A Fernandez-Martinez
email: luismonasterio@ugr.es

Carbonation of calcium-magnesium pyroxenes: Physical-chemical controls and effects of reaction-driven fracturing

The weathering of primary silicates, and their carbonation in particular, is key for the geochemical cycling of elements, strongly affecting the C cycle and the long-term regulation of the Earth's climate. The knowledge on the controlling factors and mechanisms of aqueous carbonation of primary silicates is however still far from complete. This precludes a better understanding of their chemical weathering in nature and is a strong handicap to implement effective Carbon Capture and Storage (CCS) strategies. Here, dissolution-carbonation reactions of two abundant Ca-Mg pyroxenes, augite and diopside, have been investigated in experiments conducted at hydrothermal conditions, in the presence/absence of different carbonate sources (NaHCO 3 and Na 2 CO 3 ). We show that the main reaction products are low-magnesium calcite and amorphous silica. A higher conversion of augite (~38 wt%) than diopside (~15 wt%) was achieved. The presence of abundant Fe and Al (and minor Na) in the former pyroxene strongly enhances the release of cations to the solution, and contributes to the formation of abundant secondary crystalline silicates as well as carbonates (Na-phillipsite and magnesium silicate hydrate, MSH). In particular, Na-phillipsite nucleates in etch pits exerting a crystallization pressure ~100 MPa exceeding the tensile strength of augite and causing extensive fracturing. This takes place via an interface-coupled dissolutionprecipitation mechanism, despite the bulk system being undersaturated with respect to this phase.

Limited reaction-induced fracturing was also observed following MSH precipitation within diopside crystals. Reaction-induced fracturing increases exposed reactive surface area and creates channels for solution flow, thereby contributing to the progress of the reaction via a positive feedback loop.

Ultimately, our results help to understand differences in the kinetics and mechanisms of chemical weathering of these two abundant rock forming inosilicates relevant for CCS strategies, showing that secondary phase formation (other than carbonates) are fostered by moderately alkaline pH and the presence of alkali metals, resulting in reaction-driven fracturing that enables the progress of silicate carbonation for an effective, safe, and permanent CO 2 mineral storage. We also show that under our experimental conditions the precipitation of amorphous silica and calcite cannot generate sufficient pressure as to create fracturing, an effect that limits carbonation of Mg-Ca-Fe pyroxenes.

INTRODUCTION

Weathering of primary silicate minerals caused by a range biogeochemical processes contributes to Earth´s surface modeling, soil formation, the development of biota by supplying key nutrients [START_REF] Nagajyoti | Heavy metals, occurrence and toxicity for plants: A review[END_REF] and the control of Earth´s climate over geologic time-scales by the mineralization of CO 2 via carbonation [START_REF] Walker | A negative feedback mechanism for the long-term stabilization of Earth's surface temperature[END_REF][START_REF] Pacala | Stabilization wedges: Solving the climate problem for the next 50 years with current technologies[END_REF]. Carbonation of primary silicates is a key step in the carbon cycle and follows a "Urey-type" reaction [START_REF] Urey | The planets: their origin and development[END_REF]Daval et al., 2009a;[START_REF] Lorenzo | The carbonation of wollastonite: A model reaction to test natural and biomimetic catalysts for enhanced CO 2 sequestration[END_REF][START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF],

MSiO 3 + CO 2 + H 2 O = MCO 3 + SiO 2 .nH 2 O
(1), which in the case of mafic and ultramafic minerals can be expressed by the more general reaction (Daval et al., 2009a),

M x Si y O x+2y-t (OH) 2t + xCO 2 = xMCO 3 + ySiO 2 + tH 2 O (2)
where M is an alkaline-earth metal such as Ca 2+ , Mg 2+ , or a divalent transition metal (e.g., Fe 2+ ).

These reactions highlight the key role of calcium-and magnesium-rich mafic and ultramafic rocks in Earth´s climate control [START_REF] Schott | Mechanism of pyroxene and amphibole weathering-I. Experimental studies of iron-free minerals[END_REF][START_REF] Berner | The need for mass balance and feedback in the geochemical carbon cycle[END_REF] .

Due to the alarming rising levels of anthropogenic CO 2 emissions to the atmosphere, principally caused by fossil fuel combustion, several initiatives have been developed for ex situ and in situ Carbon Capture and Storage (CCS). In this context, Geological Carbon Storage (GCS) via mineralization of CO 2 after its deep injection into mafic and ultramafic geologic formations (e.g., CarbFix pilot test, Iceland; [START_REF] Matter | Rapid carbon mineralization for permanent disposal of anthropogenic carbon dioxide emissions[END_REF]) is a promising strategy [START_REF] Lackner | Carbon dioxide disposal in carbonate minerals[END_REF]IPCC, 2014). This in situ CCS strategy can be considered the safest and most permanent way to store this greenhouse gas [START_REF] Seifritz | CO 2 disposal by means of silicates[END_REF]. In terms of ex situ mineral carbonation, the most promising strategies are aqueous-based mineral carbonation processes, such as the "pH swing" method [START_REF] Park | CO 2 mineral sequestration: physically activated dissolution of serpentine and pH swing process[END_REF], or the direct carbonation, normally achieved under circumneutral pH conditions [START_REF] Oelkers | Carbon dioxide sequestration a solution to a global problem[END_REF]Daval et al., 2009a,b;[START_REF] Lorenzo | Dissolution-Recrystallization of (Mg,Fe)CO 3 during Hydrothermal Cycles: Fe II /Fe III Conundrums in the Carbonation of Ferromagnesian Minerals[END_REF][START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF], aided by complexing agents or biomimetic processes involving the use of carbonic anhydrase, silicates, or metal organic frameworks (MOFs) to enhance the dissolution-carbonation processes during mineral replacement [START_REF] Lorenzo | The carbonation of wollastonite: A model reaction to test natural and biomimetic catalysts for enhanced CO 2 sequestration[END_REF].

Carbonation of silicates is an exothermic reaction that follows a combined dissolutionprecipitation process, whereby divalent cations are released to the solution and, in the presence of a Dissolved Inorganic Carbon (DIC) source, form secondary carbonate phases (Daval et al., 2009a,b).

Disclosing experimentally the key atomic-or molecular-scale processes and micro-to-macroscale mechanisms of these coupled dissolution-carbonation reactions is crucial to model, implement and enhance CCS processes and strategies, and to understand and model the fate of CO 2 injected during GCS.

Several studies have focused on the fundamental understanding of the mechanisms involving dissolution of silicate minerals and the subsequent precipitation of carbonate phases (e.g., [START_REF] Casey | Surface chemistry of labradorite feldspar reacted with aqueous solutions at pH = 2, 3, and 12[END_REF][START_REF] Banfield | HRTEM study comparing naturally and experimentally weathered pyroxenoids[END_REF][START_REF] Lackner | Carbon dioxide disposal in carbonate minerals[END_REF][START_REF] Ruiz-Agudo | Mechanism of leached layer formation during chemical weathering of silicate minerals[END_REF][START_REF] Ruiz-Agudo | Control of silicate weathering by interface-coupled dissolution-precipitation processes at the mineral-solution interface[END_REF][START_REF] Lorenzo | Dissolution-Recrystallization of (Mg,Fe)CO 3 during Hydrothermal Cycles: Fe II /Fe III Conundrums in the Carbonation of Ferromagnesian Minerals[END_REF][START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF]. Studies on the dissolution of primary silicates have systematically reported the formation of an amorphous and hydrated silica-rich layer covering the mineral´s surface, the so-called "leached layer", surface altered layer (SALs) or amorphous silica-rich surface layer (ASSLs), which can passivate mineral dissolution [START_REF] Casey | Leaching and reconstruction at the surfaces of dissolving chain-silicate minerals[END_REF]Daval et al., 2009a,b;[START_REF] Ruiz-Agudo | Mechanism of leached layer formation during chemical weathering of silicate minerals[END_REF][START_REF] Hellmann | Formation of amorphous silica surface layers by dissolutionreprecipitaton during chemical weathering: Implications for CO 2 uptake[END_REF][START_REF] Ruiz-Agudo | Control of silicate weathering by interface-coupled dissolution-precipitation processes at the mineral-solution interface[END_REF][START_REF] Wild | Physical properties of interfacial layers developed on weathered silicates: A case study based on labradorite feldspar[END_REF]. Furthermore, most studies on the carbonation of primary silicates have reported an additional passivation effect caused by the formation of carbonate mineral coatings on the primary mineral surface, decreasing the porosity and the permeability of the starting material and limiting the progress of the reaction [START_REF] O'connor | Aqueous mineral carbonation[END_REF];Daval et al., 2009a,b;[START_REF] Kelemen | Rates and mechanisms of mineral carbonation in peridotite: natural processes and recipes for enhanced, in situ CO2 capture and storage[END_REF]. In general, passivation resulting in a reduction of permeability and porosity of the host material will take place due to precipitation of a more insoluble phase [START_REF] Hellmann | Unifying natural and laboratory chemical weathering with interfacial dissolutionreprecipitation: A study based on the nanometer-scale chemistry of fluid-silicate interfaces[END_REF][START_REF] Ruiz-Agudo | Mechanism of leached layer formation during chemical weathering of silicate minerals[END_REF][START_REF] Wild | Physical properties of interfacial layers developed on weathered silicates: A case study based on labradorite feldspar[END_REF]. These effects play a critical role in GCS processes, controlling the dissolution rate of primary silicate materials and acting as a handicap for their effective CO 2 mineralization [START_REF] Mcgrail | Potential for carbon dioxide sequestration in flood basalts[END_REF][START_REF] Stockmann | Dissolution of diopside and basaltic glass: the effect of carbonate coating[END_REF]Daval et al., 2009a,b;[START_REF] Ruiz-Agudo | Mechanism of leached layer formation during chemical weathering of silicate minerals[END_REF][START_REF] Wild | Physical properties of interfacial layers developed on weathered silicates: A case study based on labradorite feldspar[END_REF]. However, the replacement of a mineral phase can involve precipitation of a secondary phase in a confined volume of the host material (dissolution pits, pores, and/or micro-fractures), and this can generate crystallization pressure and an associated stress [START_REF] Scherer | Crystallization in pores[END_REF][START_REF] Scherer | Stress from crystallization of salt[END_REF]) that can exceed the tensile strength of the host material resulting in fracturing of the parent phase, in turn increasing permeability and exposing fresh reactive surface [START_REF] Emmanuel | Impact of nano-size weathering products on the dissolution rates of primary minerals[END_REF]. Reaction-driven fracturing has been observed during hydration of olivine [START_REF] Kelemen | Reaction-driven cracking during retrograde metamorphism: Olivine hydration and carbonation[END_REF]Plumper et al., 2013;[START_REF] Lafay | Intracrystalline reaction-induced cracking in olivine evidenced by hydration and carbonation experiments[END_REF], in carbonation processes [START_REF] Matter | Permanent storage of carbon dioxide in geological reservoirs by mineral carbonation[END_REF];[START_REF] Kelemen | Rates and mechanisms of mineral carbonation in peridotite: natural processes and recipes for enhanced, in situ CO2 capture and storage[END_REF] and during weathering-related dissolution-precipitation replacement reactions involving volume changes (positive or negative), tensile stress generation and collapse [START_REF] Jamtveit | Accelerated hydration of the Earth's deep crust induced by stress perturbations[END_REF][START_REF] Plümper | The interface-scale mechanism of reactioninduced fracturing during serpentinization[END_REF][START_REF] Røyne | Pore-scale controls on reaction-driven fracturing[END_REF]. Positive volume changes and an associated stress can also occur upon precipitation of amorphous phases in a confined space, as exemplified by fracturing during alkali-silica reaction in cement (Rajabipour et al., 2015 and refs. therein).

