Carbon speciation and solubility in silicate melts

To improve our understanding of the Earth’s global carbon cycle, it is critical to characterize the distribution and storage mechanisms of carbon in silicate melts. Presently, the carbon budget of the deep Earth is not well constrained and is highly model‐dependent. In silicate melts of the uppermost mantle, carbon exists predomi­ nantly as molecular carbon dioxide and carbonate, whereas at greater depths, carbon forms complex polymer­ ized species. The concentration and speciation of carbon in silicate melts is intimately linked to the melt’s composition and affects its physical and dynamic properties. Here we review the results of experiments and calculations on the solubility and speciation of carbon in silicate melts as a function of pressure, temperature, composition, polymerization, water concentration, and oxygen fugacity.


INTRODUCTION
Evidence of carbon-bearing phases in the Earth's mantle includes the release of CO 2 in volcanic eruptions, dissolved CO 2 in magmatic glasses and glass inclusions (Mörner & Etiope, 2002), diamonds and carbonate minerals in mantle xenoliths (Eggler, 1987;Sobolev & Shatsky, 1990), and the existence of carbonatite and kimberlite magmas (Wyllie et al., 1990).There are two possible sources of carbon: primordial carbon and the carbon delivered by later come tary and asteroid bombardment.Primordial carbon existed in the proto-Earth and subsequently survived the moonforming impact, and its amount is currently unknown.From all existent carbon, part of it might be locked in the core, part in some deep mantle reservoir, another fraction lies at the surface, and the remaining is resurfaced after surviving subduction.To determine how much carbon may have remained in the Earth after the giant impact, the chemistry and thermodynamics of carbon in silicate (particularly, with the bulk silicate Earth composition) must be determined as a function of pressure and temper ature.Estimates of the amount of carbon exchanged between the surface and the mantle range between 30 and 130 megatons per year, and estimates of the carbon concentration stored within the core range between 0.2 and 4 wt.%(McDonough, 2003;Mookherjee et al., 2011;Wood, 1993).Carbon is mainly subducted into the Earth in the form of carbonates within metasomatically calciumenriched basaltic rock, calcified serpentinites, and sedi mentary carbonaceous ooze of the seafloor (Brenker et al., 2006).Some carbonates may survive subduction by under going transitions to denser carbonate phases (Brenker et al., 2006;Isshiki et al., 2004;Mao et al., 2011;Merlini et al., 2012;Oganov et al., 2008;Ono et al., 2005;Solomatova & Asimow, 2017).If a fraction of carbon is subducted into the lower mantle, all possible carbon sinks need to be determined.Due to carbon's low solubility in crystalline silicates (Keppler et al., 2003;Panero & Kabbes, 2008;Shcheka et al., 2006), carbon strongly partitions into silicate melts relative to silicate minerals.This chapter briefly summarizes the experiments and calculations that have been performed on carbon-bearing silicate melts and glasses, particularly the speciation and solubility of carbon as a function of pressure, with a primary goal to expose areas that remain controversial or unknown that would especially benefit from ab initio molecular dynamics simu lations.There have been at least three excellent review papers on carbon in silicate melts (see Holloway & Blank, 1994;Ni & Keppler, 2013;Webster et al., 2011), as well as several papers that have done an excellent job summa rizing, tabulating, and plotting together data from previous studies (e.g.Duan, 2014;Shishkina et al., 2014).Here, we provide a perspective from computational mineral physics on what is critical to investigate in the near future.Furthermore, we contribute our calculations on carbon ated forsterite melts to improve our understanding of dia mond formation from silicate melts.

EXPERIMENTS ON SILICATE MELTS
Experimentally, standard difficulties hinder the in situ analysis of silicate melts: absence of periodicity, which prevents refining structure and density from X-ray diffraction, and high background optical radiation, which hinders spectroscopic measurements.Glasses from quenched melts are amenable to study, but the structure may change and carbon may diffuse during quench.Nevertheless, the carbon content of quenched samples that were equilibrated with other phases (solids, liquids or gases) can be determined using a bulk analyzer, secondary-ion mass spectrometry, nuclear magnetic reso nance experiments, and most commonly, Fourier-trans form infra-red (FTIR) spectroscopy.FTIR is able to determine both CO 2 and H 2 O concentrations with a high level of accuracy if the molar absorptivity is well cali brated against absolute techniques, such as a bulk carbon analyzer.The solubility and speciation of carbon depends on the composition, oxygen fugacity, H 2 O and CO 2 con centrations, temperature, pressure, and NBO/T (the ratio between the number of Non-Bridging Oxygen atoms and Tetrahedrally-coordinated cations; this ratio is defined in slightly different ways by different authors, depending on which cations are considered tetrahedrally coordinated).
Experiments have generally been conducted in largevolume presses in the pressure range of 1-4 GPa and temperature range of 1000 °C-2000 °C.Typically, the procedure is to saturate a melt at high pressure and temper ature with CO 2 until equilibrium is reached and then rap idly quench the melt to produce a glass that ideally retains the structure of the melt.The examination of carbon spe ciation has mostly been limited on quantifying the CO 2 -to-CO 3 2-ratio as a function of composition.Unfortunately, with a few exceptions (e.g.Sen et al., 2013), experimental studies have not pursued the formation of more complex species, such as carbon-carbon polymers, organic mole cules, or even silicon-carbon and iron-carbon polymers.

