Chiara Marieni
email: chiara.marieni@get.omp.eu

Martin J Voigt

Eric H Oelkers

GEOCHIMICA et COSMOCHIMICA

Keywords:

The dissolution rates of Green Monster Mine epidote at temperatures of 25, 100 and 200 °C, and over the pH range 2-11, were determined from far-from equilibrium experiments performed in both batch and mixed-flow reactors. Epidote dissolution rates based on silicon release decrease with increasing pH to pH ~8, then increase in response to further pH increases. The apparent relative metal release rates from epidote at chemical steady-state were found to vary with pH and temperature, in part due to secondary phase formation. At 100 and 200 °C, Al is preferentially released relative to Si at alkaline pH, but preferentially retained by the solid at 2<pH<8. This behaviour is interpreted to stem from the precipitation and re-dissolution of Al oxy-hydroxides such as boehmite, diaspore, and gibbsite, as observed in solids recovered after the experiments. Calcium tends to be preferentially released compared to Si and Al at acidic and near to neutral pH. Iron was found to be retained in the solid phase due to the prompt formation of secondary Fe minerals.

Nevertheless, neither the dissolution of 20 wt% of the initial epidote mass nor the formation of secondary phases on the epidote surface substantially changed epidote dissolution rates.

As epidote i) is almost three times more Ca-rich than a typical basaltic glass, ii) preferentially releases Ca at pH typical of CO 2 -charged water injections, and iii) exhibits increasing dissolution rates as pH increases at alkaline conditions, it seems likely that the presence of epidote in altered basalts may be beneficial for the formation of calcite and other Cacarbonates during mineral carbonation efforts. In addition, the relatively rapid rates of epidote dissolution at acidic conditions suggest that epidote has a significant role in the weathering of altered mafic rocks.

INTRODUCTION

Epidote (Ca 2 FeAl 2 (SiO4) 3 (OH)) is a common secondary alteration mineral often found in veins or replacing plagioclase in hydrothermally altered basic igneous rocks at temperatures of 200 to 400 °C (e.g., [START_REF] Kristmannsdóttir | Alteration of basaltic rocks by hydrothermal activity at 100-300 °C[END_REF][START_REF] Seyfried | Hydrothermal alteration processes at midocean ridges; constraints from diabase alteration experiments, hot spring fluids and composition of the oceanic crust[END_REF]. Epidote is also a major phase in low to medium grade regional and contact metamorphic rocks [START_REF] Grapes | Epidote group minerals in low-medium pressure metamorphic terranes[END_REF]. Epidote dissolution plays a role in a number of natural and industrial processes. In nature, it can influence the weathering of volcanic terrains [START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF][START_REF] Sverdrup | Estimating field weathering rates using laboratory kinetics[END_REF] as well as the water chemistry in geothermally active areas at high temperature [START_REF] Bird | Epidote in Geothermal Systems[END_REF]. Epidote dissolution can also promote subsurface mineral carbonation efforts by releasing Ca into the fluid [START_REF] Marieni | Carbon sequestration potential of altered mafic reservoirs[END_REF]Oelkers et al., 2008a).

Relatively few studies have experimentally measured epidote dissolution rates [START_REF] Blanchard | Epidote dissolution kinetics: An experimental study at 250°C and 500 bars between pH 3.4 and pH 12[END_REF][START_REF] Kalinowski | Dissolution kinetics and alteration of epidote in acidic solutions at 25 °C[END_REF][START_REF] Nickel | Experimental dissolution of light and heavy minerals in comparison with weathering and intrastratal solution[END_REF][START_REF] Rochelle | Fluid-rock interaction in the Miravalles geothermal field, Costa Rica[END_REF][START_REF] Rose | Dissolution rates of prehnite, epidote, and albite[END_REF][START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF], and fewer explored these rates at alkaline conditions (see Table 1).

Dickson-type autoclave experiments at 250 °C and 500 bars performed by [START_REF] Blanchard | Epidote dissolution kinetics: An experimental study at 250°C and 500 bars between pH 3.4 and pH 12[END_REF] and [START_REF] Rochelle | Fluid-rock interaction in the Miravalles geothermal field, Costa Rica[END_REF] showed that Ca and Si are the main cations released to the aqueous fluid phase, whereas liberated Al and Fe tend to precipitate as sparingly soluble secondary phases such as Al oxy-hydroxides and hematite, respectively, in oxic and near to neutral pH conditions. These studies also highlighted how fluid composition changes can alter the epidote dissolution mechanism and can accelerate its dissolution. For example, [START_REF] Blanchard | Epidote dissolution kinetics: An experimental study at 250°C and 500 bars between pH 3.4 and pH 12[END_REF] reported that adding fluoride to the aqueous solution increased the Al release rate from epidote due to the formation of strong aqueous AlF complexes. Kinetic studies at lower temperatures (≤90 °C) demonstrated that epidote dissolution rates vary with fluid pH, with more rapid rates observed at low and high pH, and the slowest rates were measured at near to neutral conditions [START_REF] Kalinowski | Dissolution kinetics and alteration of epidote in acidic solutions at 25 °C[END_REF][START_REF] Nickel | Experimental dissolution of light and heavy minerals in comparison with weathering and intrastratal solution[END_REF][START_REF] Rose | Dissolution rates of prehnite, epidote, and albite[END_REF][START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF]. [START_REF] Rose | Dissolution rates of prehnite, epidote, and albite[END_REF] reported that epidote dissolution at 90 °C and pH<7 is stoichiometric with respect to Si, Al, and Ca. At pH>7, this author observed an initial preferential release of Al and Si, suggesting the formation of a Ca-enriched surface layer. Contrasting results were reported by [START_REF] Nickel | Experimental dissolution of light and heavy minerals in comparison with weathering and intrastratal solution[END_REF] and [START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF], who observed the preferential release of Al and Ca from epidote at acidic conditions. [START_REF] Kalinowski | Dissolution kinetics and alteration of epidote in acidic solutions at 25 °C[END_REF] found that in experiments at 25 °C, some cations are preferentially released in fluids with pH<7 in the order Ca>Si>Fe>Al. Such observations suggests that i) Ca ions in the interchain position are the most easily released from the epidote structure, ii) Si is released from the framework during a surface protonation reaction, iii) Al ions, having high degrees of polymerisation, are the most firmly bound cations, and iv) the dissolution behaviour of epidote is often incongruent and overall a complex process. Similar conclusions were reached by [START_REF] Barman | Weathering of silicate minerals by organic acids. I. Nature of cation solubilisation[END_REF] during their study on the effect of selected aqueous organic acids on the weathering of silicate minerals.

This study builds upon these past efforts by systematically measuring the dissolution rates of epidote as a function of temperature from 25 to 200 °C, and pH from 2 to 11. The goals of this work are 1) to complement the existing knowledge on epidote with further experimental data towards developing a predictive equation describing epidote dissolution rates, and 2) to use these results to assess the consequences of epidote dissolution rates on natural geochemical phenomena and industrial processes.

MATERIAL and METHODS

Starting solutions and materials

Experiments in this study were performed in batch and mixed-flow reactors with selected reactive fluids. All initial reactive fluids were prepared from reagent grade chemicals (HCl, NaOH, NaCl, and NaHCO 3 ) and ultrapure water (18.2 MΩ cm -1 at 25 °C, Millipore), with pH ranging from ~2 to ~11. The compositions of these fluids are reported in Table 2. All initial reactive fluids had low ionic strength (<0.1 M) to minimize possible effects of ionic strength on measured dissolution rates.

The epidote used for all the dissolution experiments originated from the Green Monster Mine, Alaska, USA. This mineral sample is relatively free of defects and impurities. Epidote is a monoclinic calcium silicate and a member of the sorosilicate group (Figure 1). Its structure is characterized by two linked silicate tetrahedra (Si 2 O 7 ), along another single Sitetrahedron and continuous chains of Al-octahedra. The chemical composition of this epidote was determined by X-ray fluorescence spectrometry (XRF) using a S2 ranger Bruker spectrometer; this composition is provided in Table 3 and consistent with Ca 2.07 Al 2.00 (Al 0.08 Fe 3+ 1.02 Mn 0.01 K 0.01 S 0.01 Ti 0.01 )Si 3.00 O 12 OH, which conforms closely with the idealized epidote formula. The epidote sample was manually ground and sieved to obtain the grain size fraction between 20 and 100 µm (Figure 2). The 20-100 µm sample was ultrasonically cleaned in alcohol and rinsed repeatedly with deionized water to remove fine particles before being dried at 50 °C. Its specific surface area was measured by multipoint Krypton adsorption BET method using a Quantachrome Autosorb-1MP, and determined to be 863±5% cm 2 /g (correlation coefficient 0.9997). Its geometric specific surface area was calculated to be 350 cm 2 /g, assuming that grains are smooth spheres with a 50 µm diameter [START_REF] Tester | Correlating quartz dissolution kinetics in pure water from 25 to 625 °C[END_REF].

Experimental methods

Epidote steady-state far-from equilibrium dissolution rates were determined from Si release rates as function of pH and temperature. At 25 °C, these experiments were performed in batch reactor systems due to the relatively slow reaction rates. At 100 and 200 °C, rates were measured using the mixed-flow reactor system illustrated in Figure 3. The initial conditions of all experiments are listed in Table 2.

Batch reactor experiments

Batch-reactor experiments were performed in 250 mL Azlon polypropylene reactors, each loaded with ~2 g of 20-100 µm sized epidote, ~150 g of initial aqueous reactive fluid, and a floating polytetrafluoroethylene (PTFE)-coated magnetic stir bar. The reactors were covered with custom-made polyether ether ketone (PEEK) lids with two sampling ports: one for the collection of liquid samples (~1 mL each) for elemental analysis via a 0.2 µm PTFE filter and syringe, and a second for in situ pH measurements. All batch reactors were immersed in a water bath, which i) was held at a constant temperature of 25±0.2 °C by a thermostat control system, and ii) was positioned on a magnetic stir plate to keep the epidote powder in suspension by stirring at ~200 rpm.

Each batch reactor was cleaned with ultrapure water and ethanol before each experiment. At the end of batch experiments, the solid reaction products were separated from the liquid by filtration through a 0.45 µm cellulose acetate membrane, rinsed with ultrapure water, and dried at room temperature. All filtered fluid samples were acidified with 0.3% Suprapur HNO 3 prior to storage and elemental analysis. Before each individual experiment or experimental series, the reactor was first cleaned with ultrapure water and ethanol, followed by filling it with ultrapure water and heating it up to 200 °C for several days. Each experiment was started by placing epidote and ultrapure water into the reactor, closing the reactor, and starting both the stirrer and the HPLC pump.

