Martin Voigt
email: martinvoigt@hi.is

Christopher R Pearce

David M Fries

Andre Baldermann

Eric H Oelkers

Magnesium isotope fractionation during hydrothermal seawater-basalt interaction

come

Introduction

The Mg isotopic composition of seawater is controlled by a combination of inputs and outputs from reservoirs with distinct isotopic compositions, and exchange processes that fractionate its three stable isotopes ( 24 Mg, 25 Mg and 26 Mg). Rivers, which transport Mg derived from the weathering of continental carbonate and silicate rocks, are thought to be the major source of Mg to the oceans, while seafloor hydrothermal systems and carbonate mineral precipitation are the dominant sinks (Tipper et al., 2006b;[START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF][START_REF] Huang | Magnesium isotopic composition of altered oceanic crust and the global Mg cycle[END_REF]. The study of marine evaporite minerals and carbonate-hosting sedimentary successions suggest that the Mg concentration of seawater varied considerably over the Phanerozoic and is currently increasing [START_REF] Horita | Chemical evolution of seawater during the Phanerozoic: Implications from the record of marine evaporites[END_REF][START_REF] Fantle | Sr isotopes and pore fluid chemistry in carbonate sediment of the Ontong Java Plateau: Calcite recrystallization rates and evidence for a rapid rise in seawater Mg over the last 10 million years[END_REF][START_REF] Higgins | Records of Neogene seawater chemistry and diagenesis in deep-sea carbonate sediments and pore fluids[END_REF]. The current and past state of the marine Mg isotopic system nevertheless remains unclear, as Mg isotope records derived from foraminifera from the past 40 Ma indicate a rapid decrease in seawater  26/24 Mg over the past ~ 15 Ma (Pogge von Strandmann et al., 2014), whereas pelagic marine carbonates from the past 80 Ma suggest only small changes in seawater  26/24 Mg over this period [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. The interpretation of such changes (or lack thereof) is challenging as the influence of the different fluxes on the Mg isotope budget remains uncertain. In particular the extent of isotopic fractionation occurring in marine hydrothermal systems is poorly constrained at present [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. Although basaltic rock dissolution in hydrothermal systems temporarily releases Mg to the fluid phase, this release is often counterbalanced by Mg-rich clay mineral precipitation. The net result of this coupled process is the almost complete removal of Mg from the seawater in high-temperature hydrothermal systems with temperatures exceeding 400 °C, as well as significant Mg removal at lower temperature conditions [START_REF] Mottl | Hydrothermal circulation through mid-ocean ridge flanks: Fluxes of heat and magnesium[END_REF][START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF].

Consequently, there is a net transfer of Mg from seawater to the oceanic crust in such settings (e.g., [START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF][START_REF] Coogan | An internally consistent, probabilistic, determination of ridge-axis hydrothermal fluxes from basalt-hosted systems[END_REF][START_REF] German | Hydrothermal processes[END_REF], and in the case of non-complete Mg removal (especially at lower temperatures) this process potentially affects the oceanic Mg isotope budget [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF].

Although the number of studies of Mg isotopes in altered oceanic basalts to date are limited [START_REF] Teng | Magnesium isotope geochemistry[END_REF][START_REF] Huang | Magnesium isotopic composition of altered oceanic crust and the global Mg cycle[END_REF][START_REF] Guo | Mg isotopic systematic and geochemical applications: a critical review[END_REF], current data suggests a wide range of Mg isotopic compositions can result from carbonate and clay mineral precipitation during low-temperature seawater alteration. A relatively strong preferential uptake of light Mg isotopes is commonly observed by Mg-containing carbonate mineral precipitation in shelf regions, such as during the dolomitization of ancient platform carbonates [START_REF] Galy | Mg isotopic composition of carbonate: insight from speleothem formation[END_REF]Tipper et al., 2006b;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF][START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]; this process has been suggested to be the main driver of past changes in seawater  26/24 Mg (Pogge von [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF]. On the other hand, Mgbearing silicate alteration minerals such as clays show a smaller degree of Mg isotopic fractionation, with most studies suggesting the preferential incorporation of heavy Mg isotopes into the non-exchangeable sites (i.e. octahedral sheets) of secondary clay minerals (Tipper et al., 2006a;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF][START_REF] Ryu | Experimental investigation of Mg isotope fractionation during mineral dissolution and clay formation[END_REF]. There is also evidence for Mg isotope fractionation in the opposite sensethe preferential incorporation of lighter Mg isotopes into the exchangeable interlayer sites of Mg-bearing clay minerals [START_REF] Pogge Von Strandmann | The influence of weathering processes on riverine magnesium isotopes in a basaltic terrain[END_REF][START_REF] Wimpenny | The behaviour of Li and Mg isotopes during primary phase dissolution and secondary mineral formation in basalt[END_REF]. This suggests that the metal ion (Mg) uptake by secondary clay minerals and the related isotope fractionation mechanism are highly dependent on the starting fluid composition (including the pH, concentration of elements required for mineral formation, and the presence or absence of seed crystals and precipitation inhibitors). Furthermore, fractionation also depends on the physicochemical and surface characteristics of the alteration mineral (such as crystal structure and bond lengths, specific surface area, surface charge, etc., [START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH) 2 ] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF][START_REF] Baldermann | Removal of Barium, Cobalt, Strontium, and Zinc from Solution by Natural and Synthetic Allophane Adsorbents[END_REF]. Such factors can be further complicated by aqueous solution speciation, as Mg isotope fractionation can occur between individual species (e.g., [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF].

