Silicate dissolution boosts the CO2 concentrations in subduction fluids

Estimates of dissolved CO2 in subduction-zone fluids are based on thermodynamic models, relying on a very sparse experimental data base. Here, we present experimental data at 1–3 GPa, 800 °C, and ∆FMQ ≈ −0.5 for the volatiles and solute contents of graphite-saturated fluids in the systems COH, SiO2–COH ( + quartz/coesite) and MgO–SiO2–COH ( + forsterite and enstatite). The CO2 content of fluids interacting with silicates exceeds the amounts measured in the pure COH system by up to 30 mol%, as a consequence of a decrease in water activity probably associated with the formation of organic complexes containing Si–O–C and Si–O–Mg bonds. The interaction of deep aqueous fluids with silicates is a novel mechanism for controlling the composition of subduction COH fluids, promoting the deep CO2 transfer from the slab–mantle interface to the overlying mantle wedge, in particular where fluids are stable over melts.

S ubduction of the oceanic lithosphere and its sedimentary cover is accompanied by devolatilization processes 1 . CO 2 removal through dissolution of carbonates occurring in altered oceanic lithosphere and its sedimentary cover, along with diapirism of slab rocks 2, 3 and/or melts 4 , provides an efficient way to recycle carbon back to the mantle wedge and, ultimately, to the Earth's surface 5,6 . However, other forms of carbon, often closely associated with silicates, have been reported in slab rocks and in particular in subduction mélanges. For instance, graphite has been described in blueschist-facies mafic rocks, metasediments and hybridized peridotites at Santa Catalina 7 , and in ophiolitic serpentinites from the Western Alps 8 , where also diamond has been found in UHP metasediments 9 . In Alpine Corsica 10 and in the Western Italian Alps 11 , reduction of carbonates during subduction results in graphite-rich metasediments and serpentinites, suggesting that graphite may become a major phase in hybridized silicate-rich subduction mélanges. Graphite has been considered to represent a refractory sink of carbon in the subducting slab, owing to its lower solubility in aqueous fluids 12 and melts 13 compared to carbonates. On the other hand, graphite dissolution mechanisms and solute transport in complex COH fluids at high pressures have remained experimentally unconstrained. Moreover, recent thermodynamic models highlight the role of graphite in subduction-zone fluids 14 and suggest that the presence of graphite is capable of modifying fluid properties and promoting the formation of C-bearing anions, possibly enhancing the complexation of major and trace elements at elevated P and T conditions 12 .
Here, we provide comprehensive experimental constraints on the composition of high-pressure graphite-saturated COH fluids in terms of dissolved CO 2 , SiO 2 , and MgO in increasingly complex petrological systems at controlled redox conditions, buffered by using the double-capsule technique and both the nickel-nickel oxide (NNO) and the fayalite-magnetite-quartz (FMQ) buffers, in order to develop a model for the interaction between deep aqueous fluids and silicates in subduction mélanges. A carbonate-free compositional range has been explored at P = 1 GPa, T = 800°C and P = 3 GPa, T = 800°C in order to focus on the role of graphite and silicates in the investigated processes. We synthesized COH fluids in equilibrium with graphite and other minerals representative of subduction mélanges, i.e., Mg-silicates (forsterite and enstatite), representative of the mantle component, and quartz, representative of the sedimentary component. Experimental products were analyzed for their volatile COH composition by quadrupole mass spectrometry (QMS) and for their Mg and Si solute load by cryogenic laser-ablation inductively coupled plasma mass spectrometry (ICP-MS). Measured data were compared to thermodynamic modeling results. Further details are provided in Methods section and as Supplementary Information. Our results suggest that the interaction of deep aqueous fluids with silicates in the presence of graphite in a subduction mélange promotes the dissolution of graphite and enhances the CO 2 contents of the fluids; this provides a new mechanism for controlling the volatile composition of COH fluids already at depths of~30 km.