Mixed-flow reactor experiments

Mixed

Once the target pressure was reached, the reactor was heated to the desired temperature, which was reached within approximately 1 h in all experiments. The first liquid samples were taken after ~24 h, and the residence time was ~13 h. Further samples were collected over time. Such samples were collected over at least three residence times to assure the reactor fluid was completely mechanically mixed [START_REF] Oelkers | The mechanism, rates and consequences of basaltic glass dissolution: I. An experimental study of the dissolution rates of basaltic glass as a function of aqueous Al, Si and oxalic acid concentration at 25 C and pH= 3 and 11[END_REF]. Once three consecutive samples were found to have identical outlet fluid Si concentrations within analytical uncertainties, Si steady-state release rates were assumed and the experiment stopped. Fluid samples were collected in three separate polypropylene vials. Two nonacidified samples (~1 g each) were taken for pH measurement at room temperature and Si analysis, followed by a ~10 g sample for elemental analysis; this latter sample was acidified with 0.3% Suprapur HNO 3 to avoid precipitation of solid phases due to temperature and pressure changes. After the completion of an individual experiment or an experimental series, the reactor was opened and the solid reaction products were separated from the liquid by vacuum filtration through a 0.45 µm cellulose acetate membrane, rinsed with ultrapure water, and dried at 50 °C.

The experiments run at 100 °C were performed in series, a common technique in mineral and rock dissolution studies (e.g., [START_REF] Flaathen | The effect of aqueous sulphate on basaltic glass dissolution rates[END_REF][START_REF] Gudbrandsson | An experimental study of crystalline basalt dissolution from 2⩽ pH⩽ 11 and temperatures from 5 to 75 °C[END_REF][START_REF] Saldi | An experimental study of magnesite dissolution rates at neutral to alkaline conditions and 150 and 200°C as a function of pH, total dissolved carbonate concentration, and chemical affinity[END_REF] that optimizes time and repetition of work. Ten consecutive dissolution experiments were performed on a single epidote powder sample. The series was started by placing the epidote powder into the titanium mixed-flow reactor, and sealing it. The first inlet fluid was passed through the reactor at a constant flow rate until Si steady-state outlet fluid compositions were observed, as described above. After the attainment of steady-state, the inlet fluid composition was changed to a fluid of different composition and a new experiment started. The first inlet solution in the series had a pH of 2, and subsequent inlet solutions had increasingly higher pH, up to pH 11. After the pH 11 experiment, a duplicate run was made with a pH 2 inlet solution to verify that the running of these experiments in series and the potential precipitation of secondary minerals did not affect the measured epidote dissolution rates. Experiments at 200 °C were run individually because at this temperature epidote would dissolve too quickly to be reused in a succeeding experiments. For each of these experiments freshly cleaned epidote powder was reacted with a single inlet fluid until steady-state Si concentrations were observed in the outlet fluid. After the attainment of steady-state, the reactor was emptied and the solids collected for further analysis. Each experiment was stopped before 10 wt% of the initial epidote was dissolved.

Analyses

The fluids from the batch reactor experiments, along with inlet and outlet fluids of mixed-flow reactor experiments were analysed for their pH and Si concentrations. Liquid pH was measured using an Orion ROSS Ultra™ pH electrode connected to a Hanna Instruments™ pH meter. The electrode was calibrated using NIST pH 4.01, 7.00 and 10.01 buffer solutions, and replicate analyses of buffers and samples showed analytical accuracy of 0.03 pH units and precision of ±0.02 pH units at room temperature. For the 25 °C experiments, the fluid pH was measured in situ, whereas the in situ pH of the fluids from the experiments at 100 and 200 °C was recalculated from the 25 °C pH measurements using PHREEQC v3 [START_REF] Parkhurst | Description of input and examples for PHREEQC version 3: a computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF], together with its carbfix.dat v1.1 thermodynamic database [START_REF] Voigt | Evaluation and refinement of thermodynamic databases for mineral carbonation[END_REF]. The same approach was used to calculate the saturation indices of potential secondary phases. Silicon concentrations of the collected fluids in each experiment were measured daily by colorimetry using the molybdate blue method [START_REF] Strickland | The preparation and properties of silicomolybdic acid. I. The properties of alpha silicomolybdic acid[END_REF] following the procedure of [START_REF] Tréguer | Manuel d'analyse des sels nutritifs dans l'au de mer[END_REF].

Measured Si concentrations have an uncertainty (two standard errors) of ±5% for measurements between 0.05 and 10 ppm. Selected output solutions from each experiment were also analysed for Ca, Al, Fe, and Si concentrations using a Horiba Ultima Expert Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES), with an analytical accuracy within 3% and precision better than ±3%, as determined by replicate analyses of certified solutions and samples, respectively. Detailed information on detection limits and data uncertainties are given in Electronic Supplementary 1 and 2, respectively. Given the lower uncertainty of ICP-OES analyses, they were preferred over colorimetric measurements to calculate elemental release and epidote dissolution rates. For the case of batch reactor experiments at 25 °C, samples for spectrometric analyses were taken only at the end of the experiments as not to significantly alter the water-rock ratio in the reactors by sampling. As such, epidote dissolution rates from these experiments were calculated using Si colorimetric results. Nevertheless, the two methodologies for aqueous Si concentration measurement are in close agreement, with a coefficient of determination R 2 of 0.99 (Electronic Supplementary 3).

Microscopic analyses on the fresh epidote powder and the solid reaction products recovered from the reactors after each experiment were performed with a Jeol JSM7800F scanning electron microscope (SEM) equipped with an electron dispersive spectroscope (EDS).

Calculation of steady-state epidote dissolution rates

Epidote dissolution rates ( ) from the results of batch reactor experiments were Note that for the experimental series at 100 °C, the epidote mass at the beginning of each experiment of the series was calculated, based on the mass of Si released from the reactor during the previous experiments of the series. This calculated mass was used for rate calculations using Equation 2.

RESULTS

Temporal evolution of reactive fluid compositions

The Si composition and pH of the reactive fluids during the 25 °C batch reactor experiments evolved significantly (Table 4,Figure 4 Insight into the epidote dissolution process can be gained by considering the relative cation abundances in the reactive fluids. This is particularly true for the experiments performed at 100 °C, where the experimental design resulted in the precipitation and subsequent re-dissolution of some secondary phases. The relative cation release rates of various elements concentrations are provided in Table 5. If the elements were released stoichiometrically, the Ca/Si and Al/Si ratios would be 0.69, and the Fe/Si ratio would be 0.34. As shown in Table 5, the Fe/Si ratios were <0.1 in each experiment. For Ca, Al, and Si, the release at 100 and 200 °C was close to stoichiometric at pH 2 and 8, respectively.

Preferential release of Ca over Al and slightly over Si was observed in the experiments performed at 3<pH<9, and up to pH 10 at 100 °C, with Ca release rates at 200 °C and pH 3 fluids up to 147 times greater than of Al. Notably, the low Al/Si ratios suggest that Al was retained in a solid phase at these conditions. In contrast, at pH above pH 8 for both 100 and 200 °C experiments, Al is observed to be preferentially released compared to Si.

Solid alteration products

The epidote grains recovered at the end of the experiments at 25 °C showed no dissolution features or secondary phases despite up to 48 days of reaction, and thermodynamic calculations indicating that the reactive fluids were supersaturated at alkaline conditions (pH≥7) with respect to Fe-oxides, Al oxy-hydroxides, and various Al-silicates including zeolites. In contrast, the reacted solids collected at the end of the experiments performed at 100 and 200 °C were substantially altered compared to the starting material (see Figure 7). SEM images showed epidote grain surfaces collected after the 100 °C experiments were severely pitted and covered with extensive Fe-oxide precipitates. These Fe-minerals formed "crusts" that partially covered the dissolved epidote surfaces, especially along the grain edges. Often, the crusts were detached from the underlying grains, which The Fe-phases were present as either single crystals or agglomerates rather than as the "crusts" observed in the solids collected from the 100 °C experiments, and differences in their morphology were observed as a function of pH. Acicular and platy Fe-oxide crystals, morphologies likely associated with hematite and goethite [START_REF] Davidson | The kinetics and mechanisms of schwertmannite transformation to goethite and hematite under alkaline conditions[END_REF], were found at acidic pH (pH≤4), whereas an octahedral habit typical of magnetite [START_REF] Saldi | Mineralogical evolution of Fe-Si-rich layers at the olivine-water interface during carbonation reactions[END_REF] was found at basic conditions (pH≥8).

Epidote dissolution rates

Epidote dissolution rates in the present study are based on Si release rates. Retrieved rates are referred to as steady-state rates, as although Si steady-state release was observed, Ca, Al, and Fe were not released in stoichiometric quantities in every experiment (Table 5). Resulting rates, together with their uncertainty and in situ pH for all experiments are listed in Table 6 and (log) of measured rates ranged from a maximum of -14.98 mol/cm 2 /s at pH 2 to a minimum of -16.07 mol/cm 2 /s at pH 7. The uncertainty on these rates was estimated to be lower than ±0.11 log units (two standard errors), based on the sum of the uncertainties associated with fluid composition, BET surface area measurements, and uncertainties of the slopes calculated during least squares regression.

At 100 °C, the total epidote mass dissolved throughout the experimental series was ~20 wt%, based on mass balance calculations using aqueous Si concentrations. The minimum epidote logarithmic dissolution rate was determined to be -14.40 mol/cm 2 /s at pH 9, which is almost two orders of magnitude higher than that observed at 25 °C and at alkaline conditions. The steady-state logarithmic rates at pH 2, determined from experiments run at the beginning and end of the experimental series, were found to be almost identical with values of -12.30 and -12.37 mol/cm 2 /s, respectively. The rate difference is within the uncertainty of the rate measurements, which for all these mixed-flow reactor experiments was estimated to be ±0.04 log unit (two standard errors), based on the sum of the uncertainties associated with fluid flow, fluid composition, and BET surface area measurements. At 200 °C, the epidote dissolution rates were found to be ~1 order of magnitude higher than corresponding rates determined at 100 °C, with a minimum logarithmic value of -13.18 mol/cm 2 /s measured around pH 8. increasing the fluid pH to ~5.5 (e.g., [START_REF] Ganor | Surface protonation data of kaolinite-reevaluation based on dissolution experiments[END_REF][START_REF] Guy | Multisite surface reaction versus transport control during the hydrolysis of a complex oxide[END_REF][START_REF] Oelkers | The surface chemistry of multi-oxide silicates[END_REF]. It is unlikely that the rapid pH increase observed during the pH 4 experiment is due to the presence of fine particles as this behaviour was not observed in the experiments performed at pH 2. In contrast, the pH decreases markedly at pH 10; this potentially occurred due to the equilibration of the reactive fluid with atmospheric carbon dioxide (CO 2 ).

Similarly, the uptake of CO 2 by the fluid may have affected the pH evolution of the reactive fluid of the experiment run at an initial pH of 12, where the slower pH decrease with time compared to the pH 10 solution can be explained by the presence of a more strongly pH buffered initial solution (Table 2). Thermodynamic calculations performed with the initial fluid composition of pH 10 and pH 12 experiments equilibrated with a partial pressure (pCO 2 ) of 0.0004 atm confirm the possibility that the observed pH decrease was due to CO 2 gas dissolution into the reactive fluid. According to these calculations, if the fluids initially having pH of 10 and 12 were equilibrated with atmospheric CO 2 , their pH would reach values of 7.00 and 9.06, respectively, and contain up to 0.1 mmol/kg and 8 mmol/kg of CO 2 , respectively.

