Carbon, carbides, carbonates and carbonatitic melts in the Earth's interior

Over recent decades, many experimental studies have focused on the effect of CO2 on phase equilibria and melting behaviour of synthetic eclogites and peridotites as a function of pressure and temperature. These studies have been of fundamental importance to understanding the origin of carbonated magmas varying in composition from carbonatitic to kimberlitic. The occurrence of diamonds in natural rocks is further evidence of the presence of (reduced) carbon in the Earth's interior. The oxygenation of the Earth's interior (i.e. its redox state) through time has strongly influenced the speciation of carbon from the mantle to mantle-derived magmas and, in turn, to the volcanic gases released to the atmosphere. This paper explains how the knowledge of the oxygen fugacity recorded by mantle rocks and determined through the use of appropriate oxy-thermobarometers allows modelling of the speciation of carbon in the mantle, its mobilization in the asthenospheric mantle by redox partial melting, and its sequestration and storage during subduction by redox freezing processes. The effect of a gradual increase of the mantle fO2 on the mobilization of C is here discussed along with the main variables affecting its transport by subduction into the mantle.

Carbon in the Earth's mantle is in exchange with the Earth's surface and the atmosphere (Kasting et al. 1993). At subduction zones carbon from sediments and altered oceanic crust is transported into the mantle and recycled to the surface on a short timescale as a result of island arc processes, but some carbon probably persists both as carbonate minerals and as elemental carbon during subduction and can be carried down to the depth of the deep upper and even lower mantle (Kelemen & Manning 2015). In contrast, basaltic magmas at mid-ocean ridges and oceanic islands bring carbon mainly in the form of CO 2 to the surface. Some of this carbon shows geochemical evidence of crustal recycling (Hauri et al. 1993) but some might result from oxidation of a reduced primordial source; that is, a source present in the mantle since accretion of the Earth (Palot et al. 2012). Our understanding of the deep carbon cycle through the mantle requires information on the mobility, solubility within mantle rocks and magmas, and knowledge of the forms in which carbon is stable at different pressure, temperature and oxygen fugacity conditions within the Earth. This information is necessary to determine how much carbon is probably stored in the mantle, and the mechanisms by which it may be cycled through the mantle and eventually reach the surface. In this paper, known forms of carbonbearing phases found in mantle rocks are first described through a selection of classic articles from the literature, followed by discussion of the carbon speciation as a function of the mantle redox state through space and time.

Current estimates of carbon in the Earth's interior
Estimates of the abundance of carbon in the Earth's interior are uncertain owing to its low solubility in mantle minerals and the outgassing at shallow depths. The amount of carbon in rockforming minerals such as olivine, orthopyroxene, clinopyroxene and garnet has been determined experimentally and found to be in the range of a few ppm (Keppler et al. 2003;Rosenthal et al. 2015). Similarly, the most abundant minerals representative of the transition zone and lower mantle (i.e. wadsleyite, ringwoodite, ferropericlase and bridgmanite) also incorporate negligible (<1 ppm) amounts of carbon (Shcheka et al. 2006;Hayden & Watson 2008). The low concentration of carbon in the abundant silicate minerals implies that it must be stored in the largest geochemical reservoir, the terrestrial mantle (Javoy et al. 1982), as a pure phase in the immobile reduced form of elemental carbon (or carbide), oxidized carbonate and the mobile form of carbonated magma. Because of the low solubility of CO 2 in magmas upon decompression with consequent devolatilization, the possibility of tracking its history from the source rock to the surface is limited to a few known undegassed lavas (e.g. Siqueiros and 2πD43 popping rocks; Le Voyer et al. 2017); alternatively, geochemical tracers and noble gases that correlate positively with the abundance of C (e.g. helium, argon, barium, rubidium and niobium; Matthews et al. 2017) are used, the concentrations of which are better constrained because of their high incompatibility in erupted lavas and sampled fumaroles. Using, then, the global average concentration of these trace elements from mid-ocean ridge basalts (MORB) and assuming typical melt fractions of 10%, such a method provides concentrations of a few tens of ppm (c. 14-50 ppm) as referred to the depleted mantle (i.e. the residual mantle source after extraction of MORB); whereas the carbon content of the bulk silicate Earth (BSE), generally determined from mantle plume-like magmas, has been proposed to vary between 500 and 1000 ppm (Marty et al. 2013).
Different forms of elemental carbon in mantle rocks: graphite, diamonds and carbides Carbon forms different accessory phases in rocks from the Earth's interior, such as graphite, diamond, iron(-nickel) and silicon carbides and either solid or liquid carbonates. Native carbon in mantle-derived rocks such as eclogites and peridotites occurs both as graphite and diamond. The origin of graphite in mantle-derived rocks is usually explained as a result of the following: (1) transformation from an original diamond-bearing assemblage to graphite owing to a re-emplacement at lower pressures observed, for example, in garnet pyroxenite layers from Beni Bousera, Morocco (Pearson et al. 1989); (2) exsolution from a C-saturated magma at reducing conditions as observed in ultramafic xenoliths from the Algerian Sahara (Kornprobst et al. 1987); or (3) as a relict of metasomatic processes such as found in peridotites from Jagersfontein (South Africa) showing multiple graphite flakes of vein-like form (Field & Haggerty 1990). Some graphite occurrences are thought to originate by assimilation from magma of carbonaceous country rocks (Ripley & Taib 1989;Barrenechea et al. 1997;Luque et al. 1998). In contrast to the processes above, where variation in pressure, temperature and bulk-rock chemistry are invoked to explain the origin of graphite, there is also evidence of crystalline carbon in exhumed blueschist metasedimentary rocks in contact with serpentinite from Alpine Corsica (France) that formed by reduction of carbonate during cold subduction (Galvez et al. 2013).