Results
CO 2 contents of fluids in equilibrium with silicates. The volatile compositions of COH fluids were measured by piercing the capsules after quench in a gas-tight vessel and then conveying the emanating gases to a quadrupole mass spectrometer (QMS) 15 . Measured data were subsequently compared with the compositions predicted by traditional thermodynamic modeling using different equations of state and mixing properties of H 2 O and non-polar species (details in Methods section). Carbon-saturated fluids were synthesized first in the pure COH system, where fluids interacted only with graphite ( Supplementary Fig. 1a). As predicted by thermodynamic modeling, all analyzed fluids are located on the graphite-saturation surfaces (black lines in Fig. 1 Si and Mg contents of fluids in equilibrium with silicates. The interpretation of the observed differences in volatile content of COH fluids that do and do not interact with silicates is not straightforward. Because, we did not find any evidence of hydration and/or carbonation reactions in the run products, our preferred interpretation is that dissolution reactions of silicates are influencing the XCO 2 of the fluid, provided that graphite is present in excess. We therefore measured additionally the dissolved Si and Mg in the synthetic COH fluids at 1 GPa and 800°C by using a modified version of the cryogenic LA-ICP-MS technique 16 . This technique was originally developed for the analysis of solutes in pure water, which is frozen in the experimental capsules and analyzed via laser-ablation ICP-MS. In the case of COH fluids, an immiscible mixture of water and non-polar gases is expected at the investigated P, T conditions 17 Fig. 1d) is 0.30 ± 0.04 mol kgH 2 O −1 , which is much lower than the quartz solubility in pure water (1.23 mol kgH 2 O −1 ref. 18 ), but much higher than previously reported quartz solubilities in H 2 O-CO 2 fluids characterized by similar XCO 2 but without graphite (0.04 mol kgH 2 O −1 ref. 19 Supplementary Fig. 1e) is much higher compared to the SiO 2 -COH system (1.24 ± 0.19 mol kgH 2 O −1 ), resembling the solubility of quartz in pure water. The solubility of forsterite and enstatite has not previously been measured in mixed H 2 O-CO 2 fluids, but it has been investigated in pure water [21][22][23][24] , amounting to 0.21-0.30 mol SiO 2 kgH 2 O -1 ref. 24 . We additionally performed a dissolution experiment of forsterite and enstatite in pure water (MgO-SiO 2 -H 2 O system; black dot in Fig. 2), obtaining very similar results (0.22 ± 0.06 mol SiO 2 kgH 2 O -1 ), clearly testifying that the solubility of forsterite and enstatite in pure water is much lower than in COH-bearing fluids.
Constraints on the increased solubility of silicates. Our solubility results indicate that in both the graphite-saturated SiO 2 -COH and MgO-SiO 2 -COH systems, the carbon dissolved in fluids does not behave merely as an inert diluent, but promotes the dissolution of silicates at the conditions of our experiments. The simplest explanation of these results is that new unexpected organic complexes containing Si-O-C and Si-O-Mg bonds are formed in addition to the solutes known experimentally, such as the Mg 2+ ion and the silica monomer and dimer 24,25 . This hypothesis is supported by the measured dissolved Mg concentrations in the MgO-SiO 2 -H 2 O and MgO-SiO 2 -COH systems. Although published experimental data are not available to date for the P-T conditions investigated, the extrapolated solubility of Mg derived from the dissolution of forsterite and enstatite in pure water should be less than 0.17 mol kgH 2 O −1 at P = 1-2 GPa and T = 900-1200°C 23 . In our experiments in pure water at 1 GPa and 800°C, dissolved Mg is slightly higher (0.28 ± 0.04 mol kgH 2 O −1 ; Supplementary Table 3). However, in COH fluids at identical P, T conditions the Mg content almost quadruples (1.08 ± 0.10 mol kgH 2 O −1 ; Supplementary Table 3).
In order to gain some insight into the possible aqueous species relevant to the different types of experimental systems reported in the present study, we used a thermodynamic model that also takes Mg-and Si-bearing dissolved species into account, in addition to neutral COH species, and therefore is suitable for the systems SiO 2 -COH and MgO-SiO 2 -COH. We first performed preliminary calculations using the aqueous speciation-solubility code EQ3 26 Table 4).
