Anna L Harrison
email: anna.harrison@queensu.ca

Pascale Bénézeth

Jacques Schott

Eric H Oelkers

Vasileios Mavromatis

Magnesium and carbon isotope fractionation during hydrated Mg-carbonate mineral phase transformations

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The carbon, oxygen, and metal isotope compositions of naturally-forming carbonate minerals are considered to be indicators of environmental conditions at the time of their formation, and the Mg isotopic compositions of minerals and fluids in particular provide valuable insight into modern weathering and element cycling processes [START_REF] O'neil | 13 C and 18 O compositions in some fresh-water carbonates associated with ultramafic rocks and serpentinites: Western United States[END_REF][START_REF] Deines | Stable carbon isotope ratios and the existence of a gas phase in the evolution of carbonate ground waters[END_REF][START_REF] Baumgartner | Stable isotope transport and contact metamorphic fluid flow[END_REF][START_REF] Deines | Carbon isotope effects in carbonate systems[END_REF][START_REF] Tipper | Mg isotope constraints on soil pore-fluid chemistry: Evidence from Santa Cruz, California[END_REF][START_REF] Wimpenny | The behaviour of Li and Mg isotopes during primary phase dissolution and secondary mineral formation in basalt[END_REF][START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[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][START_REF] Tipper | Seasonal sensitivity of weathering processes: Hints from magnesium isotopes in a glacial stream[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF][START_REF] Shirokova | Using Mg Isotopes to trace cyanobacterially mediated magnesium carbonate Precipitation in alkaline aakes[END_REF][START_REF] Beinlich | Inter-mineral Mg isotope fractionation during hydrothermal ultramafic rock alteration -Implications for the global Mg-cycle[END_REF][START_REF] Li | Magnesium isotope fractionation between brucite [Mg(OH)2] and Mg aqueous species: Implications for silicate weathering and biogeochemical processes[END_REF]Mavromatis et al., 2014a;2014b;[START_REF] Geske | The magnesium isotope (δ 26 Mg) signature of dolomites[END_REF][START_REF] Ryu | Experimental investigation of Mg isotope fractionation during mineral dissolution and clay formation[END_REF][START_REF] Hu | Resetting of Mg isotopes between calcite and dolomite during burial metamorphism: Outlook of Mg isotopes as geothermometer and seawater proxy[END_REF]Mavromatis et al., 2017a;2017b;[START_REF] Beinlich | Peridotite weathering is the missing ingredient of Earth's continental crust composition[END_REF][START_REF] Oskierski | Mg isotope fractionation during continental weathering and low temperature carbonation of ultramafic rocks[END_REF]. The isotopic composition of minerals and fluids in engineered carbon storage environments are also beginning to show promise as tracers of carbon storage and indicators of its efficiency [START_REF] Power | Biologically induced mineralization of dypingite by cyanobacteria from an alkaline wetland near Atlin, British Columbia, Canada[END_REF][START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF][START_REF] Wilson | Carbon dioxide fixation within mine wastes of ultramafichosted ore deposits: Examples from the Clinton Creek and Cassiar Chrysotile deposits[END_REF][START_REF] Wilson | Isotopic disequilibrium during uptake of atmospheric CO2 into mine process waters: Implications for CO2 sequestration[END_REF][START_REF] Wilson | Subarctic weathering of mineral wastes provides a sink for atmospheric CO2[END_REF][START_REF] Wilson | Offsetting of CO2 emissions by air capture in mine tailings at the Mount Keith Nickel Mine, Western Australia: Rates, controls and prospects for carbon neutral mining[END_REF][START_REF] Beinlich | In situ sequestration of atmospheric CO2 at low temperature and surface cracking of serpentinized peridotite in mine shafts[END_REF][START_REF] Harrison | Accelerated carbonation of brucite in mine tailings for carbon sequestration[END_REF][START_REF] Harrison | The impact of evolving mineral-water-gas interfacial areas on mineral-fluid reaction rates in unsaturated porous media[END_REF][START_REF] Hans | Sequestration of atmospheric CO2 in chrysotile mine tailings of the Woodsreef Asbestos Mine, Australia: Quantitative mineralogy, isotopic fingerprinting and carbonation rates[END_REF][START_REF] Mccutcheon | A greenhouse-scale photosynthetic microbial bioreactor for carbon sequestration in magnesium carbonate minerals[END_REF][START_REF] Oskierski | Chemical and isotopic signatures of waters associated with the carbonation of ultramafic mine tailings, Woodsreef Asbestos Mine, Australia[END_REF][START_REF] Gras | Isotopic evidence of passive mineral carbonation in mine wastes from the Dumont Nickel Project (Abitibi, Quebec)[END_REF]Oelkers et al., 2019a;[START_REF] Pogge Von Strandmann | Rapid CO2 mineralisation into calcite at the CarbFix storage site quantified using calcium isotopes[END_REF]Power et al., 2019). The robust interpretation of isotopic compositions in both natural and engineered environments requires knowledge of the mechanisms of isotopic fractionation, the magnitude of fractionation between fluids and solids, the impact of temperature on fractionation, and the stability of the isotopic compositions of the solid over time. Mineral growth rate, temperature, fluid composition, mineral structure, cation-oxygen bond strengths, and precipitation pathway exert strong controls on isotopic fractionation between solids and the fluid from which they form [START_REF] Criss | Principles of Stable Isotope Distributio[END_REF][START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF][START_REF] Mavromatis | The continuous re-equilibration of carbon isotope compositions of hydrous Mg carbonates in the presence of cyanobacteria[END_REF]Mavromatis et al., , 2017a, b;, b;[START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H4SiO4 o , H3SiO4and amorphous silica (SiO2•0.32H2O) at 25 and 75°C using the three-isotope method[END_REF]. Hydrated Mg-carbonate minerals like nesquehonite [MgCO3•3H2O] and dypingite [Mg5(CO3)4(OH)2•~5-8H2O] are commonly formed during weathering of ultramafic rock in natural and engineered systems, and have been identified as potential sinks to offset anthropogenic CO2 emissions [START_REF] Wilson | Verifying and quantifying carbon fixation in minerals from serpentine-rich mine tailings using the Rietveld method with X-ray powder diffraction data[END_REF][START_REF] Wilson | Carbon dioxide fixation within mine wastes of ultramafichosted ore deposits: Examples from the Clinton Creek and Cassiar Chrysotile deposits[END_REF][START_REF] Wilson | Subarctic weathering of mineral wastes provides a sink for atmospheric CO2[END_REF][START_REF] Wilson | Offsetting of CO2 emissions by air capture in mine tailings at the Mount Keith Nickel Mine, Western Australia: Rates, controls and prospects for carbon neutral mining[END_REF][START_REF] Boschi | Enhanced CO2-mineral sequestration by cyclic hydraulic fracturing and Si-rich fluid infiltration into serpentinites at Malentrata (Tuscany, Italy)[END_REF][START_REF] Zhao | Aqueous carbonation of natural brucite: Relevance to CO2 sequestration[END_REF][START_REF] Pronost | Carbon sequestration kinetic and storage capacity of ultramafic mining waste[END_REF][START_REF] Schaef | Brucite [Mg(OH)2] carbonation in wet supercritical CO2: An in situ high pressure X-ray diffraction study[END_REF][START_REF] Schaef | Forsterite [Mg2SiO4] carbonation in wet supercritical CO2: An in situ high-pressure Xray diffraction study[END_REF][START_REF] Assima | CO2 sequestration in chrysotile mining residues-implication of watering and passivation under environmental conditions[END_REF][START_REF] Bea | Reactive Transport Modeling of Natural Carbon Sequestration in Ultramafic Mine Tailings[END_REF][START_REF] Beinlich | In situ sequestration of atmospheric CO2 at low temperature and surface cracking of serpentinized peridotite in mine shafts[END_REF][START_REF] Felmy | Reaction of water-saturated supercritical CO2 with forsterite: Evidence for magnesite formation at low temperatures[END_REF][START_REF] Hövelmann | Direct nanoscale observations of CO2 sequestration during brucite [Mg(OH)2] dissolution[END_REF][START_REF] Loring | In situ infrared spectroscopic study of brucite carbonation in dry to water-saturated supercritical carbon dioxide[END_REF][START_REF] Montes-Hernandez | Rapid precipitation of magnesite microcrystals from Mg(OH)2-H2O-CO2 slurry enhanced by NaOH and a heat-aging step (from similar to 20 to 90 o C)[END_REF][START_REF] Harrison | Accelerated carbonation of brucite in mine tailings for carbon sequestration[END_REF][START_REF] Harrison | Influence of surface passivation and water content on mineral reactions in unsaturated porous media: Implications for brucite carbonation and CO2 sequestration[END_REF][START_REF] Harrison | The impact of evolving mineral-water-gas interfacial areas on mineral-fluid reaction rates in unsaturated porous media[END_REF][START_REF] Harrison | Changes in mineral reactivity driven by pore fluid mobility in partially wetted porous media[END_REF][START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF]Power et al., 2013a;2013b, 2014[START_REF] Harrison | Nsq = nesquehonite; Dyp = dypingite[END_REF][START_REF] Assima | Impact of temperature and oxygen availability on the dynamics of ambient CO2 mineral sequestration by nickel mining residues[END_REF][START_REF] Kristova | Carbonate mineral paragenesis and reaction kinetics in the system MgO-CaO-CO2-H2O in presence of chloride or nitrate ions at near surface ambient temperatures[END_REF][START_REF] Chaka | Ab initio thermodynamics of magnesium carbonates and hydrates in water-saturated supercritical CO2 and CO2-rich regions[END_REF][START_REF] García Del Real | Clumped-isotope thermometry of magnesium carbonates in ultramafic rocks[END_REF][START_REF] Highfield | Lowtemperature gas-solid carbonation of magnesia and magnesium hydroxide promoted by non-immersive contact with water[END_REF][START_REF] Mccutcheon | Microbially accelerated carbonate mineral precipitation as a strategy for in situ carbon sequestration and rehabilitation of asbestos mine sites[END_REF][START_REF] Gras | Isotopic evidence of passive mineral carbonation in mine wastes from the Dumont Nickel Project (Abitibi, Quebec)[END_REF][START_REF] Mccutcheon | Experimental deployment of microbial mineral carbonation at an asbestos mine: Potential applications to carbon storage and tailings stabilization[END_REF]. A variety of hydrous magnesium carbonate minerals exist and at Earth's surface conditions, their stability generally increases from more to less hydrated phases [START_REF] Langmuir | Stability of carbonates in the system MgO-CO2-H2O[END_REF][START_REF] Canterford | Some observations on the properties of dypingite, Mg5(CO3)4(OH)2 • 5H2O, and related minerals[END_REF]. Magnesite, the anhydrous Mgcarbonate phase, is the most stable Mg-carbonate mineral, but does not readily form at Earth's surface conditions [START_REF] Hänchen | Precipitation in the Mgcarbonate system-effects of temperature and CO2 pressure[END_REF][START_REF] Saldi | Magnesite growth rates as a function of temperature and saturation state[END_REF][START_REF] Saldi | An experimental study of magnesite precipitation rates at neutral to alkaline conditions and 100-200°C as a function of pH, aqueous solution composition and chemical affinity[END_REF][START_REF] Power | Room Temperature Magnesite Precipitation[END_REF][START_REF] Harrison | Nsq = nesquehonite; Dyp = dypingite[END_REF].