In contrast to what observed for graphite, the occurrence of diamonds is limited to specific rock types, mainly kimberlites but also lamproites and lamprophyres from cratonic areas (Boyd & Gurney 1986;Gurney et al. 2010), regions of the continental crust that have remained tectonically stable for at least 2.5 Gyr and are underlain by a thick lithospheric mantle extending to depths of over 200 km. Rocks considered as host for diamonds have been identified on the basis of inclusions in natural diamonds and are represented by eclogites (E-type inclusions), peridotites and websterites (P-type inclusions ;Meyer 1987;Gurney 1989;Stachel & Harris 2008). The occurrence of carbon in the form of diamond has been a major field of research because of its economic value and stimulated some of the very first high-pressure experiments (Bundy 1963;Kennedy & Kennedy 1976;Akaishi et al. 1990;Irifune et al. 2004) that aimed to explore the pressure and temperature conditions for synthesis of gem-like quality diamonds. The results from these studies combined with thermodynamic predictions (Day 2012) have been used as a geothermobarometer to constrain the equilibration pressures and temperatures of diamond-bearing rocks, in particular those rocks showing coexistence between graphite and diamond (e.g. Korsakov et al. 2010;Mikhailenko et al. 2016). Importantly, most attention has been paid to the chemical composition of minerals and fluids trapped in diamonds as a tool to understand their origin. For instance, this is the case for silicate minerals from Juina diamonds (Walter et al. 2008) and daughter minerals in fibrous diamonds (Weiss et al. 2011), both showing geochemical evidence of the passage of CO 2 -rich melts with important implications for the origin of diamonds by reduction of C-O(-H) mantle fluids.
Although rarely found in nature, carbon can be stored also as silicon carbide (Leung et al. 1990;Mathez et al. 1995;Yang et al. 2015) or as an alloying element in Fe(-Ni) metal trapped in diamonds (Jacob 2004;Kaminsky & Wirth 2011;Mikhail et al. 2014;Smith et al. 2016). The stability of Fe(-Ni)-C intermetallic alloys has been the subject of investigation in recent high-pressure experimental studies (Fei & Brosh 2014;Rohrbach et al. 2014;Stagno et al. 2014) and, in the mantle, this appears strongly dependent on the ratio between metallic iron and elemental carbon and, therefore, mostly associated with local heterogeneities in the C/Fe distribution. In fact, assuming that the deep mantle at depth below c. 300 km is saturated with 1 wt% Fe(Ni) alloy (Frost et al. 2004;, most of the elemental carbon is predicted to dissolve with concentrations up to 2 wt% in the alloy. This implies that, where elemental carbon is locally more abundant (>c. 100 ppm) than iron, carbides can be stable in the form of molten Fe 7 C 3 along with coexisting diamonds (Dasgupta & Hirschmann 2010;Rohrbach et al. 2014). Therefore, carbides would form by solid-solid reaction only in portions of the Earth's interior where iron metal and elemental carbon (either graphite of diamonds) or carbonate (Palyanov et al. 2013) are in mutual contact. Thus, one should not be surprised if the best evidence of Fe-carbides in the mantle is probably produced by solid-solid reaction at the boundary between the Fe inclusions and the diamond host at mantle conditions (Kaminsky & Wirth 2011;Smith et al. 2016). The local mantle oxidation state also plays a critical role in determining the conditions for the stability of carbide versus carbonate phases.

Carbonate minerals and CO 2 -bearing melts
Carbon occurs in the mantle in its oxidized form (e.g. C 4+ ); for example, as either solid or molten carbonate or fluid where it can be present as both molecular (CO 2 ) and ionic (CO 3 2− ) species. Carbonate minerals are usually solid solutions between calcite (CaCO 3 ), magnesite (MgCO 3 ) and siderite (FeCO 3 ) end-members strongly depending on the temperature, pressure and bulk composition (see Hammouda & Keshav 2015, and references therein). A Ca, Mg-rich phase (dolomite) is stable below 4 GPa (c. 120 km) in peridotite assemblages (Falloon & Green 1989, whereas Ca-rich solid carbonates are shown experimentally to be stable in eclogitic assemblages (Hammouda 2003;Yaxley & Brey 2004). As the pressure increases, magnesite is expected to be the stable carbonate with respect to dolomite and siderite as a consequence of the high affinity of Ca and Fe for lower mantle silicate minerals (see Fig. 1a; Hammouda 2003;Ghosh et al. 2009;Litasov & Ohtani 2009a,b, 2010Keshav & Gudfinnsson 2010;Stagno et al. 2011;Kiseeva et al. 2013). However, previous experimental studies support the observation of Mg-rich carbonates

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V. Stagno and aragonite coexisting for Mg# of the initial starting material of ≤0.6 (Fig. 1b). The presence and chemical composition of solid carbonates coexisting with mantle minerals are determining factors for the composition of near-solidus CO 2 -rich magmas formed by partial melting of carbonated eclogites and peridotites (Gudfinnsson & Presnall 2005;Hammouda & Keshav 2015, and references therein). Carbonatites are defined by the Subcommission on the Systematics of Igneous Rocks of the International Union of Geological Sciences (IUGS) as igneous rocks, either effusive or intrusive, containing more than 50% in volume of primary carbonate minerals (Streckeisen 1980); that is, the result of crystallization of a magma with less than 10 wt% of SiO 2 (Woolley & Kempe 1989). Carbonatites have been found in several localities within diverse geological settings related to either intraplate continental rifts or compressive systems such as subduction zones (for more details on the worldwide distribution, see Woolley & Kjarsgaard 2008), although a mantle origin for these liquids is not unequivocal (Koster van Groos & Wyllie 1963;Wyllie & Huang 1975;Wallace & Green 1988;Veksler et al. 1998) as they might retain evidence of crustal origin (Liu et al. 2016) and latestage assimilation processes (Lustrino et al. 2016). Primary carbonatitic melts were shown experimentally to be characterized by extremely low viscosity in the range of 0.003 and 0.01 Pa s (Kono et al. 2014;Stagno et al. 2018), other than being an important constituent of metasomatic fluids interacting with mantle silicates in peridotite xenoliths from Spitsbergen in Norway (Ionov et al. 1993); and their possible origin beneath mid-ocean ridges has been the subject of several experimental studies (Dasgupta & Hirschmann 2006 ;Stagno et al. 2013) aimed at shedding light on the seismic and electrical conductivity anomalies in the upper mantle as detected beneath the East Pacific Rise ocean ridge (Evans et al. 1999;Dunn et al. 2001;Gu et al. 2005;Gaillard et al. 2008). Kimberlitic magmas are thought to form at depths below 150 km by partial melting of a carbonated mantle rock source and are also important carriers of carbon either in the form of a dissolved CO 3 2− component in the melt, or as exsolved CO 2 or diamonds. Diamonds found in kimberlites, such as those from Lac de Gras (Canada), are known for showing morphological features typical of surface dissolution that link with the oxidizing nature of these melts (Gurney et al. 2004;Fedortchouk et al. 2005) during their ascent at conditions where diamonds become unstable. The local oxygen fugacity has, therefore, the potential to flux carbon out the Earth's interior, with implications for its residence time.