At 100 and 200 °C, the changes in the chemical composition of the reactive fluids are coherent with observations of the altered solids recovered at the end of these experiments.

A general preferential release of Ca was observed for reactive fluids with pH<9, in particular at acidic conditions, and no Ca-phase was detected or calculated to be supersaturated in these reactive fluids. Such observations suggest the exchange of Ca with protons present in the reactive fluids as previously observed for other Ca-bearing silicates such as wollastonite and diopside [START_REF] Oelkers | The surface chemistry of multi-oxide silicates[END_REF][START_REF] Schott | Formation, growth and transformation of leached layers during silicate minerals dissolution: The example of wollastonite[END_REF]. In contrast, the low Al/Si ratios of the reactive fluids at these same conditions, are likely due to the precipitation of secondary Alhydroxide phases; these fluids were calculated to be supersaturated relative to Al oxyhydroxide phases, such as boehmite, diaspore and gibbsite, at 2<pH<9. Moreover, the precipitation of such phases was confirmed directly through the analysis of the solids recovered after the experiment run at 200 °C with a pH 3 reactive fluid (Figure 7). The lack of Al-rich solid phases observed in the solids recovered from the experimental series run at 100 °C may be related to the experimental design. The running of sequential experiments with increasing pH in series likely caused the dissolution of previously formed Al-rich secondary minerals. This interpretation could explain the initial high Al concentrations in the experiment run at pH 9 (Figure 5), as the solubility of Al-containing minerals increases with pH [START_REF] Bénézeth | Aqueous high-temperature solubility studies. II. The solubility of boehmite at 0.03 m ionic strength as a function of temperature and pH as determined by in situ measurements[END_REF]. In contrast, Ca tended to be preferentially retained in the solid phase in experiment run at pH>8 at 200 °C, where Si and Al were released in a close to stoichiometric ratio (Table 5). No secondary phases were calculated to be stable in the reactive fluids used in these alkaline experiments, yet Ca-Ti-oxide crystals were detected at pH 10, and minor Na-Al-silicates at pH 8 and 10 (Figure 7). The precipitation of the Na-rich phase seems to not have significantly affected the reaction stoichiometry, with Al/Si release ratios being similar to that of the dissolving epidote. Similarly, due to the small quantity of Ca-Ti-oxide precipitated, it seem likely that this did not affect substantially the Ca/Si and Ca/Al ratios of the fluids (Table 5). The retention of Ca by the solid phase may reflect the formation of a Ca-rich surface layer on the dissolving epidote, consistent with the Ca-forproton exchange reaction at alkaline pH [START_REF] Oelkers | The surface chemistry of multi-oxide silicates[END_REF].

The relative apparent release rate of Fe is low in all experiments at both 100 and 200 °C (Table 5). The aqueous Fe 3+ released from epidote is unstable in the fluid phase for pH≥3 and Eh≥0.4, as Fe-oxides readily form [START_REF] Pourbaix | Atlas of electrochemical equilibria in aqueous solutions[END_REF]. These phases were observed in all the solids recovered after these experiments.

Effect of temperature on epidote dissolution rates

The dissolution rates of epidote at 100 °C were found to be up to ~2 log unit higher than corresponding rates at 25 °C, but only ~1 log unit lower than at 200 °C (Figure 8). The overall fastest cation release rates at 200 °C explains the observed abundant secondary phases in the solid samples recovered after the experiments run at these temperatures. For instance, the fast Al release rate at 200 °C and pH 3 leads to a more substantial supersaturation of Al oxy-hydroxide phases. In turn, supersaturation with various minerals leads to their rapid precipitation leading to the decrease of Al/Si towards zero (Table 5).

Comparison with literature data

All epidote dissolution rates determined in this study are compared with the results of previous experimental studies in Figure 9. A good consistency is evident amongst most of the different datasets. For all the studied temperature conditions, the most pH-sensitive rates were found for acidic pH as suggested by [START_REF] Nickel | Experimental dissolution of light and heavy minerals in comparison with weathering and intrastratal solution[END_REF], [START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF][START_REF] Blanchard | Epidote dissolution kinetics: An experimental study at 250°C and 500 bars between pH 3.4 and pH 12[END_REF], but in contrast to those proposed by [START_REF] Rose | Dissolution rates of prehnite, epidote, and albite[END_REF]. At 25 °C, the rates obtained in this study from batch reactor experiments are closely consistent with corresponding rates reported by [START_REF] Nickel | Experimental dissolution of light and heavy minerals in comparison with weathering and intrastratal solution[END_REF], [START_REF] Rose | Dissolution rates of prehnite, epidote, and albite[END_REF] and [START_REF] Kalinowski | Dissolution kinetics and alteration of epidote in acidic solutions at 25 °C[END_REF], but are up to ~2 log unit slower than the corresponding rates reported by [START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF]. Note that the epidote dissolution rates reported by [START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF] were obtained on the dissolution of zoisite from the sum of released base cations rather than from Si release (see Table 1). This could be the reason of such discrepancies. At 100 °C, rates determined in the present study agree well with those of [START_REF] Rose | Dissolution rates of prehnite, epidote, and albite[END_REF] at 90 °C up to pH 9. In contrast, there exist significant differences among rates reported at higher temperature [START_REF] Blanchard | Epidote dissolution kinetics: An experimental study at 250°C and 500 bars between pH 3.4 and pH 12[END_REF][START_REF] Rochelle | Fluid-rock interaction in the Miravalles geothermal field, Costa Rica[END_REF], perhaps due to the distinct buffer solutions used in the different experiments. The buffers used in the 250 °C experiments of [START_REF] Blanchard | Epidote dissolution kinetics: An experimental study at 250°C and 500 bars between pH 3.4 and pH 12[END_REF] and [START_REF] Rochelle | Fluid-rock interaction in the Miravalles geothermal field, Costa Rica[END_REF] contained acetate and Na-fluoride. The presence of these aqueous components may affect epidote dissolution rates, as has been seen for other silicate minerals (Golubev et al., 2006;Golubev and Pokrovsky, 2006;[START_REF] Harouiya | An experimental study of the effect of aqueous fluoride on quartz and alkali-feldspar dissolution rates[END_REF][START_REF] Pokrovsky | Effect of organic ligands and heterotrophic bacteria on wollastonite dissolution kinetics[END_REF][START_REF] Wolff-Boenisch | The effect of fluoride on the dissolution rates of natural glasses at pH 4 and 25°C[END_REF].

The preferential initial release of Ca at acidic pH was reported by [START_REF] Nickel | Experimental dissolution of light and heavy minerals in comparison with weathering and intrastratal solution[END_REF], [START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF], and [START_REF] Kalinowski | Dissolution kinetics and alteration of epidote in acidic solutions at 25 °C[END_REF]. Such release was also observed in this study indirectly at 25 °C from surface protonation, and directly at 100 and 200 °C through aqueous Ca measurements. As Ca ions are not part of the epidote framework, it is generally agreed that the first step of its dissolution is the relatively fast removal of alkaline earth metals at acidic conditions through proton exchange reactions (e.g., [START_REF] Guy | Multisite surface reaction versus transport control during the hydrolysis of a complex oxide[END_REF][START_REF] Oelkers | General kinetic description of multioxide silicate mineral and glass dissolution[END_REF]. In contrast, no conclusions can be made for exchange reactions of other metals because of the formation of secondary minerals.

Epidote dissolution mechanisms

The far from equilibrium dissolution rate is controlled by the fastest pathway available for breaking the slowest bond structurally crucial for the mineral. As shown for many Alsilicates, such as albite, kaolinite, and basaltic glass [START_REF] Oelkers | The mechanism, rates and consequences of basaltic glass dissolution: I. An experimental study of the dissolution rates of basaltic glass as a function of aqueous Al, Si and oxalic acid concentration at 25 C and pH= 3 and 11[END_REF][START_REF] Oelkers | The effect of aluminum, pH, and chemical affinity on the rates of aluminosilicate dissolution reactions[END_REF], the epidote dissolution mechanism is most probably associated with the breaking of the Al-O structure through Al-proton exchange reactions, after the partial liberation of the adjoining Si tetrahedra. However, given the precipitation and re-dissolution of Al-hydroxide phases in several experiments in this study, this mechanism cannot be explored in detail with the obtained dataset. Following the approach of [START_REF] Palandri | A compilation of rate parameters of water-mineral interaction kinetics for application to geochemical modeling[END_REF], a more pragmatic rate model based only on protons activity was adopted for fitting epidote rate data.

In this model, the epidote dissolution rate is expressed as the sum of terms for the dissolution mechanisms driven by H + , OH -, and independent of pH as Arrhenius-type equations:

(3)

where indicates the BET surface area normalized steady-state epidote dissolution rate at far-from equilibrium conditions, refer to pre-exponential factors, designate the activation energies, stands for the gas constant, signifies temperature in K, denotes the hydrogen ion activity, and represents the reaction orders with respect to H + .

The values for , , and were calculated for acidic (A), neutral (N), and basic (B) conditions by non-linear least squares regression of all the experimental rate data of this study simultaneously. The Levenberg-Marquardt algorithm was used for optimization, and the fitting was carried out on the log-transformed data and rate equation so that residuals of each experimental data point are effectively weighted according to a constant relative uncertainty of each rate. Only results from this study were used to calibrate the equation i) to maintain consistency with respect to experimental and analytical procedures and the epidote sample, and ii) because it is the only dataset providing epidote dissolution rates throughout most of the pH scale and at several temperatures. Data from [START_REF] Sverdrup | The kinetics of base cation release due to chemical weathering[END_REF] were not considered because rates were measured on zoisite, a Fe-depleted epidote subgroup.

The modelled epidote dissolution rates resulting from the best-fit calculations are shown in Figure 10, and the best-fit parameter values listed in Table 7 along with the parameters proposed by [START_REF] Palandri | A compilation of rate parameters of water-mineral interaction kinetics for application to geochemical modeling[END_REF]. Lower activation energies, and different reaction orders were determined for epidote dissolution in comparison to those reported in the literature by [START_REF] Palandri | A compilation of rate parameters of water-mineral interaction kinetics for application to geochemical modeling[END_REF]. Overall, the uncertainty in the fitted parameters is much lower in the acidic and neutral regions due to the greater availability of measured rates. The scatter in rates obtained at basic conditions may suggest the presence of additional mechanisms, but some of these rates could be considered as outliers based on their reported uncertainties. The rates proposed by [START_REF] Rose | Dissolution rates of prehnite, epidote, and albite[END_REF] at 90 °C for pH ~8 and ~11

have reported uncertanty of ±0.2 log units, which exceeds the average relative error in the Rose study based on the uncertanty in temperature, pH, and regression of element release data. This uncertainty estimate does not account for the uncertainty on surface area measurements. In turn, the rate measured at 25 °C in this study for the reactive fluid with initial pH of 12 has the highest uncertainty associated with the rate measurement, and may have been affected by the effect of fluid equilibration with atmospheric CO 2 that at these conditions could have led to supersaturation with respect to calcite.