The isotopic composition of hydrous Mg-carbonate minerals that form at or near Earth's surface could be an important tracer of natural weathering processes and engineered CO2 storage [START_REF] Wilson | Isotopic disequilibrium during uptake of atmospheric CO2 into mine process waters: Implications for CO2 sequestration[END_REF][START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF][START_REF] Harrison | Nsq = nesquehonite; Dyp = dypingite[END_REF][START_REF] Harrison | The impact of evolving mineral-water-gas interfacial areas on mineral-fluid reaction rates in unsaturated porous media[END_REF][START_REF] Gras | Isotopic evidence of passive mineral carbonation in mine wastes from the Dumont Nickel Project (Abitibi, Quebec)[END_REF][START_REF] Oskierski | Chemical and isotopic signatures of waters associated with the carbonation of ultramafic mine tailings, Woodsreef Asbestos Mine, Australia[END_REF][START_REF] Harrison | Nsq = nesquehonite; Dyp = dypingite[END_REF]. Such potential applications have motivated a number of studies on Mg or C isotopic fractionation between hydrous Mg-carbonate minerals and their forming fluids [START_REF] Wilson | Isotopic disequilibrium during uptake of atmospheric CO2 into mine process waters: Implications for CO2 sequestration[END_REF][START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF][START_REF] Shirokova | Using Mg Isotopes to trace cyanobacterially mediated magnesium carbonate Precipitation in alkaline aakes[END_REF][START_REF] Oelkers | The temporal evolution of magnesium isotope fractionation during hydromagnesite dissolution, precipitation, and at equilibrium[END_REF], but few have studied both Mg and C isotope behaviour together for the same mineral or the impact of temperature on fractionation. The formation process of hydrous Mgcarbonate minerals is complex, and may involve a combination of direct precipitation and transformation of less-stable precursors [START_REF] Hopkinson | The Transformation of Nesquehonite to Hydromagnesite in the System CaO-MgO-H2O-CO2 : An Experimental Spectroscopic Study[END_REF][START_REF] Sutradhar | Controlled synthesis of different morphologies of MgO and their use as solid base catalysts[END_REF][START_REF] Hopkinson | Phase transitions in the system MgO-CO2-H2O during CO2 degassing of Mg-bearing solutions[END_REF][START_REF] Ballirano | Phase transitions in the MgCO2-H2O system and the thermal decomposition of dypingite, Mg5(CO3)4(OH)2•5H2O: Implications for geosequestration of carbon dioxide[END_REF][START_REF] Kristova | Carbonate mineral paragenesis and reaction kinetics in the system MgO-CaO-CO2-H2O in presence of chloride or nitrate ions at near surface ambient temperatures[END_REF][START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF][START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF][START_REF] Ming | Synthesis and characterization of lansfordite and nesquehonite[END_REF]. This complicates the interpretation of isotopic compositions; the impact of the mineral phase transformations on isotopic fractionation has yet to be fully explored but may result in overwriting of isotopic compositions. To address these complications, we build on past studies of Mg isotope fractionation by measuring the temporal evolution of both C and Mg isotope compositions of co-existing reactive fluids and the hydrous Mg-carbonate minerals nesquehonite and dypingite during the transformation of nesquehonite to dypingite. Nesquehonite is less stable and is regarded as more hydrated than dypingite, owing to a higher H2O : Mg molar ratio (3 : 1 compared to ~1 to 1.6 : 1) despite fewer moles of water per mole of nesquehonite.

The objectives of the present study are to 1) determine the magnitude of Mg and C isotopic fractionation between nesquehonite and fluid and dypingite and fluid, 2) assess the impact of temperature on Mg and C isotope fractionation between reactive fluid and these two carbonate minerals, 3) evaluate the impact of mineral phase transformations on isotopic compositions of hydrous Mg-carbonates, 4) provide insight into the potential utility of C and Mg isotope fractionation as a proxy for Mg-carbonate precipitation when solid samples are not available, and 5) provide further insight into the mechanisms of Mg isotope fractionation between carbonate minerals and fluids.

Methods

Experimental methods and analytical techniques

The experimental protocol followed in this study is described in detail in [START_REF] Harrison | Nsq = nesquehonite; Dyp = dypingite[END_REF], in which the solubility products of nesquehonite and dypingite were determined. In the present study, the samples of the [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF] study have been further analyzed to determine the stable carbon and magnesium isotopic composition of the carbonate minerals and the fluid to which they were exposed. Briefly, experiments in our previous study [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF] were conducted at 5, 25 and 35°C, with those at 25 and 35°C being duplicated. The duplicates ran subsequently to the original and for a longer duration, to observe the complete conversion of nesquehonite to dypingite. The shorter duration experiments are referred to as "short-term" experiments, which ran for between 367-432 h, and the longer duration as "long-term" experiments which ran for between 1368-2043 h. Each experimental series consisted of a suite of nine to eleven sealed, closed-system batch reactors at each fixed temperature. Initially 0.60 g of synthetic nesquehonite with ~73 g of an aqueous solution containing 0.10 mol/L NaCl and 0.06 mol/L NaHCO3 were introduced in each reactor. The reactors (60 mL Nalgene bottles) were filled to have as little headspace as possible in order to limit exchange of C with the atmosphere (some bubbles of air could not be completely removed). The synthesis method for the initial nesquehonite is reported by [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF]. At selected times an individual reactor was sampled in its entirety to track the chemical and isotopic composition of the reactive aqueous solution, as well as changes in the mineralogical and isotopic composition of the solids. The solution was removed via a syringe, and filtered through a 0.22 µm polyethersulfone (PES) syringe filter.

Four aliquots were immediately acidified to 2% HNO3 for subsequent analysis of Mg concentrations and Mg isotopic compositions. A single aliquot was used for immediate pH measurements and subsequent alkalinity measurements. For subsequent δ 13 CDIC analysis, fluids were stored in 2 mL air-tight vials with no headspace. All fluids were refrigerated prior to subsequent analysis. Fluid pH was measured immediately after sampling using a Metrohm 913 pH-meter and a Metrohm combined electrode (6.0234.1000) that was calibrated using NIST traceable buffer solutions at each experimental temperature, with an uncertainty of approximately ±0.03 pH units.

The solids were separated from any remaining aqueous solution via vacuum filtration, and were rinsed with distilled, de-ionized water to prevent NaCl precipitation. Solids were dried at room temperature for ~48 h and stored in a desiccator prior to analysis. Dypingite was formed in situ within the reactors at 25 °C and 35 °C through transformation of nesquehonite, with long-term experiments designed to allow the complete transformation from nesquehonite to dypingite. The phase transformation was tracked by changes in aqueous solution composition and mineralogical data collected using X-ray diffraction (XRD). The mineralogical data are reported in [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF].

The alkalinity of all fluid samples was determined by HCl titration using an automated Schott Titroline Alpha Plus titrator. Long term reproducibility of alkalinity analyses was determined from repeated analysis of a standard; it was better than ±0.36 × 10 -3 mol/L (3σ).

Dissolved inorganic carbon (DIC) concentrations were calculated using the geochemical modelling program PHREEQC V.3 [START_REF] Parkhurst | Description of Input and Examples for PHREEQC Version 3 -A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport , and Inverse Geochemical Calculations[END_REF] with a modified LLNL database (modifications to the database are described in [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF]). The uncertainty introduced by the calculation of DIC is not known, but was assumed to equal that of the alkalinity measurement. Aqueous Mg concentrations were measured by atomic absorption spectroscopy (AAS) using a Perkin Elmer AAnalyst 400. The quantification and detection limits of Mg concentrations were 9.6 × 10 -8 mol/L and 2.9 × 10 -8 mol/L, respectively, and reproducibility was better than 2% based on triplicate analysis of each sample. Reported Mg concentrations represent averages of triplicate measurements of each sample during one measurement session. The temporal evolution of the chemical composition of the fluids is reported in [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF] and reproduced here (Tables 1 and2; Electronic Annex 2 Table A2).

Carbon isotope analyses

Carbon isotope analyses of the solid carbonates were performed in continuous-flow mode following the methodology of [START_REF] Breitenbach | Carbon and oxygen isotope analysis of small carbonate samples (20 to 100 µg) with a GasBench II preparation device[END_REF]. Analyses were conducted with a GasBench II coupled to a ThermoFinnigan MAT 253 mass spectrometer at the Ruhr-University Bochum. The sampled solid carbonates are hydrophilic, therefore exposure to the laboratory environment was minimized during sample preparation (i.e., weighing, transfer into vials) and analyses were performed within hours of sample preparation. Between 90 and 120 µg of sample powder was weighed into borosilicate glass vials. Samples were acid-digested at 70°C and analyzed together with international standards NBS19, IAEA603, and CO-8. Results are reported as δ 13 Csolid with respect to the Vienna PeeDee belemnite (VPDB) standard. The external standard deviation for carbon isotope ratios is <0.08‰ (n= approximately 32).