However, in this latter case, fracturing is associated with hydration of the resulting silica gel (incorporating different alkali and alkaline-earth metals). It is unknown, however, whether the latter reaction-driven fracturing occurs during primary silicate carbonation.

Despite the recent progress in the understanding of the mechanisms and kinetics of dissolution-carbonation of silicate minerals, the current knowledge regarding the effects of neutral to alkaline pH, carbonate speciation, secondary silicate formation ( Daval et al., 2009a;[START_REF] King | Effect of secondary phase formation on the carbonation of olivine[END_REF][START_REF] Sissmann | The deleterious effect of secondary phases on olivine carbonation yield: Insight from time-resolved aqueous-fluid sampling and FIB-TEM characterization[END_REF][START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF], with or without a passivation effect (i.e., the formation of an impervious layer of product phase on the parent phase) [START_REF] Ruiz-Agudo | Mechanism of leached layer formation during chemical weathering of silicate minerals[END_REF][START_REF] Ruiz-Agudo | Control of silicate weathering by interface-coupled dissolution-precipitation processes at the mineral-solution interface[END_REF][START_REF] Lorenzo | The carbonation of wollastonite: A model reaction to test natural and biomimetic catalysts for enhanced CO 2 sequestration[END_REF][START_REF] Wild | Physical properties of interfacial layers developed on weathered silicates: A case study based on labradorite feldspar[END_REF], and its impact on porosity and permeability [START_REF] Jamtveit | Accelerated hydration of the Earth's deep crust induced by stress perturbations[END_REF][START_REF] Kelemen | Rates and mechanisms of mineral carbonation in peridotite: natural processes and recipes for enhanced, in situ CO2 capture and storage[END_REF]Royne and Jamtveit, 2015), is still far from complete. Moreover, most studies on silicate mineral carbonation have focused on olivine (King et all., 2010;Daval et al., 2011), wollastonite (Di Lorenzo et al., 2018), or thermally activated serpentine [START_REF] O'connor | Aqueous mineral carbonation[END_REF], while very little attention has been paid to other abundant primary silicates such as Mg-Ca-Fe pyroxenes [START_REF] Stockmann | Dissolution of diopside and basaltic glass: the effect of carbonate coating[END_REF][START_REF] Stockmann | Do carbonate precipitates affect dissolution kinetics?: 2: Diopside[END_REF][START_REF] Bodor | Susceptibility of mineral phases of steel slags towards carbonation: mineralogical, morphological and chemical assessment[END_REF].

This study aims to determine experimentally the effects of pH, DIC source, and carbon speciation in solution under hydrothermal conditions on the carbonation of two of the most abundant clinopyroxenes in the Earth's crust. In particular, we aim to shed light onto the effect of secondary silicate mineral formation during carbonation replacement, and their effect on reactiondriven fracturing [START_REF] King | Effect of secondary phase formation on the carbonation of olivine[END_REF][START_REF] Kelemen | Rates and mechanisms of mineral carbonation in peridotite: natural processes and recipes for enhanced, in situ CO2 capture and storage[END_REF][START_REF] Lafay | Intracrystalline reaction-induced cracking in olivine evidenced by hydration and carbonation experiments[END_REF]. Finally, we strive to gather mechanistic and geochemical results of relevance for CCS strategies, GCS in particular. To achieve these goals, we studied the dissolution-carbonation processes under near-neutral to moderately-alkaline pH, of diopside (CaMgSi 2 O 6 ) and augite ((Ca,Mg,Fe 2+ ) 2 Si 2 O 6 ), two calcium and magnesium primary silicates of the group of pyroxenes, one of the most abundant groups of rock-forming minerals in the Earth's crust [START_REF] Deer | An Introduction to the Rock Forming Minerals[END_REF][START_REF] Schott | Mechanism of pyroxene and amphibole weathering-I. Experimental studies of iron-free minerals[END_REF][START_REF] Knauss | Diopside dissolution kinetics as a function of pH, CO 2 , temperature, and time[END_REF]. Pyroxenes are inosilicate minerals with a general formula XYSi 2 O 6 where X represents Na + , Ca 2+ , Mn 2+ , Fe 2+ , Mg 2+ , and Li +, and Y represents Mn 2+ , Fe 2+/3+ , Mg 2+ , Al 3+ , Cr 3+ [START_REF] Morimoto | Nomenclature of pyroxenes[END_REF][START_REF] Schott | Mechanism of pyroxene and amphibole weathering-I. Experimental studies of iron-free minerals[END_REF]. Diopside was chosen because dissolution of this mineral has been thoroughly studied [START_REF] Berner | Dissolution of pyroxenes and amphiboles during weathering[END_REF][START_REF] Schott | Mechanism of pyroxene and amphibole weathering-I. Experimental studies of iron-free minerals[END_REF][START_REF] Knauss | Diopside dissolution kinetics as a function of pH, CO 2 , temperature, and time[END_REF][START_REF] Mcgrail | Potential for carbon dioxide sequestration in flood basalts[END_REF][START_REF] Dixit | Effect of solution saturation state and temperature on diopside dissolution[END_REF][START_REF] Stockmann | Dissolution of diopside and basaltic glass: the effect of carbonate coating[END_REF], and a few studies have focused on its carbonation [START_REF] Stockmann | Do carbonate precipitates affect dissolution kinetics?: 2: Diopside[END_REF], so that it can be used as a reference clinopyroxene. In contrast, the dissolution of augite has been sparsely studied [START_REF] Mcadam | Preferential low-pH dissolution of pyroxene in plagioclase-pyroxene mixtures: Implications for martian surface materials[END_REF][START_REF] Stockmann | Do carbonate precipitates affect dissolution kinetics?: 2: Diopside[END_REF], and there are no studies on its carbonation other than the very preliminary one by [START_REF] O'connor | Aqueous mineral carbonation[END_REF].

The original features of this study are: (i) in contrast to most silicate weathering and carbonation studies, the selected pHs of this work include a wide range of natural groundwater pH (6.5 -8.5) [START_REF] Driscoll | Groundwater and Wells[END_REF], which helps to directly extrapolate our results to natural environments;

(ii) to the best of our knowledge, this is the first study performed using high purity single crystals of these pyroxenes instead of powders of these minerals, thus allowing a detailed spatially-resolved characterization of dissolution-carbonation reactions using high-resolution techniques such as X-ray micro-computed tomography (Micro-CT); (iii) we combine dissolution-carbonation processes to reveal and quantify experimentally the effect of crystallization stress of newly formed secondary silicate phases on the progress of pyroxene carbonation.

MATERIALS AND METHODS

Starting materials

Augite and diopside crystal specimens, from science museum and undetermined localities, of optical quality (i.e., high purity and transparent) were cut with a diamond saw into single crystals 1×1×1 mm in size (~0.005 g). Crystals were cut along {001}, {100} and {010} planes as corroborated by means of electron backscattering diffraction (EBSD) analysis using a field emission scanning electron microscope (FESEM, Auriga Carl Zeiss SMT).

Hydrothermal experiments

Two types of hydrothermal experiments were performed: (i) dissolution experiments in the absence of added dissolved inorganic carbon (DIC), and (ii) carbonation experiments involving the addition of DIC. Dissolution experiments were performed using 1 mL Milli-Q water (resistivity 18.2 MΩ•cm, Millipore) adjusted to pH 7.5 using NaOH (Sical). Carbonation experiments were performed in solutions prepared by mixing 1 mL Milli-Q water with 0.025 g of NaHCO 3 (pH 7.5), or 0.031 g of Na 2 CO 3 (pH of 11.5), to ensure an excess of carbonate and to achieve the desired pH values (i.e., pH = 7.5 and 11.5).

Single crystals (~0.022 mmol) were introduced in PTFE vessels (polytetrafluoroethylene, V tot = 3 mL) with 1 mL of the different solutions described above. Afterward, the PTFE vessels were introduced into hydrothermal steel reactors, sealed and heated to 150ºC for 7, 14 and 28 days.

The pressure was not independently controlled and corresponds to the vapor pressure at the experimental T. At the given time intervals, reactors were cooled at room T and opened. Crystals were separated and dried at room T. To ensure reproducibility, experiments were performed in duplicate. Note that one individual crystal was used per experiment, three different hydrothermal experiments were carried out (i.e. NaHCO 3 , Na 2 CO 3 and water) and three different sampling times were selected (i.e. 7, 14 and 28 days), a total of 36 individual experiments were performed (i.e., 18 crystals of each pyroxene were used).

Geochemical calculations and solution speciation were performed using PHREEQC computer code (version 3.3.12, USGS, Reston, VA, USA) and the llnl.dat database (Parkhurst and Appelo, 1990) to model the evolution of the Saturation Index (SI n ) and free energy (ΔG) of the different precipitates identified in our experimental conditions. Due to the absence of geochemical information for augite in any database present in this PHREEQC version, information for this phase was introduced manually following the geochemical data from [START_REF] Davidson | Thermodynamic analysis of quadrilateral pyroxenes[END_REF], [START_REF] Loucks | A precise olivine-augite Mg-Fe-exchange geothermometer[END_REF], Palandri and Kharaka (2004) and [START_REF] Pham | On the potential for CO 2 mineral storage in continental flood basalts-PHREEQC batch-and 1D diffusion-reaction simulations[END_REF] (logK=21; -ΔH = 122.775 kJ/mol).

Analysis of the solutions and solids

The pH of the starting and reacted solutions was measured using a glass electrode (Metrohm) calibrated with three standard solutions (pH = 4.01, 7.01 and 10.01 at 25 °C) with ±0.01 of uncertainty. The concentration of Ca, Mg and Si in reacted solutions was determined by ICP-OES at Centro de Instrumentación Científica (CIC-UGR, Perkin Elmer, Optima 8300) and at Institut de Sciences de la Terre (ISTerre, Varian 720ES).

In order to determine the mineralogical/structural changes undergone by the reacted samples, they were analyzed using a JASCO IRT-7100 microscope coupled to a Micro-Raman spectrometer (µ-Raman, JASCO NRS-5100) with a Nd-YAG laser (λ = 785.11 nm, 30 mW, Elforlight G4-30), spectral range 1200-100 cm -1 . Reported spectra correspond to the average of 5 measurements.

The morphology, texture and composition of solids were characterized by scanning electron microscopy (SEM, FEI Quanta 400) coupled to an X-ray energy dispersive spectrometer (EDS, xFlash Bruker) for chemical microanalysis, working at an acceleration voltage of 20 kV.

Samples reacted for 28 days were analyzed by high-resolution X-ray Micro-Computed Tomography (Micro-CT, VERSA Xradia 510, ZEISS) to disclose and quantify the spatial distribution of reactant and product phases and cracks. Scans were performed at 40 kV and 75 µA.

Data were acquired with a 4x magnification objective and a charge coupled device (CCD) sensor for a total scan time of 15 h including the collection of reference images. The voxel size achieved under these conditions was 3 µm. Analyses of Micro-CT were performed on the same crystals first analyzed by SEM-EDX to avoid any potential error on the selection of the grey-level/contrast threshold to quantify the selected phases. The image analysis was performed using the ImageJ software (Schneider et al., 2012) and Dragonfly software (Version 4.1, Object Research Systems).