To better constrain the behaviour of Mg isotopes in marine hydrothermal systems, we performed a series of experiments reacting glassy and crystalline basalt with seawater at temperatures of 250 °C and 290 °C. These temperatures are intermediate between the lowtemperature marine hydrothermal systems at <100 °C and the high-temperature axial hydrothermal systems that produce fluids of >400 °C, where necessary to 1) achieve sufficiently fast reaction progress to study this isotopic exchange in the laboratory, and 2) to avoid extremely rapid removal of Mg from the seawater into secondary phases at even higher temperatures. The two rock types were chosen to explore the potential impact that the presence of distinct mineral phases had on the chemical and isotopic evolution of the marine basaltic crust relative to the more reactive glassy components. Unlike previous experimental studies of such systems (e.g., [START_REF] Bischoff | Seawater-basalt interaction at 200°C and 500 bars: Implications for origin of sea-floor heavy-metal deposits and regulation of seawater chemistry[END_REF][START_REF] Seyfried | Hydrothermal transport of heavy metals by seawater: The role of seawater/basalt ratio[END_REF][START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-I. Experimental results for major and minor components of seawater[END_REF][START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 °C and 150 °C[END_REF][START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-II. Experimental results for Fe, Mn, and sulfur species[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300°C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] Seyfried | Hydrothermal alteration of basalt by seawater under seawater-dominated conditions[END_REF][START_REF] Seewald | The effect of temperature on metal mobility in subseafloor hydrothermal systems: constraints from basalt alteration experiments[END_REF], the temporal evolution of the aqueous Mg isotopic composition was followed during the experiments via regular sampling, enabling the behaviour of Mg isotopes during the dissolution of basalt and the formation of secondary alteration minerals to be constrained.

Methods

Experimental design

The experiments conducted in this study were designed to investigate chemical exchange during seawater-basalt interaction by reacting two types of basalt with different crystallinity with seawater in rocked closed-system Ti-reactors at 250 and 290 °C for 53 and 92 days, respectively (Fig. 1, Table 1). The basalt used consisted of either basaltic glass or crystalline powders derived from Stapafell in SW Iceland (40-80 μm size fraction, obtained by milling, sieving and subsequent cleaning from ultra-fine grains by repeated ultrasonic cleaning in ultrapure water). The specific surface areas of the glass and crystalline powders were 0.1 and 0.4 m 2 /g, respectively, as determined by the BET technique [START_REF] Brunauer | Adsorption of gases in multimolecular layers[END_REF] on a Quantachrome Autosorb 1-MP analyser using Kr gas. The chemical composition of the samples, previously reported by Oelkers and Gislason (2001) and [START_REF] Gudbrandsson | An experimental study of crystalline basalt dissolution from 2⩽pH⩽11 and temperatures from 5 to 75°C[END_REF], is provided in Table 2 and is nearly identical to that of mid-ocean ridge basalt (MORB, which, on average, contains slightly less Mg and Fe but more Si and Al compared to the basalt used in this study; [START_REF] White | Composition of the Oceanic Crust[END_REF]. Both powders were reacted with natural seawater collected from the equatorial Pacific at a depth of 350 m (EqPac cruise November 1992; [START_REF] Murray | JGOFS studies in the equatorial Pacific[END_REF]. The seawater was acidified upon collection using distilled concentrated HNO 3 to prevent the precipitation of solids and growth of organic material. The pH of the seawater required for the experiments was re-adjusted to its natural value of ~8.14 by the gradual addition of a 25 % ammonia solution (EMD Millipore Suprapur) prior to use in the experiments. The mass ratio of seawater to basaltic powder was ~10 in all experiments, in line with previous experiments and estimates for submarine hydrothermal systems [START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 °C and 150 °C[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300°C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF]. Fluid samples (~ 22 mL) were regularly retrieved from the reactor during the experiments using a sampling valve with an attached cooling apparatus that included a 0.45 μm cellulose acetate membrane filter. This sampling, which was conducted more frequently at the beginning of the experiments due to the faster rate of change expected in the measured parameters, decreased the water:rock ratio to approximately 5 by the end of the experiments. The pressure in the reactors, which was constrained by equilibrium between liquid and gas, was approximately 39 bar and 73 bar at 250 °C and 290 °C, respectively, as calculated using thermodynamic data for the H 2 O-NaCl system of [START_REF] Driesner | The system H 2 O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 °C, 0 to 5000 bar, and 0 to 1 X NaCl[END_REF] and [START_REF] Driesner | The system H 2 O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 °C, 1 to 5000 bar, and 0 to 1 X NaCl[END_REF]. Further details on the fluid sampling and experimental design used in this study are provided in Voigt et al. (2018b).

Analytical methods

Aqueous concentrations

The pH of all of the sampled fluids was measured at 22±1 °C using a Metrohm microelectrode, calibrated against pH buffers of pH 4.0, 6.9, and 9.2. The uncertainty on these pH measurements is ±0.07 pH units, based on replicate analyses. For the 250 °C experiments, aqueous Na, Mg, Si, K, Ca, Sr, Li and Fe concentrations were determined by inductively coupled plasma atomic emission spectrometer (ICP-AES, iCAP6000 Series, ThermoFisher), and by inductively coupled plasma mass spectrometry (ICP-MS, Agilent 7500ce) for the 290 °C experiments. The analytical uncertainties and detection limits of these analyses are reported in Electronic Supplementary Table 1. For the 290 °C experiments, Na concentrations were also determined by flame atomic absorption spectrometry (AAS, AAnalyst 600, Perkin Elmer). The concentrations determined for the experimental samples using the different techniques are consistent within the analytical uncertainties. Additionally, aqueous Al concentrations were determined by furnace AAS, while aqueous and Cl -concentrations were measured using ion chromatography (IC, Dionex ICS 2000). Additional details of these analytical methods can be found in Voigt et al. (2018b).