δ 13 C is defined by equation 1:

δ 7 89 = < = > ?@ > ?A B CDEFGH = > ?@ > ?A B CIDJKDLK -1O × 1000 (1)
The carbon isotopic composition of dissolved inorganic carbon (δ 13 CDIC) was measured at the Ruhr-University Bochum with a Thermo Fisher Scientific MAT253 equipped with a GasBench and a GC Pal autosampler by CTC analytics. Samples were introduced into vials that were previously flushed with He. The fluid was reacted with 65% phosphoric acid at room temperature to release the CO2. Analysis of an internal Na2CO3 standard resulted in a long-term 1σ reproducibility of ± 0.10‰ for δ 13 CDIC in the time period of 2016-2017 (n=54).

Magnesium isotope analyses

The magnesium isotopic composition of selected aqueous Mg samples from each experimental series and corresponding solids was determined following the procedure of [START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF]. Solid samples were digested in concentrated HNO3. Digested solids and acidified liquid samples were evaporated to dryness and re-dissolved in 1N HNO3.

Samples were loaded onto 10 mL Bio-Rad poly-prep columns containing AG-50W-X12 [START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF](Mavromatis et al., , 2014a(Mavromatis et al., , 2014b;;[START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Beinlich | Inter-mineral Mg isotope fractionation during hydrothermal ultramafic rock alteration -Implications for the global Mg-cycle[END_REF][START_REF] Beinlich | Peridotite weathering is the missing ingredient of Earth's continental crust composition[END_REF], as well as from other laboratories [START_REF] Bolou-Bi | Magnesium isotope compositions of natural reference materials[END_REF][START_REF] Wombacher | Separation of Mg, Ca and Fe double-spike TIMS[END_REF][START_REF] Geske | The magnesium isotope (δ 26 Mg) signature of dolomites[END_REF][START_REF] Riechelmann | Impact of diagenetic alteration on brachiopod shell magnesium isotope (δ 26 Mg) signatures: Experimental versus field data[END_REF][START_REF] Riechelmann | Echinoid skeletal carbonate as archive of past seawater magnesium isotope signatures -Potential and limitations[END_REF]Mavromatis et al., 2017a;2017c). The reproducibility of chromatographic separation was assessed by repeated analyses of selected samples and the JDo-1 (dolomite) and IAPSO seawater as shown in Table 2, and was better than 0.08‰.

Calculation of aqueous speciation and isotopic composition of carbon and magnesium aqueous species

In this study, aqueous speciation and mineral saturation states were calculated as in [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF], using PHREEQC V3 [START_REF] Parkhurst | Description of Input and Examples for PHREEQC Version 3 -A Computer Program for Speciation, Batch-Reaction, One-Dimensional Transport , and Inverse Geochemical Calculations[END_REF] and a modified LLNL database updated to include aqueous Mg-carbonate complexes. The solubility products of nesquehonite and dypingite reported in [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF] were used to calculate saturation states in the experiments. The isotopic composition of aqueous C species were calculated using fractionation factors reported in [START_REF] Zhang | Carbon isotope fractionation during gas-water exchange and dissolution of CO2[END_REF] (Table 1). In these calculations estimations of δ 13 CCO32-is based on the sum of aqueous CO3 2-and MgCO3°

species and for δ 13 CHCO3-on the sum of aqueous HCO3 -and MgHCO3 + species, in an approach similar to that used to estimate B isotope fractionation between its two aqueous species (e.g. [START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF]. This approach is used because C isotope fractionation factors for MgCO3° and MgHCO3 + aqueous species are unknown.

The isotope composition of the Mg aqueous species present in the reactive solutions was derived from the speciation calculations and the 26/24 Mg reduced partition function ratios (β) for Mg 2+ (aq) and aqueous inorganic Mg complexes reported by [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. As such the isotopic composition of aqueous species relative to the bulk isotopic composition of the reactive solution has been calculated similar to [START_REF] Mavromatis | Zinc isotope fractionation during the inorganic precipitation of calcite -towards a new pH proxy[END_REF] using the equation

R &' () 1 = S AT 34 IUIDG -∑ (8XXX/YZ [ -8XXX/YZ \ ) [^\ ×. [ . \ (2)
where δ 26 Mgi is the isotopic composition of the ith species, fi and fj are the abundance fractions of the ith species and the sum of the abundance fractions of all the other species, respectively. The aqueous species considered in these calculations included: MgCO3°, MgOH + , Mg 2+ , MgCl + , and MgHCO3 + . Estimation of lnβ functions for 5 and 35°C were made by exponential fitting of the reduced partition functions in the range of 0 to 300°C based on the values of [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. To compare, additional estimates of the lnβ functions at 25°C were conducted using the reduced partition functions calculated by [START_REF] Gao | Theoretical calculations of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]. In their study the authors propose a fractionation between MgHCO3 + (aq) and Mg 2+ (aq) of ~ 2.4‰, which is 40% lower than that proposed by [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. To estimate the isotopic composition of Mg 2+ in our experiments using the value of [START_REF] Gao | Theoretical calculations of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF], a similar 40% reduction in theoretical estimates of MgCO3 ° and MgCl + was applied (Table 2 andElectronic Annex 2).

Results

Mineral transformation

As presented previously in [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF] and shown in Fig. 1 and Table 1, nesquehonite dissolved to reach equilibrium, before transforming to dypingite at 25°C and 35°C. Note that within this study we refer to dypingite as a single mineral phase although precipitated solids may contain 5 or 8 water molecules per unit formula as reported by [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF]. At 5°C, nesquehonite did not transform into a different phase during the 1420 h experimental series. In contrast, at 25°C, minor amounts of dypingite were first detected by XRD at 359 h in the long-term experimental series, and dypingite formed between 367 h and 1086 h during the short-term experimental series (see [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF]. This change in mineral phase was also associated with a decrease in Mg concentration in the reactive fluid (Table 2). At 35°C, the transformation from nesquehonite to dypingite was more rapid than at 25°C. Dypingite was first detected at trace levels in the sample taken at 75 h from the short-term 35°C experimental series and in the sample taken after 123 h from the long-term 35°C experimental series.

Evolution of carbon isotopic composition

There were two major sources of carbon at the onset of each experiment: the carbon in the initial nesquehonite, and that in the dissolved inorganic carbon (DIC) from the NaHCO3 in the initial experimental solution. A small amount of carbon was also present in the small volume of headspace present in each reactor, however given the low concentration of CO2 in laboratory air (~400 ppm), this is estimated to represent likely <0.01% of total C in the reactors. The initial distribution of the mass of carbon between the two main sources of C, nesquehonite and DIC, is nearly equal, with ~4.38 millimoles of carbon in DIC (~73 g of a 60 mM NaHCO3 solution per reactor), and 4.34 millimoles of carbon in the initial nesquehonite (0.60 g of nesquehonite per reactor). The initial isotopic composition of the two carbon sources is very different (Table 1). Due to the large mass of nesquehonite required for the experiments, it was synthesized in two batches, leading to a minor difference in initial C isotopic composition of the solids between the short-and long-term experimental series. The δ 13 Cnsq value of the initial nesquehonite was -18.12‰ (VPDB), and -16.87‰ (VPDB) in the short-and long-term experimental series, respectively. A fresh NaHCO3 buffer solution was generated for each of the five sets of experiments in this study, therefore the initial isotopic composition of the DIC differs for each experimental run (-4.26‰ ≤ δ 13 CDIC ≤ -4.01‰, see Table 1).

At all experimental temperatures, the δ 13 CDIC values exhibited an initial decrease by the first sampling point (<12 h). In all experimental series, the δ 13 CDIC values decreased to approximately -7.5±0.3‰ as long as the mineral phase of the solid in the reactor was nesquehonite alone (Fig. 2). During the transformation of nesquehonite to dypingite in the 25 and 35°C experimental series, the δ 13 CDIC values continued to decrease (Fig. 2B and2C). A relatively constant value that averaged at -11.87±0.24‰ and -11.92 ±0.11‰ was achieved in the long-term 25 and 35°C experiments after 1157 and 600 h, respectively (Fig. 2B and2C).

This decrease in δ 13 CDIC values was accompanied by an increase in δ 13 Csolid values (Fig. 2B and 2C). At the first measured sampling point between (i.e., between 4 and 122 h depending on the experiment, the solid had moderately higher δ 13 Csolid values relative to the seed material (by 0.44 to 1.38‰) except in the short-term 35°C experiment (Table 1). During transformation of nesquehonite to dypingite, the solid phase δ 13 Csolid values continued to increase, stabilizing at an average of -7.28±0.16‰ (VPDB) (n = 2) and -7.45±0.12‰ (VPDB)

(n = 3) in the long-term 25 and 35°C experimental series, respectively (Table 1; Fig. 2). The concurrent temporal variation of the δ 13 CDIC and δ 13 Csolid values is better seen as the apparent fractionation factor between the solid and the reactive fluid which in this study is expressed as:

Δ 13 Csolid-DIC= δ 13 Csolid -δ 13 CDIC (3)
The Δ 13 Csolid-DIC is negative at all temperatures when nesquehonite is the only mineral phase present, but it changes to positive values as the transformation to dypingite progresses (Fig. 3). When nesquehonite alone was present and the δ 13 CDIC and δ 13 Csolid values were stable, the Δ 13 Cnsq-DIC had an average value of -10.15±0.37‰ (VPDB) (n = 4), -10.16±0.88‰ (VPDB) (n = 7), and -10.59±0.79‰ (VPDB) (n = 4), at 5, 25, and 35°C, respectively including both the short-and long-term experimental series. The sample taken at 123 h in the long-term 35°C experiment was excluded from calculation of Δ 13 Csolid-DIC for nesquehonite because trace dypingite was documented with XRD (Fig. 3; Table 1). The Δ 13 Cdyp-DIC values were calculated when dypingite was the only phase detected with XRD; the value was an average of 4.74±0.12‰ (VPDB) (n = 2) and 4.47±0.17‰ (VPDB) (n = 3) in the long-term 25 and 35°C experimental series, respectively. Thus no significant impact of temperature was observed for Δ 13 Csolid-fluid values.