2-
) ratio is most strongly dependent on the composition of the melt.It has been shown that carbon exists almost exclusively as CO 3 2-(rather than CO 2 ) in mafic melts, such as basalt (Fine & Stolper, 1986;Fogel & Rutherford, 1990;Shishkina et al., 2014;Thibault & Holloway, 1994), olivine melitite (Brey, 1976;Brey & Green, 1976), phono-tephrite (Behrens, 2009), nephelinite (Brooker et al., 1999;Shishkina et al., 2014), and icelandite (Jakobsson, 1997).In the sequence of basalt, andesite, rhyodacite, and rhyolite melts, Fogel and Rutherford (1990) showed a general increase in the CO 2 /CO 3 2-ratio, such that carbon exists exclusively as CO 2 in rhyolite and as CO 3 2-in basalt, while in albiteanorthite melts, Brey (1976) found that the CO 2 /CO 3 2ratio increases with increasing albite content.King and Holloway (2002) found that highly polymerized melts with high ionic porosities (>48.3%) and low nonbridging oxygen/tetrahedral oxygen (<0.3) have a higher concentration of molecular CO 2 .In melts along the NaAlO 2 -SiO 2 join (from NaAlSi 6 O 14 rhyolite rock compo sition to pure NaAlSiO 4 nepheline), Brooker et al. (1999) found that the relative and absolute abundance of CO 3 2increases with increasing NaAlO 2 /SiO 2 at the expense of CO 2 , such that carbon in NaAlSiO 4 exists almost exclu sively as CO 3 2-, whereas carbon in NaAlSi 6 O 14 exists almost exclusively as CO 2 .The total solubility of carbon decreases as NaAlO 2 is added to SiO 2 , up to a NaAlO 2 / SiO 2 ratio of about 0.5, after which the trend reverses and there is a sharp increase in the solubility of carbon.The CO 2 /CO 3 2-ratio decreases with increasing pressure at constant temperature (in other words, carbon increases coordination with pressure).The effect of temperature is subtler: at constant pressure, the CO 3 2-concentra tion decreases with increasing temperature between 1450 °C and 1600 °C and increases with increasing tem perature from 1600 °C to 1700 °C, in agreement with the results of Fine and Stolper (1985).Konschak and Keppler (2014) examined the speciation of carbon in dacite, phonolite, basaltic andesite, and alkali silicate melts using synchrotron infrared spectroscopy and dia mond anvil cells up to 1000 °C and 200 kbar, finding a correlation between NBO/T and speciation.In alkali sili cate and basaltic andesite, carbon exists exclusively as carbonate, while in dacite and phonolite, carbon exists as a mixture of CO 2 and CO 3 2-.With increasing tempera ture, the effect of composition on carbon's speciation decreases as carbon shifts from existing as CO 3 2-to CO 2 .They find that the speciation of carbon is largely insensi tive to pressure up to 200 kbar, and that composition and temperature have a much stronger effect.
The speciation of carbon in highly reduced melts is poorly understood.Whereas Morizet et al. (2010) sug gested that applying reducing conditions would not affect carbon speciation in hydrous melts, Kadik (2004) observed that carbon is dissolved primarily as atomic carbon in reduced ferrobasalt.Kadik observed direct Si-C bonds in ferrobasaltic glass using Raman spectros copy, and Sen et al. (2013) observed that carbon exclu sively bonds to silicon rather than oxygen in a reduced SiLiOC melt using nuclear magnetic resonance experi ments, giving rise to their contrary conclusions.Although it is typically expected that in shallow melts carbon will bond to oxygen to form CO 2 or CO 3 2-, it is possible that in more reduced melts and especially at higher pressures, carbon will bond directly to silicon instead of oxygen.See the computational section for theoretical evidence of Si-C bonds in pyrolitic melt.Additional experiments and specific measurements are needed to constrain the speci ation of carbon in reduced silicate melts.In summary, at lithospheric conditions, i.e. within the pressure range of 0.5-4 GPa and at temperatures below 2000 °C, the CO 2 / (CO 2 +CO 3 2-) ratio is most strongly affected by the com position, and in particular, the silica content of the melt (Figure 16.1).Carbon exists almost exclusively as CO 2 in silica-rich felsic melts (e.g., rhyolite) and as CO 3 2-in silicapoor mafic melts (e.g., basalt, olivine melitite and nephe line melts).The CO 2 /(CO 2 +CO 3 2-) ratio is also negatively correlated with pressure and generally insensitive to tem perature; there remain disagreement and insufficient data on the effect of the H 2 O content on the speciation of carbon.Additional studies are needed to refine the effect of temperature, H 2 O content, and NBO/T, as well as the effect of network-modifying cations within the melt.

Solubility of Carbon
The solubility of carbon within a silicate melt depends most strongly on pressure and composition.The effects of temperature, water content, and oxidation state are less well defined at the present time, due to discrepancies in the literature.Solubility can be difficult to measure accurately due to several factors.Hydrogen and carbon may diffuse into the silicate melt, or small amounts of melt components may dissolve into the fluid phase, affecting the measured carbon solubility.The oxidation state may change due to the capsule material, resulting in changes in carbon speciation, and thus, solubility.Furthermore, the use of different molar absorptivity standards for the CO 2 and CO 3 2-for the FTIR bands may be a source of inconsistencies in reported solubilities.
Here we summarize the current data on carbon solubility in a variety of silicate melt compositions, highlighting the need for additional high-quality experiments to resolve discrepancies and gaps in the literature.We use the term carbon solubility to encompass the cumulative solubility of CO 2 and CO 3 2-, making the distinction when necessary.There is good agreement within the experimental litera ture that carbon solubility in silicate melts increases rap idly with increasing pressure (Behrens et al., 2004;Blank,  ) as a function of silica content at 300 °C-1700 °C for melts and glasses along the NaAlO 2 -SiO 2 join from Brooker et al. (1999) (circles), andesite melts from King and Holloway (2002) (triangles), phonolite and dacite melts from Konschak and Keppler (2014) (diamonds), and mafic melts from Shishkina et al. (2014) (squares).The data from Brooker et al. (1999) and King and Holloway (2002) were obtained at 1-2 GPa and 1 GPa, respectively.Shishkina et al. (2014) did not observe any molecular CO 2 species for the range of mafic melts investigated at 1200 °C-1250 °C up to 0.5 GPa.Konschak and Keppler (2014) reported that the carbon speciation is independent of pressure in the pressure range of 3-20 GPa at temperatures of up to 1000 °C; however, Brooker et al. (1999) observed a negative correlation of CO 2 /(CO 2 +CO 3 2-) and pressure.In either case, the effect of pressure and temperature is secondary to the effect of silica content on carbon's speciation.See electronic version for color representation of the figures in this book.