In the system MgO-SiO 2 -COH, the new Mg(OH) 2(aq) complex and the predicted complexes MgHCO 3 + , MgCO 3(aq) , MgHSiO 3 + , and MgSiO 3 (aq) were used together with the silica monomer and dimer in trial calculations to predict Mg and Si solubilities. However, numerous calculations resulted in solubilities that were too low, indicating the likely need for an additional complex involving the components MgO, CO 2 , and SiO 2 in the MgO-SiO 2 -COH system compared to the carbon-free MgO-SiO 2 -H 2 O system. An analysis of the available solubility data at 800°C and 1 GPa for the MgO-SiO 2 -H 2 O and the MgO-SiO 2 -COH systems indicates that a variety of MgO-SiO 2 -CO 2 complexes might be feasible. For example, complexes involving oxidized C-species such as bicarbonate or carbonate complexes, or complexes involving reduced C-species could account for the observed solubilities. In Supplementary  Table 4, we present the results for a complex of Mg with the silicate anion and the organic anion propionate (MgSiC complex) which can be written as Mg[OSi(OH 3 )][CH 3 CH 2 COO]. This complex provides an explanation for the distinctive enhanced solubilities of Mg and Si measured in the present study. In particular, the MgSiC complex is predicted to be important in the relatively reduced systems investigated, i.e., bearing H 2 O-CO 2 fluids in equilibrium with graphite close to the C-CO 2 (CCO) buffer 29 . This complex, however, would be insignificant in the COH fluids in all previous studies of silicate solubilities that focused on unbuffered H 2 O-CO 2 fluids without graphite (i.e., above the CCO buffer), which are potentially stable up to extremely oxidizing conditions. Analogous calculations for the SiO 2 -COH system suggest the possibility of other organic complexes involving SiO 2 and reduced C-species. It is worth noting here that the stability of organic COH species in subduction-zone fluids has been recently suggested 14 . A more complete analysis of the potential importance of MgO-SiO 2 -CO 2 complexes over a wide range of temperatures and pressures is hampered by the lack of other experimental Mg-and Si-solubility data in the MgO-SiO 2 -COH and SiO 2 -COH systems. Consequently, a full equation of state characterization of the standard partial molal properties of MgO-SiO 2 -CO 2 complexes must await the development of estimation schemes for refining the properties of such complexes.
Constraints on the increase of CO 2 . Analytical results indicate that in both the SiO 2 -COH and MgO-SiO 2 -COH systems externally buffered by FMQ and NNO, dissolution reactions of either quartz/coesite and forsterite + enstatite are able to boost the CO 2 content of graphite-saturated COH fluids at elevated pressures and temperatures. No significant differences have been observed concerning the XCO 2 increase between quartz-bearing and forsterite + enstatite-bearing experiments, suggesting that dissolved Si, rather than Mg, is the major player in this boosting process. This could be attributed to the polymerized nature of silica at high pressures and temperatures 20 , which may be different from other species, for example aluminum species 30 . Our model predicts that neutral silica monomers [SiO 2 (aq)] and dimers [Si 2 O 4(aq) ] are important species at the investigated conditions (Supplementary Table 4), which is supported also by experimental data from forsterite and enstatite incongruent dissolution in pure H 2 O at 1 GPa and 700°C 24 . However, none of the models we developed was able to account for the large increase in the CO 2 solubility in the fluid that was experimentally determined in SiO 2 -COH or MgO-SiO 2 -COH systems. Several possible explanations for this novel effect can be suggested. For instance, very large amounts of HCO 3 − or CO 3 2species that would occur in the SiO 2 -bearing fluids could be converted to CO 2 through reactions of the type: However, theoretical model results indicate that at 1 GPa and 800°C insignificant amounts of HCO 3 − or CO 3 2− are present in the fluids. Actually, the association forsterite + enstatite at 0.5 GPa and 600°C buffers the pH of the coexisting aqueous fluid to between 2.5 and 4 ref. 14 . Our model predicts that at 1 GPa and 800°C the pH of the fluid is 5.57 in the MgO-SiO 2 -H 2 O system and 3.73 in the MgO-SiO 2 -COH system (Supplementary Table 4). These pH values would favor the stability of the species CO 2(aq) against HCO 3 − and CO 3 2− . Moreover, reaction (Eq. 1) is independent on the presence of silica, thus it cannot explain the influence exerted by silicate dissolution in enhancing the XCO 2 of the fluid.