The change in pH during the mineral phase transformation resulted in a shift in aqueous C speciation, with a reduction in the amount of CO3 2-(Fig. 1 and Electronic Annex 1). However, the dominant species remained HCO3 -throughout all experiments. The change in aqueous speciation implies that Δ 13 Csolid-DIC will be impacted by pH. Therefore Δ 13 Csolid-CO32-and Δ 13 Csolid-HCO3-may allow better extrapolation of the reported Δ 13 Csolid-fluid to other pH conditions. To facilitate calculation of Δ 13 Csolid-CO32-and Δ 13 Csolid-HCO3-, we have included the calculated values of δ 13 CCO32-and δ 13 CHCO3-in Table 1. These numbers are uncertain as DIC is also present as MgHCO3 + and MgCO3°, and the impact of these complexes on δ 13 CCO32-and δ 13 CHCO3-is unknown. Therefore, here we mainly discuss Δ 13 Csolid-DIC as the bulk δ 13 CDIC was measured.

Evolution of magnesium isotopic composition

The Mg isotope composition of the synthetic nesquehonite used in the experimental runs exhibits distinct values between that used in the short-term experimental series (δ 26 Mg = -1.38‰±0.08‰), and the long-term experimental series (δ 26 Mg = -1.02‰±0.08‰; Table 2) due to it being synthesized in two separate batches. The isotopic composition of the solids did not change relative to the initial nesquehonite seed material in all experiments as long as the mineral phase remained nesquehonite (Fig. 4). At 5 o C, nesquehonite did not transform to dypingite during the experimental series, and little change in isotopic composition of the solid was observed (Fig. 4A). During the mineral phase transformation from nesquehonite to dypingite, a decrease in δ 26 Mgsolid values was observed (Figs. 4B and4C). After this transformation, the in δ 26 Mgsolid values were 0.08‰ to 0.20‰ lower than the initial solid in the 25°C experiment and 0.20‰ lower than the initial solid in the 35°C experiment.

The only source of Mg in the reactors was that introduced in the initial nesquehonite.

Thus, the isotopic composition of the reactive fluids at early time in the experiments (i.e., <11 h) irrespective of reaction temperature exhibited isotopic compositions similar to that of the seed nesquehonite. At 5°C, the isotopic composition of the fluid after 12 h of reaction time was -1.36‰, equal to that of the seed material within error (Table 2 and Fig. 4A). However, by 24 h the fluid phase had higher δ 26 Mg values relative to the solid by ~0.18‰ and remained relatively constant until the end of the 5°C experimental series (Table 2), though the Mg concentration stabilized after approximately 120 h (Fig. 6A; [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF]. Similarly, after 24 h and 11 h of reaction time in the short-term experimental series conducted at 25 and 35°C respectively, the fluid phase had higher δ 26 Mg values relative to the solid when nesquehonite was still the only detectable phase. After 359 h in the long-term 25°C experimental series, when dypingite was detectable with XRD, the fluid had higher δ 26 Mg values by 0.98‰±0.05‰ relative to the corresponding solid (Fig. 4B). The δ 26 Mgfluid values remained stable for the rest of the 1607 h experimental series, albeit with a slight decreasing trend (Fig. 4B). After 311 h in the long-term 35°C experimental series, when dypingite was the dominant phase, the fluid had higher () %a/1*-./01* ), has been estimated as:

`"#$% &' () %a/1*-./01* = R &' () %a/1* -R &' () ./01* (4)
The results of these calculations are reported in Table 2 and illustrated in Fig. 5. In experiments conducted at 5°C, where the only mineral phase was nesquehonite, the

`"#$% &'
() Y%f-./01* value when the aqueous Mg concentration stabilized after 120 h was -0.13±0.03‰ (n = 3) (Table 2). In the 25 and 35°C experiments, the `"#$% under 50% of the aqueous Mg is present as these complexes after the phase transformation (Fig. 6). The formation of Mg-bearing aqueous carbonate complexes is predicted to be accompanied by an enrichment in 26 Mg of MgHCO3 + (aq) and MgCO3 o (aq) relative to Mg 2+ (aq) [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Gao | Theoretical calculations of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]. This implies that in a highly alkaline fluid, like that used in our experiments, the δ 26 Mg value of Mg 2+ (aq) is lower compared to the bulk δ 26 Mg value of the fluid (i.e., the total aqueous Mg). The isotopic composition of Mg 2+ (aq) in the experimental fluids was calculated using the 26/24 Mg reduced partition function ratios (β) of inorganic aqueous Mg species [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Gao | Theoretical calculations of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]. These calculations indicated that the δ 26 Mg value of Mg 2+ (aq) is lower relative to bulk fluid δ 26 Mg values at all experimental temperatures (Table 2). In contrast to the negative Mg isotope fractionation between solid and total Mg(aq), the fractionation between nesquehonite and Mg 2+ (aq) and dypingite and Mg 2+ (aq) was positive for all experiments (Fig. 5). The fractionation between solid and Mg 2+ (aq) was calculated as:

`2$/2 &' () %a/1*-34 Ag ($f) = R &' () %a/1* -R &' () 34 Ag ($f) (5)
The values were 0.84 ≤ `2$/2 &' () %a/1*-34 Ag ($f) ≤ 2.87 for all experimental runs (Table 2).

The aqueous speciation and calculated isotopic composition of Mg 2+ in all experiments is provided in Electronic Annex 2.

Discussion

Carbon isotope fractionation between hydrous Mg carbonates and reactive fluid

Nesquehonite dissolved to reach chemical equilibrium within ~120 h, 24 h, and 3 h in the 5, 25, and 35°C experiments, respectively (Fig. 1). However, a minor increase in δ 13 C values in the solid phase compared to the initial nesquehonite was observed within the first ~24 h of each experimental series, except the short-term 35°C experimental series, which exhibited a minor decrease in δ 13 C value (Table 1). Assuming the solid is isotopically homogeneous, its bulk isotopic composition should not change due to dissolution. The increase in δ 13 Csolid values would correspond to a decrease in δ 13 CDIC values, given an exchange of carbon isotopes between the fluid and the solid. This is consistent with a lower measured δ 13 CDIC value than predicted by dissolution alone. Similarly, an offset in Mg isotopic composition between solid and fluid was observed during net dissolution of nesquehonite, in excess of measurement error (Fig. 5; However, the lack of knowledge of fractionation factors, and large uncertainty in calculated values means the extent to which isotopic exchange occurred during the approach of nesquehonite to chemical equilibrium cannot be precisely estimated in our experimental runs.

When nesquehonite was at chemical equilibrium in all experiments, Δ 13 Cnsq-DIC was negative and remained relatively constant until the phase transformation to dypingite began (Table 1; Fig. 3). This is unlike most observations for carbonate minerals, which are typically enriched in 13 C (i.e., higher δ 13 C) compared to the DIC of the aqueous solution from which they have formed when at thermodynamic isotopic equilibrium (e.g., [START_REF] Deines | Carbon isotope effects in carbonate systems[END_REF][START_REF] Rubinson | Carbon-13 fractionation between aragonite and calcite[END_REF][START_REF] Zachmann | Cryptocrystalline magnesite[END_REF][START_REF] Romanek | Carbon isotopic fractionation in synthetic aragonite and calcite: Effects of temperature and precipitation rate[END_REF][START_REF] Wilson | Isotopic disequilibrium during uptake of atmospheric CO2 into mine process waters: Implications for CO2 sequestration[END_REF]. Nesquehonite chemical equilibrium was approached by dissolution, and there was not evidence of extensive exchange of C isotopes between fluid and solid during dissolution or at equilibrium. For example, in the 5°C experiment, nesquehonite reached chemical equilibrium within ~120 h (Fig. 1A, [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF], but the Δ 13 Cnsq-DIC values remained nearly constant after 24 h until the end of the 1420 h experiment. Although a minor amount of C isotopic exchange was suspected to occur between fluid and solid, as described above, the extent of exchange was uncertain and thus likely quite limited. It is therefore concluded that isotopic equilibrium was not likely achieved between the bulk nesquehonite and fluid at any temperature, despite achievement of chemical equilibrium.

In contrast to the C isotopic composition of nesquehonite, which likely reflects only partial isotopic exchange between fluid and solid, the isotopic composition of fluid and solid were significantly altered during the transformation to dypingite (Fig. 2). The Δ 13 Csolid-DIC values increased during the phase transformation and stabilized when dypingite was the only phase detectable. The large change in fluid and solid isotopic composition during the phase transformation indicates the formation of dypingite likely occurs via the dissolution of nesquehonite and re-precipitation from aqueous solution, facilitating substantial transfer of C (see section 4.3). A dissolution-reprecipitation process implies it is more likely that dypingite achieved C-isotopic equilibrium with the fluid compared to nesquehonite and fluid. Similarly, the small variation of the Δ 13 Cdyp-DIC value estimated for the samples collected after 1607 h at 25°C (n=2) and after 600 h at 35°C (n=3) when dypingite was at chemical equilibrium suggests isotopic equilibrium was approached (Fig. 3). Additionally, these values have been estimated from solids and corresponding fluids that equilibrated in individual batch reactors.

That means that several fluid-solid systems approached the same value. The positive Δ 13 Cdyp-DIC and Δ 13 Cdyp-HCO3-are consistent with previous abiotic studies indicating preferential uptake of 13 C in carbonate minerals [START_REF] Romanek | Carbon isotopic fractionation in synthetic aragonite and calcite: Effects of temperature and precipitation rate[END_REF][START_REF] Jimenez-Lopez | Carbon isotope fractionation in synthetic magnesian calcite[END_REF].