1993; Botcharnikov et al., 2005;Botcharnikov et al., 2007;Brooker et al., 1999;Fogel & Rutherford, 1990;Jendrzejewski et al., 1997;Shishkina et al., 2014).For example, in rhyolitic melts at 1123-1323 K, CO 2 solubility increases from roughly 120 ppm at 20 MPa to 800-1000 ppm at 140 MPa to 3700 ppm at 660 MPa (Blank, 1993;Fogel & Rutherford, 1990).In dacitic melts, the maximum CO 2 solubility increases from 800 ppm at 100 MPa to 3000 ppm at 500 MPa (Behrens et al., 2004), and in andes itic melts, the CO 2 solubility increases from 175 ppm at 50 MPa to 3300 ppm at 500 MPa (Botcharnikov et al., 2005).Similarly, in shoshonitic melts, Vetere et al. (2011) found that the concentration of CO 2 (in the form of carbonate) increased from 307 ppm at 50 MPa to 2932 ppm at 400 MPa.Thus, there is a consensus that more carbon species can dissolve in silicate melts with increasing pressure, and thus with increasing depth.There is also a strong dependence of the carbon solubility on the composition of the silicate melts, most notably affected by the degree of polymerization (Brooker et al., 2001a;Brooker et al., 2001b;Mysen et al., 2009;Shishkina et al., 2014) and concentration of CaO (Brey, 1976;Holloway, 1976;Iacono-Marziano et al., 2012;King & Holloway, 2002;Moore, 2008;Papale et al., 2006;Shishkina et al., 2014).Holloway (1976) observed that carbon solubility is posi tively correlated with the Ca/(Ca+Mg) ratio.Brey (1976) found that the solubility of carbon in olivine melitite (8.3-9.5 wt.% CO 2 ) is much higher than in albite-anorthite (1.6-2.5 wt.% CO 2 ), for which the solubility increases slightly with increasing anorthite content.Brooker et al. (2001aBrooker et al. ( , 2001b) observed a negative correlation with MgO content and a positive correlation with NBO/T.King and Holloway (2002) found that carbon solubility is negatively correlated with the Si+Al mole fraction and positively correlated with cations that have a large Gibbs free energy of decarbonation or a high charge-to-radius ratio (e.g.Ca).Alkalis have also been found to have a positive corre lation with the solubility of CO 2 (Behrens et al., 2009;Lesne et al., 2011;Vetere et al., 2014), although the rela tionship is more complex.Shishkina et al. (2014) found that at 500 MPa and the H 2 O content extrapolated to 0 wt.%, the CO 2 concentration increases from tholeiite (~3400 ppm) to alkali basalt (~5200 ppm), to basanite (~7400 ppm), to phonotephrite (~8500 ppm), to nephe linite (~14000 ppm).To describe the complex relationship between composition and carbon solubility, Shishkina et al. formulated a modified Π parameter (originally pro posed by Dixon, 1997, for a limited range of silica con tents) using eight compositions of silicate melt combined with previous data sets.The Π parameter in Shishkina et al. is defined as the ratio between the freely diffusing cations and the tetrahedral network, (Ca 2+ + 0.8K + + 0.7Na + + 0.4Mg 2+ + 0.4Fe 2+ )/(Si 4+ + Al 3+ ), as reflecting the degree of polymerization of the melt.The relationship between the natural log of the solubility of CO 2 and Π was found to be 1.167*lnP + 0.671* Π + 0.65 (where P is pressure), obtained from the linear regression of 48 values of CO 2 solubilities at 50-500 MPa.The newly formulated Π parameter in Shishkina et al. is the most rigorous parameterization of the compositional effect on carbon solubility at the present time.
Although most studies demonstrate a negative correla tion between total carbon solubility and H 2 O content (Behrens et al., 2004;Blank et al., 1993;Botcharnikov et al., 2005;Botcharnikov et al., 2006;Fogel & Rutherford, 1990;Mattey, 1991;Moussallam et al., 2016;Pan et al., 1991;Pawley et al., 1992;Shishkina et al., 2010;Stolper & Holloway, 1988;Tamic et al., 2001), several studies observed a positive correlation (Behrens et al., 2004;Behrens et al., 2009;Iacono-Marziano et al., 2012;King & Holloway, 2002;Jakobssen, 1997).Below about 2 × 10 4 ppm H 2 O, there is generally a weak correlation between the H 2 O and CO 2 concentrations, while at higher H 2 O concentration the CO 2 solubilities tend to drop (Ni & Keppler, 2013).For example, at 2 kbar and 1250-1300 °C, the CO 2 solubility in basaltic and rhyolitic melts plateaus around 1000 ppm CO 2 up to around 2 × 10 4 ppm H 2 O, gradually dropping to 0 ppm CO 2 by 5 × 10 4 ppm H 2 O in basaltic melt (Botcharnikov et al., 2005;Shishkina et al., 2010) and by 5.6 × 10 4 ppm H 2 O in rhyolitic melt (Tamic et al., 2001).On the other hand, King and Holloway (2002) observed a total CO 2 solubility increase by about 0.06 wt.% per wt.% of H 2 O in andesite glass at 10 kbar and 1300 C: as the H 2 O concentration increased from 0 to 3.4 wt.%, molecular CO 2 decreased from 0.07 to 0.01 wt.% and CO 3 2-increased from 0.25 to 0.57 wt.%.Iacono-Marziano et al. (2012) hypothesized that a positive corre lation between CO 2 and H 2 O concentrations may be due to NBO formation, which promotes CO 3 2-formation, thus increasing the total carbon solubility.The solubility data of icelandite from Jakobssen (1997) shows no trend with H 2 O when plotted against dissolved CO 2 (Ni & Keppler, 2013), whereas there is a positive trend when plotted against dissolved CO 2 normalized to the CO 2 partial pressure.Nevertheless, the majority of studies see a negative correlation and it is not clear at the present time what is responsible for the discrepancy in these studies.