Implications for natural processes

The calculated epidote dissolution rates show that this mineral, as many other aluminosilicate solid phases (e.g., [START_REF] Casey | Dissolution rates of plagioclase at pH= 2 and 3[END_REF][START_REF] Gudbrandsson | An experimental study of crystalline basalt dissolution from 2⩽ pH⩽ 11 and temperatures from 5 to 75 °C[END_REF][START_REF] Oelkers | The mechanism, rates and consequences of basaltic glass dissolution: I. An experimental study of the dissolution rates of basaltic glass as a function of aqueous Al, Si and oxalic acid concentration at 25 C and pH= 3 and 11[END_REF], is relatively rapid at acid weathering conditions. This means that the presence of epidote is most likely to have a significant impact on the weathering of soils, as suggested by [START_REF] Sverdrup | Calculating field weathering rates using a mechanistic geochemical model PROFILE[END_REF], in particular of epidote-bearing rocks, such as mafic reservoirs. Moreover, it appears that aqueous Al concentration is a major rate inhibitor of the dissolution of many aluminosilicate minerals, such as feldspars, muscovite, and kaolinite (e.g., [START_REF] Oelkers | The effect of aluminum, pH, and chemical affinity on the rates of aluminosilicate dissolution reactions[END_REF]Oelkers et al., 2008b). As such, the rapid dissolution of epidote, with its high relative aluminium content (Table 8), could lead to the increase of aqueous fluid Al activity during its dissolution. This aluminium could slow the weathering rates of other minerals. Such effect needs to be taken into account during the evaluation of mineral dissolution in weathering profiles.

Implications for carbon storage

Mineral storage in mafic and ultramafic rocks through mineral carbonation has been considered by a plethora of studies. To date there is only one on-going industrial scale mineral carbonation, the CarbFix project in Iceland. This project is successfully mineralizing water-dissolved CO 2 through its reactions with fresh and altered basalt in the subsurface.

The carbon storage potential of fresh mafic rocks, such as basalt has been quantified by numerous experimental, modelling, and field studies (e.g., [START_REF] Clark | Experimental observations of CO 2 -water-basaltic glass interaction in a large column reactor experiment at 50 °C[END_REF][START_REF] Dessert | Basalt weathering laws and the impact of basalt weathering on the global carbon cycle[END_REF][START_REF] Galeczka | An experimental study of basaltic glass-H 2 O-CO 2 interaction at 22 and 50°C: Implications for subsurface storage of CO 2[END_REF][START_REF] Gislason | Carbon Storage in Basalt[END_REF][START_REF] Godard | Geological carbon capture & storage in mafic and ultramafic rocks[END_REF][START_REF] Goldberg | Carbon dioxide sequestration in deep-sea basalt[END_REF][START_REF] Gunnarsson | The rapid and cost-effective capture and subsurface mineral storage of carbon and sulfur at the CarbFix2 site[END_REF][START_REF] Gysi | Numerical modelling of CO 2 -water-basalt interaction[END_REF][START_REF] Gysi | CO 2 -water-basalt interaction. Low temperature experiments and implications for CO 2 sequestration into basalts[END_REF][START_REF] Kelemen | In situ carbonation of peridotite for CO 2 storage[END_REF][START_REF] Marieni | Experimental study on mafic rock dissolution rates within CO2-seawater-rock systems[END_REF][START_REF] Matter | Rapid carbon mineralization for permanent disposal of anthropogenic carbon dioxide emissions[END_REF][START_REF] Paukert | Reaction path modeling of enhanced in situ CO 2 mineralization for carbon sequestration in the peridotite of the Samail Ophiolite, Sultanate of Oman[END_REF][START_REF] Rosenbauer | Carbon sequestration via reaction with basaltic rocks: Geochemical modeling and experimental results[END_REF][START_REF] Schaef | Carbonate mineralization of volcanic province basalts[END_REF][START_REF] Snaebjörnsdóttir | Reaction path modelling of in-situ mineralisation of CO 2 at the CarbFix site at Hellisheidi, SW-Iceland[END_REF][START_REF] Snaebjörnsdóttir | Carbon dioxide storage through mineral carbonation[END_REF][START_REF] Wolff-Boenisch | Dissolution of basalts and peridotite in seawater, in the presence of ligands, and CO 2 : implications for mineral sequestration of carbon dioxide[END_REF]. These studies generally highlight the advantage of basalt for this purpose due to the fast release rates of cations such as Ca, which are crucial for mineral carbonation. However, many potential basaltic reservoirs for CO 2 mineral storage contain altered mafic rocks, particularly in geothermal systems (e.g., [START_REF] Browne | Hydrothermal alteration in active geothermal fields[END_REF] and ophiolites (e.g., [START_REF] Gillis | Patterns and processes of alteration in the lavas and dykes of the Troodos ophiolite, Cyprus[END_REF]. These rocks contain abundant secondary Cabearing silicates, such as epidote and amphiboles, which have also the potential to provide the cations necessary for mineral carbonation. Epidote is one of the main high temperature (>200 °C) alteration products of Ca-rich plagioclase; it can constitute up to 50 vol% of a crystalline basalt [START_REF] Marieni | Carbon sequestration potential of altered mafic reservoirs[END_REF]. Its Ca/Si ratio is higher than that of basalt, Ca-amphiboles such as actinolite, Ca-pyroxene such as diopside, and the common Caplagioclases, labradorite and anorthite (see Table 8). As such, it only takes ~20 tons of epidote to mineralize 1 ton of CO 2 as calcite compared to ~40 tons required by the Stapafell basaltic glass [START_REF] Oelkers | The mechanism, rates and consequences of basaltic glass dissolution: I. An experimental study of the dissolution rates of basaltic glass as a function of aqueous Al, Si and oxalic acid concentration at 25 C and pH= 3 and 11[END_REF]. Furthermore, the absence of Mg in epidote may limit the precipitation of some pore filling clays and chlorite, which compete with carbonate minerals for pore space. Note that results from the experiments performed in this study at 100 °C confirmed that Fe-oxide precipitates do not slow the epidote dissolution at pH 2 even after the dissolution of ~20 wt% of this mineral. As such, it seems unlikely that these precipitates will slow epidote dissolution in natural systems. In contrast, the Al/Si ratio of epidote is almost twice that of crystalline and glassy basalts (see Table 8), but is similar or lower than that of the Ca-pyroxene and the Ca-plagioclases. The high Al content of epidote could be a disadvantage for carbon storage because of the inhibitory effect of aqueous Al concentrations on dissolution rates of many aluminosilicate minerals, as discussed above.

A comparison of epidote dissolution rates with corresponding basaltic glass dissolution rates is presented in Figure 9. Epidote dissolution rates calculated from Si release rates at 25 °C are from one to three orders of magnitude lower than those of basaltic glass [START_REF] Gislason | Mechanism, rates, and consequences of basaltic glass dissolution: II. An experimental study of the dissolution rates of basaltic glass as a function of pH and temperature[END_REF]. The difference in these rates at 100 °C is somewhat lower at acidic pH, which represent the conditions of CO 2 -charged aqueous fluid injections in the current CarbFix project (e.g., [START_REF] Snaebjörnsdóttir | Reaction path modelling of in-situ mineralisation of CO 2 at the CarbFix site at Hellisheidi, SW-Iceland[END_REF], but increases again at 200 °C. However, the availability of divalent cations, such as Ca 2+ , Fe 2+ , and Mg 2+ , required for the mineralization of CO 2 must be considered to constrain carbon mineral storage efficiency.

The comparison of Ca release rates from epidote as well as from the other Ca-bearing silicates provide a more accurate comparison in this context (Figure 11). The higher Ca content in the epidote brings its predicted release rates closer to those of the other Casilicates. Ca release rates from epidote at 25 °C match, within one log unit of uncertainty, the Ca release rates from numerous other common silicate phases up to pH 8, and at 100 °C are as fast as basaltic glass rates up to pH 5. The observation that epidote can release Ca as fast as a fresh plagioclase suggests that alteration minerals can play a significant role in the carbon mineralization process, and that the absence or limited availability of the fresh basaltic glass in some systems can be overcome by the abundance of divalent metal rich secondary phases. Furthermore, the preferential release of Ca at pH<9 discussed above and the relatively fast pH increase from acidic towards alkaline conditions even at low temperature due to metal-proton exchange reactions, such as in the 25 °C experiments with initial reactive fluid pH of 4 (Figure 4), could further promote the precipitation of calcium carbonate (e.g., [START_REF] Snaebjörnsdóttir | Reaction path modelling of in-situ mineralisation of CO 2 at the CarbFix site at Hellisheidi, SW-Iceland[END_REF].

CONCLUSIONS

Epidote dissolution rates have been measured as a function of pH at temperatures from 25 to 200 °C. The major results include:

a) The epidote dissolution rates vary with pH in a manner similar to many other aluminosilicate minerals, where rates decrease with increasing pH at acidic conditions, minimize at near to neutral pH, and then increase with increasing pH at alkaline conditions (e.g., Hellman, 1994;[START_REF] Lammers | Muscovite dissolution kinetics as a function of pH at elevated temperature[END_REF].

b) The results on epidote dissolution rates from this study agree with those previously reported by [START_REF] Nickel | Experimental dissolution of light and heavy minerals in comparison with weathering and intrastratal solution[END_REF] and [START_REF] Kalinowski | Dissolution kinetics and alteration of epidote in acidic solutions at 25 °C[END_REF].

c) Scanning electron microscope images of precipitated secondary minerals were provided as a function of pH and temperature, highlighting the predominance of Fe-oxides at every pH condition along with the supersaturation of Al oxy-hydroxide phases at acidic pH.

d) Alteration products precipitated on epidote grains do not appear to alter epidote dissolution rates even after the removal of ~20 wt% of the initial sample mass in ~80 days of sequential experiments at different pH.

e) Epidote, as well as many other aluminosilicate minerals, dissolves rapidly at acidic conditions so that its presence may have a major impact on weathering rates of mafic rocks.

f) Divalent metal-rich secondary phases such as epidote can play a significant role in the carbon mineralization process due to the abundance of Ca in its structure, and Ca preferential release at acidic pH typical of CO 2 -charged fluid injections. Such observations extend the applicability of this storage approach to additional geologic systems.

FIGURES

Figure 1: Epidote crystal structure a) in 3D, and b) down the b axis of the monoclinic unit cell. Data from [START_REF] Gabe | A reinvestigation of the epidote structure: confi rmation of the iron location[END_REF]. [START_REF] Gislason | Mechanism, rates, and consequences of basaltic glass dissolution: II. An experimental study of the dissolution rates of basaltic glass as a function of pH and temperature[END_REF] refers to basaltic glass (BG) dissolution rates.