Moreover, the Δ 13 Cdyp-DIC value estimated in this study at 25°C of 4.74±0.12‰ is in fairly good agreement with those reported by [START_REF] Mavromatis | The continuous re-equilibration of carbon isotope compositions of hydrous Mg carbonates in the presence of cyanobacteria[END_REF] (2.1 to 4.0‰) and [START_REF] Wilson | Isotopic disequilibrium during uptake of atmospheric CO2 into mine process waters: Implications for CO2 sequestration[END_REF] (3.8±1.4‰). The large range in 13 Cdyp-DIC in [START_REF] Mavromatis | The continuous re-equilibration of carbon isotope compositions of hydrous Mg carbonates in the presence of cyanobacteria[END_REF] study is attributed to precipitation occurring across a range of saturation states with respect to dypingite, compared to the close-to-equilibrium conditions in the present experiments.

Magnesium isotope fractionation between hydrous Mg carbonates and reactive fluid

The average `"#$% (2012) study for the dypingite-fluid system within uncertainty (i.e., -1.35±0.27‰). Similarly, the Mg isotope fractionation between natural hydromagnesite and the forming fluid in Lake Salda (Turkey) exhibits a similar `"#$% &' () %a/1*-./01* as observed in this study for dypingite of about -1.0±0.1‰ [START_REF] Shirokova | Using Mg Isotopes to trace cyanobacterially mediated magnesium carbonate Precipitation in alkaline aakes[END_REF]. Dypingite and hydromagnesite have similar crystal structures, but differ in the degree of hydration and crystallinity. Close fractionation factors for these two minerals is plausible. The higher degree of hydration of Mg in dypingite compared to hydromagnesite suggests that Mg isotope fractionation may respond differently to growth rate effects between the two minerals, even if equilibrium fractionation factors were similar (c.f., [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]. Thus, as was observed for C, the Mg isotopes are more likely to have obtained equilibrium between dypingite and fluid than nesquehonite and fluid. Notably, however, the time of stabilization of C and Mg isotopic compositions differed. The carbon isotopic composition in both fluid and solid stabilized more rapidly than Mg isotopes when nesquehonite was present. A measurable effect on the C isotope compositions was observed earlier than for Mg when the phase transformation began at 25 and 35°C, yet the Mg isotope compositions stabilized earlier than C isotope compositions as the phase transformation completed (Tables 1 and2). This difference in time of stabilization of isotope compositions might reflect differences in relative fluid and solid reservoir sizes (i.e., moles of C are approximately equal in solid and fluid whereas there is more Mg in the solid than fluid), differences in the rate of exchange of C compared to Mg, or different distances from equilibrium. For example, a greater amount of C might be required to exchange before isotopic equilibrium is achieved. We could not distinguish these effects using our data, however, it is important to note that Mg and C isotopes may not achieve equilibrium over the same timescale owing to a variety of factors.

An interesting feature of the experimental results is that the `2$/2 &' () %a/1*-34 Ag ($f) calculated using Eq. 5, exhibits positive values, while the `"#$% &' () %a/1*-./01* is negative for all the experiments (Fig. 5). The positive value for solid-Mg 2+ fractionation indicates that the solid is enriched in the heavier 26 Mg isotope relative to aqueous Mg 2+ , despite the solid being depleted in 26 Mg compared to the bulk aqueous Mg. Unlike our observations for the hydrated Mg-carbonates, the formation of the anhydrous phases magnesite and dolomite are accompanied by depletion of the solid phase in 26 Mg relative to aqueous Mg 2+ [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Li | Experimental calibration of Mg isotope fractionation between dolomite and aqueous solution and its geological implications[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. Solid phase depletion in 26 Mg relative to bulk fluid Mg has also been observed during the incorporation of Mg in calcite and aragonite as a trace element or impurity [START_REF] Li | Magnesium isotope fractionation during precipitation of inorganic calcite under laboratory conditions[END_REF][START_REF] Saulnier | Mg isotope fractionation during calcite precipitation: An experimental study[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]Mavromatis et al., , 2017aMavromatis et al., , 2017c;;[START_REF] Wang | Experimental calibration of Mg isotope fractionation between aragonite and seawater[END_REF]. This 26 Mg depletion in the solid phase has been attributed to the shorter average Mg-O bond length of the hexa-coordinated aqueous Mg 2+ compared to the Mg-O bond length in the solid phase. The fluid phase Mg-O bond length of hydrated aqueous Mg 2+ is ~2.08/2.11Å [START_REF] Pavlov | Hydration of beryllium, magnesium, calcium, and zinc ions using density functional theory[END_REF][START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF] whereas in anhydrous carbonate minerals this bond length is consistently longer; 2.101 Å in magnesite [START_REF] Schauble | First-principles estimates of equilibrium magnesium isotope fractionation in silicate, oxide, carbonate and hexaaquamagnesium(2+) crystals[END_REF], 2.115 Å in dolomite [START_REF] Antao | Cation disorder in dolomite, CaMg(CO3)2, and its influence on the aragonite+magnesite<-> dolomite reaction boundary[END_REF]) and between 2.11 and 2.16 Å in Mg-calcite [START_REF] Finch | Coordination of Sr and Mg in calcite and aragonite[END_REF][START_REF] Pinilla | Equilibrium magnesium isotope fractionation between aqueous Mg 2+ and carbonate minerals: Insights from path integral molecular dynamics[END_REF]. Owing to the large variation of the Mg-O bond length in hydrous Mg-carbonates, a direct correlation between this parameter and Mg isotope fractionation is not straightforward. For example, nesquehonite is comprised of disordered corner-sharing MgO6 octahedra where Mg is directly coordinated to two water molecules and the Mg-O bond distance in the unit cell ranges between 2.01 and 2.14 Å [START_REF] Giester | The crystal structure of nesquehonite, MgCO3• 3H2O, from Lavrion, Greece[END_REF].

Therefore, it is difficult to assess whether a positive or negative fractionation between Mg 2+ and solid should be expected. Nevertheless, the positive `2$/2 &' () *+,-34 Ag ($f) values for dypingite in our study are in excellent agreement with those reported previously for hydromagnesite by [START_REF] Oelkers | The temporal evolution of magnesium isotope fractionation during hydromagnesite dissolution, precipitation, and at equilibrium[END_REF]. These authors studied the evolution of Mg isotope fractionation between hydromagnesite and reactive fluid in experiments that lasted up to 574 d in carbonate-buffered solutions and presented bulk δ 26 Mg values of the fluid and solid phase.

Here, we calculate the magnesium isotope fractionation between hydromagnesite and aqueous Mg 2+ for selected samples from the Oelkers et al. ( 2018) study, under the assumption that hydrated magnesium carbonates form by incorporation of Mg 2+ . It should be noted, however, that the formation mechanism of these carbonates is not known, and may not be limited to Mg 2+ incorporation only. Using the reduced partition functions presented by [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF] in combination with Eq. 5 for the samples Hmgs-1.17, Hmgs-2.13, Hmgs-3. growth by incorporation of complexed Mg. In our study, aqueous speciation and mineral composition of the solid changed over time. Thus, it was not possible to conclude whether Mg isotope fractionation was mainly controlled by crystallographic (i.e., bond length) or fluid speciation factors. Nevertheless, it was clear that isotopic compositions obtained during growth of a metastable phase are overwritten during replacement by a secondary, more stable phase.

Finally, it is important to note that the aqueous species-specific `2$/2 &' () %a/1*-34 Ag ($f)

values calculated using Eq. 5 are strongly dependent on the accuracy of the first-principle calculations of β-values for the Mg isotope fractionation among aqueous species and may therefore be somewhat uncertain. For example, in this study the isotopic composition of Mg 2+ has been calculated based on the β-values reported in [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF] and those of [START_REF] Gao | Theoretical calculations of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF]. The [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF] calculations considered only the first hydration shell of the Mg aquo ion and small clusters of water molecules. The importance of the shell configuration can be seen in the absolute values of the lnβ functions; for a cluster of 6 water molecules the lnβ functions takes a value of 24.78 ‰, whereas for 18 water molecules it takes a value of 23.96 ‰ at 25°C [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF]. Similarly, the fractionation factors between the aqueous species Mg 2+ and MgHCO3 + have an offset of 40% in values reported by Schott et al. Moreover, there are no available data on the theoretical values of the reduced partition function ratios for Mg in hydrated Mg carbonates thus considerable uncertainty is implied for the actual values of `2$/2 &' () %a/1*-34 Ag ($f) in these solids.

Implications for the formation mechanisms and the application of isotopic composition of hydrous Mg carbonates

The mechanisms of hydrous Mg-carbonate mineral formation are not well-known and often involve transformation from less-hydrated precursors [START_REF] Davies | The transformation of nesquehonite into hydromagnesite[END_REF][START_REF] Hopkinson | The Transformation of Nesquehonite to Hydromagnesite in the System CaO-MgO-H2O-CO2 : An Experimental Spectroscopic Study[END_REF][START_REF] Hopkinson | Phase transitions in the system MgO-CO2-H2O during CO2 degassing of Mg-bearing solutions[END_REF][START_REF] Ballirano | Phase transitions in the MgCO2-H2O system and the thermal decomposition of dypingite, Mg5(CO3)4(OH)2•5H2O: Implications for geosequestration of carbon dioxide[END_REF][START_REF] Kristova | Carbonate mineral paragenesis and reaction kinetics in the system MgO-CaO-CO2-H2O in presence of chloride or nitrate ions at near surface ambient temperatures[END_REF][START_REF] Harrison | Influence of surface passivation and water content on mineral reactions in unsaturated porous media: Implications for brucite carbonation and CO2 sequestration[END_REF][START_REF] Harrison | The impact of evolving mineral-water-gas interfacial areas on mineral-fluid reaction rates in unsaturated porous media[END_REF][START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF][START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF]. As observed in this study, the phase transformation between hydrated Mg-carbonate minerals is accompanied by a change in isotopic composition. The large change in the C and Mg isotopic composition of the solid and fluid phase (Figs. 2 and4) during the mineral phase transformation reveals that there is extensive exchange of atoms during this process. This isotopic exchange indicates that the mineral phase transformation mainly occurs via a dissolution-reprecipitation mechanism. The complete alteration of crystal morphology as observed by [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF] is consistent with bulk dissolution-reprecipitation of entire crystals, in contrast to observations of microscale replacement in anhydrous biogenic carbonates [START_REF] Pederson | Diagenesis of mollusc aragonite and the role of fluid reservoirs[END_REF][START_REF] Casella | Experimental diagenesis: insights into aragonite to calcite transformation of Arctica islandica shells by hydrothermal treatment[END_REF]. The overwriting of isotopic compositions during the phase transformation implies that the use of the isotopic composition of hydrous magnesium carbonates as a tracer of initial formation conditions or original source of CO2 must be approached with some caution. The measured solid composition may reflect the fluid composition at the time of a phase transformation, rather than that of the fluid during the time of initial mineral precipitation.