Finally, all reacted crystals were thoroughly crushed using an agate mortar (grain size < 200 µm) and analyzed by X-Ray Diffraction (XRD) using an X'Pert PRO diffractometer (PANalytical) with the following instrumental parameters: Cu Kα-radiation (λ = 1.5405 Å), 40 mA current, 45 kV tension, 3-70°2θ measurement range, 4 s per step, and 0.04°2θ step size. Prior to analysis, powder samples were placed on zero-background Si sample holders. Diffraction patterns were analyzed using the computer software HighScore Plus 2.2.4 (PANalytical) and minerals were identified matching the experimental diffraction peaks with those included in the Joint Committee for Powder Diffraction Standards (JCPDS) PDF-2 database. For the quantification of the crystalline products, we used the Rietveld method [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF] and the crystal structures provided by the American Mineralogist Crystal Structure Database (Table S1) using HighScore Plus 2.2.4 (PANalytical). To corroborate the accuracy of the XRD Rietveld quantification, the normalized extent of carbonation (ξ n ) was calculated for Rietveld analyses and for mass balance analyses using the equation (Daval et al. 2009b):

(3) where and are the wt% of calcite and pyroxene (diopside or augite) determined by Rietveld analysis or mass balance calculation, and and are the molecular masses (g•mol -1 ) of calcite and pyroxenes respectively, yielding dimensionless ξ n .

To calculate the amount of Si-bearing amorphous phases obtained after 28 days of reaction, mass balance calculations were performed using the data obtained by Rietveld analysis of reacted solids and the results of ICP-OES chemical analysis of solutions, as follows:

(4) where is the molar % of Si from the reacted (dissolved) pyroxene obtained from the Rietveld analyses and the values of the initial mass of pyroxene in the experiments, is the molar Si concentration in solution obtained by ICP-OES analyses and is the molar % of Si precipitated in the Na-phillipsite phase obtained by Rietveld analysis. A detailed description of the mass balance calculations is presented in Supplementary Material. Note that Na-phillipsite is the only crystalline secondary silicate that we could identify in our runs. The difference in concentration obtained, Δm, is interpreted here as the Si contained in the Si-bearing amorphous phases (amorphous silica and magnesium silicate hydrate, see below).

Selected crystals were analyzed to identify amorphous phases by Fourier transform infrared spectroscopy using an attenuated total reflectance sample holder (ATR-FTIR, Jasco), spectral range 4000 -400 cm -1 , and step size of 0.48 cm -1 . Reported spectra correspond to the average of 72 measurements.

RESULTS

Evolution of solution chemistry during dissolution-carbonation experiments

In all systems studied here, augite runs systematically presented a higher release of Ca, Mg and Si to the solution as compared to diopside runs (Figure 1).

Evolution of the solution chemistry in water runs

In water (initial pH 7.5) significant amounts of alkaline-earth metals were released from both pyroxenes and remained in solution after 28 days of reaction (Figure 1a-d), an effect that can be related to the relatively large extent of dissolution of the starting material and the very limited DIC source (i.e., CO 2 present in the head space (1.2 cm 3 ) of the reactor). A slight decrease in the total concentration of Ca and Mg at 14 days, followed by a further increase was observed in water experiments, while the pH increased up to 14 days and subsequently decreased (pH 8.6 in augite and pH 9 in diopside runs). These results suggest that, after an initial period of pyroxene dissolution, Ca-Mg bearing carbonates formed within 14 days (corroborated by the analysis of reacted solids, see section 3.2). Precipitation of carbonates releases protons [START_REF] O'connor | Aqueous mineral carbonation[END_REF][START_REF] Rodriguez-Navarro | Formation of amorphous calcium carbonate and its transformation into mesostructured calcite[END_REF], causing a decrease in pH and, therefore, a renewed dissolution of the primary silicate to feed cations to the solution. If only Mg-Ca carbonate were precipitated, Si in solution should display a constant increase due to the two dissolution steps. However, Figures 1e and1f show that in the case of diopside runs, Si in solution showed a constant concentration during the whole experimental runs, whereas in augite systems, the concentration of Si presented an initial plateau between 7 and 14 days, matching the pH rise, and a later increase with a pH decrease. We suggest that in both runs, formation of amorphous silica (SiO 2am ) took place, which is consistent with previous works on pyroxene dissolution [START_REF] Schott | Mechanism of pyroxene and amphibole weathering-I. Experimental studies of iron-free minerals[END_REF][START_REF] Dixit | Effect of solution saturation state and temperature on diopside dissolution[END_REF][START_REF] Mcadam | Preferential low-pH dissolution of pyroxene in plagioclase-pyroxene mixtures: Implications for martian surface materials[END_REF]. Time-resolved variations in Si concentration during augite dissolution should be explained by the precipitation of an additional Si-bearing phase (Na-Phillipsite, Figure 1e) that fostered further release of Si from the parent phase.

Evolution of the solution chemistry in NaHCO 3 runs

Ca release to the solution from both pyroxenes in NaHCO 3 runs presented a first increase until 14 days, less pronounced in diopside runs, and a subsequent decrease caused by the precipitation of secondary Ca-bearing phases, as corroborated by XRD (see section 3.3). Mg release in augite runs showed a slight increase after 14 days of reaction. Logarithmic scale was used to unravel time differences (Figure S1). It can be observed a decrease up to 14 days and a further increase after 28 days of reaction. However, due to measurement error, we cannot infer a real increase or a more stable behavior. For this reason, we assume, in agreement with XRD results

(Figure S9 and S11), a constant release of Mg from augite and the subsequent formation of a Ca-Mg secondary phase. In the case of diopside, the release of Mg showed a decreasing trend between 7 and 28 days in logarithmic scale (Figure S1), not observable using a linear scale figure (Figure 1). It can be assumed a constant sink of Mg, probably caused by the precipitation of Mg-calcite. The Si concentration in solution in NaHCO 3 systems was the lowest measured in this work as compared with the Na 2 CO 3 and water runs, suggesting an important precipitation of Si-bearing secondary phases. It must be noted that the starting pH was the same in water and NaHCO 3 solutions, however, water systems underwent a higher pH increase over the first 14 days of reaction. We hypothesize that the higher level of carbonate precipitation in NaHCO 3 runs and the associated higher proton release led to such a limited pH rise in this run.

Evolution of the solution chemistry in Na 2 CO 3 runs

In Na 2 CO 3 runs, the concentration of Si in solution was up to two orders of magnitude higher than in the other systems. This result is consistent with the pH-dependent solubility of silica, which increases significantly at highly alkaline pHs [START_REF] Fleming | Silicic acid ionization and calculation of silica solubility at elevated temperature and pH application to geothermal fluid processing and reinjection[END_REF][START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF]. Interestingly, the Si concentration in augite runs was higher than in diopside runs. This suggests that the dissolution rate of augite is higher than that of diopside, and that a secondary Sibearing phase formed in diopside runs.

Evolution of the dissolution rates of pyroxenes

Dissolution rates of pyroxenes were calculated based on Si concentration in solution at the three sampling times (Figure S2). All our results show rates (LogR from -10.5 down to -13) that are in partial agreement with those reported in the literature (LogR from -9 down to -11 mol.m -2. s -1 ) (Daval et al. 2010;[START_REF] Dixit | Effect of solution saturation state and temperature on diopside dissolution[END_REF]).Yet they were systematically lower, especially in the case of NaHCO 3 runs where our rates were two order of magnitude lower. This shows that in our closed system we were closer to equilibrium than in other studied systems (flow-through experiments). Our results are also consistent with the fact that we have precipitation of siliconcontaining secondary phases, which reduced the silicon content in solution, and as a consequence, the values of LogR.

Characterization of solids reacted in water

Reacted augite

XRD patterns showed small changes after reaction of augite with water for 28 days (Figure 2a).

Rietveld analyses (Figure 2b) showed less than 15 wt% of augite replacement by: low Mg-calcite

(2.61 wt%), Na-phillipsite (~11 wt%) and iron oxides (hematite, 2.16 wt%). Na-phillipsite is a zeolite composed by Na, Al and Si, with the possibility of Mg, Ca and K incorporation (theoretical

formula: (Na,K,Ca) 1-2 (Si,Al) 8 O 16 •6H 2 O).
Hematite was also present from the early stages of reaction, showing a continuous but minor increase in concentration over time due to Fe release from the parent phases and the decrease in the solubility of iron oxides and hydroxides with increasing pH [START_REF] Schwertmann | Solubility and dissolution of iron oxides[END_REF] causing fast precipitation. µ-Raman analyses confirmed the precipitation of calcite (Figure 2c) showing the translational lattice mode (T) at 286 cm -1 , the ѵ 4 -symmetric CO 3 deformation at 717 cm -1 and the ѵ 1 -symmetric CO 3 stretching band at 1085 cm -1 [START_REF] Gunasekaran | Raman and infrared spectra of carbonates of calcite structure[END_REF]. Hematite was also identified by µ-Raman showing bands at 326 cm -1 , 449 cm -1 and 570 cm -1 corresponding to hematite E g , E u , and E g vibrations, respectively [START_REF] Bersani | Micro-Raman investigation of iron oxide films and powders produced by sol-gel syntheses[END_REF][START_REF] Chamritski | Infrared-and Raman-active phonons of magnetite, maghemite, and hematite: a computer simulation and spectroscopic study[END_REF]. SEM-EDS analysis of augite crystals reacted for 28 days showed fractures filled by a secondary Na-rich silicate, Na-phillipsite as demonstrated by XRD analysis (Figure 1d-e and S1). EDS point analyses (Figure S4 and Table S2) confirmed the presence of this zeolite phase with empirical formula Na 1.95 Mg 0.05 Al 3.21 Si 4.79 O 16 •6H 2 O. Despite the lack of added DIC, a small amount of calcite was observed (Figure S5). The formation of calcite suggests that the CO 2 present in the head space of the reactor (1.2 cm 3 ) dissolved in the solution forming HCO 3 -, which upon dissociation, supplied CO 3 2-ions that, in the presence of Ca 2+ ions, caused the precipitation of calcite and the release of H + . This is consistent with the pH and Ca 2+ concentration evolution in solution analyses (Figure 1a andd). SEM-EDS analysis of calcite showed that this phase included Mg. To unravel the actual content of Mg in calcite, the lattice parameters of calcite were calculated by Rietveld refinement and the Mg content was determined according to [START_REF] Goldsmith | Relation between lattice constants and composition of Ca-Mg carbonates[END_REF] (Table S3). The calculated Mg amount in calcite was 8 mol%. Silica gel was also identified by SEM-EDS analysis (Figure S6) in dissolving areas, such as small fractures and etch pits. Micro-CT analysis showed the presence of two secondary phases (identified by their contrast due to differences in X-ray attenuation), already identified in the same crystals using SEM-EDS. In Figure 2f, the red phase is amorphous silica and the green one is Na-phillipsite. It can be observed that precipitates were present inside the reacted crystals filling fractures that in some cases cross-cut the whole pyroxene crystal. Image analysis of Micro-CT results showed 23 wt% augite replacement by 14.3 wt% Na-phillipsite and 8.7 wt% amorphous silica. These values do not agree with the mass balance for silicon calculated using Eq. ( 4): a deficit of Si in the solution was detected that should be present as a precipitate. We suggest that the amorphous SiO 2 content obtained from Micro-CT analysis actually included calcite and amorphous silica due to the resolution constraints of the Micro-CT equipment. Mass balance was recalculated using the values obtained by Micro-CT total amount of augite dissolved and the concentration of Si and Ca in solution, yielding 2.16 wt% SiO 2 and 2.61 wt% calcite. If we normalize the phase contents obtained by Rietveld analysis to the amorphous silica and calcite determined by mass balance calculations, the corrected values for the quantitative analysis are 83.97 wt% augite, 9.86 wt% Na-phillipsite and 0.85 wt% hematite (Table 1). Thus, we assume that due to the resolution constraints of our Micro-CT equipment, the amounts of Na-phillipsite and CaCO 3 + amorphous SiO 2 were slightly overestimated.