Characterisation of solids

The mineralogical composition of the unreacted basalt powders and of the solids recovered from the reactors were analysed by powder X-ray diffraction (PXRD, PANalytical X'Pert PRO, Co-Ka radiation at 40 kV and 40 mA). Briefly, the solid materials were mixed with 20 wt-% of ZnO as the internal standard, then randomly oriented preparations were created using the top loading technique and subsequently examined in the range 4-85º 2Θ using a step size of 0.02º 2Θ/s with a count time of 1 s/step. Rietveld-based phase quantification was performed applying the PANalytical X'Pert HighScore Plus software and the pdf-4 database. For further analysis of the neo-formed clay minerals, the < 2 µm size fraction was separated by centrifugation. Subsequently, oriented mounts were created as described in [START_REF] Baldermann | The Fe-Mg-saponite solid solution series a hydrothermal synthesis study[END_REF], and analysed in the range 3-30º 2Θ using a step size of 0.02º 2Θ/s and a count time of 2 s/step on a Philips PW 1830 diffractometer (Cu-Ka radiation, 40 kV and 30 mA), each under air dried conditions, after solvation with ethylene glycol (EG)

and after heating of the specimens to 550ºC for 1 h. The chemical composition and hydration state of the saponite-type precipitates were estimated from EG-solvated preparations using the program Sybilla© developed at ChevronTexaco [START_REF] Baldermann | The Rate and Mechanism of Deep-Sea Glauconite Formation at the Ivory Coast -Ghana Marginal Ridge[END_REF]. In addition, the basalt powders and reaction products were analysed by scanning electron microscopy (SEM) using a Jeol JSM 6360LV equipped with an electron dispersive spectroscope (EDS).

Isotopic composition measurements

The Mg isotopic compositions of basalt and liquid samples were determined by multiple collector inductively coupled plasma mass spectrometry (MC-ICP-MS) using a ThermoFisher Neptune at the National Oceanography Centre, Southampton. The solid samples were first dissolved in a mixture of bi-distilled HNO 3 and HF at 130 °C, evaporated to dryness, and re-dissolved in double-distilled HCl. Prior to analysis, Mg was purified using ion-exchange chromatography with a protocol adapted from Pogge von Strandmann et al.

( 2008; 2012). For this, a sample aliquot containing 2000 ng Mg was evaporated to dryness and re-dissolved in 200 µL of 0.8 mol/kg aqueous HNO 3 before loading onto pre-cleaned Bio-Rad AG50W-X12 (200-400 mesh) resin equilibrated with 0.8 mol/kg HNO 3 in a Savillex 30 mL column to a height of 8.5 cm. Cations other than Mg were eluted using a total volume of 51 mL of 0.8 mol/kg aqueous HNO 3 , followed by the elution of Mg in 20 mL of 2 mol/kg aqueous HNO 3 . To ensure a 100 % yield, this elution protocol was tested using the IAPSO seawater standard, the DSM3 Mg standard [START_REF] Galy | Magnesium isotope heterogeneity of the isotopic standard SRM980 and new reference materials for magnesium-isotope-ratio measurements[END_REF] as well as the BCR-2 basaltic rock standard and SCo-1 shale standard from the USGS; each showed Mg isotopic compositions in close agreement with previously reported values (Table 3). The column procedure was repeated 2-3 times to achieve a sufficient purity for Mg analyses, which was confirmed by measurement of Li, Na, Mg, Al, K, Ca, Ti V, Mg, Fe, Ni, Sr, Sn and Pb concentrations using a ThermoFisher X-Series ICP-MS. Despite the efficiency of this procedure, complete removal of Ca was not achieved for four samples (BSW04-03, BSW05-07, BSW07-03, and BSW07-04), resulting in isobaric interferences during the MC-ICP-MS measurements; these analyses were corrected as described below.

Purified samples were introduced to the MC-ICP-MS in 3 % aqueous HNO 3 via a standard injection system (SIS). Thirty measurements with a combined integration time of 252 s were made per sample. The samples, containing ~600 ppb Mg typically yielded 24 Mg beam intensities of ~13.5 V. Mass fractionation occurring during the measurements was corrected using the sample-standard bracketing technique, and values are reported as relative to the DSM3 standard [START_REF] Galy | Magnesium isotope heterogeneity of the isotopic standard SRM980 and new reference materials for magnesium-isotope-ratio measurements[END_REF]. Similar to the method outlined by [START_REF] Paton | Improved laser ablation U-Pb zircon geochronology through robust downhole fractionation correction[END_REF], the drift of standard measurements was modelled using smoothed cubic splines instead of simple linear interpolations for a more accurate representation of changes in standard measurements based on statistical methods.

Uncertainties in this drift model and overdispersion correction were estimated using Monte Carlo simulations, so that the given uncertainties were propagated from uncertainties in the sample and standard measurements. All samples were run in duplicate, and their weighted means and propagated uncertainties are given in [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Teng | Magnesium isotope geochemistry[END_REF]. The magnitude of 2 standard deviations of the measurements made during this study varied from 0.07 ‰ to 0.24 ‰. The higher variability is reflected in the uncertainties propagated using the method described above.

Isobaric interference effects incurred during analysis from the residual Ca in four samples (BSW04-03, BSW05-07, BSW07-03, and BSW07-04) were corrected by assuming that observed deviations of the measured δ 26/24 Mg and δ 25/24 Mg values from the mass dependent fractionation line [START_REF] Young | Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[END_REF] were caused by 48 Ca interference with the 24 Mg signal. This enabled the measured δ values to be corrected by back-tracking to the 'true' values that were consistent with mass dependent fractionation (see Supplementary Fig. 1).

Two of the affected samples were analysed by MC-ICP-MS after two and three repeats of the ion-exchange separation, which lead to an increasingly better, but not complete, Ca removal.

For both samples, these two individual analyses are consistent with the same corrected δ 26/24 Mg and δ 25/24 Mg. Furthermore, the analysis after three separation runs indicates a smaller amount of 48 Ca (Supplementary Fig. 1), consistent with the assumption that the deviations are caused by Ca interference. Propagation of uncertainties in this inversion was performed using Monte Carlo simulations, so that the uncertainties given for δ 26/24 Mg and δ 25/24 Mg of the corrected samples include uncertainties of the interference correction.

Results

Evolution of the liquid phase composition

General chemical trends

The elemental composition of the experimental seawater changed significantly during its reaction with basalt (Table 4). The rate of change was higher at 290 °C than at 250 °C, and faster reaction progress, as monitored by the temporal evolution of reaction fluid compositions, was also observed for the experiments performed using basaltic glass compared to those using crystalline basalt as the reactant, even though the initial surface area of the crystalline material (determined using the BET technique) was approximately 4 times higher.