The speciation of carbon as a function of pressure, temperature and Earth's mantle redox state To date, many experimental studies have been performed to investigate the structural stability of pure carbonate minerals (Biellmann et al. 1993;Isshiki et al. 2004;Oganov et al. 2008;Mao et al. 2011;Boulard et al. 2012;Cerantola et al. 2017) and their melting (Tao et al. 2013;Solopova et al. 2014;Shatskiy et al. 2015a,b) as well as melting of CO 2 -bearing mineral mantle assemblages as a function of pressure and temperature, respectively (for a detailed reference list see Hammouda & Keshav 2015). All these experimental studies, however, assume the stability of carbonate minerals at depth, neglecting the possibility that elemental carbon rather than carbonate can be the stable carbon phase depending on the availability of oxygen in the interior of the Earth. An alternative and more dynamic approach to understanding the state of carbon at depth is to consider the oxygen fugacity required for carbonate (liquid or solid) to be stable versus elemental carbon. The fO 2 in the Earth's interior is buffered by the local abundant silicate minerals and is dependent on the pressure and temperature. Only when the fO 2 required for the carbon-carbonate equilibrium crosses the local fO 2 buffered by the mantle rocks will oxidation of diamonds to solid carbonates occur and, at solidus T, CO 2 -rich magmas can form. In the next section, we will review some recent studies on the calibration of oxy-thermobarometers that are widely used to determine the oxidation state of mantle peridotites and eclogites and, thus, model the speciation of carbon throughout the Earth's interior. In addition, some redox reactions of interest for the speciation of carbon down to the lower mantle will be discussed.

The oxygen fugacity and its application in experimental petrology
The oxygen fugacity ( fO 2 ), or partial pressure of oxygen (Eugster 1957), is the thermodynamic variable that indicates the chemical potential (i.e. availability) of oxygen in those reactions where both reagents and products contain the same element(s) but with different oxidation states. These reactions are termed redox reactions and their graphical representations are univariant curves in log fO 2 -temperature diagrams. At a given temperature, above this curve the oxidized phase of an assemblage is stable, whereas below it the reduced phase is stable (see Fig. 2). Rock-forming minerals are widely characterized by the presence of heterovalent elements, such as iron, chromium and vanadium. Their occurrence in oxidized or reduced form can be used to infer the redox state at which certain rocks have equilibrated. An important goal in experimental geochemistry is, therefore, to investigate the behaviour of these elements with respect to the fO 2 and develop interpretative models to understand the change of redox conditions in the Earth and how this might have influenced the speciation of carbon (Delano 2001;Li & Lee 2004;Aulbach & Stagno 2016).
The fO 2 in experiments performed at high pressure and temperature is monitored mainly following two techniques: the first is based on the use of solid minerals or metal-metal oxide couples (e.g. Fe-FeO, Re-ReO 2 , Mo-MoO, Ni-NiO, etc.) that buffer the oxygen fugacity at certain known values calculated using the relative thermodynamic data and equation of states; the second approach employs noble metals as redox sensors to effectively measure the unknown oxygen fugacity of the run products  (Luth 1993); EMOG, enstatite-magnesite-olivine-graphite, and EDDOG, enstatite-dolomite-diopside-olivine-graphite buffers (Stagno & Frost 2010); IW, iron-wüstite buffer (O'Neill 1987); C-COH, graphite-COH fluid (Ulmer & Luth 1991); MsOCP, moissanite-olivine-graphiteenstatite (Ulmer et al. 1997).

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Carbon speciation in the Earth's interior recovered from a given pressure and temperature. In more detail, these techniques can be summarized as follows.
(1) Double capsules are used, where an outer capsule (e.g. of Re) contains a metal oxide (e.g. ReO 2 ) buffer and H 2 O and an inner capsule contains the sample plus H 2 O. A Pt inner capsule ensures permeability of H 2 between the buffering outer and the inner capsules. By buffering the fH 2 in the outer capsule the fO 2 of the inner capsule is fixed (Eugster & Wones 1962;Ulmer & Luth 1991).