Reacted diopside

In the case of diopside subjected to dissolution in water at pH 7.5, XRD and Rietveld analyses (Figure 3a and S7) showed no major differences between unreacted and reacted samples, except for the presence of 1.23 wt% Mg-Calcite (12 mol% Mg, Table S3), also confirmed by SEM-EDS analyses (Figure 3b-c). As mentioned above, calcite precipitation could have been caused by the presence of CO 2 in the head space of the reactor. µ-Raman analyses also confirmed the precipitation of this carbonate (Figure 3d). In addition, SEM-EDX and XRD analyses confirmed the presence of hematite (0.4 wt%). Rietveld analyses showed a very limited replacement of diopside by secondary phases (< 2 wt%) and, in contrast with augite runs, no secondary crystalline silicates were detected.

However, SEM-EDS analyses showed the presence of Ca-and Mg-free Si-rich precipitates in dissolution pits and on the surface of diopside, which we interpret as silica gel (Figure 3e). Micro-CT analyses (Figure S8) showed silica gel (2.7 wt%) after 28 days of reaction, but only on the surface of the reacted material. As in the case of the augite run, mass balance calculations were performed to unravel the actual SiO 2 content. This analysis shows that the value obtained by Micro-CT analysis was overestimated, because our equipment could not differentiate between calcite and amorphous silica (identified by XRD and SEM-EDS, respectively) as they show no detectable Xray attenuation contrast. Rietveld calculations were normalized to the 1.7 wt% amorphous SiO 2 calculated by mass balance yielding 96.73 wt% diopside, and 1.23 wt% calcite (Table 1). In contrast with augite runs, no pervasive fractures were identified by SEM or micro-CT analyses.

Apparently, while the formation of secondary crystalline silicate phases induces fracturing, this is not the case for the precipitation of amorphous silica (see discussion section).

3.3

Characterization of solids reacted in sodium bicarbonate solutions

Reacted augite

XRD-Rietveld results (Figure 4a and S9) show that the reaction of augite in NaHCO 3 solution led to the formation of Na-phillipsite and calcite, as also occurred in the case of water. However, augite replacement was substantially higher (36.9 wt%) and secondary phases formation reached maximum values as compared with the whole set of experimental results: 12.7 wt% Na-phillipsite (value very similar to water runs) and 22.3 wt% calcite. Importantly, the mass balance between Si in solution (Figure 1c) and reacted augite from Rietveld analysis showed an excess of Si that would be incorporated into an additional secondary Si-bearing phase, which was not detected by XRD or SEM-EDS analyses. Based on the results of water runs (see above), we suggest that the missing Si was incorporated into amorphous silica. Rietveld analyses were thus normalized to the 2.1 wt% of newly formed amorphous silica calculated from mass balance (Table 1). SEM-EDS analyses (Figure 4b,c) showed massive pervasive fracturing of the starting augite crystals and confirmed the presence of abundant Na-phillipsite and calcite precipitated within the fractures and on the surface of the starting material. Well-developed rhombohedral calcite crystals ~8 µm in size with surfacedecorated iron-oxides were also identified. Calcite formation was confirmed by µ-Raman analyses (Figure 4d). Micro-CT analyses (Figure 4e) confirmed that the secondary phases precipitated within the fractures cross-cutting the crystal and in the pores of the host augite crystal. Interestingly, Naphillipsite precipitated directly in contact with the fracture walls, filling the fractures inwards and fully covering the surface of the walls. In contrast, calcite crystals appeared on the surface of the pyroxene crystal and filling the cracks in contact with the Na-phillipsite (Figure S10), evidencing a first precipitation of the zeolite and the subsequent formation of calcite. However, it cannot be ruled out the possibility that, once the cracks appeared caused by the first precipitation of Na-phillipsite, calcite started to precipitate contemporaneously to this zeolite. It should be noted that in this run the amount of newly formed iron oxides reached the highest value of all experiments (2.01 wt%).

Reacted diopside

XRD-Rietveld analyses (Figures 5a andS11) of diopside showed a much higher level of replacement (12.6 wt%) by newly formed phases in NaHCO 3 solution than in water, but this value was significantly lower than that of augite reacted in bicarbonate solutions. Calcite was the most abundant secondary phase, showing a progressive increase up to 11.7 wt% over the whole span of the experiment, whereas iron oxides were, in all experiments, under 1 wt%. Mass balance calculations showed that a fraction of precipitated Si was missing. As in the previous cases, this is interpreted as amorphous silica gel not detected by XRD. Quantitative Rietveld analysis results

were normalized using the 1.27 wt% of amorphous SiO 2 calculated from mass balance (Table 1).

Calcite precipitation was confirmed by µ-Raman (Figure 5b) showing the characteristic bands at 286 cm -1 , 717 cm -1, and 1085 cm -1 , plus additional diopside bands, due to the relatively high beam penetration depth. These inosilicate bands include: the symmetrical stretching vibration of bridging oxygen in Si-O-Si (Si-O br ) at 663 cm -1 , the symmetrical stretching vibration of non-bridging oxygen in Si-O (Si-O nbr ) at 1012 cm -1 and, in the lower frequency region, four bands at 206 cm -1 , 316 cm -1 , 350 cm -1 and 385 cm -1 corresponding to the Ca/Mg-O vibrations [START_REF] Buzatu | The Raman study of single-chain silicates[END_REF].

Precipitation of calcite and iron oxides was also confirmed by SEM-EDS analyses (Figure 5c andd). Rhombohedral calcite crystals were observed on the surface and within dissolution pits of the diopside substrate. EDS analyses of calcite crystals showed a high Mg content (Figure 5c). From XRD analysis, the Mg content in calcite was determined to be 14.8 mol%. The highest Mg content in calcite was observed in these runs, whereas in pure water a higher Mg content was observed in diopside than in augite runs. Similar to the pure water systems, and in contrast with augite runs, diopside crystals did not show massive pervasive fracturing as in the case of augite runs (inset in Figure 5d). As a result, no secondary phases were detected in the interior of diopside crystals by Micro-CT.

Characterization of solids reacted in sodium carbonate solutions

Reacted augite

After 28 days, the formation of Mg-calcite (12 mol% Mg) was detected in augite samples along with hematite, whose content increased almost linearly with reaction time (Figures 6a andS12a).

Augite replacement in the Na 2 CO 3 system was the lowest observed here (7.95 wt%). Mg-calcite reached 6.9 wt%, in good agreement with Micro-CT analyses (7.7 wt%). Mg-calcite was principally present as rhombohedral crystals ~16 µm in size on the surface of the starting material and inside surface cracks and dissolution pores (some extending deep into the pyroxene crystal), as shown by SEM-EDS analyses (Figure 6b,c) and Micro-CT (Figure 6d). However, pervasive fracturing was not observed within reacted augite crystals (Figure 6d). Furthermore, no Si-bearing secondary phases were identified.

Reacted diopside

XRD results (Figures S12b andS13) showed minimal replacement of diopside (2.25 wt%)

in Na 2 CO 3 solution by low-magnesium calcite crystals (4 mol% Mg, the lowest value of all runs).

SEM-EDS analysis of solids collected after 7 days of reaction (Figure 7a) showed the presence of a gel-like Mg-and Si-rich surface precipitate with no Ca, in addition to rhombohedral crystals of calcium carbonate. Moreover, EDS analyses showed that the apparently amorphous Mg-silicate had a Mg/Si ratio of 0.72, in good agreement with mass balance calculations yielding a Mg/Si ratio of 0.63. The Mg/Si ratio was calculated by mass balance as follows:

(5)

where is the mol % of Mg from the dissolved pyroxene obtained from the Rietveld analyses, is the Mg concentration in solution obtained by ICP-OES analyses and is the mol % of Mg precipitated in the Mg-containing crystalline phases obtained by Rietveld analysis using a Pseudo-Voigt (n=0.5) for peak fitting and refinement. The difference in concentration obtained, Δ Mg , is interpreted here as the Mg contained in the Mg+Si-bearing amorphous phase.

Such values are in full agreement with the typical Mg/Si ratios observed for magnesium silicate hydrate (MSH) gels (0.6-0.9) [START_REF] Lothenbach | Magnesium and calcium silicate hydrates[END_REF][START_REF] Bernard | Effect of magnesium on calcium silicate hydrate (CSH)[END_REF]. After 28 days of reaction (Figure 7b), the MSH gel suffered a morphological transformation to a more condensed (less porous and more compact) structure constrained within the limits of surface cracks, and filling dissolution pits of diopside. Calcite crystals were associated with MSH on the surface and within etch pits of the pyroxene (Figure 7b). Micro-CT (Figure 7c) analyses showed the distribution of MSH along the dissolution areas and within the pores formed on the surface of diopside, but also in several small cracks extending from the surface to the interior of the crystal (without cross-cutting the whole crystal). Micro-CT based calculation of MSH + calcite content yielded 9.7 wt% of both phases. If we subtract from this value the Rietveld value obtained for calcite, the MSH content should be 7.45 wt%. However, mass balance did not match these values, showing an excess of Si in the system. Additional mass balance calculations were performed considering the Si and Mg content in solution, yielding a MSH content of 5 wt%. Rietveld analyses were normalized to this value (Table 1). Calcite could not be differentiated from MSH using micro-CT due to analytical constraints (i.e., under our experimental conditions, the X-ray contrast of these two phases is very similar, so our micro-CT analysis could not differentiate them).

MSH precipitation was confirmed by FTIR analyses (Figure 7d) showing the broad ѵ-OH stretching around 3400 cm -1 and the δ-OH bending at ~1615 cm -1 of water as well as a weak band at ~1240 cm -1 attributed to the Q 3 stretching vibration of Si-O bonds, and a band at ~1180 cm -1 corresponding to the ѵ 3 vibration of the Si-O bond in fresh MSH gels, which is red-shifted from the typical ѵ 3 Si-O band of calcium silicate hydrate (CSH) at 945 cm -1 [START_REF] Ashraf | Carbonation behavior of hydraulic and non-hydraulic calcium silicates: potential of utilizing low-lime calcium silicates in cement-based materials[END_REF][START_REF] Lothenbach | Magnesium and calcium silicate hydrates[END_REF]. The presence of a carbonate phase was also confirmed by the ѵ 3 band at ~1458 cm -1 [START_REF] Ashraf | Carbonation behavior of hydraulic and non-hydraulic calcium silicates: potential of utilizing low-lime calcium silicates in cement-based materials[END_REF][START_REF] Gunasekaran | Raman and infrared spectra of carbonates of calcite structure[END_REF]. Calcite bands at 874 and 713 cm -1

were not detected due to the overlapping of the broadband of ѵ as Si-O-Si vibration of diopside [START_REF] Omori | Analysis of the infrared absorption spectrum of diopside[END_REF][START_REF] Mozgawa | Vibrational spectra of aluminosilicate structural clusters[END_REF]. To further corroborate the presence of MSH, µ-Raman analyses were performed (Figure 7e). The bands of diopside were detected, as well as the bands corresponding to O-H-O vibrations at 219 cm -1 , O-Si-O bending at 354 cm -1 and Si-O-Si symmetrical bending at 450 and 661 cm -1 , corresponding to MSH [START_REF] Lothenbach | Magnesium and calcium silicate hydrates[END_REF][START_REF] Bernard | Effect of magnesium on calcium silicate hydrate (CSH)[END_REF].