Alternatively, a change in fCO 2 at fixed fH 2 imposed by the buffers could result from a change in fH 2 O or fO 2 associated with dissolved silica. In our double-capsule experiments, silicate dissolution reactions in both the MgO-SiO 2 -COH and SiO 2 -COH systems proceed together with the dissolution of graphite. In the pure COH system, the dissolution of graphite at the investigated relatively oxidizing conditions is controlled by the reaction C þ 2H 2 þ2O 2 ! CO 2 þ2H 2 O (see Eq. 12 in Methods section; Supplementary Fig. 4) until the fugacity of H 2 in the inner capsule, containing a COH fluid, equals that in the outer capsule, containing C-free water in equilibrium with the NNO or the FMQ buffers. The equilibrium constant of the reaction above is: Our experimental data (runs COH70 and COH69 in Supplementary Table 1) and the thermodynamic model of Zhang and Duan (ZD09mod in Supplementary Table 2; details in Methods section) allow retrieving K in the pure COH system at 1 GPa and 800°C resulting both in the NNO-and the FMQbuffered experiments a value of log K = 37.5, assuming log fH 2 NNO = 1.775 and log fH 2 FMQ = 1.889, and log fO 2 = −14.28 (inner capsule buffered by NNO) and log fO 2 = −14.31 (inner capsule buffered by FMQ), respectively.
The observed increase in fluid XCO 2 in SiO 2 -COH and MgO-SiO 2 -COH systems will result in an increase of fCO 2 . Therefore, it is convenient to express Eq. 2 as a function of fCO 2 : By fixing log fH 2 and log K, fCO 2 is expressed as a function of the two variables fO 2 and fH 2 O, which can be represented as two tri-dimensional surfaces, one calculated for log fH 2 NNO (Fig. 3a) and one calculated for log fH 2 FMQ (Fig. 3b). In order to move from the fCO 2 of the pure COH system (green dots in Fig. 3 Table 5). However, in view of the absence of redox sensitive components in the minerals under investigation, even small variations of fO 2 are highly unlikely in our experimental system and therefore we suggest that a decrease in fH 2 O is the culprit of the observed increase in fCO 2 in the MgO-SiO 2 -COH and SiO 2 -COH systems. By using the H 2 O fugacity coefficient from Zhang and Duan 31 (1.579 at 1 GPa and 800°C), we are able to calculate the decrease in water activity (aH 2 O), assuming that

Dissolution of graphite and silicates in subduction mélanges.
Our results suggest that the silica component derived from the dissolution of either magnesium silicates or quartz/coesite alone, even in absence of carbonates, controls the composition of deep COH fluids in equilibrium with graphite, in particular enhancing their CO 2 content when compared to SiO 2 -free systems. This mechanism could be effective especially in cold subduction zones, where subsolidus conditions prevail, and particularly in subduction mélanges, where silicate minerals and graphite 10 are thought to be abundant and flushed by aqueous fluids originating from the dehydration of the subducted lithosphere 32,33 (Fig. 4). Independently from the occurrence of carbonates, the dissolution of silicates can boost the dissolution of graphite in the subduction mélange in the form of volatile CO 2 dissolved in COH fluids by up to + 30% compared to silicate-free systems. These CO 2 -rich fluids will interact with the overlying mantle rocks, influencing metasomatic processes, carbonation/decarbonation reactions, and the melting temperatures of rocks in the mantle wedge 3 . From this perspective, the fact that fluid inclusions in shallow-mantle xenoliths are often dominated by CO 2 over water 34 could be an effect of the inherited CO 2 -rich composition of slab-derived fluids, and does not necessarily require extensive diffusional hydrogen loss from the inclusion to the host mineral. Moreover, as this CO 2 boosting effect cannot be predicted by available thermodynamic models that have been used to estimate the amount of CO 2 recycled from subducted carbon-bearing   Additional experiments investigating more complex, carbonatebearing systems as well as an improved quantification of the content of graphite and organic matter in subducted sediments are required to better quantify the impact of this novel mechanism on the global carbon flux.

Methods
Investigating the fluid composition in COH-bearing systems. Several experimental studies investigated separately the effect of the volatiles H 2 O 35-38 and CO 2 39-42 on subsolidus and melting relations in peridotitic systems at uppermantle conditions. Only few studies considered the effect of the simultaneous occurrence of H 2 O and CO 2 or more generally, the influence of COH fluids on the peridotitic systems 3,43,44 . The H 2 O/CO 2 ratio in COH fluids is crucial because it affects the location of carbonation/decarbonation reactions and the position of the solidus. However, the H 2 O/CO 2 ratio of the fluid in equilibrium with mantle minerals has mainly been estimated through thermodynamic modeling 3 , using equations of state of simple H 2 O-non-polar gas systems 45,46 (e.g., H 2 O-CO 2 -CH 4 ), equations that do not consider the complexity related to dissolution processes 47 .