(2) Capsules of materials such as Fe, Re and BN have been shown to influence the redox state of samples (Wendlandt et al. 1982;McCammon & Ross 2003), although a fluxing phase (i.e. a circulating fluid) is necessary to ensure homogeneous fO 2 conditions inside the whole capsule.
(3) Buffering solid assemblages such as a mixture of Re and ReO 2 can be added (about 15-20 wt%) to the starting material (Rubie 1999). In this case, the fO 2 of the experiment is buffered by the solid assemblage only if both metal and metal oxide phases coexist and are in mutual contact with the surrounding mineral assemblage. The circulation of a fluid phase would also help to buffer the fO 2 all over the sample.
Obviously, the choice of the metal-metal oxide depends on its potential reactivity with the experimental starting materials, which would limit its applicability. (4) Noble metal alloys (e.g. platinum group elements (PGE), Au and Ag) are used as sliding redox sensors where the fO 2 is measured (not buffered), which normally comprise an Fe-bearing metal alloy (Huebner 1971;Taylor et al. 1992).
The first three experimental techniques allow investigation of the dependence of a variable (e.g. Fe 3+ /ΣFe in minerals, element partitioning, C-O-H fluid speciation, melting temperature) with respect to the buffered (imposed) known fO 2 . In contrast, the application of noble metals (mainly platinum and iridium) employed as redox sensor is more appropriate when the fO 2 buffered by a mineral assemblage is quantitatively not known, meaning that its variation as a function of P-T needs to be determined (i.e. the univariant curve in the log fO 2 versus T or P diagram), or when the fO 2 buffered by a solid mineral assemblage (although it can be calculated using a proper thermodynamic dataset of the mineral endmembers (Luth 1993) involved) needs to be verified owing to its use at extrapolated P-T conditions or owing to the disappearance of a phase (e.g. by melting). A practical example is given by the coexistence of graphite (diamond) and carbonate along with mantle silicates in peridotite (known by the acronym EDDOG/D) and eclogite (DCDG/D) mineral assemblages as follows: and Equilibria (1) and (2) are both chosen to represent the fO 2 at which carbon is present either as graphite (or diamond, C 0 ) or carbonate (C 4 + ) along with mantle mineral assemblages. The fO 2 buffered by both equilibria was calibrated based on a set of thermodynamic data for each pure phase by Eggler & Baker (1982) and Luth (1993), respectively (Fig. 2). However, the fO 2 buffered by equilibria involving solid carbonates is applicable only at temperatures below their melting temperature. Above the melting (solidus) temperature, the fO 2 will be buffered by similar equilibria to (1) and (2) where the solid carbonate is replaced by the CO 2 -rich silicate-bearing melt. Because thermodynamic data are complex to determine and not available for liquid carbonates, the composition of which varies as the temperature increases toward more and more SiO 2 -rich liquids, accurate measurements of the fO 2 at each P and T are necessary. These can be made by adding 3-5 wt% of pure Ir (or Pt) metal as a redox sensor to the starting material. During the high P-T experiment, FeO from the coexisting phases (i.e. equilibria (3) and (4)) is reduced to Fe 0 and alloys with the Ir metal. The activity of Fe in the alloy is adjusted to the value buffered by the presence of carbonate melt and graphite (or diamond; equilibria (1) and (2)) at a given P and T. The resulting lowering of the activity of the Ir (Pt) metal component is a consequence of the redox conditions imposed by the carbon-carbonate equilibrium as a function of pressure and temperature and the melt composition. The fO 2 at which carbon and carbonate coexist within synthetic peridotite and eclogite assemblages (1) and (2) at high P-T of the experiments is, thus, calculated using the simultaneous mineral equilibria and Fe 3 Al 2 Si 3 O 12 ¼ Al 2 SiO 5 þ 2SiO 2 þ 3Fe þ 1:5O 2 : garnet kyanite coesite alloy (4) The fO 2 of the above equilibria is then calculated with the formulae þ log a olivine Fe 2 SiO 4 À log a SiO 2 À 2log a alloy Fe (5) and log f O 2 ¼ ÀDrG P,T [4] 1:5RT ln(10) À 2log a alloy Fe þ 2 3 log a garnet Fe 3 Al 2 Si 3 O 12 : (6) A gradual decrease of the measured fO 2 buffered by equilibria (1) and (2) is observed as result of the increased SiO 2 content of the carbonated melt with temperature in contrast to thermodynamic calculations of the fO 2 buffered by the appropriate subsolidus peridotitic and eclogitic assemblage (Stagno & Frost 2010;Stagno et al. 2015).