Figure 10: Best-fit epidote dissolution rates as a function of pH and temperature, along with this study and literature data [START_REF] Kalinowski | Dissolution kinetics and alteration of epidote in acidic solutions at 25 °C[END_REF][START_REF] Nickel | Experimental dissolution of light and heavy minerals in comparison with weathering and intrastratal solution[END_REF][START_REF] Rose | Dissolution rates of prehnite, epidote, and albite[END_REF].

Figure 11:

Ca release rates from Ep-epidote, BG-basaltic glass [START_REF] Gislason | Mechanism, rates, and consequences of basaltic glass dissolution: II. An experimental study of the dissolution rates of basaltic glass as a function of pH and temperature[END_REF], CB-crystalline basalt [START_REF] Gudbrandsson | An experimental study of crystalline basalt dissolution from 2⩽ pH⩽ 11 and temperatures from 5 to 75 °C[END_REF], Amp-actinolitic amphibole [START_REF] Critelli | Dissolution rates of actinolite and chlorite from a whole-rock experimental study of metabasalt dissolution from 2≤pH≤12 at 25 °C[END_REF], Px-diopside pyroxene [START_REF] Brantley | Chemical Weathering Rates of Pyroxenes and Amphiboles in[END_REF][START_REF] Golubev | Experimental determination of the effect of dissolved CO 2 on the dissolution kinetics of Mg and Ca silicates at 25 °C[END_REF], and Plg-labradoritic plagioclase (modified by Gudbrandsson et al., 2011 from Chou and[START_REF] Chou | Steady-state kinetics and dissolution mechanisms of albite[END_REF] at 25 (a), 100 (b) and 200 °C (c), as a function of pH. The release rates were determined by combining the dissolution rates with the stoichiometric concentrations of Ca in each phase. The eluent solution is pumped to a chamber with the mineral sample in suspension, and the dissolved reaction products diffuse from the mineral chamber across dialysis membranes to the outer eluent flow [1] Based on Si release [2] Based on sum of released base cations [START_REF] Palandri | A compilation of rate parameters of water-mineral interaction kinetics for application to geochemical modeling[END_REF].

Acidic Neutral Basic

This

  -flow reactor experiments were performed in 200 mL titanium Parr™ reactors, each loaded with ~1 g of the 20-100 µm sized epidote and ~200 g of ultrapure water. A high pressure liquid chromatography (HPLC) pump injected the inlet fluid into the reactor at a flow rate of ~0.25 g/min (uncertainty ±2%); under these conditions, the time required to completely exchange the fluid in the reactor, known as residence time, was approximately 13 h. The fluid exited the reactor through a 2 µm titanium filter positioned inside the reactor, an external cooling system, and a back pressure regulator. The back pressure regulator was loaded with argon to a pressure of 2 or 22 bar for the 100 or 200 °C experiments, respectively, to avoid water vaporisation inside the reactor. A heater was used to maintain the experimental temperature at 100 or 200 °C, and a thermocouple placed in a thermowell monitored the temperature inside the reactor with an uncertainty of ±1 °C. A mechanical stirring system, consisting of an external stirring motor connected to a titanium magnetic drive and impellor located inside the reactor, kept the epidote grains in suspension at a stirring rate of ~200 rpm. All the other components of the system in contact with the fluid including tubing and valves were made of titanium.

  calculated from measured reactive fluid Si concentrations by first calculating the slope of a least-squares fit of the total mass of Si in the fluid, , as a function of elapsed time . Here, was calculated by multiplying the aqueous Si concentration by the mass of the fluid in the reactor at the time of the sampling, which was monitored throughout the entire duration of the experiments. In total, less than 10 wt% of the reactive fluid was removed during sampling from each experiment. Rates were then calculated using (1) where corresponds to the stoichiometric number of moles of Si in each mole of epidote, denotes the specific BET surface area of the epidote in the reactor, and stands for the initial mass of epidote in the reactor. Rates in this study were normalized to the measured BET specific surface area to allow their direct comparison with literature data. Steady-state epidote dissolution rates for mixed-flow reactor experiments were determined using (2) where refers to the fluid flow rate, designates the concentration of Si in the outlet fluid, and 3.0 again corresponds to the Si stoichiometric number of moles of Si in one mole of epidote. The fluid flow rate was monitored throughout the experiments, and the mass of epidote dissolved during each experiment was determined from mass balance calculations.

  ). Silicon concentrations rapidly increased at the beginning of each experiment; this increase subsequently slowed from the third day to an approximately linear increase with time. The fastest Si release rate was observed during the experiment with initial fluid pH of 2, where the dissolved Si concentration reached values of up to 0.24 mmol/kg, which is approximately 5 times more than in the experiment with an initial pH of 12. The experiments run at intermediate initial fluid pH values attained lower aqueous Si concentrations ranging from 0.02 to 0.04 mmol/kg. A near constant pH was observed throughout the whole duration of the experiment run with an initial fluid pH of 2. In the experiment with initial fluid pH of 7 and 8, the pH progressively increased from this initial pH, whereas in the experiment with initial fluid pH of 12, the pH progressively decreased, reaching the value of 10.28 after 48 days. Finally, the pH of the reactive fluids of the experiments run with an initial pH of 4 and 10 exhibited a rapidly changing pH in the first 48 h, attaining values of 5.50 and 8.00, respectively, remaining stable afterwards. Cation concentrations measured at the end of each experiment showed that Ca was preferentially released from the solid relative to Al, Fe and Si in the experiments run at initial pH values ranging from 4 to 10. Iron concentrations were observed to be ~0.1 mmol/kg higher than Si in the experiment run with initial fluid pH of 2, but were close or below the detection limit in all the other experiments. At 100 and 200 °C, the measured pH of outlet fluids was identical to those of inlet fluids within analytical uncertainties due to the experimental design, as the continuous injection of initial fluid buffers potential pH changes induced by fluid-mineral interactions. In contrast, the major element concentrations measured throughout the mixed-flow reactor experiments exhibit distinct behaviours depending on pH, and to a lesser extent as a function of temperature (see Figure 5 and Figure 6) as described in detail below. Aluminum -At 100 °C, the maximum reactive fluid Al concentrations, ~0.27 mmol/kg, were observed in the most acidic fluids; measured dissolved Al concentrations decreased progressively as the imposed reactive fluid pH is increased towards neutral pH in succeeding experiments, reaching values lower than 0.01 mmol/kg in near to neutral pH conditions, and maintaining similar levels at alkaline conditions (pH>9). A notable decrease of aqueous Al concentrations as function of time was detected in the experiment run at pH 9 (Figure 5). At 200 °C, a different Al behaviour was observed: Al concentrations increased with increasing pH from below the detection limit at pH 3 to ~0.08 mmol/kg at pH 10. Calcium -In contrast to Al, no significant difference was found in the relative Ca release rates as function of temperature. The highest reactive fluid Ca concentrations were observed in the most acidic reactive fluids; 0.27 mmol/kg of Ca was present in 100 °C and pH 2 fluids, and 0.52 mmol/kg in 200 °C and pH 3 fluids. Ca concentrations progressively decreased with increasing reactive fluid pH up to pH ~8, then remaining close to zero or even below detection limit at more alkaline conditions. Iron -The Fe concentrations were below the detection limit in most of the sampled reactive fluids. Measurable fluid Fe concentrations with values ≤0.03 mmol/kg were found at 100 °C in experiments performed in fluids having a pH of 2, 3, and 4, and at 200 °C only in reactive fluids at pH 10. Silicon -Dissolved silicon concentrations in the reactive fluids tended to be highest at acidic conditions, at a minimum at near to neutral pH, and then increasing again at alkaline pH. At 100 and 200 °C, the highest reactive fluid Si concentrations were observed at pH 2 and 3, with values up to 0.37 and 0.68 mmol/kg, respectively; the lowest Si concentrations at pH 9 and 8 with values of 0.003 and 0.03 mmol/kg, respectively.

  could be a result from the post-experimental quenching and sample preparation. No sign of the precipitation of other secondary phases was detected even though PHREEQC calculations suggested the supersaturation of the reactive fluids with respect to Al oxyhydroxides such as boehmite, diaspore, and gibbsite in the epidote runs at pH 3, 4, and 5.Moreover the Al/Si ratios of the reactor fluids was less than that of the dissolving epidote, suggesting the removal of Al from the fluid phase at these conditions. At 200 °C, extensive alteration was evident, with numerous epidote grains reduced to dimensions below their original size, the presence of dissolution features on both grain surfaces and edges, and the presence of several secondary minerals. At acidic conditions, crystalline Al oxy-hydroxides were detected in the solids collected from the experiment run in pH 3 reactive fluids. These were not observed in the experiments run at pH 4 although the reactive fluid was supersaturated with respect to boehmite, diaspore, and gibbsite, as indicated by thermodynamic calculations. At alkaline conditions, minor fibrous Na-Al-silicates were found in the solids collected at the end of experiments performed in the fluids having an initial pH of 8 and 10, with Na coming from the inlet fluids. Hexagonal Ca-Ti-oxides were observed at pH 10. Fe-oxides were detected in all of the solids collected from the 200 °C experiments.

plotted in Figure 8 .

 8 Epidote dissolution rates tend to decrease with increasing pH under acidic conditions, minimize at near to neutral conditions, and then increase with further increases in pH. Steady-state epidote dissolution rates for the experiments at 25 °C, were obtained by linear regression of the temporal evolution of reactive fluid Si concentrations. Rates are based on this temporal evolution after day 7 of each experiment to avoid any anomalous initial element release rates. The total mass of epidote dissolved during each of these 25 °C experiments was determined to range from 0.2 to 2 wt% of the initial mass, based on the total reactive fluid Si concentrations and mass balance calculations. The base-10 logarithm

  At 25 °C, despite significant variations in the Si concentrations as function of pH, and supersaturation of the reactive fluids with respect to several secondary minerals at steadystate conditions, no alteration products were observed. Moreover, substantial pH changes were observed in the batch reactor experimental fluids for those experiments having initial reactive fluid pH of 4 and 10. The rapid pH change at acidic conditions suggests a major role of surface protonation in epidote dissolution, with metal-proton exchange reactions

Figure 2 :

 2 Figure 2: Scanning electron micrographs of the initial epidote used for the dissolution experiments performed in this study. The grain size fraction of this epidote is between 20 and 100 µm.

Figure 3 :

 3 Figure 3: Experimental systems used for A) batch reactor experiments at 25 °C, and B) mixed-flow reactor experiments at 100 and 200 °C. A water bath with thermostat control and the couple magnetic plate-stir bar were used during the batch reactor experiments to maintain the set temperature and the grains in suspension, respectively, within the polypropylene reactors. In the mixed-flow experiments, a high pressure liquid chromatography (HPLC) pump was employed to deliver the inlet fluid to the heated titanium reactor, where the solution was mechanically stirred, while the outlet fluid exited through a back pressure regulator, placed after the cooling system.