Another fundamental property of H 2 O-bearing fluids at high-pressure conditions is the capacity to transport dissolved species 18 . The amount of solutes from rock-forming minerals in aqueous fluids increase with increasing pressure 23, 48-50 until the fluid becomes no longer distinguishable from a silicate melt and a supercritical liquid is formed 51,52 The solubility of forsterite and enstatite has been measured in pure water up to 1.5 GPa and at T = 700-1300°C 24 . Experimental data on mineral dissolution in mixed H 2 O-CO 2 fluid are available only for quartz 19,20,53 , albite 54 , and diopside 55 and suggests that solubility decreases with increasing content of CO 2 in the fluid.
The aim of the paper is to provide for the first time experimental constraints on the composition of high-pressure COH fluids in equilibrium with graphite in terms of both volatile content and dissolved solutes in increasingly complex petrological systems at controlled fO 2 conditions. Fluids have been investigated in equilibrium with graphite only in the system COH, with graphite + quartz/coesite in the system SiO 2 -COH and with graphite + forsterite + enstatite in the system MgO-SiO 2 -COH. Two different experimental setups and analytical techniques were employed to determine the volatile composition and the solubility of minerals in COH fluids at P = 1.0 and 3.0 GPa, and T = 800°C. These conditions were selected for sake of simplicity to avoid the presence of carbonates (magnesite) in the system MgO-SiO 2 -COH and the consequent complexities related to carbonate dissolution. In particular, the link between H 2 O/CO 2 ratio (derived analytically by means of a quadrupole mass spectrometer [QMS] 15 ) and silicate dissolution (investigated by cryogenic laser-ablation inductively coupled plasma mass spectrometry [LA-ICP-MS] 56 ) is highlighted here and compared with thermodynamic calculations.
Bulk compositions and starting materials. COH fluids were generated starting either from oxalic acid dihydrate (OAD; H 2 C 2 O 4 ·2H 2 O) or an equivalent mixture of 1:1 oxalic acid anhydrous (OAA; H 2 C 2 O 4 ) + water ( Supplementary Fig. 1). OAD was employed in the experimental runs aimed at investigating the COH volatile composition by means of the capsule-piercing QMS technique 15 (QMS experiments; Supplementary Fig. 1a−c). The dissociation of oxalic acid at high temperature is given by the reaction: Instead of OAD, OAA + Cs-doped (590 µg g −1 ) water was employed as fluid source in experiments on mineral solubility in COH fluids (LA-ICP-MS experiments; Supplementary Fig. 1d, e), to ensure the presence of an internal standard (Cs) for LA-ICP-MS data quantification 56 The thermal dissociation of OAA at high-temperature conditions generates a CO 2 -H 2 fluid according to the reaction: The addition of a proper amount of Cs-doped water in the capsule allowed to obtain a starting fluid composition with XH 2 O = 0.5 for the LA-ICP-MS experiments too.
Graphite (ceramic-grade powder, checked for purity and crystallinity by X-ray powder diffraction and scanning electron microscopy) was added in all experiments to ensure carbon saturation of the COH fluid. In SiO 2 -COH and MgO-SiO 2 -COH experiments, natural quartz powder (Supplementary Fig. 1c) and a mixture of synthetic forsterite and enstatite ( Supplementary Fig. 1b) were added respectively, with fluid/solid ratios of about 0.2 by weight. Forsterite and enstatite were synthesized from dried nano-crystalline Mg(OH) 2 (Sigma-Aldrich, 99.9% purity) and silicon dioxide (Balzers, 99.9% purity), mixed in stoichiometric proportions, pelletized and loaded in a vertical furnace at 1500°C for 24 h. Synthesis products were ground in ethanol for 1 h, dried and characterized by Xray powder diffraction analysis (Bruker, AXS D8 Advance, ETH Zurich; Philips X'pert MPD, University of Milan). The resulting composition of the mixture, derived by Rietveld analysis, is forsterite 83.2 wt%, enstatite 16.7 wt%, and cristobalite 0.1 wt%. Run products were characterized using scanning electron microscopy and electron microprobe WDS analyses (Jeol JXA 8200). Silica polymorphs (quartz/coesite) were identified by X-ray diffraction analysis.