Quantitative comparison of the carbonation extent

To better assess the carbonation extent of the different starting materials, values determined by Rietveld refinement (ξ n RR ) were plotted as a function of mass balance values (ξ n MB ) (Eq. 3) (Figure S14). Extents of carbonation determined by both methods are listed in Table 1. The slope and correlation coefficient of the linear regression of the corresponding data (N=3) for both analyses were close to 1, showing that the ξ n values obtained by Rietveld analysis are in excellent agreement with those obtained by mass balance analysis. These results support, on the one hand, that Rietveld analysis is an accurate method for quantitative crystalline phase analysis, even in the case of mineral phases present in very small amounts, and on the other hand, it gives extra reliability to our experimental work.

Discussion

Effect of pH and secondary phases precipitation during dissolution-carbonation

Dissolution kinetics of inosilicate minerals are positively correlated with [H + ] (e.g., [START_REF] Schott | Mechanism of pyroxene and amphibole weathering-I. Experimental studies of iron-free minerals[END_REF][START_REF] Mcadam | Preferential low-pH dissolution of pyroxene in plagioclase-pyroxene mixtures: Implications for martian surface materials[END_REF][START_REF] Schott | Formation, growth and transformation of leached layers during silicate minerals dissolution: The example of wollastonite[END_REF]. Therefore, the concentration of released divalent metals susceptible to contribute to the carbonation reaction is expected to be higher at close-toneutral than at highly alkaline pHs. However, carbonate precipitation is dependent on

[CO 3 2- ],
which increases with pH (for a given value of DIC). Thus, a proper balance between these two key parameters (i.e. [CO 3

2-] and pH), is of paramount importance to reach the highest possible carbonation yield. In our case, this is achieved in sodium bicarbonate solution for both minerals studied here. If dissolution is considered the rate limiting step of the carbonation reaction, the highest replacement should be observed in the pure water run and the lowest replacement should take place in Na 2 CO 3 solutions. This holds true for augite experiments (Table 1). However, a higher level of diopside replacement was achieved in Na 2 CO 3 than in water runs (Table 1), which points to the existence of another kinetic limiting step.

Regarding free energy calculations (Eq. S2 and S3 and Table 2), it was observed that all systems had a negative free energy, enabling the dissolution of the pyroxenes. It is important to note that, systematically, ΔG values of augite were lower (more negative) than those of diopside, resulting in higher expected dissolution rates and therefore, a higher augite replacement by secondary phases, as we observed experimentally in all runs.

Calculation of Saturation Index (SI cal ) from measured concentrations in ICP-OES analyses using PHREEQc (Figure 8) shows that the highest calcite supersaturation is reached for augite in NaHCO 3 runs. Due to the similar behavior of SI cal for both pyroxenes, results for diopside SI modeling are not shown here. Low magnesium calcite (~8-10 mol%) presents a slightly lower solubility product than pure calcite [START_REF] Morse | Partition coefficients in calcite: Examination of factors influencing the validity of experimental results and their application to natural systems[END_REF]). Thus, we can expect a slight increase of the calculated SI cal due to the Mg content, favoring Mg-calcite precipitation. Furthermore, the precipitation of calcium carbonate causes a pH decrease (Figure 1) by proton release, which would foster further pyroxene dissolution. Thus, our model is in good agreement with our experimental results showing that in NaHCO 3 runs calcite precipitation reached the highest yield as compared to the other systems (24.6 wt% in augite and 11.7 wt% in diopside). To explain why the Mg content in precipitated calcite was maximum in diopside reacted in NaHCO 3 runs, and minimum in diopside reacted in Na 2 CO 3 runs, we suggest that at neutral-to-moderately alkaline pH (bicarbonate and water runs), the higher [Ca 2+ ]/[CO 3

2-

] ratio (closer to unity) as compared to higher pH runs (with

higher [CO 3 2-
]) in addition to the high SI cal could enable faster calcite growth favoring Mg incorporation [START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]. In addition, because Mg was incorporated in MSH, a phase which according to our SEM-EDX and micro-CT observations preceded the formation of Mg-calcite in diopside runs with Na 2 CO 3 solution, there was a lower amount of Mg available to be incorporated into calcite.

In agreement with [START_REF] Gadikota | Chemical and morphological changes during olivine carbonation for CO 2 storage in the presence of NaCl and NaHCO 3[END_REF], who showed that the addition of NaHCO 3 during ex situ CCS fostered the carbonation of Ca-Mg silicates due to its buffer effect, we also observe enhanced silicate dissolution-carbonation in NaHCO 3 runs due to the relatively constant pH of the reaction (7.5 < pH < 9). This relatively constant moderately alkaline pH enhances the dissolution of the pyroxenes as compared to a strongly alkaline pH. As a consequence, dissolution of these silicates increases the amount of alkaline-earth metal ions fed to the solution susceptible to react with CO 3 2-ions. This is one factor that helps to explain why we obtain the highest levels of calcium carbonate precipitation in bicarbonate runs. But it is not the only one (see below).

Regarding iron oxide precipitation, PHREEQc calculations (Figure S15) show that under the whole pH range of our experiments, hematite was supersaturated. Therefore, precipitation of Feoxides was expected right after Fe release following dissolution of the starting materials, in agreement with [START_REF] Schwertmann | Solubility and dissolution of iron oxides[END_REF]. As in the case of Mg-calcite, precipitation of Fe-oxides should also favor the progress of the dissolution/carbonation according to Le Chatelier's principle.

Regarding secondary silicate phases, amorphous silica, MSH and Na-phillipsite precipitated in our experiments despite the fact that the bulk solution was undersaturated with respect to the latter. Our analysis of the solution chemistry evolution and SEM-EDS observations revealed that amorphous silica was precipitated after a moderate alkalization in NaHCO 3 and water runs.

Amorphous SiO 2 was found within etch pits and as isolated precipitates on the surface of the pyroxene crystals. The formation of etch pits and their filling by amorphous silica reveals that a coupled dissolution-precipitation reaction at the mineral-fluid interface (i.e., interface-coupled dissolution-precipitation, ICDP) was at work [START_REF] Putnis | Mineral replacement reactions[END_REF][START_REF] Ruiz-Agudo | Mechanism of leached layer formation during chemical weathering of silicate minerals[END_REF], 2016).

According to previous works (i.e., Daval et al., 2009a;[START_REF] Ruiz-Agudo | Mechanism of leached layer formation during chemical weathering of silicate minerals[END_REF][START_REF] Wild | Physical properties of interfacial layers developed on weathered silicates: A case study based on labradorite feldspar[END_REF], replacement processes taking place at the mineral-fluid interface result in strong compositional gradients and important pH differences between the bulk solution and the mineral-fluid interface.

Such gradients enable the precipitation via an ICDP mechanism of secondary phases, thermodynamically not possible in the bulk solution [START_REF] Putnis | Mineral replacement reactions[END_REF], thus explaining the observed formation of amorphous silica (as well as the other two secondary silicates, as discussed below)

despite the fact that this phase was unsaturated in the bulk solution.

Under the highly alkaline pH of the Na 2 CO 3 runs, we detected no amorphous silica precipitation; however, the highest Si concentration in solution was reached (Figure 1). This result is consistent with the nearly exponential increase in silica solubility at pH > 9 [START_REF] Fleming | Silicic acid ionization and calculation of silica solubility at elevated temperature and pH application to geothermal fluid processing and reinjection[END_REF][START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF], not favoring its precipitation. On the other hand, because pyroxene dissolution rates decrease with increasing pH [START_REF] Schott | Formation, growth and transformation of leached layers during silicate minerals dissolution: The example of wollastonite[END_REF], the Si release rate was substantially lower in highly alkaline systems than in moderately alkaline ones.

Augite dissolution-carbonation at neutral-to-moderately alkaline pH, led to the precipitation of Na-phillipsite. Previous works have reported the precipitation of secondary Na-phillipsite (commonly associated with amorphous Si-rich glass) during low-T hydrothermal weathering of basic and ultrabasic rocks rich in aluminum-augite in pelagic environments [START_REF] Glaccum | Na, K)-phillipsite: Its stability conditions and geochemical role in the deep sea[END_REF][START_REF] Iyer | Composition and genesis of zeolitic claystones from the Central Indian Ocean Basin[END_REF]. To model the evolution of the Saturation Index of Na-phillipsite (SI phi ) at our experimental conditions, PHREEQc calculations were performed, showing values of SI phi < 0 (undersaturation) for all relevant pH values (i.e., pH ≥ 7.5) in our studied systems (Figure 8). The latter indicates that it was not thermodynamically possible to precipitate this phase, contrary to our experimental observations. As in the case of the precipitation of SiO 2(am) above discussed, if a sufficiently high Na, Al and Si release rate is achieved, a high supersaturation will be reached at the mineral-fluid interface as to enable the heterogeneous precipitation of Na-phillipsite on the dissolving augite via an ICDP mechanism. In this respect, it is important to underline that a high solute concentration can be achieved within the constrained volume of etch pits formed during pyroxene dissolution [START_REF] Plümper | The interface-scale mechanism of reactioninduced fracturing during serpentinization[END_REF], and their pore surface will offer a large amounts of sites for heterogeneous nucleation [START_REF] Scherer | Crystallization in pores[END_REF][START_REF] Putnis | Mineral replacement reactions[END_REF][START_REF] Emmanuel | Impact of nano-size weathering products on the dissolution rates of primary minerals[END_REF][START_REF] Schiro | Damage mechanisms of porous materials due to in-pore salt crystallization[END_REF]. Altogether, these combined effects would favor the observed precipitation of Naphillipsite.

In our previous work [START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF] we showed the formation of a secondary Ca+(Na/K)-bearing silicate (pectolite) during pseudowollastonite carbonation under equivalent conditions to those in this work. Other studies on pyroxenes and olivine carbonation demonstrated the formation of secondary crystalline Ca and Mg silicates [START_REF] King | Effect of secondary phase formation on the carbonation of olivine[END_REF][START_REF] Sissmann | The deleterious effect of secondary phases on olivine carbonation yield: Insight from time-resolved aqueous-fluid sampling and FIB-TEM characterization[END_REF], which fostered carbonation by the effect of side-reactions, as also shown here, but underlined that divalent metal incorporation into the secondary silicates was a handicap for an effective CCS [START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF]. In our case, the observed incorporation of small amounts of Mg in Na-phillipsite will also pose a handicap, yet very limited, for effective carbonation of augite (Table S3).

The amount of Na + in Na 2 CO 3 runs was double that in NaHCO 3 runs, and orders of magnitude higher than in water runs. However, no Na-aluminosilicates precipitated in the former runs. This is likely due to the low dissolution rates of pyroxenes under strongly alkaline pH, preventing the build-up of sufficient supersaturation at the mineral-fluid interface as to enable Naphillipsite precipitation despite the higher Na content. The lack of secondary crystalline silicates in Na 2 CO 3 solutions during augite carbonation led to the lowest level of replacement and calcite yield.