The choice of including kyanite in equilibrium (4) is mainly motivated by the need to balance the excess of Al from the involved almandine component, although also supported by its presence in diamantiferous eclogites (Smyth 1980;Mikhailenko et al. 2016). Because Al 2 SiO 5 and SiO 2 are pure phases in natural eclogites (e.g. Mikhailenko et al. 2016), the fO 2 in (6) is calculated fixing the activity of these phases at unity, and a olivine Fe 2 SiO 4 , a alloy Fe , a SiO 2 and a garnet Fe 3 Al 2 Si 3 O 12 are the activities of the Fe 2 SiO 4 component in olivine, Fe in Fe-Ir alloy and the Fe 3 Al 2 Si 3 O 12 component of garnet, respectively, calculated using the appropriate activity-composition models (Stagno & Frost 2010;Stagno et al. 2015). DrG P,T is the standard state Gibbs free energy change of pure end-member equilibria (3) and (4), determined at the pressure and temperature of interest from the thermodynamic data (i.e. formation enthalpy, entropy, heat capacity, thermal expansivity, molar volume) and the equation of state of each mineral end-member (details have been given by Stagno & Frost 2010;Stagno et al. 2015). A full formulation of the DrG P,T has been given by Cemič (2005), where Δ r H 298 , Δ r S 298 , Δ r C p and Δ r α are the enthalpy and entropy of formation, heat capacity and thermal expansivity changes of the 378 V. Stagno reaction (Fei 1995;Fabrchanaya et al. 2004 ); Δ r V is the volume change of a reaction, i is the ambient pressure and temperature volumes times their appropriate thermal expansivity and β is the compressibility. is the activity coefficient of Fe in the alloy determined using symmetric binary Margules terms provided in the literature (Schwerdtfeger & Zwell 1968;Kessel et al. 2003). Many noble metals that form solid solutions with Fe can be employed as a redox sensor. Fe-Ir and Fe-Pt are preferred because Fe is likely to exist in the face-centred cube (FCC) structure over the experimental pressure and temperature range of multi-anvil applications. Further, the solubility of C in Ir and Pt has been shown to be negligible at least in the recovered run products (Stagno et al. 2011(Stagno et al. , 2015. Importantly, timescales of the order of 12-24 h are required for the equilibrium fO 2 to be obtained. Although an important aspect in facilitating equilibrium is to keep the grain size of the initial Ir and Pt metals at c. 5 µm to accelerate the diffusion of Fe from the surrounding silicate minerals, the equilibration becomes sluggish at subsolidus temperatures, with consequent unequilibrated fO 2 (Stagno et al. 2015). A further source of uncertainty is represented by the possible overestimation of XFe in the alloy caused by secondary X-ray fluorescence near grain boundaries (Llovet & Galan 2003). For instance, an overestimation of the XFe mole fraction in the alloy by ±0.01 (i.e. ±0.4 wt% Fe) would result in a difference in the calculated fO 2 of about ±0.3 log units. The presence of oxides measured in the alloy, such as SiO 2 and CaO, probably results from the contribution of nearby silicates, and it can be used to evaluate the quality of the electron microprobe measurements on the redox sensor alloy.
The mantle redox state and the speciation of carbon over time and ranging in age from c. 3.8 to c. 2.6 Ga. The knowledge of the fO 2 recorded by these rocks is made possible through the use of oxy-thermobarometers; that is, redox equilibria representative of peridotitic and eclogitic mantle mineral assemblages where Fe in the form of Fe 2+ and Fe 3+ occurs both as reagents and products as follows: The Gibbs free energy change of these chemical equilibria was calibrated experimentally at P-T applicable to mantle depths employing the redox sensor technique (O'Neill 1987;Ballhaus et al. 1991;Gudmundsson & Wood 1995;Stagno et al. 2013Stagno et al. , 2015. The use of these oxy-thermobarometers requires measurements of the Fe 3+ content in natural Cr-bearing spinel (equation (9)), and garnet (equations (10) and (11)) in addition to the chemical composition of the coexisting silicates. Figure 3 shows the Fe 3+ content of Cr-spinel and garnet of natural mantle peridotites and eclogites available in the literature plotted as a function of the calculated fO 2 . The positive correlation between Fe 3+ /ΣFe of spinel or garnet and the log fO 2 is evident and brings into consideration that most of the spinel peridotite xenoliths are more oxidized than garnet peridotite and eclogites. Natural spinels are characterized by averaged Fe 3+ /ΣFe contents of 22(±8)%, whereas garnets from peridotites and eclogites show much lower averaged contents of c. 8 (±5)% and 4(±3)%. Because of the coexistence of many of these xenoliths with graphite and/or diamonds, the correlation between Fe 3+ /ΣFe and the mantle redox state reflects the chemical potential of these rocks to reduce or oxidize volatile phases such as C through the general net redox reaction where Fe 3+ and Fe 2+ refer to the ferric and ferrous iron of the bulkrock. Indeed, a similar equilibrium can be written replacing C 0 and C 4+ with H 2 and H + , N 3− and N 2 , and S 2− and S 6+ , respectively, to describe the buffering effect of Fe-bearing silicates on the speciation of (less abundant) volatiles. The redox state of the lithospheric mantle as a function of equilibrated depth is shown in Figure 4, where most of the peridotitic xenoliths plot in the diamond and graphite stability field possibly along with C-O(-H) fluids or melts from carbonatitic to kimberlitic in composition. The fO 2 required for carbide phases to coexist along with mantle silicates would be 7-8 log units below the FeNi precipitation curve (Fig. 4) as predicted by Schmidt et al. (2014). In contrast, most of the fibrous diamonds show inclusions of daughter minerals probably crystallized from a CO 2 -rich melt (the growth medium) suggesting, therefore, an fO 2 for their formation near the equilibrium between diamonds and molten carbonate between −1 and −2.5 log units at P-T conditions of the cratonic geotherm (44 mW m −2 is here taken as reference). In addition, the oxidation state of most of the eclogitic rocks is shown to plot in the diamond stability field within a range of fO 2 values consistent with those of peridotite xenoliths. A few eclogitic xenoliths from the Lace kimberlites (Aulbach et al. 2017) appear reduced (log fO 2 between FMQ −4 and FMQ −5, where FMQ is fayalite-magnetite-quartz buffer) and might have coexisted, therefore, with CH 4 -rich fluids. Such overlap might reflect either 379 Carbon speciation in the Earth's interior Fe 3+ depletion of the protolith or the result of metasomatism. A more detailed explanation is given below.