In LA-ICP-MS experiments, a layer of diamond powder (grain size 20 µm) serves as a trap for collecting the COH fluids in equilibrium with solids ( Supplementary Fig. 1d). In the model, these fluids interact with slices of rocks bearing forsterite + enstatite (mantle-derived) and graphite + quartz (sedimentary slab cover). Because of the quadratic growth, small changes in water fugacity/activity due to dissolution of silicates and the consequent release of organosilicon complexes, can enhance the CO 2 content in COH fluids, even in the absence of carbonates, as long as graphite is present. Such fluids will flush the overlying mantle wedge, influencing metasomatic and/or melting processes Experimental conditions and apparatus. Capsules were welded shut in a frozen steel holder to avoid overheating. Capsules were reweighed to ensure no fluid loss during welding occurred. Sintered MgO rods were employed to embed the capsule, surrounded by a graphite heater, Pyrex glass and NaCl. A rocking piston-cylinder apparatus was used to reach high-pressure and high-temperature conditions. The rocking piston-cylinder is a regular end-loaded piston-cylinder, which allows forward and backward rotation of 180°during the experimental run, thus inverting its position in the gravity field. Chemical inhomogeneity within the capsule is in fact common in fluid saturated experiments. The rocking piston-cylinder overcomes this problem 57 as the rotation of the sample induces Rayleigh−Taylor instabilities, forcing the fluid to migrate and causing chemical re-homogenization. Pressure calibration of the rocking apparatus is based on the quartz to coesite transitions 58 at P = 3.07 GPa and T = 1000°C, and P = 2.93 at T = 800°C (accuracy ± 0.01 GPa and ± 5°C). Temperature was measured with a K-type thermocouple located within 0.6 mm from the top of the capsule and is considered accurate to ± 5°C.
Buffering strategy and thermodynamic modeling. Because the volatile composition of graphite-saturated COH fluids is dependent on the redox state of the system, all experiments were performed using a conventional double-capsule design to constrain the chemical potentials ( Supplementary Fig. 1).
The outer Au capsule (OD = 5 mm in QMS experiments; OD = 3 mm in LA-ICP-MS experiments contains a buffering mixture of either Ni + NiO + H 2 O (NNO) or fayalite + magnetite + quartz + H 2 O (FMQ; ferrosilite + magnetite + coesite at 3 GPa, 800°C). As long as all phases are present in the buffering mixtures, they fix the fugacity of H 2 (fH 2 NNO , fH 2 FMQ ) through the reactions: The inner Au 60 Pd 40 capsule (OD = 2.3 mm), which contains the COH fluids in equilibrium with graphite ± quartz/coesite ± forsterite + enstatite, is permeable to hydrogen. Therefore, the fugacity (and, thus, the chemical potential) of H 2 is expected to be homogeneous and identical in the inner and in the outer capsules. Indirectly, also all the other species composing the COH fluid will be externally buffered, including oxygen. However, since the inner capsule contains a mixed COH fluid instead of pure water, the oxygen fugacity in the inner capsule will be lower compared to that fixed in the outer capsule. The fugacities of oxygen and hydrogen fixed in the outer capsule by both NNO and FMQ were calculated employing Perple_X 59 (http://www.perplex.ethz.ch) using the thermodynamic data set of Holland and Powell 60 Table 2). Subsequently, we calculated the speciation of the graphite-buffered COH fluid in the inner capsule for fH 2 fixed by both NNO and FMQ through thermodynamic modeling using (i) the software package Perple_X 59 (based on Gibbs free energy minimization) and the EoS of Connolly and Cesare 45 (Perple_X EoS n. 11) (CC93 in Supplementary Table 2 Table 2 for modeling at 1-3 GPa and 800°C). Depending on the thermodynamic models used, predicted fluids are characterized by the following ΔFMQ values:  Table 2). In fact, the equilibration of the COH fluid in the inner capsule is accomplished by these coupled reactions: which can be condensed to the following graphite-consuming reactions: In conclusion, the equilibration of the COH fluid at run conditions implies that CO 2 is produced in the inner capsule by oxidation of graphite. As a consequence, the XCO 2 of the COH fluid in the inner capsule increases until equilibrium in fH 2 is reached between the inner and outer capsules (Supplementary Fig. 4).