Magnesium was constantly removed from the liquid through basalt-seawater interaction and reached levels below the detection limit after 7 days in the basaltic glass experiment at 250 °C, while the final aqueous Ca concentrations were higher than the initial seawater in both experiments (Fig. 2). Similar to Mg, the initially present in the seawater was removed from the liquid over time. A pH of 3.7 and 4.9 was attained in the crystalline basalt experiments at 250 °C and 290 °C, respectively, before increasing to approximately pH 9.5. In contrast, the pH values did not decrease significantly in the basaltic glass experiments before they increased to similar values as in the crystalline basalt experiments (Fig. 2). Significant

Magnesium isotopic compositions

The basaltic glass used in this study had a  26/24 Mg composition of -0.28±0.18 ‰, while the crystalline basalt had a slightly lower value of -0.38±0.18 ‰ (uncertainties listed here reflect the 95% confidence interval, corresponding to ~2 standard errors). These values are thus identical within uncertainty, and are in agreement with the value of -0.30±0.03 ‰ obtained by [START_REF] Wimpenny | The behaviour of Li and Mg isotopes during primary phase dissolution and secondary mineral formation in basalt[END_REF] for the Stapafell basaltic glass. The seawater used as reactant had a starting  26/24 Mg composition of -0.86±0.07 ‰, which is identical within uncertainty to the  26/24 Mg value of -0.83±0.09 ‰ for seawater recommended by [START_REF] Teng | Magnesium isotopic compositions of international geological reference materials[END_REF]. Starting from the initial seawater composition, the liquid evolved towards isotopically lighter compositions (Fig. 2, Table 4): In the 250 °C basaltic glass experiment  26/24 Mg initially decreased to -1.02±0.19 ‰ during the first 24 h, then decreased to -3.27±0.87 ‰ between days 4 and 7 before the aqueous Mg concentrations became too low for isotopic analysis. In the corresponding crystalline basalt experiment, a fluid  26/24 Mg value of -1.11±0.13 ‰ was reached within the first 14 days. The next sample, taken after 21 days of total elapsed time, had a  26/24 Mg composition of -0.79±0.14 ‰, then decreased again to -1.26±0.41 ‰ at the end of the experiment (Fig. 2). At 290 °C, the fluid that was reacted with basaltic glass decreased to a  26/24 Mg value of -1.07±0.07 ‰ within the first day, while later samples did not contain sufficient Mg for isotopic analysis. At the same temperature, seawater reacted with crystalline basalt showed a slight decrease in  26/24 Mg values to -1.01±0.07 ‰ within 4 days, followed by a drop to -1.63±0.29 ‰ and another slow decrease to -1.75±0.08 ‰ after 35 days.

Solid alteration products

The basalt powders used as reactants were significantly altered during the experiments. SEM images of the solids recovered from the reactors after the experiments were terminated (Fig. 3) show that the basalt grains were completely covered by alteration minerals with honeycomb-like structures, which is typical for smectite clays (e.g., [START_REF] Fiore | Smectite formation in rhyolitic obsidian as inferred by microscopic (SEM-TEM-AEM) investigation[END_REF]. Furthermore, anhydrite was formed during all experiments (Voigt et al., 2018b). The massive formation of smectite minerals was confirmed by quantitative PXRD analyses (Table 5, Fig. 4). Modelling of XRD patterns obtained from EG-solvated, oriented clay films enabled the smectite clays to be identified as trioctahedral ferrous saponite with Na ions occupying mainly the exchangeable interlayer sites (Fig. 4). The ferrous saponite precipitated in this study contains approximately 0.46 to 0.67 atoms per formula unit (a.p.f.u.) octahedral Fe in the experiments with crystalline basalt, and from 0.71 to 0.98 a.p.f.u. octahedral Fe in the basaltic glass experiments (Table 5; Supplementary Fig. 3). Furthermore, PXRD data suggest that minor analcime/heulandite type zeolite formed during the two basaltic glass experiments.

At 290 °C, plagioclase (close to albitic composition) and minor proportions of mixed-layer chlorite-smectite minerals were formed in the experiment with basaltic glass according to the PXRD analyses (Table 5, Fig. 4).

Discussion

Evolution of liquid chemistry and alteration reactions

The reaction of basalt with seawater under hydrothermal conditions in our experiments caused the rapid and abundant precipitation of ferrous saponite and minor anhydrite, which removed Mg as well as Na, OH, Al, Si, Fe, and Sr from the fluid (Voigt et al., 2018b).

A number of studies have previously concluded that the evolution of fluid pH in such systems is controlled by the relative importance of two competing processes: (1) The uptake of alkalinity (i.e. OH -groups) along with Mg, Si and Fe by secondary hydrous minerals, which drives a drop in pH as seen in the beginning of the experiments with crystalline basalt; and (2) leaching of Ca and other cations from the basalt causing pH and aqueous Ca concentrations to increase after Mg removal was near complete [START_REF] Bischoff | Seawater-basalt interaction at 200°C and 500 bars: Implications for origin of sea-floor heavy-metal deposits and regulation of seawater chemistry[END_REF][START_REF] Seyfried | Hydrothermal transport of heavy metals by seawater: The role of seawater/basalt ratio[END_REF][START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 °C and 150 °C[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300°C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] Seyfried | Hydrothermal alteration of basalt by seawater under seawater-dominated conditions[END_REF]. The stronger increase in pH observed in this study compared to previous experiments and marine high-temperature hydrothermal fluids (Fig. 2; [START_REF] Seyfried | Low temperature basalt alteration by sea water: an experimental study at 70 °C and 150 °C[END_REF][START_REF] Seyfried | Experimental seawater-basalt interaction at 300°C, 500 bars, chemical exchange, secondary mineral formation and implications for the transport of heavy metals[END_REF][START_REF] German | Hydrothermal processes[END_REF] is possibly related to the uptake of HCl by the gas phase enabled by the high salinity, and/or the presence of small amounts of NH 3 introduced during the pH adjustment of the seawater used in the experiments (see Voigt et al., 2018b). The low initial pH in the crystalline basalt experiments also explains the prolonged period of Fe enrichment in the liquid (released from basalt), after which it was incorporated into the saponite clays as indicated by their high octahedral Fe contents (cf. section 3.2) and the absence of secondary Fe-hydroxide minerals. Fluid enrichment in Fe is also consistent with trends observed in natural marine hydrothermal fluids (e.g., [START_REF] German | Hydrothermal processes[END_REF]. Furthermore, the correlation between the total mass of precipitated smectite and the estimated structural Fe content of saponite formed in experiments with basaltic glass and crystalline basalt (Table 5) suggests that a Fe-poor saponite was initially precipitated, followed by an increasing more Fe-rich saponite during subsequent mineral growth.