The effect of temperature on the solubility of carbon is also poorly constrained.Generally, carbon solubility seems to be weakly dependent on temperature, such that the sign of the trend depends on the composition.For example, it has been shown that carbon solubility decreases weakly with increasing temperature for albitic melts (Blank & Brooker, 1994;Brooker et al., 1999;Stolper et al., 1987) and decreases strongly for rhyolitic melts at 0.1 GPa (Blank, 1993;Fogel & Rutherford, 1990;Ni & Keppler, 2013).Eitel and Weyl (1932) observed a negative dependence in sodium metasilicate melts at 750 atm, and Pearce (1964) observed pronounced negative temperature dependence in Na 2 O-SiO 2 melts at 1 atm.However, Brooker et al. (1999) observed a slight increase in solubility with increasing temperature for NaAlSiO 4 and no dependence for melts with compositions between NaAlSi 4 O 10 and NaAlSi 6 O 14 .In more mafic composi tions, there is even less consensus.Brey and Green (1976) observed a slight negative relationship in olivine melilitite at 3 GPa with 9% CO 2 dissolved at 1450 °C, 8.5% at 1550 °C, and 8.3% at 1650 °C, while Mysen et al. (1976) observed a strong positive correlation with temperature at 1400-1700C above 1 GPa.Pan et al. (1991) demon strated that carbon solubility is temperature-independent in tholeiitic basalt melt at 1-1.5 GPa and 1300 °C-1600 °C.It is possible that there are discrepancies in the effect of temperature due to different quenching methods and/or quality of the glass as an analog for certain com positions.In any case, additional studies are needed to constrain the effect of temperature on carbon solubility.At least at uppermost mantle pressures and temperatures, increasing oxygen fugacity increases the solubilities of carbon and hydrogen (Kadik, 2004;Morizet et al., 2010;Stanley et al., 2011).Morizet et al. (2010) found a strong positive correlation between carbon solubility and oxidation state in haploblastic glasses at 1250 °C and 200-300 MPa, finding that the CO 2 content changes from 680 to 1320 ppm between ΔFMQ -2.6 and ΔFMQ + 2.6 independently of H 2 O content changing from 1.3 to 4.0 wt.%.Stanley et al. (2011) found that the CO 2 content increases from 51 ppm at IW to 510 ppm at IW + 1 in a synthetic melt based on the Adirondack-class Humphrey basalt, at 1-2.5 GPa and 1400 °C-1625 °C.At greater depths, however, the relationship between oxygen fugacity and carbon solubility is unknown.It has been hypothe sized that carbon may behave like oxygen in reduced high-pressure melts (Sen et al., 2013) and possibly result in an increase in solubility.

SIMULATIONS OF SILICATE MELTS
It remains a great challenge to experimentally measure the structural properties of melts at simultaneously high pressures and temperatures.The majority of experiments require quenching of the melt prior to analysis, which may change the local structure and coordination environ ment of the atoms, as well as the volatile concentration (Behrens & Nowak, 2003;Brey, 1976;Guillot & Sator, 2011).Additionally, experiments on carbon solubility and speciation in silicate melts have mostly been limited to pressures of up to 4 GPa and temperatures of up to 2000 °C, while calculations can determine the precise behavior of atoms and directly calculate thermodynamic properties at a wide range of pressures and temperatures.
On the other hand, the atomistic simulations have strong size limitations, as they typically contain a few hundred atoms in a periodically repeated simulation box.This may be somehow mitigated by long simulation times and large number of configurations, in a push to cover as much as possible from the configurational space.
Molecular dynamics calculations can be performed with classical or ab initio methods.In classical molecular dynamics, the forces between atoms are calculated from empirical interatomic potentials, whereas in ab initio molecular dynamics, forces are determined from electronic structure calculations (e.g. with density functional theory).In both cases, the motions of the atoms are calculated with Newton's second law and are treated classically.Due to computational expense, ab in itio molecular dynamics are limited by the number of atoms and duration of the simulation; the latter can be orders of magnitude higher than for classical molecular dynamics.The level of accuracy of classical molecular dynamics depends on the quality of the parametrization of the interatomic potentials, which depends on the accu racy of the reference data.Furthermore, extrapolation to pressure-temperature conditions beyond the conditions of the reference data decreases the accuracy of the poten tials.Although ab initio molecular dynamics depends on several approximations (e.g., the exchange-correlation energy and the treatment of core electrons), it is based on first principles in the sense that it does not require param eterization with experimental data.For the case of highpressure, high-temperature silicate melts, the reference data is scarce or nonexistent, especially within the large range of pressure and temperature conditions of planetary interiors, and so ab initio methods are presum ably more reliable.For example, Vuilleumier et al. (2015) found that their classical simulations were not sufficiently viscous, as the atomic diffusion coefficients were larger than experimental values.They also found disagreement in the CO 2 concentration as a function of composition when comparing their results from classical simulations to ab initio simulations, concluding that the empirical force fields need to be improved.Furthermore, the ratio of CO 2 to CO 3 is severely overestimated with classical molecular dynamics in the calculations of Guillot and Sator (2011) (see section 3.2).Thus, even though empirical methods allow for a larger number of atoms and longer simulation duration, experimental results on carbon spe ciation are far better reproduced with ab initio methods.The effect of cell size (i.e., number of atoms) on carbon speciation in ab initio molecular dynamics simulations is not currently well understood.