This emphasizes that the formation of secondary silicate phases is crucial to promote carbonation of primary silicates [START_REF] Monasterio-Guillot | Reaction of pseudowollastonite with carbonate-bearing fluids: Implications for CO 2 mineral sequestration[END_REF].

The lack of Na-phillipsite precipitation in diopside runs can be easily explained considering the absence of Al in the elemental composition of this mineral. However, other crystalline secondary Ca and/or Mg silicates could in theory be formed after diopside dissolution at neutral to moderately alkaline pH, as observed for instance after carbonation of olivine [START_REF] King | Effect of secondary phase formation on the carbonation of olivine[END_REF]Sissman et al., 2013) and wollastonite (Daval et al. 2009a,b). In our closed systems, however, diopside shows a lower dissolution rate than augite, as demonstrated by our ICP-OES analyses and the % replacement achieved after 28 days of reaction (Figure 1 and Table 1). Therefore, both the slow kinetics of Si release to the solution, and the limited amount of dissolution pits/pores formed on diopside as to favor heterogeneous nucleation of secondary crystalline silicates, seem to have contributed to the reduced yield of secondary phases observed here at moderately alkaline pH.

The contrasting behavior of diopside as compared to augite in Na 2 CO 3 solution is also exemplified by the formation of MSH in the case of diopside runs. As indicated above, secondary Mg-bearing silicate phases could be interpreted as a handicap for effective CO 2 capture. However, Rietveld and mass balance analyses showed that carbonation yield of diopside during Na 2 CO 3 experiments was double than that of water runs, in contrast to augite that reached similar carbonate yield in both runs (Table 1). The formation of MSH after dissolution of a Mg-Ca-pyroxene is not totally unexpected under our experimental conditions, because MSH is stable at moderately alkaline pH (p≈ 7.5) [START_REF] Bernard | Effect of magnesium on calcium silicate hydrate (CSH)[END_REF]. The formation of MSH has been previously reported during olivine carbonation at 170 ºC [START_REF] Sissmann | The deleterious effect of secondary phases on olivine carbonation yield: Insight from time-resolved aqueous-fluid sampling and FIB-TEM characterization[END_REF]). However, the Mg/Si ratio reported by [START_REF] Sissmann | The deleterious effect of secondary phases on olivine carbonation yield: Insight from time-resolved aqueous-fluid sampling and FIB-TEM characterization[END_REF] was much higher (Mg/Si = 3.72) as compared to our experimental result (Mg/Si ~ 0.7). We suggest that this difference is due to the molar concentration of Mg in the starting material (double in forsterite that in our pyroxenes), and to the higher dissolution rate of olivine as compared with diopside [START_REF] Schott | Formation, growth and transformation of leached layers during silicate minerals dissolution: The example of wollastonite[END_REF]. Following [START_REF] Sissmann | The deleterious effect of secondary phases on olivine carbonation yield: Insight from time-resolved aqueous-fluid sampling and FIB-TEM characterization[END_REF] and [START_REF] Lothenbach | Magnesium and calcium silicate hydrates[END_REF], PHREEQc calculations were performed using talc as a proxy to MSH,

showing that such a Mg-rich silicate was supersaturated in the Na 2 CO 3 solution and, therefore, precipitation was expected. In this respect, we demonstrate that the precipitation of MSH during diopside carbonation can foster its dissolution leading to enhanced Ca release. This effect helps to explain why a higher amount of calcite was precipitated in this run as compared to the water run (i.e., effect of side reactions). We suggest that the absence of MSH formation in augite during Na 2 CO 3 runs is due to the higher dissolution rate of this phase as compared with diopside, resulting in higher compositional gradients at the mineral interface that promoted the formation of Mg-calcite as a Mg sink, instead of a Mg-rich silicate phase. Note that SEM-EDX analysis demonstrates that MSH formation precedes calcite formation on the surface of diopside, showing that the kinetics of dissolution and carbonate precipitation in this system were sluggish.

To summarize, our results show that the formation of non-carbonate secondary precipitates (i.e., Na-phillipsite, hematite, Magnesium Silicate Hydrates and amorphous silica), fostered the dissolution and subsequent carbonation of the starting material. Altogether, our experimental results demonstrate that the formation of secondary silicates (and oxides) played a key role in silicate carbonation due to the importance of side reactions on enhanced dissolution of primary silicates and on the subsequent effective carbonation (e.g., Frugier et al., 2008, and references therein).

Effect of reaction-driven fracturing

There is also another crucial effect associated with the precipitation of secondary phases that strongly contributed to enhance augite and diopside carbonation: reaction-induced fracturing. In all runs where Na-phillipsite precipitated, augite crystals showed massive pervasive fracturing (Figure 2d-f and Figure 4b ande), whereas no such massive fracturing was observed in the rest of the reacted crystals, with the exception of diopside run at high pH where some fracturing was observed associated with MSH precipitation. As mentioned above, Na-phillipsite precipitation started in the (wedge-like) etch pits or pre-existing surface cracks/pores of the host material, and continued by filling cracks generated by the crystallization of this phase. This reaction-driven fracturing is critical for the advancement of the carbonation process, resulting in the highest replacement and carbonate yields observed here. It is also expected to have an impact during GCS not just because Ca-Mg-Al pyroxenes are abundant in target rock-formation, but also because in such formations pore water is typically saline, showing high Na concentrations and neutral-to-moderately alkaline pHs [START_REF] Matter | Rapid carbon mineralization for permanent disposal of anthropogenic carbon dioxide emissions[END_REF], and volcanic glass and plagioclase dissolution may act as an additional Al source, which may favor secondary Na-aluminosilicate formation likely resulting in fracturing.

Due to the difference in chemical potential between ions in solution and in a solid phase, a pressure can be exerted by a solid crystallizing in a supersaturated solution, and such a crystallization pressure can be transmitted to confining surfaces such as the walls of pores or cracks.

The crystallization pressure in pores large enough that curvature effects can be neglected is defined by [START_REF] Correns | Growth and dissolution of crystals under linear pressure[END_REF][START_REF] Scherer | Crystallization in pores[END_REF][START_REF] Steiger | Crystal growth in porous materials-I: The crystallization pressure of large crystals[END_REF]

, ( 6
)
where n is the number of ions forming the solid phase, R is the gas constant, T is the temperature, IAP is the ion activity product, k sp is the solubility product (IAP/k sp is the supersaturation, β) and V m is the crystal molar volume. Eq. ( 6) shows that Δp depends on supersaturation, which acts as a driving force for crystallization pressure generation [START_REF] Schiro | Damage mechanisms of porous materials due to in-pore salt crystallization[END_REF]. In general terms, the free energy change ΔG r associated with the formation of a new phase within a subcritical crack, such as dissolution pits or pre-existing surface cracks in the pyroxenes, can lead to a significant Δp if a positive molar volume difference ΔV s exists between the reactant and product phases, as predicted by thermodynamics,

Pressures of up to 300-400 MPa have been predicted using Eq. ( 7) for common reactions such as olivine replacement by serpentine [START_REF] Kelemen | Reaction-driven cracking during retrograde metamorphism: Olivine hydration and carbonation[END_REF] or alkali-silica reaction (ASR) in cement [START_REF] Ichikawa | Modified model of alkali-silica reaction[END_REF].

Failure of materials due to crystallization pressure generation within an elastic material using an energy criterion will take place when the strain energy imposed by the growing crystals is higher than the strain energy obtained during an uniaxial tensile strength test [START_REF] Espinosa-Marzal | The chemomechanics of crystallization during rewetting of limestone impregnated with sodium sulfate[END_REF], i.e., when σ c > σ T , where σ c is the critical stress and σ T is the tensile strength. One way to determine σ c involves the calculation of using Eq. ( 6). In our experiments, however, the supersaturation at which Na-phillipsite crystallized is unknown, so we cannot calculate σ c using this approach. However, we can estimate the stress required for the opening of a flaw or subcritical crack (e.g., a notch-or wedge-like dissolution pit or pre-existing crack) following crystallization pressure generation by a newly formed phase in such a confined space using fracture mechanics.

The critical stress can be calculated knowing the critical stress intensity (or fracture toughness) of a particular solid, and for a particular flaw geometry. Here, we can consider the case of a semicircular flaw normal to the face exposed to the solution of a solid of semi-infinite length undergoing internal pressurization [START_REF] Jacobsen | Concrete-ice abrasion mechanics[END_REF], as the geometry that can best represent surface etch pits and preexisting surface cracks in pyroxene crystals (Figure 9a). In this case and for mode-I fracturing, the stress intensity is (Tada et al., 1993),

where σ is the internal stress within the flaw (or tensile stress pulling apart the surfaces of the flaw), c is the radius of the semicircular flaw, and  is the angle of the flaw with respect to the solid surface. For a crack normal to the surface, the peak stress is at =/2, and the critical stress to reach the critical stress intensity K Ic is [START_REF] Jacobsen | Concrete-ice abrasion mechanics[END_REF],

Because no actual K Ic value for augite single crystals has been reported, we have calculated K Ic according to the Griffith's criterion for a brittle material under plane strain using the equation (Griffith, 1920), ( 10)

where E is the Young modulus, ν is the Poison ratio, and γ is the surface energy (2γ is the energy required to create new surfaces at the crack tip). In the case of augite, the reported values of E and ν are 143.76 GPa [START_REF] Aleksandrov | The elastic properties of pyroxenes[END_REF] and 0.25 [START_REF] Ji | Composition and tectonic evolution of the Chinese continental crust constrained by Poisson's ratio[END_REF], respectively. Due to the scarcity of (reliable) reported values for γ of augite, we have used two different ones which help us to establish a lower and upper bound of K Ic for this pyroxene. The values are: 0.4 J m -2 reported for augite by [START_REF] Miller | Adhesion and the Surface Energy Components of Natural Minerals and Aggregates[END_REF], and the theoretical value of 1.19 J m -2 for augite calculated using the equation [START_REF] Gilman | Direct measurement of the surface energies of crystals[END_REF]

, ( 11
)
where a is the atomic radius (or interatomic distance) of the atoms laying in the cleavage plane (here this value is taken as the average bond distance between oxygen and metal cations in M1 (i.e., Al, Fe, Ti) and M2 (i.e., Ca, Mg) positions, equal to 2.28 Å; [START_REF] Cameron | Structural and chemical variations in pyroxenes[END_REF], and d 0 is the d-spacing of {hkl} cleavage planes (i.e., weakest bond) in a particular crystal, which is d 110 = 6.42 Å for the main {110} cleavage planes of augite. The fact that the theoretical value of γ for augite calculated using Eq. ( 11) is nearly identical to the surface energy value of 1.2 J m -2 reported for aegirine [START_REF] Li | Surface properties and floatability comparison of aegirite and specularite by density functional theory study and experiment[END_REF] give us confidence about the reliability of our calculation method. Note that augite and aegirine are isostructural and form a solid solution, so it is not unexpected for their surface energy values to be very similar. Using the γ values 0.4 and 1.19 J m -2 , Eq. ( 10) yields the following K Ic values: 0.35 MPa m ½ and 0.61 MPa m ½ , respectively. For comparison, we have also considered the K Ic value of 1.28 MPa m ½ reported for a diopside ceramic [START_REF] Herman | Influence of vitrified bond structure on radial wear of cBN grinding wheels[END_REF]. With the exception of the lowest value, the rest fall within the range of K Ic values reported for common silicate single crystals including olivine, quartz, feldspars, garnets and Al 2 SiO 5 polymorphs [START_REF] Atkinson | Subcritical crack growth in geological materials[END_REF][START_REF] Whitney | Hardness, toughness, and modulus of some common metamorphic minerals[END_REF].