Magnesium isotope fractionation

The changes in aqueous  26/24 Mg during the experiments likely reflect the combined effects of isotopic fractionation during saponite precipitation and the Mg release from basalt dissolution. Consequently, an assessment of the extent of isotope fractionation into the alteration products requires an estimate of the amount of Mg released from basalt dissolution, which is later scavenged by clay mineral formation. Here, we estimate these values from mass balance relationships between aqueous and solid phase Mg, assuming that all Mg released from basalt dissolution is precipitated into a single alteration phase (i.e. saponite). It is also assumed that no significant Mg is taken up by the low-NaCl vapour phase that is present at the end of the experiments, as the vapour pressure of Mg is significantly lower than that of Na (Lide, 2003); thus Mg is only expected to be present in trace quantities in the vapour phase under the experimental conditions used in this study [START_REF] Driesner | The system H 2 O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 °C, 1 to 5000 bar, and 0 to 1 X NaCl[END_REF][START_REF] Driesner | The system H 2 O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 °C, 0 to 5000 bar, and 0 to 1 X NaCl[END_REF]. The amount of Mg released from basalt dissolution was estimated from mass balancing the components Mg, Ca and SO 4 . We assume that Ca and are only removed from the liquid by precipitation into anhydrite. The latter assumption is likely not entirely satisfied, especially during the later stages of the experiments, when Ca could be incorporated into one or more of the other observed alteration phases (saponite, zeolites, and albitic plagioclase).

Therefore, the calculated amounts of Mg released from basalt dissolution (symbols in Fig. 5a,b) and Mg incorporation into smectite are likely minimum estimates.

Based on the mass balance constraints described above, the evolution of  26/24 Mg during the experiments was modelled using an incremental isotope mass balance model, allowing for isotopic fractionation during the precipitation of a single Mg-incorporating mineral (saponite). A constant isotopic fractionation factor describing irreversible isotopic fractionation during smectite precipitation (i.e. the smectite does not react with the liquid after precipitation) is assumed in this model, and is defined as

Consequences for the marine Mg isotopic budget

Recent studies of the marine Mg isotopic budget suggest that variations in carbonate mineral formation (such as dolomitization) and riverine inputs have exerted a major influence on the composition of seawater through time [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF], and that a decrease in seawater  26/24 Mg over the past ~15 Ma may have been driven by a decrease in the extent of dolomite precipitation [START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF]. Although the influence of Mg-clay formation in marine hydrothermal environments and in marine sediments on the global marine budget has been proposed by [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF] and [START_REF] Dunlea | Cenozoic global cooling and increased seawater Mg/Ca via reduced reverse weathering[END_REF], the magnitudes of these effects are poorly constrained at present, and are expected to vary as a function of the degree of Mg where … reflects the contributions of other fluxes on the marine Mg budget (e.g. Tipper et al., 2006b;[START_REF] Pogge Von Strandmann | Modern and Cenozoic records of seawater magnesium from foraminiferal Mg isotopes[END_REF][START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF]. Assuming that irreversible isotopic fractionation occurs in a closed system, it can be shown (Appendix B) that for a given fraction f of Mg removal from the seawater, the isotopic evolution can be described by

(4.3)
This function has its maximum of at f=0 and is shown in Fig. 6a for , which is the mean of our experimental best fit weighted by the inverse of their variance. Since , the effect of Mg isotope fraction in these clays is proportional to (4.4)

illustrating that the effect of clay precipitation on the marine budget is largest at for a constant , and is zero at both no clay mineral precipitation and complete Mg removal (Fig. 6b).

This result shows that the impact of Mg isotopic fractionation during smectite formation in high-temperature marine hydrothermal systems on the marine Mg isotopic budget may be low, as Mg is almost quantitatively removed from the seawater during hydrothermal reactions (e.g., [START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-I. Experimental results for major and minor components of seawater[END_REF][START_REF] Elderfield | Fluid and geochemical transport through oceanic crust: a transect across the eastern flank of the Juan de Fuca Ridge[END_REF][START_REF] Coggon | Linking basement carbonate vein compositions to porewater geochemistry across the eastern flank of the Juan de Fuca Ridge, ODP Leg 168[END_REF][START_REF] German | Hydrothermal processes[END_REF]. Using the mean of our best fit fraction factor, the isotopic difference between seawater and clays due to irreversible precipitation is approximately for an 80 % removal of Mg from seawater (see Fig. 6), which is assumed to be the minimum value for high temperature hydrothermal systems, and it often approaches 100 % [START_REF] Mottl | Hydrothermal circulation through mid-ocean ridge flanks: Fluxes of heat and magnesium[END_REF][START_REF] German | Hydrothermal processes[END_REF].