Thus far, there have been five studies on carbonated sil icate melts using molecular dynamics simulations.The two first studies were conducted at pressure and tempera ture conditions of the upper mantle: Guillot and Sator (2011) implemented classical molecular dynamics to quantify the solubility of carbon in rhyolite, MORB, and kimberlite melts at 2-15 GPa and 1473-2273 K; and Vuilleumier et al. (2015) used a combination of classical and ab initio molecular dynamics to study the speciation of carbon in basaltic and kimberlitic melts with ~20 wt.% CO 2 at 2073 K and 12 GPa.Subsequently, simulations at lower mantle pressures and temperatures were conducted.Ghosh et al. (2017) used ab initio molecular dynamics to examine the speciation of carbon in MgSiO 3 melt with 5-16 wt.% CO 2 at 2200-6000 K and 140 GPa, while Ghosh and Karki (2017) examined the transport prop erties of MgSiO 3 melt with 16.1 wt.% CO 2 at 2200-5000 K up to 140 GPa.Most recently, Solomatova et al. (2019) used ab initio molecular dynamics to examine the specia tion and polymerization of carbon in pyrolite melt with 5-10 wt.% CO 2 at 3000-5000 K up to 140 GPa.The com positions and carbon concentrations of the ab initio molecular dynamics simulations are summarized in Table 16.1.
In this chapter, we add our simulations on pure and carbonated Mg 2 SiO 4 forsterite melt at 3000 K and up to 120 GPa.We have worked on several distinct composi tions: Mg 2 SiO 4 , Mg 2 SiO 4 +C, Mg 2 SiO 4 +CO 2 , and Mg 2 SiO 4 +MgCO 3 , and study the effect of carbonation on the melt properties as well as the differences between the various carbon species.We have employed the Qbox package (Gygi, 2018).We start the calculations with solid Mg 2 SiO 4 forsterite.Forsterite, the Mg-end member term of the mineral olivine, has an orthorhombic structure with 4 formula units per unit cell, namely 28 atoms.We consider a 2x1x2 supercell containing 112 atoms.After static structural relaxation, we perform a moleculardynamics calculation on the solid, raising the tempera ture well above the melting point.Once we reach melting, we decrease the temperature and thermalize the melt at the desired value closer to realistic telluric conditions.Here, we performed a high-pressure study along the 3000 K isotherm.All simulations are NVT type, meaning the Number of particles, the Volume of the simulation box, and the Temperature are kept constant.This is numeri cally simpler than the NPT ensemble, where pressure instead of volume is fixed.Temperature is controlled via a Nose-Hoover thermostat, and the time step of the sim ulations is 0.75 fs.Temperature is monitored throughout the simulations to maintain fluctuations within a couple hundred degrees above and below the average 3000 K.We compute the electronic density and wave functions sam pling the Brillouin zone in the reciprocal space using only the Γ point.We add carbon in the silicate melt as C atoms, CO 2 molecules, or MgCO 3 groups.The addition of the supplementary atoms is done in the interstitial pores of the melt at low pressure.CO 2 is added as a linear mole cule, and MgCO 3 as a Mg cation about 2 Å apart on top of a CO 3 triangular anionic group.The new melts are first thermalized for one full picosecond in order to dissipate the interatomic forces and equilibrate the strains and then compressed along the 3000 K isotherm up to lowermantle pressures.

Solubility of Carbon Dioxide in the Silicate Melt
Guillot and Sator (2011) observed a strong positive correlation of carbon solubility with pressure.For example, at 1673 K, carbon solubility in a basaltic melt increased from 2 wt.%CO 2 at 2 GPa to 30 wt.% CO 2 at 10 GPa.A weak negative correlation with temperature was observed and the effect of temperature increases with increasing pressure, such that at 2 GPa, there is almost no Table 16.1 Carbon concentrations in the simulated melts using ab initio molecular dynamics, expressed as the formula units of carbon species added, wt.% of carbon species added, wt.% of C and mol% of C. The chosen carbon concentrations of 1.4-4.7 wt.% C reflect the range of carbon present in carbonaceous chondrites (0-6 wt.% C) (Pearson et al., 2006) 2003;Mattey, 1991;Pan et al., 1991;Thomsen & Schmidt, 2008).For example, both Guillot and Sator (2011) and Mattey (1991) predict CO 2 solubility in basaltic melt of 1.5 wt.% at 2 GPa and 1673 K.At 3.5 GPa and 1573 K, Thomsen and Schmidt (2008) report a CO 2 solubility of 5 wt.%CO 2 in a complex carbonatite melt, similar to the value of 6 wt.% CO 2 at 3.5 GPa and 1673 K predicted by Guillot and Sator (2011).The solubility is also weakly correlated with silica content, only becoming noticeable above about 10 GPa.The solubility of CO 2 at 10 GPa and 2273 K is about 25 wt.% in basalt and 24 wt.% in rhyolite, while at 15 GPa and 2273 K, the solubility of CO 2 is about 37 wt.% in basalt and 34 wt.% in rhyolite.Although Guillot and Sator (2011) predict excellent agreement of solubility with experiments, the form in which carbon exists (CO 2 vs. CO 3

2-
) is significantly different than experi mental observations (see below).