Figure 4 :

 4 Figure 4: Temporal evolution for all the batch reactor experiments run at 25 °C of (a) reactive fluid pH, (b) Si concentrations determined from both colorimetric analyses (circles) and ICP-OES analyses (diamonds), and (c) cation concentrations determined from ICP-OES analyses (diamonds) of the final fluid sample as a function of reactive fluid pH. The uncertainty in measured values, which in this study represent the 95% confidence interval (or two standard errors), is approximated by the symbol size.

Figure 5 :

 5 Figure 5: Temporal evolution of reactive fluid concentrations for the experiments performed at 100 °C. Ca, Al and Fe concentrations were measured using ICP-OES analyses, whereas Si concentrations were measured using both colorimetric and ICP-OES analyses. Fe concentrations were below the detection limit of 0.1µmol/kg in the experiments run at pH 6, 9, 10 and 11. The uncertainty in measured values, which in this study represent the 95% confidence interval (or two standard errors), is approximated by the symbol size. Note the different concentration scales on the y-axis of experiments run at pH 2 and 3.

Figure 6 :

 6 Figure 6: Temporal evolution of reactive fluids concentrations for the experiments performed at 200 °C. Ca, Al and Fe concentrations were measured using ICP-OES analyses, whereas Si concentrations were measured using both colorimetric and ICP-OES analyses. Fe concentrations were below the detection limit of 0.1µmol/kg in the experiments run at pH 3, 4, and 8. The uncertainty in measured values, which in this study represent the 95% confidence interval (or two standard errors), is approximated by the symbol size. Note the different concentration scale on the y-axis of the experiment run at pH 3.

Figure 7 :

 7 Figure 7: Scanning electron micrographs of the solids recovered after various experiments performed in this study. At 100 °C, dissolution features on epidote grain (a), and Fe-oxide "crusts" covering partially or entirely the epidote surface (b and c), particularly along the grain edges. At 200 °C and acidic pH, highly altered epidote grains (d) often covered by Feoxide agglomerates and Al-hydroxide crystals (e and f). At 200 °C and basic pH, Fe oxide crystals with the octahedral habit typical of magnetite(g, h, and i), fibrous Na-rich silicates (h and i), and hexagonal Ca-Ti-oxides (i). The scale is provided below every image.

Figure 8 :

 8 Figure 8: Steady-state epidote dissolution rates based on the Si release rates determined in the present study as a function of pH, for batch reactor experiments at 25 °C, and mixedflow reactor experiments at 100 and 200 °C. The rate uncertainty of measured rates, which in this study represent the 95% confidence interval (or two standard errors), is approximated by the symbol size.

Figure 9 :

 9 Figure9: Epidote (Ep) dissolution rates from this study compared to previously reported epidote dissolution rates and with basaltic glass dissolution rates as a function of pH at 25 (a),90-100 (b), and 200-250 °C (c) as a function of pH. Note, data from[START_REF] Gislason | Mechanism, rates, and consequences of basaltic glass dissolution: II. An experimental study of the dissolution rates of basaltic glass as a function of pH and temperature[END_REF] refers to basaltic glass (BG) dissolution rates.

Table 1 :

 1 Summary of epidote dissolution rates reported in the literature. Batch reactor experiments are indicated with "B", dialysis with "D", mixed-flow with "MF", and flow-through with "FT". Epidote dissolution rates are expressed as logarithm of rates in mol/cm 2 /s.

	Reference	Type	T	pH	Ionic strength	log r	[1]	log r	[2]
				(°C)		(mol/kg)	(mol/cm 2 /s)	(mol/cm 2 /s)
	Nickel (1973) *	MF	25	0.2	0.78	-14.23	-
					3.6	0.0003	-15.17	-
					5.6	deionized water	-15.80	-
					10.6	0.0004	-15.44	-
	Sverdrup (1990) **	MF	25	3.0	-	-		-13.6
					3.0	-	-		-13.9
					3.5	-	-		-14.5
					4.5	-	-		-14.9
					5.2	-	-		-16.2
					5.5	-	-		-15.9
					6.2	-	-		-16.1
					10.5	-	-		-16.3
	Rose (1991)	B	25	1.29	0.12	-15.31	-
					1.39	0.10	-15.53	-
					2.52	0.07	-15.80	-
					3.51	0.06	-16.02	-
					4.10	0.04	-16.17	-
					5.05	0.06	-16.15	-
	Kalinowski et al. (1998)	D	a	25	1.99	0.01	-15.19	-
					2.99	0.001	-15.63	-
					3.00	0.0005	-15.64	-
					4.05	0.0001	-15.72	-
					4.12	0.0001	-15.65	-
					6.50	deionized water	-15.93	-
		FT	25	1.08	0.1	-14.49	-
					2.01	0.01	-14.73	-
					2.98	0.001	-15.36	-
					3.03	0.001	-15.42	-
					4.02	0.0001	-16.19	-
					4.05	0.0001	-16.00	-
					6.48	deionized water	-16.29	-
	Rose (1991)	B	90	1.29	0.12	-12.72	-
					1.40	0.10	-12.90	-
					2.50	0.07	-13.20	-
					2.50	0.07	-13.27	-
					3.47	0.06	-13.42	-
					3.47	0.06	-13.42	-
					3.47	0.06	-13.53	-
					4.38	0.04	-13.58	-
					5.50	0.06	-13.55	-
					6.62	0.08	-13.80	-
					7.75	0.09	-13.89	-
					8.64	0.07	-14.05	-
					10.82	0.12	-12.83	-
	Rochelle (1990)	B	250	6.0	deionized water	-13.28	-
					6.3	0.2	-11.94	-
					7.3	0.2	-12.83	-
	Blanchard (1994)	B	250	4.5	0.20	-12.70	-
					3.4	0.20	-12.59	-
					5.2	0.20	-13.13	-
					12.27	0.07	-13.22	-
					10	0.09	-13.38	-

* Ionic strength calculated from inlet solutions with PHREEQC v3 (carbfix database) ** Values graphically determined from figures as reported by

Kalinowski et al. (1998) a

Table 2 :

 2 List of initial conditions for each experiment performed in this study. The pH 866 reported in the table for experiments at 25 °C are from in situ pH measurements. The pH for 867 experiments at 100 and 200 °C, and all the ionic strengths (IS) were recalculated with 868 PHREEQC for in situ conditions, from the pH measurements at room temperature and the 869 initial solution compositions. 870

	Exp. ID	Elapsed time	Initial mass	Initial pH	Inlet fluid composition	IS
		(h)	(g)			(mol/kg)
	Batch reactor experiments at 25 °C
	Ep25_2		2.03	2.19	10 mmol/kg HCl	0.0100
	Ep25_4		2.05	4.20	0.1 mmol/kg HCl	0.0001
	Ep25_7		2.01	6.99	0.1 mmol/kg HCl, 0.3 mmol/kg NaHCO3	0.0003
	Ep25_8		2.02	8.15	0.001 mmol/kg NaOH, 1.1 mmol/kg NaHCO3	0.0011
	Ep25_10		2.00	9.78	0.1 mmol/kg NaOH	0.0001
	Ep25_12		2.02	11.89	11 mmol/kg NaOH	0.0112
	Mixed-flow reactor experiments at 100 °C
	Ep100_2		1.01	2.05	10 mmol/kg HCl	0.0100
	Ep100_3		0.92	3.05	1 mmol/kg HCl, 8.6 NaCl	0.0095
	Ep100_4		0.88	4.05	0.01 mmol/kg HCl, 9.4 NaCl	0.0095
	Ep100_5		0.87	5.05	0.01 mmol/kg HCl, 9.5 NaCl	0.0095
	Ep100_6		0.87	6.32	0.1 mmol/kg HCl, 0.2 mmol/kg NaHCO3, 9.2 NaCl	0.0094
	Ep100_8		0.87	7.71	0.001 mmol/kg NaOH, 1.1 mmol/kg NaHCO3, 8.6 NaCl	0.0096
	Ep100_9		0.87	9.19	1 mmol/kg NaOH, 8.6 NaCl	0.0095
	Ep100_10		0.87	10.19	10 mmol/kg NaOH	0.0100
	Ep100_11		0.86	11.02	80 mmol/kg NaOH	0.0793
	Ep100_2B		0.86	2.05	10 mmol/kg HCl	0.0100
	Mixed-flow reactor experiments at 200 °C
	Ep200_3		1.03	3.06	1 mmol/kg HCl, 9.4 mmol/kg NaCl	0.0103
	Ep200_4		1.07	4.06	0.1 mmol/kg HCl, 9.9 mmol/kg NaCl	0.0100
	Ep200_8		1.03	7.61	0.001 mmol/kg NaOH, 1.1 mmol/kg NaHCO3, 9.1 NaCl	0.0101
	Ep200_9		1.05	9.21	10.1 mmol/kg NaOH	0.0100
	Ep200_10		1.06	9.75	50 mmol/kg NaOH	0.0443
	871

Table 3 :

 3 Chemical composition of the investigated epidote in the present study obtained by XRF.

		wt%		moles
	SiO 2	37.32	Si	3.00
	TiO 2	0.19	Ti	0.01
	Al 2 O 3	21.94	Al	2.08
	Fe 2 O 3	16.78	Fe	1.02
	Mn 2 O 3	0.16	Mn	0.01
	MgO	0.01	Mg	<0.001
	CaO	23.99	Ca	2.07
	K 2 O	0.06	K	0.01
	SO 3	0.14	S	0.01
	LOI	1.82	O	13.41

Table 5 :

 5 Summary of averaged pH, Si concentrations, and cation release ratios in the outlet aqueous solutions at steady-state for each mixed-flow reactor experimental run. The pH reported in the table were recalculated with PHREEQC for in situ conditions, from the pH measurements at room temperature and the outlet solution compositions at steady-state. Often the Fe/Si stoichiometric ratio is not available because values of Fe concentrations are below the detection limit (0.1 µmol/kg). The uncertainties on Si measurements are listed and represent the 95% confidence interval (or two standard errors). The full data is provided in Electronic Supplementary Table2.

	Exp. ID	pH	Si	Uncertainty	Ca/Si	Al/Si	Fe/Si	Ca/Al
			(mmol/kg)	(mmol/kg)
	Stoichiometric ratios of the epidote used in this study	0.69	0.69	0.34	0.99
	Mixed-flow reactor experiments at 100 °C
	Ep100_2	2.11	0.370	0.007	0.71	0.72	0.06	0.99
	Ep100_3	3.12	0.047	0.001	0.91	0.53	0.10	1.73
	Ep100_4	4.32	0.020	<0.001	1.14	0.01	0.01	79.83
	Ep100_5	5.64	0.011	<0.001	1.32	0.05	-	31.98
	Ep100_6	6.54	0.007	<0.001	1.40	0.12	-	12.16
	Ep100_8	7.61	0.004	<0.001	1.39	1.55	-	0.89
	Ep100_9	9.19	0.003	<0.001	1.53	1.61	-	1.08
	Ep100_10	10.19	0.05	<0.001	0.92	0.34	-	2.69
	Ep100_11	11.02	0.007	<0.001	0.03	0.14	0.01	0.22
	Ep100_2B	2.09	0.242	0.003	0.71	0.72	0.08	0.99
	Mixed-flow reactor experiments at 200 °C
	Ep200_3	4.37	0.656	0.009	0.76	0.01	-	147.14
	Ep200_4	5.47	0.105	0.002	0.67	0.06	-	11.47
	Ep200_8	7.58	0.042	0.001	0.79	0.72	-	1.12
	Ep200_9	9.03	0.052	<0.001	0.14	0.73	0.001	0.19
	Ep200_10	9.75	0.087	0.001	0.01	0.90	0.004	0.02

Table 6 :

 6 Steady-state far from equilibrium epidote dissolution rates based on the Si release all the experiments performed in this study. The pH provided for batch-reactor experiments represents the pH average from the fluid samples used to calculate the epidote dissolution rates with linear regression (see Table4). The two standard error uncertainties are ±0.11 and ±0.04 log unit for rates obtained from the batch and mixed-flow reactor experiments, respectively.