Conversely, for low temperature alteration, Mg removal is less complete and reaches down to f=0 [START_REF] Fisher | Seamounts as Conduits for Massive Fluid, Heat, and Solute Fluxes on Ridge Flanks[END_REF]. In their marine Mg budget model, Higgins and Schrag (2015) adopted a value of for the isotopic difference between seawater and Mg-clays, (2018). However, Mg isotopic fractionation is expected to more pronounced at lower temperatures (e.g., [START_REF] Teng | Magnesium isotope geochemistry[END_REF], thus these values are qualitatively in agreement.

In comparison, the influence of carbonate precipitation on the Mg isotopic budget of the oceans is approximately an order of magnitude higher due to its larger isotopic fractionation factor of [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF], even considering a higher Mg flux at mid-ocean ridges compared to that of marine carbonate formation. Nevertheless, both carbonate formation and clay precipitation with incomplete Mg-removal from the seawater are crucial when constraining the global marine Mg cycle using isotopes, as suggested by [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF] and [START_REF] Huang | Magnesium isotopic composition of altered oceanic crust and the global Mg cycle[END_REF].

Conclusions

The evolution of aqueous  26/24 Mg was followed during basaltic glass and crystalline The values determined in this study are in agreement with independent field and experimental evidence for similar silicate minerals (Tipper et al., 2006a;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF][START_REF] Wimpenny | Investigating the behaviour of Mg isotopes during the formation of clay minerals[END_REF], and provide the first constraint on the  26/24 Mg composition of smectite forming under hydrothermal conditions. The observation that smectite preferentially incorporates isotopically heavy Mg is opposite to the trend seen in carbonates [START_REF] Galy | Mg isotopic composition of carbonate: insight from speleothem formation[END_REF]Tipper et al., 2006b;[START_REF] Higgins | Constraining magnesium cycling in marine sediments using magnesium isotopes[END_REF][START_REF] Teng | Contrasting lithium and magnesium isotope fractionation during continental weathering[END_REF][START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Huang | Magnesium isotopic composition of altered oceanic crust and the global Mg cycle[END_REF], thus highlights the potential utility of Mg isotopes in fluids as tracers of the formation of these different mineral types (e.g., [START_REF] Oelkers | Using stable Mg isotope signatures to assess the fate of magnesium during the in situ mineralisation of CO 2 and H 2 S at the CarbFix site in SW-Iceland[END_REF]. Furthermore, the magnitude of Mg fractionation observed during clay formation in this study is in good agreement with the previously estimated effects of Mg isotopic fractionation in low-temperature marine hydrothermal systems on the marine Mg budget [START_REF] Higgins | The Mg isotopic composition of Cenozoic seawaterevidence for a link between Mg-clays, seawater Mg/Ca, and climate[END_REF][START_REF] Huang | Magnesium isotopic composition of altered oceanic crust and the global Mg cycle[END_REF], significantly reducing uncertainties in the modelling of the Mg isotopic compositional evolution in the marine Mg cycle.

and solving for the change in isotopic composition of the reactant, gives Conversely, Bothner-By and [START_REF] Bothner-By | Fractionation of the carbon isotopes in decarboxylation reactions. III. The relative rates of decomposition of carboxyl C 12 and C 13 mesitoic acids[END_REF] showed that the isotopic composition of the total accumulated product follows the relationship where designates the isotopic ratios of the accumulated product which can be solved in a similar way to give the difference as

Figures

Fig. 1: Schematic design of Ti-autoclaves used for the experiments in this study. The Tiautoclaves were rocked to ensure mixing of the solids with the seawater. The cooling apparatus attached to the valve allowed fluid samples to be taken during the experimental run. Both curves are plotted for , the mean (weighed by the inverse of their variance) of our experimental best fit values. The latter value, scaled by the fraction of Mg in the product, f, is shown as well by the green curve in (b) to qualitatively show the effect of Mg isotope fractionation in such a system on the marine budget.).

  concentrations of aqueous Fe (2.4 mmol/kg and 4.7 mmol/kg at 250 °C and 290 °C, respectively, Supplementary Fig.2) were reached and sustained in the experiments with crystalline basalts, while the liquids had an acidic pH. Measurable quantities of aqueous silica were present in all experiments from the first sample (which was taken after ~24 h), stabilizing at 10-15 mmol/kg after decreasing from slightly higher values (20 and 25 mmol/kg at 250 °C and 290 °C, respectively). Aluminium concentrations in the liquid remained low (8 mol/kg with a standard deviation of 5 mol/kg), but were higher compared to the initial seawater. Aqueous Na and Cl concentrations increased significantly at the end of most experiments: The last two fluid samples collected from the experiments performed with basaltic glass at 250 °C had ≈17 % higher Cl concentrations compared to seawater, and both experiments at 290 °C showed a similar trend (with an up to 33 % increase). This can be explained by the formation of low-NaCl vapour due to the removal of liquid by sampling from the autoclaves, leading to an enrichment of solutes in the liquid phase (cf.Voigt et al., 2018b for a detailed discussion). The reduced liquid volume due to this effect is taken into account in the mass balance calculations presented below, where estimates of the amount of low-NaCl vapour were determined using thermodynamic relationships for the H 2 O-NaCl system reported byDrieser (2007) andDrieser and Heinreich (2007). To a lesser extent, uptake of H 2 O due to the formation of hydrated minerals leads to the same effect.