Carbon Coordinated by Oxygen
Guillot and Sator (2011) found that the proportion of CO 3 2-increases with increasing pressure and decreases with increasing temperature relative to CO 2 .Although experiments on quenched mafic melts have shown that carbon exists exclusively as CO 3 2-(e.g.Fogel & Rutherford, 1990;Shishkina et al., 2014;Thibault & Holloway, 1994), Guillot and Sator predicted a significant CO 2 content (CO 2 /[CO 2 +CO 3 2-]~0.6at 1873 K), noting that a lowtemperature extrapolation to 300 K would agree with the experimental results, implying that the speciation (and thus, solubility) of carbon in the recovered silicate glasses (i.e.quenched silicate melt) is not an accurate representa tion of the high-temperature silicate melt.The implica tion is that the experimental results on carbon-bearing silicate glasses are unreliable.However, when the CO 2 / (CO 2 +CO 3 2-) ratio is plotted for the computational studies on carbon-bearing MgSiO 3 (Ghosh et al., 2017) and carbon-bearing pyrolite (Solomatova et al., 2019), the concentrations of CO 2 are substantially lower than in Guillot and Sator (2011) at comparable temperatures (Figure 16.2).For example, at 2-3 GPa, Ghosh et al. (2017)  ) at 2273 K in MORB.The discrepancy bet ween the computational studies may be best explained by the difference in methodology.Guillot and Sator (2011) used classical molecular dynamics on a CO 2 saturated composition (~25 wt.% CO 2 at 10 GPa), but Ghosh et al. ), as a function of pressure and temperature.Guillot and Sator (2011) predict significantly more CO 2 relative to CO 3 2-in MORB melt than Ghosh et al. (2017), Solomatova et al. (2019), and this study in enstatite melt (en), pyrolite melt (py), and forsterite melt (fo), if an extrapolation to lower temperatures is made.In fact, the high CO 2 /(CO 2 +CO 3 2-) ratios predicted by Guillot and Sator (2011) at 2273 K are only achieved at 5000 K in Ghosh et al. (2017) and Solomatova et al. (2019).Experiments on basaltic melts at 1-4 GPa and 1000-2200 K observe no CO 2 (Fine & Stolper, 1986;Fogel & Rutherford, 1990;Shishkina et al., 2014;Thibault & Holloway, 1994), in agreement with Ghosh et al. (2017) and in disagreement with Guillot and Sator (2011).See electronic version for color representation of the figures in this book.
for the kimberlitic melt, but with classical molecular dynamics, the ratio is approximately 0.2 for both melts, higher than what is predicted with classical molecular dynamics.At similar conditions (~10-15 GPa and 2200 K), Ghosh et al. (2017) observed essentially no CO 2 in MgSiO 3 melt, similar to the results of Vuilleumier et al. (2015) for kimberlitic melt with ab initio molecular dynamics.
In carbonated forsterite melts, the fate of carbon depends on its entry state in the system and, consequently, on the oxidation state of the melt.The general tendency is that the coordination of carbon by oxygen increases with increasing pressure.In forsterite melt with carbon species added as CO 2 and MgCO 3 , carbon exists almost exclu sively in the form of CO 3 2-and increases in coordination to CO 4 4-with increasing pressure such that carbon in the melt is mostly CO 4 4-at core-mantle boundary pressures.In forsterite with reduced carbon added, carbon exists as a mixture of C, CO, and CO 2 ; with increasing pressure, carbon increases coordination to CO 3 2-.At lower-mantle pressures, carbon in the reduced forsterite melt exists as an approximately even mixture of CO, CO 2 , and CO 3 2-with no CO 4 4-.The relative proportions of CO 2 , CO 3 2-, and CO 4 4-are similar at all mantle pressures regardless of the melt chemistry (pyrolite, enstatite, or forsterite), as dem onstrated in Figure 16.3.

Carbon Complexes
Although at ambient pressure carbon exists in silicate melts exclusively in unpolymerized forms (e.g.CO, CO 2 , and CO 3 2-), with increasing pressure it becomes increas ingly polymerized (i.e. a higher fraction of carbon atoms are bonded to other carbon atoms) and the carbon species increasingly complex (Ghosh et al., 2017;Solomatova et al., 2019).For example, in pyrolite with 3.35 wt.% CO, nearly none of the carbon is polymerized while at 0 GPa, whereas most of the polymerized carbon exists in C 2 O, C 2 O 2 , and C 2 O 3 molecules at ~60 GPa and predominantly as C 2 O 2-6 and C 3 O 4-6 molecules at ~115 GPa and 4000 K (Solomatova et al., 2019).At 12 GPa and 2073 K, Vuilleumier et al. (2015) observed that about 3.7% of all carbon species in basalt + 20 wt.% CO 2 are C 2 O 5 , which means that 7% of carbon atoms are bonded to another carbon atom, similar to pyrolite + 9.82 wt.% CO 2 , in which 5% of carbon is polymerized (Solomatova et al., 2019), and MgSiO 3 + 16.1 wt.%, in which 7% of carbon is polymerized (Ghosh et al., 2017), at an equivalent pressure and 4000 K (Figure 16.3).
The polymerization of carbon is inversely dependent on temperature because of the increase in entropy with decreasing polymerization.At 3000 K and 20 GPa, pyrolite with 3.35 wt.% CO has 45% of its carbon poly merized, whereas at 5000 K only about 3% of its carbon is polymerized (Figure 16.4;Solomatova et al., 2019).In addition to the carbon-carbon polymerization, the degree of clustering between carbon atoms and other cations (predominantly, iron and silicon) also increases with increasing pressure (Figure 16.4).The predisposi tion of carbon to bond directly to iron suggests that carbon would follow iron during segregation of an ironrich metallic liquid during core formation in the early Earth, both prior to and after the moon-forming impact.