However, our experimental results indicate only a partial alteration of isotopic compositions at chemical equilibrium between nesquehonite and fluid on our experimental timescales, in contrast to observations of significant Ca isotopic exchange between calcite and fluid under chemical equilibrium (Oelkers et al., 2019b). This likely results from the very low rate of exchange of water molecules in the hydration sphere of aqueous Mg compared to aqueous Ca [START_REF] Pokrovsky | Surface chemistry and dissolution kinetics of divalent metal carbonates[END_REF]. The experimental observations suggest that extensive exchange of isotopes between fluid and Mg-carbonate solids requires mineral transformation, or perhaps longer timescales than used in our experiments.

Stable carbon isotopic compositions of Mg-carbonate minerals have been used to assess the processes by which carbon is stored and cycled during weathering at Earth's surface conditions in Mg-rich rock [START_REF] Power | Biologically induced mineralization of dypingite by cyanobacteria from an alkaline wetland near Atlin, British Columbia, Canada[END_REF][START_REF] Power | A depositional model for hydromagnesite-magnesite playas near Atlin, British Columbia, Canada[END_REF][START_REF] Power | Magnesite formation in playa environments near Atlin, British Columbia, Canada[END_REF][START_REF] Wilson | Carbon dioxide fixation within mine wastes of ultramafichosted ore deposits: Examples from the Clinton Creek and Cassiar Chrysotile deposits[END_REF][START_REF] Wilson | Isotopic disequilibrium during uptake of atmospheric CO2 into mine process waters: Implications for CO2 sequestration[END_REF][START_REF] Wilson | Subarctic weathering of mineral wastes provides a sink for atmospheric CO2[END_REF][START_REF] Wilson | Offsetting of CO2 emissions by air capture in mine tailings at the Mount Keith Nickel Mine, Western Australia: Rates, controls and prospects for carbon neutral mining[END_REF][START_REF] Beinlich | In situ sequestration of atmospheric CO2 at low temperature and surface cracking of serpentinized peridotite in mine shafts[END_REF][START_REF] Harrison | Accelerated carbonation of brucite in mine tailings for carbon sequestration[END_REF][START_REF] Hans | Sequestration of atmospheric CO2 in chrysotile mine tailings of the Woodsreef Asbestos Mine, Australia: Quantitative mineralogy, isotopic fingerprinting and carbonation rates[END_REF]2016;[START_REF] Harrison | Nsq = nesquehonite; Dyp = dypingite[END_REF][START_REF] Shirokova | Using Mg Isotopes to trace cyanobacterially mediated magnesium carbonate Precipitation in alkaline aakes[END_REF][START_REF] Mccutcheon | A greenhouse-scale photosynthetic microbial bioreactor for carbon sequestration in magnesium carbonate minerals[END_REF][START_REF] Mccutcheon | Carbon sequestration in biogenic magnesite and other magnesium carbonate minerals[END_REF][START_REF] Mervine | Carbonation rates of peridotite in the Samail Ophiolite, Sultanate of Oman, constrained through 14 C dating and stable isotopes[END_REF][START_REF] Falk | Controls on the stable isotope compositions of travertine from hyperalkaline springs in Oman: Insights from clumped isotope measurements[END_REF][START_REF] Harrison | The impact of evolving mineral-water-gas interfacial areas on mineral-fluid reaction rates in unsaturated porous media[END_REF][START_REF] Gras | Isotopic evidence of passive mineral carbonation in mine wastes from the Dumont Nickel Project (Abitibi, Quebec)[END_REF]. The Mg isotopic composition of fluids and solids could also help distinguish between Mg-carbonate and Mg-clay formation in both subsurface and near-surface CO2-capturing environments (Oelkers et al., 2019a;[START_REF] Oskierski | Mg isotope fractionation during continental weathering and low temperature carbonation of ultramafic rocks[END_REF]. Knowledge of the direction and magnitude of isotope fractionation, and degree of alteration of Mg and C isotopic compositions post-deposition, will facilitate more robust interpretation of measured Mg and C isotopic compositions during both engineered and natural carbon-storing processes. These isotopic compositions can be used to help assess the type of Mg-bearing precipitate that formed if solid samples cannot be directly accessed for analysis (e.g., subsurface CO2 storage). For example, Mg-clay precipitation can reduce the CO2 storage capacity of storage reservoirs by removing the amount of Mg available to precipitate with CO2 [START_REF] Rigopoulos | Carbon sequestration via enhanced weathering of peridotites and basalts in seawater[END_REF]Oelkers et al., 2019a). Thus, robust identification of clay precipitation versus Mg-carbonate precipitation using a combination of Our results also highlight the importance of considering the speciation of the fluid when interpreting isotopic compositions measured in the solid. As a growing body of research demonstrates [START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF][START_REF] Stamm | The experimental determination of equilibrium Si isotope fractionation factors among H4SiO4 o , H3SiO4and amorphous silica (SiO2•0.32H2O) at 25 and 75°C using the three-isotope method[END_REF], the speciation of a cation in solution can strongly impact the apparent direction and extent of fractionation. In our experiments, a negative Mg isotope fractionation between solid and bulk fluid is measured. However, a positive `2$/2 &' () %a/1*-34 Ag ($f) between solid and the Mg 2+ aquo species is calculated. This is attributed to the extensive complexation of aqueous Mg by dissolved carbonate species. The difference between measured mineral -bulk fluid isotopic fractionation and the corresponding calculated mineral -Mg 2+ aquo species fractionation may be lessened or increased depending on the fluid composition, thus Mg isotope compositions may also be useful indicators of fluid pH and dissolved inorganic carbon concentration given further study under controlled fluid composition.

Conclusion

In this study we examined the fractionation of C and Mg isotopes during the transformation of nesquehonite to dypingite at 5, 25, and 35°C. These minerals are common weathering products in ultramafic environments and are of interest for their capacity to store CO2 securely. Experiments revealed that nesquehonite did not transform to dypingite at 5°C, and isotopic equilibrium between nesquehonite and solution may not have been achieved for C or Mg. At 25°C and 35°C nesquehonite dissolved to reach equilibrium and subsequently transformed to dypingite. The phase transformation occurred by dissolution-reprecipitation and caused the initial isotopic composition of both the solid and fluid to be overwritten.

Extensive isotopic exchange of both Mg and C during the phase transformation indicated that isotopic equilibrium between solid and fluid may have been obtained for dypingite. The Δ 13 Cdyp-DIC was 4.74±0.12‰ (VPDB) and 4.47±0.17‰ (VPDB) at 25 and 35°C, respectively.

The ∆ &' () *+,-./01* between solid and the bulk fluid was -0.76‰, and -0.98±0.08‰ for the 25 and 35°C experiments, respectively. In contrast to the isotope fractionation measured between solids and bulk aqueous Mg, the calculated isotope fractionation between dypingite and the Mg 2+ aquo species was positive. This indicates that aqueous speciation may impact the fractionation between Mg-carbonates and fluids. There were no significant impacts of temperature on either C or Mg isotope fractionation between fluid and solid. These data will help improve interpretation of carbon and magnesium isotope compositions measured in natural and engineered ultramafic weathering environments, and may help to trace the fate of anthropogenic CO2 during engineered CO2 storage efforts by identification of the type of Mgbearing precipitate.

  δ 26 Mg values by 0.98‰±0.06‰ relative to the corresponding solid, and remained relatively stable for the rest the experimental series. The stabilization of the Mg isotopic composition in the fluid phase in the 25 and 35°C experimental series corresponded to times for which significant amounts of dypingite was detected, although nesquehonite was still present in the solid phase at the time of Mg isotope stabilization in the fluid phase (Table2). That is, the Mg isotope composition of the fluid stabilized before the mineral transformation was complete.Magnesium isotope fractionation between the Mg-bearing solids and the reactive fluid,

`

  17±0.05‰ (n=5), and -0.07±0.10‰ (n=4), respectively, when the mineral phase was nesquehonite alone and the Mg concentrations had stabilized in the fluid (after 24 h and 3 h in the 25 and 35 C experiments, respectively;[START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF] Figure 6A; Table2).During the transformation of nesquehonite to dypingite, the `"#$% &' () %a/1*-./01* values became progressively lower. In both the long-term 25 and 35°C experimental series, the +,-./01* were calculated for samples for which dypingite was the only phase detected with XRD, although `"#$% &' () %a/1*-./01* values stabilized when nesquehonite was still present in the samples. The `"#$% &' () *+,-./01* were -0.76 ‰ (n = 1) and -0.98 ± 0.08‰ (n = 2), respectively (Table2).Owing to the high concentration of dissolved inorganic carbon in the experiments (i.e., ~60 to 81 mM; see Electronic annex Fig A1), ~50% of the aqueous Mg is present as MgHCO3 + (aq) and MgCO3 o (aq) in the reactive fluids prior to the phase transformation, and just

`

  -./01* values of the experiments where nesquehonite was the sole phase in the reactor and the Mg concentrations in the fluid stabilized were -0.13±0.03‰ (n=3), -0. 17±0.05‰ (n=5), and -0.07±0.10‰ (n=4), for the 5, 25, and 35°C experiments, respectively (Fig.4and Table2). The measured `"#$% &' () %a/1*-./01* between nesquehonite and reactive fluid are somewhat smaller in magnitude compared to that reported previously.To our knowledge, Mg isotopic fractionation between nesquehonite and fluid is only reported by[START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF]. They conducted precipitation experiments of hydrous Mg carbonate in the presence of Gloeocapsa sp. cyanobacteria at 25°C and measured a -./01* value of -0.63‰ for nesquehonite, though this value is based on a single sample. In addition, the reactive fluid from which nesquehonite precipitated in the study of[START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF] was supersaturated with respect to amorphous magnesium carbonate (AMC;[START_REF] Purgstaller | Solubility investigations in the amorphous calcium magnesium carbonate system[END_REF]. Differences in `"#$% &' () Y%f-./01* values between this previous study and the present study may also reflect a lack of attainment of isotopic equilibrium in the present study, as postulated for C isotopes in these experiments. The dissolution and replacement of nesquehonite by dypingite facilitated extensive exchange of Mg between the fluid and solid, as also observed for C isotopes. After the mineralogical transformation the average values of `"#$% &' () *+,-./01* for dypingite were -0.76‰ (n=1) and -0.98±0.08‰ (n=2) for the 25 and 35°C experiments, respectively. These values are in relatively good agreement with the values reported in the Mavromatis et al.