  A for model details). The resulting model can be interpreted as a Rayleigh type fractionation process, whereby the changes in  26/24 Mg are primarily driven by smectite precipitation from a limited volume of liquid. The possibility of coincident Mg isotopic fractionation occurring during basaltic glass dissolution was suggested by experiments of[START_REF] Wimpenny | The behaviour of Li and Mg isotopes during primary phase dissolution and secondary mineral formation in basalt[END_REF] and for Si isotopes by data of[START_REF] Ziegler | Natural variations of δ 30 Si ratios during progressive basalt weathering, Hawaiian Islands[END_REF]. However, it was possible to reproduce the Mg isotope trends observed in our experiments without including isotope fractionation during basalt dissolution, and preliminary model runs that did include constant isotopic fractionation during the release of Mg from basalt dissolution did not significantly improve the model fit (resulting in values similar to those presented below). In contrast, it was found that different fractionation factors for the two experimental temperatures applied in this study were necessary to explain the isotopic trends with this mass balance model. The results, shown in Fig. 5c-d, reproduce the major trends seen in the experimental  26/24 Mg data: The  26/24 Mg composition of the fluid decreased slowly during the early stages of the experiments following the preferential incorporation of heavy Mg into smectite ( ). The short-lived increase in liquid  26/24 Mg values observed in the 250 °C crystalline basalt experiment may be attributed to the release of isotopically heavy Mg from basalt dissolution (as can be seen from the mass balance and strongly increasing fluid Ca concentrations, Figs. 1 and 3), which likely results from an increase in Al removal from the fluid into secondary minerals when pH increases. Conversely, the strong decrease of  26/24 Mg in the liquid towards the end of the experiments is caused by the irreversible (Rayleigh-type) nature of the Mg fractionation into smectite. The best estimate and uncertainty (i.e. analytical uncertainties propagated through the model, 95 % confidence intervals) for (defined as ) is at 250 °C and at 290 °C. These values are similar to the value obtained experimentally by Wimpenny et al. (2014) for brucite at 80 °C, which is used as an analogue to describe Mg incorporation into clay minerals, and are qualitatively in agreement with a decrease in the magnitude of isotopic fractionation with increasing temperature. They are also consistent with the fractionation factor of determined during synthetic lizardite and kerolite formation at 250 °C by Ryu et al. (2016), as well as with the behaviour of Mg during saprolite formation in the context of diabase weathering, as Teng et al. (2010) suggested fractionation factors of around for smectite-rich saprolite at Earth surface temperatures. The preferential enrichment of smectite in heavier Mg isotopes is also in agreement with the deepsea pore-fluid data of Higgins and Schrag (2010), who observed a decrease in pore-fluid  26/24 Mg with depth at some sites, indicative of the presence of an isotopically enriched Mg sink (likely clay minerals) relative to the pore-fluid. Our results also support the conclusions drawn by Huang et al. (2018), who studied the Mg isotope compositions of oceanic crustal rocks that have been subjected to low-temperature alteration, and inferred a preferential incorporation of heavy Mg isotopes in sections where saponite formation occurred. Furthermore, silicate soil samples from the Southern Tibetan Plateau show higher  26/24 Mg values compared to associated silicate host rocks, a difference that can be attributed to silicate rock weathering (Tipper et al., 2006a). Conversely, the direction of Mg isotope fractionation observed in this study is opposite to the results of Pogge von Strandmann et al. (2008), who suggested that secondary minerals such as talc and chlorite preferentially uptake isotopically light Mg from high pH fluids. Variations in Mg isotope fractionation factors during clay mineral formation can be explained by a number of parameters, including temperature, the mineral composition, reaction kinetics, and fluid speciation. For example, Schott et al. (2016) showed that the presence of organic complexes in seawater can have significant effects on Mg aqueous speciation in seawater and thus Mg isotopic fractionation during mineral precipitation. The speciation of aqueous Mg in our experiments, as calculated with PHREEQC (Parkhurst and Appelo, 2013) together with the CarbFix database (Voigt et al., 2018a) at the experimental temperatures (Fig. 5g-h), is dominated by the MgCl + complex, representing between 66 and 90 mol% of the total aqueous Mg in the initial seawater, while the Mg 2+ complex is estimated to have an abundance of 10 to 20 mol%, and the initially present aqueous MgSO 4 (up to 16 mol%) decreased with the rapid SO 4 removal from seawater. The degree to which the fractionation factors determined in this study might be affected by aqueous Mg speciation remains unresolved at present.

  removal in these settings. Our experimental results provide the first evidence for Mg isotope fractionation during clay formation in intermediate temperature hydrothermal settings, and imply that the return of isotopically light fluids that have undergone partial Mg removal into clay minerals to seawater might significantly impact  26/24 Mg mass balance.The potential effect of Mg isotope fractionation in these systems on the marine Mg budget (here called E Clays ) is a combination of: (i) the isotopic composition (i.e. the  26/24 Mg value) of the precipitated clay minerals relative to seawater; and (ii) the flux of Mg

-

  , while[START_REF] Huang | Magnesium isotopic composition of altered oceanic crust and the global Mg cycle[END_REF] adopted a value of based on the average composition of altered oceanic crust at Site 801. The fractionation factors determined under our experimental conditions are -(Fig. 6), which is slightly smaller than the values adopted by Higgins and Schrag (2015) and Huang et al.

  basalt-seawater interaction experiments at temperatures of 250 °C and 290 °C under saturated vapour pressure. The solid alteration phases recovered after termination of the experiments mainly consisted of ubiquitous saponite (a trioctahedral Mg-smectite) and minor anhydrite. Trends in the chemical evolution of the fluid composition sampled during the experiments were similar to those observed at marine hydrothermal systems. During the experiments, Mg was released into the liquid phase from basalt dissolution, while the precipitation of alteration minerals such as smectite removed Mg from the liquid, leading to a steady decrease in aqueous Mg concentrations in all experiments. A model of Mg isotopic evolution during the experiments, which assumes irreversible (Rayleigh-type) fractionation during precipitation into smectite concurrent with Mg release from basalt dissolution, can fully explain the trends observed in the experimentally determined fluid  26/24 Mg compositions. The retrieved fractionation factors of indicate that isotopically heavy Mg is preferentially incorporated into the smectite, explaining the drop in liquid  26/24 Mg when aqueous Mg concentrations approach zero.

Fig. 2 :

 2 Fig. 2: Aqueous concentrations of Ca, Mg, as well as  26/24 Mg and pH of seawater reacting with basaltic glass and crystalline basalt at temperatures of 250 °C (left side) and 290 °C (right side). The errors bars show the 95 % confidence intervals, which are smaller than the symbol size where no error bars are shown.