The oxidation state of the melt has a significant effect on the types of species present (Ghosh et al., 2017;Solomatova et al., 2019).For example, the abundance of  The oxygen fugacity of the melt is negatively correlated with the degree of carbon-carbon polymerization, as well as the degree of direct carbon-iron and carbonsilicon bonding.Thus, more carbon will bond to other carbon atoms and other cations, such as iron and silicon, in a more reducing environment.Indeed, as Figure 16.4 shows, there is a considerably larger amount of direct carbon-iron bonds for the pyrolite + CO compositions than for the pyrolite + CO 2 compositions.The same is true, and maybe even more pronounced, for the carbonsilicon bonds in case of the forsterite + C compared to forsterite + CO 2 .The pyrolite + CO 2 and forsterite + CO 2 show similar behavior, suggesting once more that the oxygen fugacity and/or the state of entry of C into the system are the dominant factors determining its spe ciation.These findings are in agreement with experi mental studies that observed direct carbon-silicon bonds in reduced ferrobasalt melt (Kadik, 2004) and reduced SiLiOC melt (Sen et al., 2013).

Elemental Diffusivities
Ghosh and Karki (2017) examined the transport properties of MgSiO 3 enstatite melt with 16.1 wt.% CO 2 at 2200-5000 K up to 140 GPa and found that the addition of carbon increases the diffusivity rates of all elements.However, the diffusivity rates of cations in more complex melts, such as basalt and kimberlite at 12 GPa and 1273 K (Vuilleumier et al., 2015) and pyrolite up to 140 GPa and 3000-5000 K, appear to be unaf fected by the presence of carbon (Figure 16.5).The dif fusion rates of oxygen and magnesium are nearly identical in carbonated pyrolite and carbonated enstatite, while silicon and carbon appear to have higher diffusion rates in carbonated pyrolite than in carbon ated enstatite, indicating that as network formers, silicon and carbon are more mobile in the less polymer ized pyrolite melt relative to the more polymerized enstatite melt.There is good agreement in the change of slope of the elemental diffusivities with pressure at around 5 GPa and 4000 K in the different melts.At 3000 K, the diffusion rates of magnesium, silicon, carbon, and oxygen increase with decreasing polymeri zation of the melt: enstatite < pyrolite < forsterite .5 Elemental diffusivities of magnesium, silicon, oxygen and carbon at 4000 K in pure pyrolite melt ("pure py"), pure enstatite melt ("pure en"), pyrolite melt with 3.35 wt.% CO ("py + 3 wt.%CO"), pyrolite melt with 5.16 wt.% CO 2 ("pyr + 5 wt.%CO 2 "), pyrolite melt with 6.48 wt.% CO ("py + 6 wt.% CO"), pyrolite melt with 9.82 wt.% CO 2 ("py + 10 wt.% CO 2 "), and enstatite melt melt with 16.1 wt.% CO 2 ("en + 16 wt.%CO 2 ").Pyrolite data is from Solomatova et al. (2019) and enstatite data is from Ghosh and Karki (2017).See electronic version for color representation of the figures in this book.
(Figure 16.6).When the atoms are more strongly bound in a silicate network, their diffusion rates are lower.et al. (2019) found that K 0 is generally positively correlated with the degree of oxidation and negatively correlated with temperature and carbon concentration; K' 0 is positively correlated with the degree of oxidation, temperature, and carbon concentration.Table 16.2 lists the equation of state parameters for a wide range of melts.Solomatova et al. find that the density difference between carbon-bearing and carbon-free pyrolite melts is larger at low pressure (where the density ratio of carbonated pyrolite to pure pyrolite ranges from 0.90 to 0.97 at 0 GPa), while above 10-20 GPa the densities converge, resulting in a density ratio of about 0.98-1.Consequently, carbon-bearing melts would be expected to be relatively less buoyant at lower-mantle pressures than at pressures of the upper mantle.

Diamond Formation
From a strict thermodynamical point of view, dia monds should not exist on the surface of the Earth.We find them naturally in rocks because they form at depth and are brought to the surface by uprising molten rock (magmas).Some of these diamonds coming from the deep mantle contain geochemical and mineralogical keys to the functioning of the entire silicate mantle.Hence, understanding their formation is fundamental to tracing the cycles of matter inside our planet.The formation of diamonds in Earth's deep mantle is poorly understood due to the limitations of experimental methods and our inability to access the diamond-forming depths of the mantle.Diamonds likely form in a wide range of pressuretemperature regimes and chemical environments (Cartigny et al., 2001;Kaminsky, 2012;Meyer, 1985).In the uppermost mantle, diamonds are thought to form during metamorphic reactions (Boyd & Finnerty, 1980), metasomatism (Shee et al., 1982;Sverjensky & Huang, 2015) and in magmatic processes (Meyer, 1985).It has .6Elemental diffusivities of magnesium, silicon, oxygen, and carbon at 3000 K in pure pyrolite melt ("pure py"), pure enstatite melt ("pure en"), pyrolite melt with 3.35 wt.% CO ("py + 3 wt.%CO"), pyrolite melt with 5.16 wt.% CO 2 ("py + 5 wt.%CO 2 "), forsterite melt with 4.09 wt.% C ("fo + 4 wt.%C"), forsterite melt with 7.25 wt.% CO 2 ("fo + 7 wt.%CO 2 ") and forsterite melt with 13.52 wt.% CO 2 ("fo + 14 wt.%CO 2 "), and enstatite melt melt with 16.1 wt.% CO 2 ("en + 16 wt.%CO 2 ").Pyrolite data is from Solomatova et al. (2019), forsterite data is from this study, and enstatite data is from Ghosh and Karki (2017).See electronic version for color representation of the figures in this book.