(

  2016) compared toGao et al. (2018) at 25°C (see Fig 5B). This variation may stem from the absolute value of partition reduction functions (β) that generally should be more accurate with the use of larger cluster models. In addition, it is not known whether the 40% offset between the[START_REF] Schott | The control of carbonate mineral Mg isotope composition by aqueous speciation: Theoretical and experimental modeling[END_REF] study and the[START_REF] Gao | Theoretical calculations of equilibrium Mg isotope fractionations between minerals and aqueous solutions[END_REF] study is valid for all aqueous species.

C

  and Mg isotopes could prove a valuable tool to trace the efficacy of CO2 removal technologies. The use of these isotopes to assess carbon-storing processes cannot be accomplished without knowledge of the fractionation factors for the different carbonate minerals that can form. Thus, the `"#$% &' () %a/1*-./01* and Δ 13 Csolid-DIC determined in our study can be used to help determine whether Mg-carbonate minerals are forming during engineered CO2 storage, particularly in Earth's near-surface environments when hydrous Mgcarbonate mineral formation is favoured. Despite the overwriting of previous isotopic compositions during mineral transformation, the observed isotopic fractionation between the hydrated magnesium carbonates and fluid may still be useful indicators of ongoing mineral weathering and carbon mineralization reactions.

Figure 1 .

 1 Figure 1. Temporal evolution of pH and saturation indices of dypingite and nesquehonite at

Figure 2 .

 2 Figure 2. Temporal evolution of stable carbon isotope composition of solids and reactive

Figure 3 .

 3 Figure 3. Temporal evolution of the carbon isotope fractionation between solid and reactive

Figure 4 .

 4 Figure 4. Temporal evolution of the Mg isotope composition of solids and reactive fluids at

Figure 5 .

 5 Figure 5. Temporal evolution of Mg isotope fractionation between solid and bulk reactive

a

  Values used to calculate Δ 13 Csolid-fluid between nesquehonite and fluid and dypingite and fluid are indicated by the labels Δ 13 Cnsq-fluid and Δ 13 Cdyp-fluid, respectively. 1080 b Denotes the δ 13 C values of seed nesquehonite and NaHCO3 buffer solution used in each experiment.

  The presence of DIC in the initial experimental fluids means that the δ 13 CDIC values should reflect mixing between initial dissolved carbon, and that provided to solution when nesquehonite dissolves. As the nesquehonite has δ 13 Csolid values that are lower than the initial δ 13 CDIC values, isotopically conservative dissolution would result in a change in δ 13 CDIC to lower values. This expected reduction in δ 13 CDIC values is nominally consistent with observations during the approach of nesquehonite to chemical equilibrium (Table1). However, it has been observed that isotopic DICnsq is the contribution to the DIC concentration from nesquehonite dissolution. The mixing model assumes an isotopically homogeneous initial solid. Solving Equation 6 for R 89 7 ijk,m indicates that the measured δ 13 CDIC values are generally lower than calculated values, but within error, for all temperatures (Table1). A lower measured δ 13 CDIC value compared to that predicted from the simple mixing model implies that isotopic fractionation may be occurring during net

	R 89 7 ijk,m × no7 m = (R 89 7 ijk,1 × no7 1 ) + (R 89 7 Y%f,1 × no7 Y%f )	(6)

fractionation can occur during net dissolution and at chemical equilibrium (e.g.,

[START_REF] Subhas | Catalysis and chemical mechanisms of calcite dissolution in seawater[END_REF] Oelkers et al., 2019b;[START_REF] Gorski | Stable mineral recrystallization in low temperature aqueous systems: A critical review[END_REF][START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF]

. To assess whether the observed change in δ 13 CDIC values is consistent with conservative input of C isotopes from nesquehonite dissolution alone, or if fractionation of the isotopes also occurs, we applied a mixing model (Eq. 6):

where t and i denote reaction time and initial values, respectively and nesquehontie dissolution, but given the high degree of uncertainty, this cannot be stated definitively based on measured δ 13 CDIC values.

Table 2

 2

). Together, these observations indicate another process in addition to nesquehonite dissolution may have occurred and resulted in C isotope fractionation. Isotopic exchange during net dissolution and at chemical equilibrium have been observed for other minerals. The exchange of isotopes between fluid and solid can result due to exchange of surface species, trace precipitation occurring during bulk dissolution, or stable mineral recrystallization (e.g.,

[START_REF] Gorski | Low temperature stable mineral recrystallization of foraminiferal tests: Implications for the fidelity of geochemical proxies[END_REF][START_REF] Gorski | Stable mineral recrystallization in low temperature aqueous systems: A critical review[END_REF][START_REF] Mavromatis | Barium isotope fractionation during witherite (BaCO3) dissolution, precipitation and at equilibrium[END_REF] 2017b;[START_REF] Subhas | Catalysis and chemical mechanisms of calcite dissolution in seawater[END_REF]

.

  4 and Hmgs-4.7 in the Oelkers et al. (2018) study, values of `2$/2 &' () %a/1*-34 Ag ($f) of 2.08, 2.57, 2.88 and 2.65‰ are determined, respectively (Electronic Annex 2 Table A1). The selected samples represent the longest incubation time for which bulk fluid δ 26 Mg values were available and likely denote closest to isotopic equilibrium conditions. The positive

	`2$/2

&' () %a/1*-34 Ag ($f) calculated for hydromagnesite in the

[START_REF] Oelkers | The temporal evolution of magnesium isotope fractionation during hydromagnesite dissolution, precipitation, and at equilibrium[END_REF]

study are consistent with our observations for dypingite, though larger (see Table

2

). It can be concluded therefore, that hydrated Mg-carbonate minerals should be enriched in the Mg isotope of higher mass ( 26 Mg) relative to aqueous Mg 2+ . Observations of depletion of hydrated Mg-carbonate minerals in 26 Mg therefore suggest aqueous speciation effects, or

  ). The measurement

	Experiment	Time	δ 13 Csolid (‰)	δ 13 CDIC (‰)	δ 13 CCO32-(‰)	δ 13 CHCO3-(‰)	Δ 13 Csolid-DIC (‰) a	Mineralogical composition c	pH	DIC (mol/L; ×10 -2 ))	DIC from nsq dissolution (mol/L; ×10 -2 ))	Mixing model estimated δ 13 CDIC (‰)	Uncertainty on mixing model δ 13 CDIC (‰)
	5	0 b	-18.12	-4.02	-7.08	-3.83	-14.10		8.25	6.00
		12	-17.67	-7.34	-9.93	-6.68	-10.33 (Δ 13 Cnsq-DIC)	Nsq	9.41	7.49	1.49	-6.82	1.27
		24	-17.52	-7.24	-9.86	-6.61	-10.28 (Δ 13 Cnsq-DIC)	Nsq	9.39	7.75	1.75	-7.20	1.23
		1085	-17.46	-7.86	-10.46	-7.21	-9.60 (Δ 13 Cnsq-DIC)	Nsq	9.39	8.14	2.13	-7.72	1.18
		1420	-18.06	-7.68	-10.03	-6.78	-10.38 (Δ 13 Cnsq-DIC)	Nsq	9.59	7.62	1.62	-7.02	1.25
	25_short	0 b	-18.12	-4.01	-5.89	-3.88	-14.10		8.15	5.97
		4	-17.68	-7.08	-8.66	-6.65	-10.59 (Δ 13 Cnsq-DIC)	Nsq	9.20	7.52	1.55	-6.92	1.27
		12	-18.22	-7.2	-8.78	-6.77	-11.02 (Δ 13 Cnsq-DIC)	Nsq	9.20	7.31	1.34	-6.59	1.30
		24	-17.79	-7.28	-8.86	-6.85	-10.51 (Δ 13 Cnsq-DIC)	Nsq	9.19	7.50	1.53	-6.89	1.27
		49	-17.05	-7.39	-8.97	-6.96	-9.66 (Δ 13 Cnsq-DIC)	Nsq	9.19	7.52	1.55	-6.92	1.27
			-18.16	-7.40	-8.97	-6.96	-10.77 (Δ 13 Cnsq-DIC)	Nsq	9.20	7.54	1.57	-6.95	1.26
			-17.98	-7.84	-9.42	-7.41	-10.13 (Δ 13 Cnsq-DIC)	Nsq	9.19	7.59	1.62	-7.02	1.26
	25_long	0 b	-16.87	-4.26	-6.15	-4.14	-12.61		8.23	5.92
			-15.49	-7.07	-8.63	-6.62	-8.40 (Δ 13 Cnsq-DIC)	Nsq	9.23	7.23	1.31	-6.54	1.23
			-9.42	-10.53	-12.26	-10.25	1.11	Nsq+Dyp	8.94	7.77	n.a.	n.a.	n.a.
		1157	-7.53	-11.59	-13.37	-11.36	4.06	Dyp+Nsq	8.82	7.80	n.a.	n.a.	n.a.
		1607	-7.16	-11.97	-13.75	-11.74	4.82 (Δ 13 Cdyp-DIC)	Dyp	8.81	7.93	n.a.	n.a.	n.a.
		2043	-7.39	-12.04	-13.79	-11.78	4.65 (Δ 13 Cdyp-DIC)	Dyp	8.90	7.68	n.a.	n.a.	n.a.
	35_short	0 b	-18.12	-4.23	-5.51	-4.12	-14.10		8.11	5.96
		5	-18.36	-7.25	-8.34	-6.95	-11.11 (Δ 13 Cnsq-DIC)	Nsq	9.12	7.24	1.27	-6.68	1.32
		7	-18.07	-7.23	-8.31	-6.92	-10.84 (Δ 13 Cnsq-DIC)	Nsq	9.14	7.21	1.24	-6.63	1.32
		11	-18.24	-7.25	-8.34	-6.95	-10.99 (Δ 13 Cnsq-DIC)	Nsq	9.11	7.27	1.30	-6.72	1.31
			-17.16	-8.04	-9.13	-7.74	-9.12	Nsq+Dyp	9.12	7.33	n.a.	n.a.	n.a.
			-11.94	-9.96	-11.09	-9.70	-1.98	Nsq+Dyp	9.02	7.46	n.a.	n.a.	n.a.
			-9.78	-10.99	-12.19	-10.80	1.21	Dyp+Nsq	8.84	7.61	n.a.	n.a.	n.a.
	35_long	0 b	-16.87	-4.12	-5.39	-4.00	-12.61		8.08	5.96
		26	-16.09	-6.67	-7.74	-6.35	-9.42 (Δ 13 Cnsq-DIC)	Nsq	9.17	7.06	1.10	-6.11	1.26
			-15.46	-7.5	-8.60	-7.21	-7.96	Nsq (trace dyp)	9.09	7.26	n.a.	n.a.	n.a.
			-12.9	-10.63	-11.80	-10.41	-2.28	Nsq+Dyp	8.90	7.66	n.a.	n.a.	n.a.
			-10.01	-11.46	-12.66	-11.27	1.46	Dyp+Nsq	8.80	7.37	n.a.	n.a.	n.a.
			-7.32	-11.87	-13.11	-11.72	4.55 (Δ 13 Cdyp-DIC)	Dyp	8.64	7.77	n.a.	n.a.	n.a.
			-7.56	-11.85	-13.10	-11.71	4.28 (Δ 13 Cdyp-DIC)	Dyp	8.65	7.65	n.a.	n.a.	n.a.
		1368	-7.48	-12.06	-13.29	-11.90	4.58 (Δ 13 Cdyp-DIC)	Dyp	8.72	7.51	n.a.	n.a.	n.a.