We experimentally verified the fluid composition predicted by thermodynamic modeling, by retrieving analytically the XCO 2 ratio by means of QMS technique 15 , summarized in the next section. At both P = 1 GPa, T = 800°C and P = 3 GPa, T = 800°C measured and calculated ratios are concordant within errors with ZD09mod for both NNO-and FMQ-buffered experiments performed in the COH system ( Supplementary Tables 1 and 2; Supplementary Fig. 2). Therefore, we conclude that this model can reproduces experimental data in the pure COH system. In the SiO 2 -COH and MgO-SiO 2 -COH systems, literature data and the new experimental data discussed in this paper demonstrate that dissolved Mg-bearing and Si-bearing species resulting from dissolution reactions taking place between solid phases and COH fluids occur in addition ( Fig. 2; Supplementary Table 3). By retrieving the XCO 2 in these systems analytically using the capsule-piercing QMS technique 15 , we have demonstrated that the thermodynamic calculations outlined above, which do not take into account these dissolved species, cannot be applied to predict the fluid composition in complex systems, in particular those bearing silicates.
The aqueous speciation and solubility calculations in the investigated silicatebearing systems were carried out using mass balance, charge balance, and mass action expressions in the code EQ3 26 . The equilibrium constants involving aqueous ions, water, and minerals were calculated using the DEW model 27  Analysis of volatiles. Here, we provide a brief summary of the technique used to measure the volatile composition of the COH fluids in the inner capsule. The full description and the validation of the technique is provided in Tiraboschi et al. 15 Quenched COH fluids are extracted from the inner capsule and conveyed to a quadrupole mass spectrometer (QMS). The capsule-piercing device consists of an extraction vessel (reactor) that is heated by an electric furnace to T = 80°C to transform liquid water into water vapor. The reactor, made of Teflon, is composed of a basal part, where the capsule is placed, and a top part, where a steel pointer is mounted. The piercing is executed by screwing the basal part on to the top part until the pointer penetrates the capsule. The capsule, partially embedded in epoxy, is mounted on a steel support, designed to oppose the rotation exerted by the steel pointer during the piercing operation. The furnace design includes a pilot hole in the base part that permits screwing the reactor with a hex key while placed in the furnace. Openings on the top of the reactor allow the carrier gas (ultrapure Ar) to flow inside it and to generate vent or vacuum conditions. The presence of O-rings ensures a tight seal. The reactor is connected to a QMS by a heated line (80°C) to avoid condensation of water on the metal tubes. The pressure conditions in the line and in the reactor are monitored through high-resolution sensor gauges ( ± 1 mbar precision). The temperatures of the line, reactor and furnace are monitored with Ktype thermocouples. Line and reactor pressures and temperatures are recorded by a Eurotherm Nanodac data recorder with PID control. The internal volume of the reactor was calibrated against the distance h between the basal and the top part. P-T-V conditions in the reactor at the time of piercing are used to retrieve the total moles, n, of gases released from the capsule, following the ideal gas law n = RT/PV.
For the calibration of the QMS, standard gas mixtures of known compositions were utilized: (i) 80 vol% Ar, 10 vol% CO 2 , 10 vol% O 2 ; (ii) 80 vol% Ar, 10 vol% CH 4 , 10 vol% CO; and (iii) 90 vol% Ar, 10 vol% H 2 . Water calibration is performed by loading a known amount of water (typically 1 µl) with a micro-syringe inserted through a silicon septum present at the top into the reactor. The calibration allows performing quantitative analyses of H 2 O, CO 2 , CH 4 , CO, H 2 , and O 2 . Uncertainties for major species were typically~1% for H 2 O and CO 2 , and~10% for CO. After piercing has occurred, gases are conveyed to the QMS by opening a valve. For every m/z channel, the QMS counts are measured every 5 s for 310 steps, for a total of 1550 s of measurement time. The moles of gases were obtained by comparing the areas of the m/z peaks with those of the standards, using a least-squares regression method. Monte Carlo simulations provided the propagation of uncertainties for each species, which corresponds to measurement uncertainty of the sample and can be represented as a probability distribution plot in ternary COH diagrams.
