T*<sub>p</sub> values significantly lower than 1,900 K. A partially molten layer could remain stable for long geological ages, because melts can be neutrally buoyant at mantle depths within a couple of hundred kilometres above the 410 km mantle discontinuity<sup>39,40</sup>.