The redox profile of the subducted slab and the transport of carbon to the deep mantle
The subduction of carbon back into the mantle is an important natural form of carbon sequestration and recycling (Kelemen & Manning 2015). The residence time, storage and flux in or out of carbon in the eclogitic portions of the slab mainly depend on the redox conditions buffered by the surrounding mineral phases represented by equilibrium (11). Carbonate minerals subducted into the deep mantle can undergo important polymorphic transformations such as that from rhombohedral dolomite-I to triclinic dolomite-II at 17 GPa to dolomite-III at c. 35 GPa, which makes them an important carrier of C down to the lower mantle (Mao et al. 2011). Subducted carbonates are also exposed to melting processes at variable depths depending on the bulk-rock chemistry and P-T path (Hammouda & Keshav 2015). A recent experimental study by Thomson et al. (2016) showed that melting of a carbonated MORB is expected to occur at depth between c. 330 and 580 km with the production of Na-bearing carbonatitic melts representing, therefore, a 'barrier' to further subduction of carbonate minerals. Although these melts are important metasomatic agents potentially responsible for the refertilization of the asthenospheric mantle (Rosenthal et al. 2014), the interaction with the surrounding Fe metal-saturated mantle can cause their reduction to diamonds by redox freezing (Rohrbach & Schmidt 2011). Inclusions in superdeep diamonds such as majorite and Ca-silicates (Thomson et al. 2016) were claimed to form by interaction of alkali-rich carbonatitic melts and reduced asthenospheric mantle. Importantly, the fate of the subducted carbonates at depth is also strongly linked with the intrinsic redox state of the oceanic slab buffered by Fe-bearing phases such as clinopyroxene and garnet. These minerals can significantly become oxidized and, thus, incorporate a large amount of Fe 3+ as a result of increasing depth (i.e. pressure) at the expense of the surrounding available oxygen (Stagno et al. 2015). This form of oxygen sequestration from Fe-bearing minerals can result in reduced portions of the subducted slab with diamond being the stable C form even at an fO 2 higher than that required for diamonds to be stable in peridotites (i.e. fO 2[DCDG/D] > fO 2[EMOG/D] ) as in Fig. 2; Luth 1993). A tentative reconstruction of the redox state of the subducted slab as a function of depth is shown in Figure 5a and b. Fig. 4. Log fO 2 (normalized to the FMQ buffer) calculated for mantle xenoliths using oxy-thermobarometers (9), (10) and (11). The blue curve is the oxygen fugacity calculated for equilibrium (1) along a cratonic geotherm of 44 mW m −2 that defines the stability field for diamond (or graphite) and solid (liquid) carbonate. The purple and pink curves indicate equilibrium fO 2 between diamonds and a carbonate-silicate and kimberlitic melt, respectively, calculated along a cratonic geotherm. The orange line is the FeNi precipitation curve (Frost & McCammon 2008). References are as in Figure 3.  5. (a) The fO 2 of subducted eclogitic rocks is calculated along a hot subduction geotherm assuming bulk Fe 3+ /ΣFe ratios of 12% that describes the ratio determined for modern-day MORB glasses (Cottrell & Kelley 2011) and for different bulk chemical compositions for synthetic eclogites in the literature (GA1, Yaxley & Green 1994;SLEC, Dasgupta et al. 2005;OTBC, Hammouda 2003). The fO 2 at which carbonate minerals or melts would reduce to graphite or diamond within eclogitic rock is also shown (bold black dashed line; Luth 1993). In (b) the fO 2 is determined for an eclogitic assemblage with a MORB bulk composition along a hot and cold subduction geotherm as for the Andes and Honshu respectively (Syracuse et al. 2010). In (c) the fO 2 is determined for an eclogitic assemblage with a MORB bulk compositions with Fe 3+ /ΣFe ratio of 0.07, 0.12 and 0.17.

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V. Stagno Here, the variation of fO 2 is calculated using the equilibrium (equation (11)) for an eclogitic slab with different bulk composition ( Fig. 5a; GA1, Yaxley & Green 1994;SLEC, Dasgupta et al. 2005;OTBC, Hammouda 2003), different temperature regime ( Fig. 5b; cold and hot subduction, Syracuse et al. 2010) and different Fe 3 + /ΣFe content to reflect the different oxidation state of the MORB protolith ( Fig. 5c; Cottrell & Kelley 2011) along with the fO 2 at which C and carbonate can coexist (Stagno et al. 2015). Although the effect of bulk-rock chemistry (Fig. 5a) mainly reflects on the composition of coexisting clinopyroxene and garnet used to calculate the fO 2 from equilibrium (11), carbonate minerals (or carbonatitic melts) are predicted to be stable down to the transition zone or lower mantle as a consequence of either the hot regime of the slab or its high ferric iron content inherited by the subducted altered oceanic crust or late-stage oxidizing processes. In both cases, diamonds in eclogites are expected to form at depths of 200-400 km, when the fO 2 buffered by the Fe-bearing silicate minerals crosses the appropriate carbon-carbonate equilibrium (dashed black line). Ancient subduction in the early Earth was probably inefficient in transporting carbonates to depth owing to the predicted hot regime (Brown 2006), which would have caused decarbonation or melting at shallow conditions (c. 30-70 km; Dasgupta & Hirschmann 2010). Alternatively, the low potential of oxidation of the slab (low Fe 3+ /ΣFe) might have contributed to near-surface reduction of subducted carbonates to graphite (Fig. 5c), thus preventing CO 2 outgassing. Both scenarios would be in contrast to an origin of kimberlitic magmas during the Archean as in case of the Wawa kimberlites (Kopylova et al. 2011), therefore supporting their extreme rarity in the initial stage of Earth's history (Stern et al. 2016).