Fig. 3 :

 3 Fig. 3: Scanning electron microscopy images of (a) the basaltic glass used as starting material and (b)-(d) solids recovered from the experiment reacting basaltic glass with seawater at 250 °C, showing a layer of smectite clay minerals covering the surface of the altered basalt as well as minor precipitated anhydrite grains. Images of the crystalline basalt are shown inVoigt et al. (2018b).

Fig. 4 :

 4 Fig. 4: PXRD patterns of starting materials and reacted solids from experiments with basaltic glass (a) and crystalline basalt (b). Note the presence of amorphous phases in all samples with basaltic glass. The hkl-reflections correspond mainly to ferrous saponite. Zincite (20 wt.%; bars) was used as an internal standard. Fe-sap = ferrous saponite; Chl-Smc = chloritesmectite; Zeo = analcime/heulandite; Pl = plagioclase ± albite; Anh = anhydrite; Qz = quartz; Ol = olivine; Aug = augite. Fig. 5: Estimated mass of Mg released from basalt dissolution and precipitated into alteration minerals, as calculated by mass balance (a,b, see text for details), (c,d) modelled aqueous  26/24 Mg during the experiments reacting basalt with seawater (dashed curves), (e,f) measured Mg concentrations in the liquid and (g,h) relative abundance (mol%) of the Mg 2+ and MgSO 4 species in the fluid samples as calculated with PHREEQC. The errors bars and shaded areas show the 95 % confidence intervals, which are smaller than the symbol size where no error bars are shown.

Fig. 6 :

 6 Fig. 6: Plot of the difference between the Mg isotopic composition of the reacting seawater (SW) and its initial composition, --, blue curve, and between the

Table 4 .

 4 The long-term 2 standard deviations in  26/24 Mg determinations at the National Oceanography Centre, Southampton is 0.07 ‰, similar to other studies[START_REF] Pogge Von Strandmann | Variations of Li and Mg isotope ratios in bulk chondrites and mantle xenoliths[END_REF][START_REF] Pogge Von Strandmann | Lithium, magnesium and silicon isotope behaviour accompanying weathering in a basaltic soil and pore water profile in Iceland[END_REF]

Acknowledgements

This research was supported by the CO2-REACT Marie Curie Actions Initial Training Network which was funded by the European Union's Seventh Framework Programme under grant agreement no 317235. The authors would like to thank Frederic Candaudap, Aurélie Marquet, Alain Castillo, Pascal Gisquet, Thierry Aigouy, Stephanie Mounic, Mathieu Benoit, Carole Causserand, Manuel Henry, Jonathan Prunier, Matt Cooper, and Agnes Michalik for help with analyses and technical assistance. We would also like to thank Deirdre Clark, Jan Přikryl, and Sigurður Reynir Gíslason for providing the Stapafell basalt, as well as Catherine Jeandel for providing the seawater. Finally, we thank Damon Teagle for his editorial support plus Ed Tipper and two anonymous reviewers for their insightful and helpful comments.

Appendix A. Details of the mass balance model calculations

The Mg fractionation factors for the formation of smectite from the aqueous fluids were generated from the solutions to a set of simulation differential equations. Solutions to these differential equation system were calculated numerically with the NDSolve function of Wolfram Mathematica, and the maximum likelihood (expressed here as

) are calculated based on the minimum inverse variance weighted squared errors using the Nelder-Mead method [START_REF] Nelder | A simplex method for function minimization[END_REF]. The corresponding uncertainties are propagated using Monte Carlo simulations where the 95 % confidence intervals are calculated from the quantiles. As mass balance constraints require inclusion of 25 Mg into the equations, are calculated internally based on and the kinetic mass-dependent fractionation law [START_REF] Young | Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance[END_REF], which was used as opposed to the equilibrium mass fractionation law due to the relatively fast kinetics of the involved processes. However, due to the small difference between the two fractionation laws, the choice does not significantly affect the model results. The mean covariance between measured  25/24 Mg and  26/24 Mg, 0.81, was included in the uncertainty propagation calculations. To account for the generation of low-NaCl vapour due to sampling from the reactors towards the ends of the experiments, all mass balance calculations account for the vapour volume estimated using the thermodynamics of the H 2 O-NaCl system [START_REF] Driesner | The system H 2 O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 °C, 1 to 5000 bar, and 0 to 1 X NaCl[END_REF][START_REF] Driesner | The system H 2 O-NaCl. Part I: Correlation formulae for phase relations in temperature-pressure-composition space from 0 to 1000 °C, 0 to 5000 bar, and 0 to 1 X NaCl[END_REF].

The evolution of Mg dissolution and precipitation during the experiments (symbols in Fig. 5a-b) were estimated using the Steffen interpolation method [START_REF] Steffen | A simple method for monotonic interpolation in one dimension[END_REF] to establish a smooth trend while preserving the monotonicity. The elemental mass balance model furthermore allows estimation of molar ratios of elements incorporated into secondary phases during the experiment based on the evolution of fluid composition and the inferred amounts of basalt dissolution. We calculated the molar ratio of (Si+Al)/(Mg+Fe) taken up into secondary minerals, which is 4/3≈1.33 in case of saponite, lower than the mean (weighed by the inverse of the variance) of the corresponding value in our experiments of 2.37±0.87.

However, the uncertainty of this parameter is relatively high, as can be seen in Supplementary

Appendix B. Irreversible isotopic fractionation in a closed system

Isotopic fractionation occurring during a reaction where the product is immediately isolated from the reactant can be described by where and designate the isotopic ratios of the reactant and of an increment of the product during the reaction, respectively. The reaction progress is commonly expressed as fractional yield, defined as , where and are the masses of the product and of the reactant before the reaction, respectively. The composition of the reactant evolves according to where and designate the isotopic ratios of the reactant after reaction progress f and at the beginning, respectively, as shown by [START_REF] Bigeleisen | Theoretical and Experimental Aspects of Isotope Effects in Chemical Kinetics[END_REF]. Substituting

Tables Table 1: Experimental parameters of the basalt-seawater experiments.

Supplementary Figures

Supplementary Fig.