Table 2 . Magnesium isotope composition of fluids and solids over time. 1088

 2 Values used to calculate Δ 26 Mgsolid-fluid between nesquehonite and fluid and dypingite and fluid are indicated by the labels Δ 26 Mgnsq-fluid and Δ 26 Mgdyp-fluid, respectively.

				Fluid			Solid
	Experiment	Time (h)	δ 25 Mg	2σ	δ 26 Mg	2σ	δ 25 Mg	2σ	δ 26 Mg	2σ	Δ 26 Mgsolid-fluid a	Calculated δ 26 Mg 2+ (aq) b	Δ 26 Mgsolid-Mg2+	Mineralogical composition c	Mg (mol/L; ×10 -2 )
	5						-0.71	0.05	-1.38	0.08				Nsq
			-0.72	0.03	-1.36	0.01	-0.69	0.02	-1.33	0.02	0.03	-4.00	2.67	Nsq	1.290
			-0.64	0.04	-1.20	0.02	-0.72	0.01	-1.39	0.03	-0.19	-3.85	2.45	Nsq	1.269
			-0.64	0.01	-1.21	0.06	-0.91	0.03	-1.36	0.00	-0.15 (Δ 26 Mgnsq-fluid)	-4.21	2.45	Nsq	1.505
			-0.65	0.03	-1.24	0.02	-0.69	0.04	-1.34	0.03	-0.10 (Δ 26 Mgnsq-fluid)	-3.92	2.57	Nsq	1.498
			-0.66	0.05	-1.25	0.02	-0.71	0.02	-1.38	0.06	-0.13 (Δ 26 Mgnsq-fluid)	-4.25	2.87	Nsq	1.502
	25_short						-0.71	0.05	-1.38	0.08				Nsq
			-0.64	0.02	-1.22	0.04	-0.71	0.01	-1.33	0.01	-0.11	-3.90	2.57	Nsq	1.094
			-0.67	0.06	-1.29	0.08	-0.73	0.05	-1.41	0.07	-0.12 (Δ 26 Mgnsq-fluid)	-3.93	2.52	Nsq	1.197
			-0.59	0.01	-1.13	0.03	-0.68	0.04	-1.32	0.08	-0.19 (Δ 26 Mgnsq-fluid)	-3.79	2.47	Nsq	1.183
			-0.66	0.02	-1.23	0.05	-0.74	0.09	-1.44	0.08	-0.21 (Δ 26 Mgnsq-fluid)	-3.89	2.44	Nsq	1.192
			-0.62	0.03	-1.19	0.04	-0.73	0.05	-1.42	0.09	-0.23 (Δ 26 Mgnsq-fluid)	-3.87	2.46	Nsq	1.216
			-0.57	0.05	-1.09	0.08	-0.78	0.05	-1.50	0.05	-0.41	-3.74	2.24	Nsq+Dyp	1.113
	25_long						-0.54	0.02	-1.02	0.08				Nsq
			-0.50	0.04	-0.95	0.00	-0.55	0.02	-1.06	0.01	-0.11 (Δ 26 Mgnsq-fluid)	-3.63	2.57	Nsq	1.098
			-0.13	0.03	-0.24	0.05	-0.61	0.00	-1.22	0.01	-0.98	-2.47	1.25	Nsq+Dyp	1.119
			-0.15	0.04	-0.29	0.05	-0.61	0.04	-1.21	0.01	-0.92	-2.31	1.10	Dyp+Nsq	1.065
			-0.16	0.01	-0.34	0.05	-0.58	0.03	-1.10	0.05	-0.76 (Δ 26 Mgdyp-fluid)	-2.36	1.26	Dyp	1.051
	35_short						-0.71	0.05	-1.38	0.08				Nsq
			-0.64	0.02	-1.27	0.06	-0.69	0.05	-1.33	0.07	-0.06 (Δ 26 Mgnsq-fluid)	-3.93	2.60	Nsq	1.063
			-0.65	0.02	-1.27	0.07	-0.71	0.04	-1.35	0.01	-0.08 (Δ 26 Mgnsq-fluid)	-3.95	2.60	Nsq	1.047
			-0.64	0.02	-1.22	0.06	-0.73	0.03	-1.42	0.08	-0.20 (Δ 26 Mgnsq-fluid)	-3.87	2.45	Nsq	1.050
			-0.47	0.04	-0.92	0.08	-0.73	0.04	-1.38	0.05	-0.46	-3.58	2.20	Nsq+Dyp	1.054
			-0.33	0.02	-0.67	0.03	-0.78	0.04	-1.51	0.05	-0.84	-3.16	1.65	Nsq+Dyp	1.048g
			-0.20	0.02	-0.38	0.06	-0.75	0.01	-1.43	0.07	-1.05	-2.60	1.18	Dyp+Nsq	0.900
	35_long						-0.54	0.02	-1.02	0.08				Nsq
			-0.53	0.01	-0.99	0.08	-0.50	0.02	-0.94	0.01	0.05 (Δ 26 Mgnsq-fluid)	-3.71	2.76	Nsq	1.044
			-0.36	0.03	-0.70	0.05	-0.58	0.05	-1.10	0.06	-0.40	-3.31	2.21	Nsq (trace Dyp)	1.057
			-0.20	0.05	-0.43	0.05	-0.67	0.01	-1.26	0.05	-0.83	-2.73	1.47	Nsq+Dyp	1.138
			-0.11	0.04	-0.18	0.08	-0.61	0.04	-1.18	0.08	-1.00	-2.28	1.11	Dyp+Nsq	1.048
			-0.10	0.02	-0.18	0.03	-0.62	0.04	-1.21	0.01	-1.03 (Δ 26 Mgdyp-fluid)	-2.06	0.84	Dyp	0.930
			-0.16	0.02	-0.29	0.02	-0.64	0.02	-1.21	0.01	-0.92 (Δ 26 Mgdyp-fluid)	-2.20	0.99	Dyp	0.885
	Standards
	DSM3		0.00	0.03	0.00	0.04
	CAM-1		-1.35	0.05	-2.64	0.06
	OUMg		-1.45	0.06	-2.80	0.08
	IAPSO		-0.42	0.05	-0.83	0.07
	JDo-1		-1.23	0.04	-2.41	0.08
	a

cMineralogical composition determined by XRD as reported in[START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35°C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF]. Nsq = nesquehonite; Dyp = dypingite. When more than one phase present, the dominant phase is reported first.

Acknowledgments

We are grateful to Jérôme Chmeleff for his support with MC-ICP-MS analyses. We thank Sebastian Breitenbach and Sylvia Riechelmann for conducting carbon isotopic analyses.

We would like to acknowledge the Associate Editor, Matthew Fantle, Adrian Immenhauser, Chris Romanek and two anonymous reviewers for their helpful suggestions that improved this paper. This study benefited from the financial support of the ISIFoR Carnot institute (Institute for the Sustainable Engineering of Fossil Resources) under the project SERPCARB AAP-2016, by the French national programme LEFE/INSU and by a Marie Skłodowska-Curie Individual Fellowship awarded to ALH under grant agreement number 701478 (DryMIN) under the European Union's Horizon 2020 program.

error is smaller than the symbols unless otherwise shown. The grey dashed line indicates the approximate timing of onset of the phase transformation from nesquehonite to dypingite.

Electronic Annex 2.

Includes Table A1. Speciation of aqueous Mg and calculated isotopic composition of Mg 2+ (aq), ! "#$" %& '( )*$+,-./ 01 , and ! 23#) %& '( )*$+,-45$6 8$5+, and Table A2. Fluid composition of all experimental timepoints.