Analysis of solutes. The solute content in the fluid was measured employing the cryogenic LA-ICP-MS technique also known as the "freezing technique" 56 , which is applied for the first time on double capsules bearing COH fluids. The recovered experimental capsule is mounted on a freezing stage, which consists of a stack of two Peltier elements, surrounded by plastic to thermally insulate the elements from the atmosphere 61 . The sample holder is placed on a copper block, in direct contact with the Peltier elements and cooled to T~−35°C. The conventional freezing technique has been updated using a cutter blade mounted on a steel support. This device allows cutting longitudinally double capsules by fastening a screw that pushes the cutter blade via a steel block through the capsule. During this operation, the capsule is enclosed in a copper holder. Once the capsule is cut open, the cutting device is removed from the freezing stage together with the upper part of the capsule holder including the top part of the capsule. The upper half of the capsule is investigated using a binocular microscope, while the lower part remains frozen on the stage during the entire laser-ablation analytical session that follows immediately.
Analyses were performed using a 193 nm ArF GeoLas Pro excimer laser system coupled to an ELAN DRCD-e quadrupole mass spectrometer at University of Bern. We analyzed the diamond trap for 24 Mg, 25 Mg, 26 Mg, 29 Si, 62 Ni, 133 Cs, 195 Pt, and 197 Au, using a 60 µm beam diameter,~13 J/cm laser fluency, and 5 Hz repetition rate. Data were acquired in blocks of up to~10 individual sample analyses bracketed by three analyses of the standard NIST SRM610, placed in the ablation chamber with the sample. Background was taken for~50 s and the sample signal, on the diamond trap or on the solid residue, was collected for~20 s. LA-ICP-MS data reduction employed the SILLS software 62 and in-house spreadsheets to calculate solute concentrations, employing rigorous limit of detection filtering 63 for each element and each measurement individually.
The cryogenic technique has been originally developed for analyzing the solute content of aqueous fluids. Cesium, introduced in the starting materials, is employed as an internal standard for data quantification, because it is a highly incompatible element that fractionates completely into the aqueous fluid phase at the given residual mineralogy. In our experiments, we introduced a known amount of water solution doped with 590 µg g −1 Cs [as Cs(OH) 2 ]. As the initial Cs/H 2 O ratio is fixed, once the Cs concentration in the fluid phase coexisting with minerals at run P and T is known, solute concentrations of the fluid can be calculated 56 . However, compared to experiments bearing aqueous fluids, our double-capsule, COHbearing experiments are more complex, because the initial Cs/H 2 O is not fixed, as the water content in the inner capsule is variable, depending on P, T and fH 2 -fO 2 conditions (Eqs. 11 and 12). In fact, in double-capsule arrangements H 2 is a mobile component that can be added or removed from the system through diffusion in and out of the inner capsule. This implies that the initial Cs concentration cannot be used as an internal standard. This value needs to be corrected taking into account the change in total water mass present in the inner capsule relative to initial amount of loaded water, as a consequence of fluid XCO 2 re-equilibration at the fH 2 -fO 2 conditions imposed by the buffers. If H 2 O is consumed during fluid reequilibration at run conditions, Cs concentration in the residual water increases; if H 2 O is produced, Cs concentration decreases (Supplementary Fig. 3). We estimated the corrected Cs concentration at run P and T using a model, which assumes that fluid equilibration at the hydrogen fugacity conditions imposed by the buffers NNO and FMQ is governed only by H 2 mobility and no hydration or carbonation reactions occur in the capsule charge. As long as these two assumptions are valid, it is possible to estimate the amount of Cs in the inner capsule in the following way considering a classic dilution equation: where C i Cs is the initial concentration of Cs in the aqueous solution loaded into the capsule (590 µg g −1 ) and C f Cs is the final concentration of Cs after fluid equilibration at fH 2 conditions. V i H 2 O and V f H 2 O are the initial and final volumes of water. The volume of water is proportional to the moles according to: (VH 2 O, volume of water; nH 2 O, number of molesof water; V mol H 2 O, molar volume of water).
Considering that at fixed pressure and temperature conditions the molar volume of water is constant, we obtain the following dilution equation: The final Cs concentration in the aquesous fluid fraction will be given by: As n i H 2 O is known (the initial amount of water charged into the capsule), this equation can be solved as long as n f H 2 O is constrained, through equation: where XH 2 O f is the final H 2 O/(CO 2 + H 2 O) ratio measured by QMS analysis, and XH 2 O i is the initial H 2 O/(CO 2 + H 2 O) ratio retrieved on the basis of the amounts of water and OAA charged into the capsule. Solute concentrations in the aqueous fraction of the COH fluid at run P and T can thus be calculated ( Fig. 2; Supplementary Table 3).
Data availability. The authors declare that the data supporting the findings of this study are available within the article.