	Exp. ID	pH	log rBET
			(mol/cm 2 /s)
	Batch reactor experiments at 25 °C
	Ep25_2	2.09	-14.98
	Ep25_4	5.52	-15.82
	Ep25_7	7.29	-16.07
	Ep25_8	8.19	-15.78
	Ep25_10	7.75	-15.85
	Ep25_12	11.26	-16.11
	Mixed-flow reactor experiments at 100 °C
	Ep100_2	2.11	-12.30
	Ep100_3	3.12	-13.13
	Ep100_4	4.32	-13.47
	Ep100_5	5.64	-13.71
	Ep100_6	6.54	-13.89
	Ep100_8	7.61	-14.22
	Ep100_9	9.19	-14.40
	Ep100_10	10.19	-14.09
	Ep100_11	11.02	-14.06
	Ep100_2B	2.09	-12.37
	Mixed-flow reactor experiments at 200 °C
	Ep200_3	4.37	-12.03
	Ep200_4	5.47	-12.84
	Ep200_8	7.58	-13.18
	Ep200_9	9.03	-13.10
	Ep200_10	9.75	-12.88

Table 7 :

 7 Epidote dissolution rate parameters used in Equation 3 in this study, compared to those proposed by

Table 8 :

 8 Atomic Ca/Si, Al/Si, and Ca/Al ratios of epidote, basaltic phases, Ca-amphibole actinolite, Ca-pyroxene diopside, and Ca-bearing plagioclases (here indicated as "Plg").

		Reference	Ca/Si	Al/Si	Ca/Al
	Epidote	This study	0.69	0.69	0.99
	Basaltic glass	Oelkers and Gislason (2001)	0.26	0.36	0.72
	Crystalline basalt Gudbrandsson et al. (2011)	0.27	0.33	0.83
	Actinolite	Critelli et al. (2014)	0.37	0.12	3.18
	Px-Diopside	Brantley and Chen (1995);	0.50	-	-
		Golubev et al. (2005)
	Plg-Labradorite	Deer et al. (1963)	0.25	0.67	0.38
	Plg-Anorthite	Deer et al. (1963)	0.50	1.00	0.50

Acknowledgements

We would like to thank Dr. Giuseppe Saldi, Alain Castillo, Carole Causserand, and Stephane Le Blond du Plouy for experimental, technical, and analytical assistance. Helpful reviews from the Executive Editor Dr. Catalano, the Associate Editor Dr. Anovitz, and two anonymous reviewers are very much appreciated. This research has been carried out within the CarbFix2 project that has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 764760.

Table 4: Summary of chemical compositions of the reactor fluid samples taken during the batch reactor experiments at 25 °C and used to calculate the epidote dissolution rates with linear regression (the full data is provided in Electronic Supplementary


P Géhanne

S Rohart

A Thiaville

V Jeudy

Strength and length-scale of the interaction between domain walls and pinning disorder in thin ferromagnetic films

Keywords: numbers: 75, 78, Fg,64, 60, Ht

We explore the magnetic-field-driven motion of domain walls with different chiralities in thin ferromagnetic films made of Pt/Co/Pt, Au/Co/Pt, and Pt/Co/Au. From the analysis of domain wall dynamics, we extract parameters characterizing the interaction between domain walls and weak pinning disorder of the films. The variations of domain wall structure, controlled by an in-plane field, are found to modify the characteristic length-scale of pinning in strong correlation with the domain wall width, whatever its chirality and the interaction strength between domain walls and pinning defects. These findings should be also relevant for a wide variety of elastic interfaces moving in weak pinning disordered media.

I. INTRODUCTION

The controlled motion of magnetic textures such as chiral domain walls (DWs) [1] or skyrmions resulting from the Dzyaloshinskii-Moriya interaction (DMI) [2] are at the basis of potential applications of spintronic devices [3]. However, magnetic textures are very sensitive to weak pinning due to ubiquitous inhomogeneities of magnetic materials, which strongly reduces their velocity and produces stochastic universal behaviors [4,5]. Despite numerous recent studies [6][7][8][9][10][11] focusing on the dynamics of pinned chiral magnetic textures, their interaction with weak pinning disorder is far from being understood.

DWs are well known to present universal behaviors [12][13][14] similar to those encountered by interfaces in a wide variety of other physical systems. Those behaviors can be described by minimal statistical-physics models [15][16][START_REF] Agoritsas | proceedings of the International Workshop on Electronic Crystals[END_REF] as an interplay between interface elasticity, weak pinning, thermal activation, and a driving force f . The dynamical regimes of interfaces strongly depend on the relative magnitude of the drive f compared to a depinning threshold force f d . In the creep regime (f < f d ), the velocity follows an Arrhenius law v ∼ e -∆E/(k B T ) , where the barrier height presents an asymptotic power law behavior ∆E ∼ f -µ with the force f close to zero. At and just above the depinning threshold, the velocity presents a power law variation with the temperature

v(f = f d ) ∼ T ψ and drive v(f > ∼ f d ) ∼ (f -f d ) β
, respectively. The critical exponents µ, ψ, and β are universal (i.e. material and temperature independent). Their values characterize the universality class of the motion and reflects the dimension of the interface and embedding medium, the range of elasticity and the interaction with pinning defects. In ultrathin films with perpendicular anisotropy, a perpendicular magnetic field H can serve as an isotropic driving force (H ∝ f ). A large major- * vincent.jeudy@universite-paris-saclay.fr ity of experimental studies on DW dynamics reported in the literature [START_REF] Jeudy | [END_REF] is compatible with the theoretical predictions (µ = 1/4, ψ = 0.15, and β = 0.25) for short range (random bond) interactions between pinning disorder and DWs. However, the minimal models ignore the exact structure of interfaces and the characteristic length-scale of pinning is a parameter chosen arbitrarily [START_REF] Agoritsas | proceedings of the International Workshop on Electronic Crystals[END_REF]19]. Since the seminal work of Lemerle et al. [12] on the creep motion, basic issues such as the length-scale and the strength of interaction between DW and defects in magnetic materials remain open.

Recent experiments on the creep motion of chiral DWs have evidenced the correlations between the DW magnetic texture and its dynamics. In thin films with perpendicular anisotropy, the DMI results in an in-plane effective magnetic field H DMI pointing in the direction perpendicular to the DW. The DMI field combined with an in-plane field H x can be used to adjust the in-plane component of magnetization direction in the DW and to control the DW magnetic structure. The recent observation of asymmetric expansion of initially circular domains [6] has lead to precise investigations of the variation of DW width, energy and stiffness [8][9][10][11] with the direction and magnitude of the in-plane and DMI fields and to re-examine more generally the creep motion of chiral DWs [11]. Rather accurate descriptions of the shape of the velocity curves versus in-plane field are now obtained [10,11]. The proposed models discuss the variations of creep barrier height ∆E with the DW energy [6][7][8][9][10][11]. Surprisingly, the interaction between the DW and random pinning disorder is assumed to be independent of DW's magnetic structure.

Here, we evidence a strong correlation between the variation of DW width controlled by an in-plane field and the characteristic length of pinning, in films with three different chiralities. Our argument is organized as follows. We first extract the material and in-plane field dependent pinning parameters controlling DW dynamics, from the self-consistent analysis proposed in Ref. [13,14]. We then numerically compute the variation with in-plane and DMI fields of the DW energy and width. The latter are compared to the variation of pinning range and strength deduced from the pinning parameters via scaling relations [START_REF] Jeudy | [END_REF].

II. EXPERIMENTAL TECHNIQUES

The samples are Pt/Co/Pt, Pt/Co/Au, and Au/Co/Pt films (with thicknesses of 5 nm for Pt and Au and 0.9 nm for Co, nominally) with perpendicular magnetic anisotropy, which have been grown by e-beam evaporation in ultra high vacuum on Si(001)/SiO 2 (100 nm)/Ta(5 nm) templates. They present (111) oriented crystallites with a typical grain size of 15 nm [20]. The micromagnetic parameters characterizing the films are detailed in Table I. The DW displacement was observed by polar Kerr microscopy. The in-plane magnetic field H x controlling the magnetization direction in the DW was generated by two large coils supplied with DC current. The out-of-plane field H used to move DW was produced by a small coil (diameter ≈ 1 mm) placed in the close vicinity of the films and supplied by pulses of duration ∆t between 1 µs and 10 ms. The explored range of µ 0 H x (±187 mT) and µ 0 H(0 -120 mT) was limited by the nucleation of multiple domains, which impedes measurement of DW displacement. The DW velocity v corresponds to the ratio ∆x/∆t, where ∆x was exclusively measured in the direction of H x (see the inset of Fig. 1(c)).

III. UNIVERSAL DOMAIN WALL DYNAMICS

The velocity curves obtained for the three films and different values of µ 0 H x are reported in Fig. 1. For their analysis, we used the self-consistent description of the creep and depinning regimes [13,14,[START_REF] Jeudy | [END_REF]21,22]:

v(H) = v(H d ) exp(-∆E k B T ) creep : H < H d v(H d ) x0 ( T d T ) ψ ( H-H d H d ) β depinning : H > ∼ H d , (1)
where

∆E = k B T d ((H/H d ) -µ -1)
is the energy barrier of the creep regime and the depinning law is the asymptotic velocity behavior in the limit of negligible contribution of thermal fluctuations [14]. In Eq. 1, µ = 1/4, β = 0.25, and ψ = 0.15 are universal critical exponents and x 0 = 0.65 a universal constant [14] characterizing the quenched Edwards Wilkinson universality class [14,15,23] and are therefore fixed. The nonuniversal parameters are the characteristic height of effective pinning barrier k B T d and coordinates of the depinning threshold (corresponding to ∆E → 0) H d and v(H d ). Those three parameters depend on the film magnetic and pinning properties, and external parameters as the in-plane field, and the temperature [START_REF] Jeudy | [END_REF]. As it can be observed in Fig. 1 a-c, all the fits of Eqs. 1, obtained with only three fitting parameters, present a good agreement with the velocity curves (see Refs. [START_REF] Jeudy | [END_REF] for details on the fitting procedure). This finding is compatible with the results reported for a large variety of other magnetic materials [13,14,[START_REF] Jeudy | [END_REF]21,22] and confirms that chiral and non-chiral DWs follow very similar universal behaviors as predicted in Ref. 11 for the creep regime.