been proposed that many of the diamonds interpreted to have originated in the transition zone and lower mantle formed from subducted carbon (Burnham et al., 2015;Pal'yanov et al., 2002;Walter et al., 2011;Zedgenizov et al., 2015).However, it is likely that a fraction of super deep diamonds, many of which may have never reached the surface, formed during the crystallization of the mantle after the moon-forming impact in the Hadean and subsequently during the Archaean and Proterozoic eons (Gurney et al., 2010;Helmstaedt et al., 2010).There have been a few computational ab initio studies exam ining the behavior of carbon in silicate melts with a focus on carbon coordination by oxygen (Ghosh et al., 2017;Guillot & Sator, 2011;Vuilleumier et al., 2015); however, there have been no computational studies characterizing the genesis of diamonds in pyrolitic melts.The analysis of diamonds in metamorphic rocks pro vides some information on the depths at which the dia monds formed and the mechanisms by which they grew.For example, octahedral diamonds in peridotitic and eclogitic rocks displayed a spiral growth mechanism, indicating that the crystal moved freely in carbon-bearing silicate melt (Bulanova, 1995).The formation and growth of diamonds has been experimentally observed in a kim berlitic melt at 1800 °C-2200 °C and 7-7.7 GPa (Arima et al., 1993), and from dolomite+iron through carboniron redox reactions (Dorfman et al., 2018).However, the coordination of carbon in the melt and the mechanism of subsequent polymerization of carbon could not be deter mined due to limitations in experimental techniques.
Although redox reactions, such as the oxidation of methane or reduction of carbon dioxide, have been consid ered a necessary step for the formation of diamonds, it has been recently shown that diamonds can form from a reac tion of carboxylates (e.g.acetate [CH 3 COO -]) with water at constant oxygen fugacity (Sverjensky et al., 2014;Sverjensky & Huang, 2015).In pyrolitic melts, Solomatova et al. (2019) observed various oxo-carbon species, such as C 2 O 2 , i.e. eth ylenedione, and C 2 O 4 , i.e. oxalate, (Figure 16.5), suggesting that in the presence of hydrogen, the formation of dia monds from acetate is possible.These polymerized carbon chains are reminiscent of carboxylates and may be consid ered precursors to the formation of diamonds.This sug gests a mechanism for diamond formation in pyrolitic melts Table 16.2Equation of state parameters for silicate melts with varying concentrations of carbon.We compare our results to the experimental studies on carbon-bearing peridotitic and basaltic melts (Sakamaki et al., 2011[not in refs]; Ghosh et al., 2007Ghosh et al., [2009Ghosh et al., or 2017?]?]).An isothermal fourth-order Birch Murnaghan equation of state was fitted to the pressure-density data sets for the pyrolite and carbonated Mg 2 SiO 4 melts.An isothermal third-order Birch Murnaghan equation of state was used to fit the pressure-volume data for Mg 2 SiO 4 (this study), MgSiO 3 (Ghosh et al., 2017), peridotite (Sakamaki et al., 2011[no]) and basalt (Ghosh et al., 2007[no]).
at large depths that does not necessitate the direct formation of oxygen-free carbon clusters; instead, diamond embryos on the nano scale could form through a pathway involving polymerized hydrocarbons, as described in Sverjensky et al. (2014) and Sverjensky and Huang (2015).

CONCLUSIONS
Experiments on silicate melts have demonstrated that at 1-4 GPa and 1000 °C-2000 °C, both the solubility and speciation of carbon depend most strongly on pressure and composition.Carbon solubility increases rapidly with small increases in pressure and is generally positively correlated with the concentration of CaO in the melt, while the CO 2 /(CO 2 +CO 3 2-) ratio is negatively correlated with pressure and is highly sensitive to the silica content, such that carbon exists almost exclusively as CO 2 in silicarich felsic melts (e.g.rhyolite) and as CO 3 2-in silica-poor mafic melts (e.g.basalt).Meanwhile, molecular dynamics simulations of silicate melts at 0-140 GPa and 1400-5000 K have come to a general conclusion that there is a strong positive correlation of carbon solubility with pressure, a weak negative correlation of solubility with temperature, and a positive correlation of CO 2 /(CO 2 +CO 3 2-) with tem perature.Simulations predict that the concentration of CO 2 sharply decreases at the expense of CO 3 2-with increasing pressure between 0 and 5 GPa, in agreement with experimental observations; between 10 and 140 GPa, pressures above what has been achieved by most experiments on carbonated silicate melts, CO 4 4-species appear and their concentration increases with increasing pressure at the expense of CO 2 +CO 3 2-.Here we also demonstrate a need for high-pressure high-temperature experiments on carbonated multicom ponent silicate melts to confirm the computationally pre dicted carbon-carbon polymerization, carbon-silicon bonding, and carbon-iron complexes.Ab initio computa tional studies on CO 2 -H 2 O-bearing silicate melts would help understand the effect of water on carbon's speciation and solubility.The detailed effect of composition and polymerization in complex silicate melts needs to be deter mined both experimentally and computationally, to thor oughly understand the speciation and solubility of carbon in the interior of the Earth.Finally, to constrain the carbon concentration of Earth's interior, it is crucial to determine the fraction of carbon that was retained in the planet after the Giant Impact via calculations on the vol atility of carbon in pyrolitic-type melt and of partitioning between the molten magma ocean and molten core.

Figure 16 . 4
Figure 16.4 Formation of carbon complexes as a function of pressure in simulations on enstatite melt (en; Ghoshet al., 2017); pyrolite melt (py;Solomatova et al., 2019) and forsterite melt (fo; this study) at 3000 K (dotted lines), 4000 K (solid lines), and 5000 K (dashed lines).Left column (a, c, e) includes melts with more reduced carbon species (C and CO); right column (b, d, f) includes melts with more oxidized species (CO 2 and MgCO 3 ).Gray regions mark pyrolite with 3 wt.%CO (left column) and pyrolite with 5 wt.%CO 2 (right column).The degree of carbon-carbon, carbon-iron, and carbon-silicon polymerization generally increases with increasing pressure and decreasing oxidation state of the melts.See electronic version for color representation of the figures in this book.
, which are regarded as the building blocks of our planet.