The mantle redox state and carbon extraction over time
The determination of the oxidation state of the asthenospheric mantle and subducting slab at depth has important implications for the mobilization and sequestration of carbon over time. Carbonate melts in the Earth's interior formed by oxidation of diamonds when the fO 2 buffered by the coexisting Fe-bearing silicates represented by the equilibria (10) and (11) intercepts the fO 2 at which carbon can coexist with carbonate as in equation (1) and (2). In Figure 4 the fO 2 for the stability of carbonate with respect to graphite or diamond in peridotitic rocks is calculated along a representative cratonic geotherm, and Figure 5 shows the fO 2 at which carbon and carbonate would coexist along a subducted slab taking into account important variables such as the different MORB chemical composition, P-T path and Fe 3+ /ΣFe ratio of the protolith. The possibility for C-bearing rocks to melt is, therefore, dependent not only on the local thermal regimes but also, more importantly, on the temporal evolution of the mantle redox state that promotes oxidation of the refractory carbon to carbonate, promoting, therefore, redox melting processes (Stagno et al. 2013). Therefore, it is of fundamental importance to investigate the variation of the mantle redox state through time to better understand the mobilization of deep carbon through the history of the Earth.
Geochemical tracers such as the V/Sc ratio of erupted basalts have been widely used to claim the constancy of the mantle redox state over the last 3.8 Gyr (Li & Lee 2004;Scaillet & Gaillard 2011) to conditions where C is stable in the form of C 4+ . Based on the reconstruction of the mantle oxidation state over time using the V/Sc of Archean eclogites as representative of early metabasalts, Aulbach & Stagno (2016) highlighted the possibility that the mantle underwent a gradual, rather than sudden, oxidation process during which the fO 2 was raised by c. 1 log unit to the modern MORB during the last 3.8 Gyr. Despite the large uncertainties in their fO 2 determinations, a similar conclusion was reached by Nicklas et al.
(2018) through partitioning measurements of V in komatiites. Figure 6 is a schematic illustration that summarizes the redox melting of a diamond-bearing asthenospheric mantle from the Archean (Fig. 6a-d) to the present ( Fig. 6e and f ). The fO 2 of the mantle, which is indicated by straight lines calculated as a function of different Fe 3+ /ΣFe, is shown to increase toward shallower depths as a result of the decompression on the volume change of equation (10) until the carbon-carbonate equilibrium (i.e. equilibrium (1)) is crossed and carbonatitic melts form by redox melting. This probably happened during the early Archean (3 Ga) when, owing to the hot mantle adiabat and the low Fe 3+ /ΣFe (assumed to be 2% for a reduced upper mantle), carbonate-silicate melts formed at about FMQ −2 log units at c. 100 km depth. Small amounts of carbonated silicate melts could be produced owing to the limited amount of carbon (c. 10 ppm in the case of reduced Early Earth; Dasgupta 2013), which, once entirely oxidized, led the Archean mantle redox state to further increase to the fO 2 indicated by the Archean MORB (FMQ −1.5 log units) represented by the Lace metabasaltic eclogite (Aulbach & Stagno 2016). Figure 6c and d shows that the thickness that undergoes redox melting strictly depends on the initial mantle Fe 3+ /ΣFe ratio and carbon content according to equilibrium (12). The gradual increase of Fe 3+ in the bulk asthenospheric mantle through time owing to subduction of oxidized material (Arculus 1985) resulted in the deepening of the redox melting with consequent decrease in the fraction of carbonatitic melts and their dilution during ascent ( Fig. 6e and f). The composition of these magmas remains strictly controlled by the temperature and pressure, varying from carbonatitic to carbonate-silicate to basalts during upwelling with an increase in the melt fraction from less than 0.01 vol% to c. 10 vol%. It is expected, therefore, that the rheological properties of these melts such as viscosity and ascent rate will continuously change upon upwelling as they dilute to the more abundant MORB by about three orders of magnitude (Kono et al. 2014;Stagno et al. 2018). The drawn models have a two-fold implication: (1) that the oxidation state of MORB does not reflect the mantle oxidation state at the source, although it is linked to it (see Sorbadere et al. 2018, after reading Ballhaus 1993; (2) that larger volumes of CO 2 -rich melts could have formed at shallower conditions during the Archean when the convective mantle was less oxidized and more 'hot', to then become less and less abundant to the present as a result of dilution at depth.

The carbon speciation in the transition zone and lower mantle
Previous experimental studies provided evidence of metal saturation at pressures compatible with the transition zone and the lower mantle, which implies that diamond is the most stable form of carbon in the Earth's deep interior (Frost et al. 2004;. The discovery of crystallized carbonated melts (Walter et al. 2008), calcite (Brenker et al. 2007), dolomite (Bulanova et al. 2010) and other carbonate minerals (Kaminsky 2012) all trapped in natural sub-lithospheric diamonds provided an alternative view of the deep mantle as characterized by higher oxygen fugacities where metal iron would not exist. Estimates of the fO 2 at which carbonate and diamond can coexist (e.g. the trapped carbonate inclusions in diamonds) can be determined through thermodynamic calculations (see equations (5)-(7)) using similar equilibria to equations (1) and (2) but employing the appropriate high-pressure polymorphs (wadsleyite or ringwoodite, coesite or stishovite, clinoenstatite, etc.). As an example, the equilibrium is chosen to represent the coexistence of magnesite and diamond in the lower mantle along with periclase intended here as a component 381 Carbon speciation in the Earth's interior of ferropericlase. Unfortunately, thermodynamic calculations of the fO 2 can result in contrasting results owing to uncertain available data used to describe the compressibility of mineral end-members as a function of pressure and temperature (i.e. bulk modulus and its pressure derivative). This is the case shown in Figure 7, where two different log fO 2 versus pressure trends are obtained depending on Fig. 6. (a-f) Thermodynamic prediction of the variation of the mantle oxidation state upon decompression obtained using equilibrium (10), and consequent depth at which the redox melting would occur. Detailed calculations have been given by Stagno et al. (2013) and Aulbach & Stagno (2016).