Figure 9b shows the variation of the critical stress (σ c ) vs. the radius of the semicircular flaw (c) calculated using Eq. ( 9), for the three K Ic values indicated above. Using the measured value of c = 32±3 µm for the case of augite subjected to crack opening following precipitation of Naphillipsite in wedge-like each pits (measurements performed on SEM images, see Figure 9c-e), and the three K Ic values above indicated (ordered from lowest to highest value), Eq. ( 9) yields values of σ c equal to 53±6, 93±10, and 196±20 MPa, respectively. The first value is rather low, likely because the low surface energy reported for augite by [START_REF] Miller | Adhesion and the Surface Energy Components of Natural Minerals and Aggregates[END_REF] using contact angle measurements is affected by surface reaction during measurement (i.e. SiO 2am formation). The σ c value obtained for the case of the augite ceramic is likely higher than that expected for a single crystal, as monomineralic aggregates tend to have higher K Ic values than single crystals [START_REF] Van Noort | The force of crystallization and fracture propagation during in-situ carbonation of peridotite[END_REF]. The σ c value obtained using the calculated surface energy for augite seems to be the most realistic. Despite the uncertainties in the above reported values of critical stress σ c , values in the order of 100 MPa are apparently necessary for fracture opening in augite single crystals, meaning that crystallization of Na-phillipsite has to exert Δp values higher than ~100 MPa within dissolution pits or preexisting cracks on the surface of augite crystals.

Our analysis yields σ c values of the same order of magnitude, but smaller than those calculated for reaction-driven fracturing associated with olivine serpentinization (~300 MPa) [START_REF] Kelemen | Reaction-driven cracking during retrograde metamorphism: Olivine hydration and carbonation[END_REF]Plumper et al., 2013). In any case our calculated σ c values are necessarily larger than the tensile strength of (unconstrained) augite crystals, otherwise no reaction-driven fracturing would have been observed. Note that while the theoretical maximum tensile strength for a crystal is ~E/10 (i.e., ~15 GPa for augite), the actual value is typically much lower because of the presence of flaws [START_REF] Idrissi | Low-temperature plasticity of olivine revisited with in situ TEM nanomechanical testing[END_REF], explaining why fracturing of augite is observed under the calculated σ c values. To the best of our knowledge, the tensile strength of augite single crystals has not been reported. However, a spalling fracture stress of 58 MPa (equivalent to tensile strength failure under very high strain rates) has been reported for an augite-rich (65%) peridotite [START_REF] He | Characteristic of dynamic tensile fracture in augiteperidotite[END_REF]. This stress can be considered as a lower bound for the stresses actually resulting in fracturing of our augite single crystals upon Na-phillipsite crystallization.

Using Eq. ( 6), and the most reliable critical stress of 93 MPa obtained here using fracture mechanics, a supersaturation  = 2.69 for Na-phillipsite (NaAlSi 3 O 8 •3H 2 O, n = 4, and V m = 149.69 cm 3 mol -1 ; data from [START_REF] Blanc | A generalized model for predicting the thermodynamic properties of clay minerals[END_REF] crystallization within augite is obtained (at 423 K). Such a relatively high, yet reasonable  value, corresponding to a SI phi of 0.42, underlines that the supersaturation that can be reached at the mineral-solution interface during an ICDP process can be significantly high, even when the bulk system is undersaturated to a particular phase, as shown here by our PHREEQc modeling. If we consider a lower bound for the crystallization pressure equal to the dynamic tensile strength of augite-rich peridotite (58 MPa), then a  value of 1.85 is calculated from Eq. ( 6), which also demonstrates that for fracture generation a significant but reasonable supersaturation has to be generated at the mineral-solution interface in dissolution pits. Still, there is a potential problem regarding the calculated crystallization pressure: for a crystal to transmit such a pressure to a confining surface, a fluid (few nm thick) has to exist between the crystal and the confining surface, so that a disjoining pressure must exist that is at least equal to such a crystallization pressure [START_REF] Scherer | Stress from crystallization of salt[END_REF]. It is not clear whether a fluid would not be squeezed out leading to direct contact between the crystals and the confining wall under a crystallization pressure of several tens or even hundred MPa, so that no crystallization pressure can be transmitted. In this respect, [START_REF] Zheng | Effects of confinement on reaction-induced fracturing during hydration of periclase[END_REF] report that confining pressures higher than 30 MPa prevented reactioninduced fracturing during the hydration of MgO (which can in theory generate crystallization pressure values of over 1 GPa). This was interpreted assuming that the liquid was squeezed out of the reaction interface, and no disjoining pressure could be developed. Yet, this could be also due to relaxation of crystallization pressure through viscous creep due to the fact that brucite is a mechanically weak mineral. Disjoining pressures higher than 75 MPa have been predicted by [START_REF] Ortoleva | Water films at grain-grain contacts: Debye-Hückel, osmotic model of stress, salinity, and mineralogy dependence[END_REF] to explain pressure solution at crustal depth of over 5 km. It can thus be argued that in our experiments effective disjoining pressures of the same order of magnitude of predicted crystallization pressures can be attained. Alternatively, it could be argued that a significantly lower crystallization pressure (few tens of MPa) could easily develop in our system, and generate stress on the surrounding confining fluid within an etch pit as to trigger a phenomenon of stress corrosion [START_REF] Ciccotti | Stress-corrosion mechanisms in silicate glasses[END_REF], enabling the opening of a crack at the tip of wedge-like dissolution pits or pre-existing cracks at crystallization pressures significantly lower than those calculated here.

Once crack opening has taken place, further propagation of the cracks would take place by additional crystallization of Na-phillipsite within such a constrained space, provided that such a phase crystallizes at a sufficiently high supersaturation. The fact that our SEM and micro-CT images show augite crystals cross-cut by fractures completely filled by Na-phillipsite, leading to a very wide fractures (widths of more than several tens of μm) is direct evidence that crystallization pressure was exerted, enabling fracture propagation. This should be facilitated by the fact that once fractures have been opened, the effective bulk modulus will be a fraction of the modulus of the intact crystal.

A similar approach could be used to calculate the effective pressure and supersaturation at the onset of MSH crystallization within diopside crystals, leading to its fracturing. In this case, however, the level of reaction-driven fracturing was more limited (i.e., no large, cross-cutting fractures were observed), but in any case, reaction-driven stresses larger than the tensile strength of diopside had to be generated to produce the observed fractures filled by MSH. Because MSH is an amorphous gel-like material, and its solubility should be relatively high, a sufficient high supersaturation as to create enough crystallization pressures to fracture diopside is unlikely.

However, it could be argued that fracturing takes place not by crystallization pressure generation, but most likely via an expansion mechanism similar to that observed for ASR resulting in cement fracturing [START_REF] Rajabipour | Alkali-silica reaction: current understanding of the reaction mechanisms and the knowledge gaps[END_REF]. Amorphous silica gel hydration can reportedly result in pressures of over 20-30 MPa (Reinhardt and Mielich, 2012) and, in theory, pressures of up to 400

MPa could be generated during alkali-silica reaction (ASR, [START_REF] Ichikawa | Modified model of alkali-silica reaction[END_REF]. If a stress corrosion effect takes place concurrently, fracture opening and propagation would likely take place even at the relatively low gel hydration pressures above indicated.

Large amounts of calcite were identified within fractures generated in the NaHCO 3 system during augite carbonation. It could therefore be argued that calcite crystallization also contributed to fracture generation, as reported for newly formed carbonates during primary silicate mineral carbonation [START_REF] Kelemen | Rates and mechanisms of mineral carbonation in peridotite: natural processes and recipes for enhanced, in situ CO2 capture and storage[END_REF][START_REF] Kelemen | Reaction-driven cracking during retrograde metamorphism: Olivine hydration and carbonation[END_REF]. However, due to the no contact between calcite and the fracture walls cross-cutting augite crystals observed in the Micro-CT analyses (Figure 4e), as well as SEM-EDS (Figure 4b) results showing that Na-phillipsite is directly in contact with augite walls, whereas calcite precipitated on the surface of the pyroxene and in contact with the newly formed zeolite, we conclude that calcite did not generate the cracks but likely contributed to their widening.

The fact that no pervasive fractures were observed in any other experiments despite the precipitation of calcite and amorphous silica, demonstrates that the supersaturation at the onset of crystallization of these phases within preexisting cracks and newly-formed dissolution (wedge-like) etch pits was not high enough to generate an effective pressure higher than the tensile strength of the pyroxene crystals. Similarly, possible expansion due to amorphous silica gel by a process similar to ASR, was not sufficient to create any fracturing.

In addition to the above-mentioned mechanisms, other reaction-driven fracturing mechanism have been proposed. [START_REF] Jamtveit | Accelerated hydration of the Earth's deep crust induced by stress perturbations[END_REF] explored the idea that fracture generation was caused by tensile stress generation due to solid volume decrease during mineral dissolution. However, this kind of process is ruled out here based on the absence of fracture generation during augite and diopside reactions in runs were no Na-phillipsite or MSH precipitated, but still dissolution occurred and a certain degree of replacement was obtained. [START_REF] Zhu | Experimental evidence of reaction-induced fracturing during olivine carbonation[END_REF] suggested that volume expansion of carbonated areas in porous granular aggregates of olivine, could induce tensile stresses and associated fracturing in non-reacted areas resulting in a crack pattern very similar to dryingcracks. However, such an effect is not observed in any of our experiments. Note that Zhu et al.

(2016) experiments showed intergranular cracks whereas our experiments resulted in intragranular cracks.

Typically, precipitation of newly formed phases during replacement reactions such as silicate carbonation can passivate the reaction by decreasing the reactive surface area in turn reducing porosity and permeability (e.g. [START_REF] Emmanuel | Impact of nano-size weathering products on the dissolution rates of primary minerals[END_REF][START_REF] Lorenzo | Dissolution-Recrystallization of (Mg,Fe)CO 3 during Hydrothermal Cycles: Fe II /Fe III Conundrums in the Carbonation of Ferromagnesian Minerals[END_REF].

Dissolution processes without crack development can create porosity and increase the reactive surface area [START_REF] Lafay | Intracrystalline reaction-induced cracking in olivine evidenced by hydration and carbonation experiments[END_REF], especially if wormholing (channelized dissolution) takes place [START_REF] Ott | Wormhole formation and compact dissolution in single-and two-phase CO 2 -brine injections[END_REF]. However, our results show that in the case of the studied pyroxenes, dissolution without pervasive cracking does not enable a significant advance of the replacement reaction.

Conversely, our results demonstrate that reaction-driven fracturing due to crystallization pressure generation [START_REF] Scherer | Crystallization in pores[END_REF][START_REF] Schiro | Damage mechanisms of porous materials due to in-pore salt crystallization[END_REF] likley associated with stress corrosion, or amorphous MSH gel expansion, is critical for the advance of silicate dissolution and carbonate precipitation, because it increases the permeability of the substrate and the available reactive surface area [START_REF] Kelemen | Rates and mechanisms of mineral carbonation in peridotite: natural processes and recipes for enhanced, in situ CO2 capture and storage[END_REF][START_REF] Kelemen | Reaction-driven cracking during retrograde metamorphism: Olivine hydration and carbonation[END_REF].