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V. Stagno the equation of state (EoS) data used for magnesite. For this reason, Stagno et al. (2011) determined experimentally the fO 2 at which diamond and magnesite can coexist in mineral assemblages consisting respectively of wadsleyite (or ringwoodite) plus clinoenstatite, and ferropericlase plus bridgmanite synthesized at pressures from 16 to c. 50 GPa using the redox sensor technique described above. These values were found to be about 2 log units above the iron-wüstite (IW) buffer, which implies that diamonds hosting carbonate inclusions are witnesses of more oxidized conditions in the deep interior than previously thought. From Figure 7, it can be noted that by extrapolating these measured values at high pressures of 100 GPa or so, magnesite is expected to be stable along with diamonds and Fe (maybe with some dissolved C), which is in agreement with the observed stability of magnesite (Isshiki et al. 2004) at lower mantle depths. More importantly, the presence of about 9000 ppm of C in the form of magnesite would be required to raise the fO 2 in the lower mantle by 2 log units relative to the IW buffer, causing, therefore, oxidation of 1% Fe metal (Rohrbach & Schmidt 2011) and incorporation of about 60% and about 2% of Fe 3+ /Fe tot in bridgmanite and ferropericlase, respectively (Stagno et al. 2011). Whether carbonates (solid or liquid) can be stable in the transition zone or lower mantle in subducted MORB-like lithologies strictly links with the role of coexisting Fe-bearing redox-sensitive minerals such as majoritic garnet, tetragonal almandine-pyrope phase (TAPP), new hexagonal aluminous (NAL) phase, calcium-ferrite (CF) and bridgmanite phases. These phases are all possible candidates for incorporating large amounts of Fe 3+ at transition zone and lower mantle conditions during subduction, leading to the formation of sub-lithospheric diamonds from the oxidized CO 2bearing fluids. Potential equilibria such as equations (1) and (2) might be written that involve some of these phases plus carbonate and diamond. However, to date no experimental studies have been performed to determine the effect of fO 2 , pressure and temperature on their Fe 3+ content (i.e. their redox buffering capacity).

Conclusions
For decades, the experimental investigation of melting processes in the interior of the Earth has relied mostly on the effect of volatile elements in their oxidized state where C has been considered to be stable as CO 2 at any depth, playing, therefore, the major role in lowering the melting temperature of mantle rocks and causing the formation of carbonate magmas. However, the redox state of the Earth's interior has played a major role in controlling the oxidation and reduction of C species and its geodynamic cycle over time, and the evolution of the mantle redox state can be investigated through the application of oxy-thermobarometry on dated mantle rocks. Such studies, along with the mineralogical findings in (sub) lithospheric diamonds, have raised several important questions, such as: When does carbon turn into carbonate at mantle conditions? What is the minimum amount of oxygen required to oxidize elemental carbon to CO 2 within natural deep mineral assemblages? Has the increase of the mantle redox state been a gradual process or did it occur all at once? Is it possible to link the mantle redox state to the volcanic eruptive style and the migration rate of magmas from the mantle up to the surface? The seismic evidence of low-velocity zones is often referred to the presence of incipient melting processes, but this would imply stagnation of melt rather than fast ascent rate (Stagno et al. 2018). Are Fe-bearing minerals valid indicators of oxidized conditions and melting processes in the hidden deep mantle?
Recent studies have provided geochemical evidence of a gradual increase in fO 2 (Aulbach & Stagno 2016;Nicklas et al. 2018) in contrast to the general view that the mantle retained a constant fO 2 of IW +4(±1) (Scaillet & Gaillard 2011) over the last 4 Gyr (Trail et al. 2011). Figure 8 summarizes the redox state of the Earth's mantle from the fO 2 of abyssal peridotites (Frost & McCammon 2008), present-day and Archean MORB (Aulbach & Stagno 2016), and diamonds with (Mg,Fe)O inclusions that are variable in Fe# [Fe/(Fe + Mg)] for which the fO 2 is inferred by the presence of carbonate inclusions (Kaminsky 2012) through Figure 7. The fO 2 of Earth at the time of equilibration (separation) between mantle and core is also shown in Figure 7 (green circle; . Interestingly, this figure indicates that the mantle redox state is distinct between the lower and the upper mantle, as well as heterogeneous in both Creservoirs with fO 2 values ranging up to c. 5 log units relative to the IW buffer. This implies that the mobilization of carbon over time Fig. 7. Experimental measurements of the fO 2 (relative to IW) v. pressure for magnesite and diamond to coexist (blue dashed line), along with transition zone and lower mantle mineral phases obtained using the IrFe alloy redox sensor and compared with thermodynamic calculations through (equation (13)) changing EoS data for magnesite (Fiquet et al. 1994;Ross 1997;Litasov et al. 2008). The dark shaded region indicates the fO 2 of the mantle after Frost & McCammon (2008) and Stagno & Frost (2010) calculated along a mantle adiabat to 10 GPa. Fig. 8. Log fO 2 v. Fe# (Fe/(Fe + Mg)) of mantle rocks (orange rectangle) and ferropericlase inclusions in superdeep diamonds (blue area) along with that of the Earth at the core-mantle separation (green circle; . The pink shaded area refers to fO 2 (between 3 and 5 log units to IW) of present-day MORB.

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Carbon speciation in the Earth's interior does not necessarily require a mantle great oxidation event to occur (c. IW +1); in contrast, local chemical heterogeneities, pressure effect on the carbon-carbonate equilibria and kinetics of the redox reactions such as equation (12) might have played a key role over time.