Origin of the differences in carbonation behavior of diopside and augite

Despite their very similar chemical composition and structure, augite and diopside display a very different dissolution and carbonation behavior. In particular, a systematically higher extent of augite dissolution and carbonation was observed (Table 1). Previous studies showed that augite has a higher dissolution rate than diopside over a whole range of pHs [START_REF] Mcadam | Preferential low-pH dissolution of pyroxene in plagioclase-pyroxene mixtures: Implications for martian surface materials[END_REF][START_REF] Schott | Formation, growth and transformation of leached layers during silicate minerals dissolution: The example of wollastonite[END_REF]. Furthermore, previous works on dissolution of iron-bearing pyroxenes [START_REF] Siever | Dissolution kinetics and the weathering of mafic minerals[END_REF][START_REF] Hoch | The effect of iron content and dissolved O 2 on dissolution rates of clinopyroxene at pH 5.8 and 25 C: preliminary results[END_REF] showed that they present a higher dissolution rate than noniron-bearing pyroxenes due to the formation of highly insoluble Fe-oxides and hydroxides that shift the equilibrium to the product side. In particular, [START_REF] Hoch | The effect of iron content and dissolved O 2 on dissolution rates of clinopyroxene at pH 5.8 and 25 C: preliminary results[END_REF] showed that the higher dissolution rate of augite as compared with diopside was related to the oxidation of iron present in higher amounts in the former clinopyroxene. Our augite crystals include 2.3 mol% Fe, while diopside includes 1.7 mol% Fe. The higher Fe content in augite likely contributed to its faster dissolution according to the effect indicated above. Furthermore, we suggest that the presence of Na and Al in augite contributed both to a faster release of divalent metals and silicate species to the solution and to the formation of secondary Na-aluminosilicates, thereby increasing the overall dissolution rate of this pyroxene [START_REF] Berger | Dissolution rate of a basalt glass in silica-rich solutions: implications for long-term alteration[END_REF]. Altogether, our results suggest that the presence of Al and the faster and ultimately higher release of Si, Fe, alkali, and alkaline-earth metals to the solution in the case of augite fostered, on the one hand, the shift of the dissolutioncarbonation reaction to the products side and, on the other hand, the precipitation of secondary phases in etch pits and surface pores/cracks at a sufficiently high supersaturation as to generate crystallization pressure sufficient to result in massive fracturing and a significant increase in reactive surface area. These two effects created a strong positive dissolution-precipitation feedbackloop in the case of augite, which was not so strong in the case of diopside, thereby explaining the observed higher conversion and carbonate yield.

Conclusions

The implications of the results obtained during this work are manifold. A critical aspect highlighted by our results is the important role of secondary phase precipitation on the advancement of the reactions, not contemplated in the conversion of pyroxenes into carbonates. The formation of secondary iron oxides and crystalline and amorphous secondary silicates provides a free energy contribution to the system, allowing the progress of the carbonation reaction. The high amounts of secondary phases observed in augite experiments with DIC in solution enhanced the progress of the reaction as compared with pure water, while in diopside systems, the small amount of secondary phases did not enhance this progress. These results show that the presence of DIC in the system is crucial for the progress of the reaction, acting as a generator of secondary phases that contribute to shift the reaction towards the product side, but the effectiveness of this process is strongly dependent of the specific crystal chemistry of the pyroxenes.

Also, we show the formation of secondary phases filling dissolution pits and fractures whose precipitation was, in theory, thermodynamically not possible in our systems. This demonstrates that these latter transformations could only be achieved by an interface-coupled dissolution-precipitation mechanism, where supersaturation with respect to specific phases could be reached at the interface between the mineral and the solution [START_REF] Putnis | Mineral replacement reactions[END_REF], Putnis 2014, Ruiz-Agudo et al. 2012, 2016).

Another important outcome of this work was the effect of pH in the systems' evolution. The advancement of the reaction was strongly pH-dependent, showing higher dissolution rates in moderately-alkaline than in strongly alkaline pH systems. This effect has a direct impact on the formation of secondary phases, fostering their precipitation in large amounts in the former case and hampering the progress of the reaction in the latter.

Our experimental results also demonstrate that the in-pore crystallization of secondary crystalline phases (Na-phillipsite) and, to a lesser extent amorphous ones (MSH), is responsible of the fracture generation and propagation during dissolution-carbonation processes. We show that the reaction-driven fracturing derives from crystallization pressure, and in the case of MSH, most likely due to gel expansion. In both cases stress corrosion should also contribute to the observed crack development. Reaction-driven fracturing is shown to be crucial for the progress of the dissolution/carbonation reaction, because it exposes fresh reactive mineral surface and enables fluid transport within pyroxene crystals. The calculated critical stress for pyroxene (augite) fracture is ~100 MPa. This value implies that fracturing will likely occur during clinopyroxene carbonation in real GCS scenarios, down to a depth of ~4 km, when the lithostatic pressure equals such pressure.

Note that if the lithostatic pressure (plus pore fluid pressure) were higher than the stress associated to secondary silicate formation, then no fracturing would take place [START_REF] Malvoisin | Control of serpentinisation rate by reaction-induced cracking[END_REF]. Our results therefore show that reaction-driven fracturing of pyroxenes would be a major contributor to CO 2 mineral capture during standard low-to-medium depth GCS.

Finally, we experimentally demonstrate that the amount of Al, Fe (and Na) ions in the pyroxenes has a strong effect during dissolution-carbonation processes, explaining why augite, which includes a higher Fe, Na, and Al content than diopside, shows the highest dissolution rate and the highest conversion and carbonate yield.

Altogether, these results provide relevant information to be considered for the enhancement of the GCS using silicate carbonation strategies. In particular, this study sheds light on the Tables Table 1. Results of the quantitative Rietveld analysis (wt%) after normalization to amorphous phase content determined using mass balance analysis. Data for pyroxene samples after 28 days of reaction. The last two columns report the extent of carbonation (i.e., mass fraction of pyroxene converted into calcium carbonate) calculated using Rietveld refinement (ξn RR ) and mass balance (ξn MB ).

Reactant Augite Diopside

Figure 1 .

 1 Figure 1. Chemistry of solutions during augite and diopside dissolution and carbonation. Error bars show standard deviation of both replicas. Total concentration of aqueous calcium (a), magnesium (c) and silicon (e) in augite experiments; Total concentration of aqueous calcium (b), magnesium (d) and silicon (f) in diopside experiments; pH of augite (h) and diopside (i) experiments. Solid lines are used as a guide to the eye.

Figure 3 .

 3 Figure 3. Products of the reaction of diopside in water (pH 7.5): (a) Time evolution of the crystalline phases content determined by XRD Rietveld analysis (error bars show standard deviation). (b) SEM-EDS compositional map showing calcite (Cal) crystals in the dissolution pits of diopside (Di) after 14 days reaction. (c) SEM image and EDS compositional variation of Ca, Si and C along the red line in (b). (d) µ-Raman spectra of calcite crystal formed on our experiment, along with that of calcite reference (RRUFF database). (e) SEM-EDS compositional map showing diopside (Di) after 28 days of reaction including a Si-bearing phase (SiO 2 ) inside a dissolution pit and on the surface of the pyroxene. The inset shows the SEM image of the reacted diopside crystal.

Figure 4 .

 4 Figure 4. Products of the reaction of augite in NaHCO 3 solution: (a) Time evolution of the crystalline phases content determined by XRD Rietveld analysis (error bars show StDev). (b) SEM image of augite (aug) crystal after 28 days of reaction, overlaid with EDS compositional map showing phillipsite (phi) and a few crystals of calcite (cal) inside the fractures and on the augite surface. The inset shows the SEM image of the reacted crystals displaying pervasive craking. (c) SEM-EDS compositional map showing calcite (cal) crystals on the surface of augite (aug) and iron oxides (Fe-Ox) in dissolution areas. (d) µ-Raman spectra of newly formed calcite (the spectra of reference calcite -RRUFF database-is also shown). (e) Micro-CT image showing in red the 3D distribution of phillipsite (phi) and in purple that of calcite (cal) in an augite crystal after 28 days of reaction. The red dotted line on the left image represents the virtual cut displayed on the right image.

Figure 7 .

 7 Figure 7. Products of the reaction of diopside in Na 2 CO 3 solution: (a) SEM-EDS compositional map showing a proto magnesium silicate hydrate (MSH) and calcite particles (cal) on the surface of diopside (di). The right SEM image shows the entire crystal after reaction. (b) SEM-EDS compositional map showing MSH in the dissolution pits and fractures of diopside (di) with calcite crystals (cal). (c) Micro-CT image showing the 3D distribution of MSH (red) and calcite (purple) in diopside crystal after 28 days of reaction. The red dashed line in the left image represents the virtual cut performed to observe the inside of the crystal, shon on the right image. (d) FTIR spectra of the diopside before and after 28 days reaction in Na 2 CO 3 solution. (f) µ-Raman spectra of the diopside reacted 28 days in Na2CO 3 solution showing the bands corresponding to MSH (Lothenbatch et al., 2015) and the spectrum of diopside from RRUFF database.

Figure 8 .Figure 9 .

 89 Figure 8. PHREEQC simulations of saturation index (SI) evolution vs. pH for calcite and sodium zeolite during augite mineral replacement reaction at equilibrium. The red dashed line represents equilibrium (i.e., SI = 0).

  The composition of diopside crystals used in this study is Ca 0.97 Mg 0.84 Fe 0.17 Si 2 O 6 , whereas that of augite crystals is Na 0.05 Ca 0.86 Mg 0.76 Fe 0.23 Ti 0.07 Al 0.3 Si 1.7 O

6 , as calculated from ICP-OES analysis after acid digestion of the unreacted mineral (see details below). No minor phases were detected by X-ray diffraction (XRD) in diopside crystals. However, rutile (TiO 2 ) traces were detected in the augite crystals (see below).

Phillipsite-Na Hematite Calcite SiO 2 MSH ξ n

						RR	ξ n MB
	Water	83.97	9.86	0.85	2.61 2.16	0.0016 0.0018
	NaHCO 3 61.93	12.39	2.01	21.71 2.09	0.1669 0.1842
	Na 2 CO 3 96.34	0	1.05	2.65	0.0131 0.0147
	Water	96.73		0.37	1.23 1.62	0.0004 0.0004
	NaHCO 3	86.32		0.81	11.5 1.27	0.0328 0.0379
	Na 2 CO 3	93.09			2.13	5.01 0.0011 0.0012

Table 2 .

 2 Free energy (kJ.mol -1 ) values for all experiments calculated using PREEQC and experimental values obtained by ICP-OES of the ionic concentration in solution and measured pH after each experiment.

ACKNOWLEDGMENTS

This research has been funded by the Spanish Government (grant CGL2015-70642-R), the European Commission (ERDF funds), the Junta de Andalucía (research group RNM-179), and the University of Granada (Unidad Científica de Excelencia UCE-PP2016-05). LMG acknowledges funding by the Spanish Government FPI (Grant BES-2016-078468). We thank Prof. George W.

Scherer for his comments and suggestions regarding reaction-driven stress generation. We also thank the personnel of the Centro de Instrumentación Científica (CIC; University of Granada) and the personnel of the ISTerre for assistance with ICP-OES, Micro-CT, and SEM analyses. The use of the analytical chemistry platform of ISTerre is acknowledged.

importance of the silicate mineral composition of rock formations during in situ CCS, showing the importance of secondary (alumino)silicate formation on reaction-driven fracture development, providing flow channels and fresh reactive surface areas to improve the carbonation reaction.