IV. INTERACTION BETWEEN DOMAIN WALL AND DEFECTS

Having discussed universal behaviors, we can now focus on the obtained non-universal parameters (see Fig. 1 d-e). (Here, we do not discuss the values of v(H d ) since it is partly determined by the contribution of DW dynamics in the flow regime at the threshold H d [START_REF] Jeudy | [END_REF].) Note that the in-plane field H x tilts the magnetization in the domains on both sides of the DW, which reduces the driving field to

H = H 1 -(H x /H K0 ) 2
, where H K0 is the anisotropy field [24]. To account for this effect [START_REF]As Hx remains significantly smaller than HK 0 , the contribution of the magnetization tilting is small: the difference between uncorrected and corrected values of ξ is less than the size of the data points of Fig[END_REF], the depinning field H d has to be rescaled to H d consequently.

Surprisingly, the values of H d and T d vary with the inplane magnetic field H x . This strongly suggests that the pinning properties of DWs depend on with their magnetic texture, in contrast to the usual assumption found in the literature [6,[8][9][10][11]. In order to understand the variations of H d and T d , we shall discuss the DW pinning at the microscopic scale and, more precisely, compare the effect of the in-plane field on the DW energy and width and on the strength and length-scale of pinning (see Fig. 2).

To predict accurately the variation of DW energy and structure with in-plane and DMI fields, we have decided not to use simplified descriptions of DWs [6,[8][9][10][11]. We have calculated the magnetization profile M (x) of a DW whose plane is ⊥ H x , from numerical micromagnetic calculations (MuMax3 [START_REF] Vansteenkiste | [END_REF]), using the parameters reported in Table I [START_REF]The numerical calculations were performed on 1024×1×1 cubic cells[END_REF]. In addition, an analytical model leading to very similar results has been developed [START_REF] Géhanne | [END_REF]. For the DW width, we use both the geometrical Hubert [START_REF] Hubert | Theorie der Domänenwände in geordneten Medien[END_REF] ∆ H and dynamic Thiele [START_REF] Thiele | [END_REF][START_REF] Thiaville | Spin dynamics in confined magnetic structures iii[END_REF] ∆ T definitions. ∆ H corresponds to half of the distance separating the intersections between the slope of M z (x) at the domain wall center (x = 0) and its value in the domains [START_REF] Thiele | [END_REF][START_REF] Thiaville | Spin dynamics in confined magnetic structures iii[END_REF]. The predicted variations of ∆ H (H x ), ∆ T (H x ) and σ(H x ) are reported in Fig. 2 and follow the expected behaviors. As the DMI field is perpendicular to the DW plane (i.e. H DMI H x ), its contribution is essentially to shift the curves by -H DMI . For H x varying from -H DMI , the magnetization within the DW progressively switches from Bloch ( M ⊥ H x ) to Néel configuration ( M H x ). As the DW width increases due to the Zeeman contribution (∝ -µ 0 M • ( H x + H DMI )), the DW energy decreases. Additionally, H x tends to tilt the magnetization in the domains on both sides of the DW: M x (x → ±∞)/M s = H x /H K0 . This reduces the angular variation of the magnetization within the DW and provokes a divergence of ∆ H (H x ) and ∆ T (H x ) and a vanishing σ(H x ) for H x → ±H K0 .

M z (x → ±∞). ∆ T is defined as ∆ T = 2M 2 s / (d -→ M /dx) 2 dx
In order to discuss the DW pinning at the microscopic scale with in-plane field H x , we use standard scaling arguments [12,19]. The free energy of a DW segment of length L, deformed over a distance u [11,12] can be written as δF (L, u) = δF elas (L, u) -δF pin (L, ξ) -δF z (L, u), where δF elas = σtu 2 /L is the elastic energy produced by the increase of DW length and, δF z = 2µ 0 M s HtLu is the gain of Zeeman energy due to magnetization reversal. The DW stiffness σ is, at this stage, assumed to be given by the DW surfacic energy. For a weak disorder producing fluctuations of DW energy, the pinning term can be written δF pin = f pin √ nξLξ, where f pin and ξ are the characteristic force and range of the DW-defects interaction, respectively and, n is the density of pinning defects per unit surface area. Here we go beyond the conventional relation ξ ∝ b (≈ 1/ √ n) used throughout in the literature [12]: we reintroduce a clear distinction between the characteristic length-scale of the pinning disorder b, which is fixed by the material inhomogeneities, and the range ξ of the DW-defects interaction, which may vary with the DW structure [START_REF] Nattermann | [END_REF] as shown in the following discussion. For a short seg-ment length (L < L c ), the DW is too rigid to follow the random pinning potential (δF elas (L, u) > δF pin ). The segment is collectively pinned by a set of pinning defects. The characteristic collective pinning lengthscale can be deduced from δF elas (L c , ξ) ∼ δF pin (L c , ξ), which reads L c ∼ (ξ/n) 1/3 (σt/f pin ) 2/3 . For L > L c , the pinning energy is larger than the elastic energy: a DW can be seen as a set of rigid segments of length L c , whose orientation follows the random pinning landscape. In order to depin a rigid segment, the magnetic field H has to reach a threshold field H d . The latter can be determined from δF pin (L c , ξ) ∼ δF z (L c , ξ), which leads to H d ∼ nξ/L c f pin /(2µ 0 M s t). Then, assuming [START_REF] Jeudy | [END_REF] that the pinning barrier height is given by k B T d ∼ δF pin (L c , ξ), we obtain the scaling relations:

ξ ∼ (k B T d ) 2 /(2µ 0 H d M s σt 2 ) 1/3 , (2)
f pin ∼ 1 √ nξ 2µ 0 H d M s tk B T d , (3)
which relate the characteristic range ξ and force f pin of the DW-defect interaction, to the measured depinning field H d (µ 0 H x ) and temperature T d (µ 0 H x ) (see Fig. 1 d-e) and the predicted DW surface energy σ(µ 0 H x ) (see Fig. 2 b). The variation with in-plane field of ξ and f pin , deter-mined from the measurements of H d , T d (see Fig. 1 d-e), the predictions for σ(µ 0 H x ) (see Fig. 2 b) and Eqs 2-3, are shown in Fig. 2. For a comparison with the predicted variations of the DW width, the values of ξ were rescaled with a constant factor, which is the only free parameter. As it can be observed in Fig. 2 a, the variations with inplane field of the pinning range ξ(µ 0 H x ) present strong correlations with the predictions for both ∆ H and ∆ T : the agreement is very good for the Pt/Co/Au except for µ 0 H x > 100 mT and it is even better for the Pt/Co/Pt and Au/Co/Pt films. The DMI field seems to essentially modify the value of µ 0 H x at which a minimum of DW width (and pinning range) is observed and no chiral contribution of pinning can be evidenced. Those observations suggest that the range of the DW-defect interaction is close to the DW width. As a direct consequence, the characteristic length-scale of pinning defects (b ≈ 1/ √ n) should be close to or smaller than the DW width [START_REF] Nattermann | [END_REF], which rules out the approximation considering DW as one dimensional line [12,33] interacting with remote defects (∆ H and ∆ T b). Let us now discuss the pinning force f pin , whose variations with in-plane field is reported in Fig. 2 b. Here also, the only free parameter is the rescaling factor. As it can be observed, the pinning force follows rather well the variations of σ(H x ). This is expected since the weak pinning of DWs results from fluctuations of DW energy, whose amplitude should decrease as σ decreases. An additional contribution is the increase of DW width, which (for b < ∆) is predicted to reduce the strength of pinning interaction [34,[START_REF] Soucaille | De l'importance de l'interaction de Dzyaloshinskii-Moriya sur la dynamique sous champ des parois de domaines magnétiques dans des films désordonnés[END_REF].

V. CONCLUSION

In conclusion, variations of the range and the strength of pinning following modifications of the wall static structure have been evidenced. This effect, observed on magnetic domain walls with chiral structure submitted to large hard-axis magnetic fields, should be relevant for elastic interfaces moving in weak pinning disordered media [16,[START_REF] Agoritsas | proceedings of the International Workshop on Electronic Crystals[END_REF] in a wide variety of others systems.

  , and the DMI field µ0HDMI deduced from SQUID, Kerr anisometry, and velocity measurements, respectively. The effective anisotropy constant K0 is calculated from K0 = µ0HK 0 Ms/2. The values of the DW width parameter (∆0 = A/K0) and the DW Bloch energy (σ0 = 4A/∆0) are obtained assuming a stiffness constant A = 16 pJ/m. The interface DMI energy D is calculated from D = µ0HDMI Ms∆0. The numbers in parenthesis are the error bars.

Figure 1 .

 1 Figure 1. Domain wall dynamics. DW velocity versus out-of-plane magnetic field µ0H measured for the (a) Pt/Co/Au, (b) Au/Co/Pt, and (c) Pt/Co/Pt films and for different values of the in-plane field µ0Hx. The solid and dash lines are predictions for the creep and depinning regimes (see Eqs. 1). The stars correspond to the coordinates of the depinning thresholds (H d , v(H d )). A good agreement with the data is obtained up to the cross-over between the depinning and flow regimes [14], which can be observed at µ0Hx = 0 mT for Pt/Co/Au (µ0H > 70 mT) and Pt/Co/Pt (µ0H > 90 mT). The curves (d) and (e) correspond to the variation with µ0Hx of the rescaled depinning field (H d , see the text) and temperature (T d ) deduced from the fit of Eqs. 1. Insert of c: Displacement of DW in the Au/Co/Pt film produced by a magnetic field pulse (µ0H = 3 mT, ∆t = 1 µs) for µ0Hx = 48 mT. The diameter of the darkest circle is 60 µm.

Figure 2 .

 2 Figure 2. Pinning of domain wall at microscopic scale. (a) Domain wall widths ∆H (solid line) and ∆T (dash line), and rescaled correlation length of the pinning ξ versus in-plane magnetic field µ0Hx, for the three films. For each film, the values of ξ deduced from Eq. 2 were rescaled by constant (≈ min(ξ)/min(∆T )) indicated in parenthesis to highlight the strong correlation between the DW width and ξ(µ0Hx). (b) Domain wall energy per unit length σt (left vertical scale, solid line) and the rescaled pinning force fpin (right vertical scale) versus µ0Hx. For each film, the values of fpin deduced from Eq. 3 were rescaled in order to set max(fpin) ≈ max(σt)/10.

Table I .

 I Micromagnetic parameters. For each material, the table indicates the magnetization saturation Ms, the anisotropy field µ0HK 0

	Material	Ms (MA/m)	µ0HK 0 (mT)	µ0HDMI (mT)	K0 (kJ/m 3 )	∆0 (nm)	σ0 (mJ/m 2 )	D (mJ/m 2 )
	Pt/Co/Pt	1.62(0.04)	580(10)	0(10)	470(14)	5.8(0.1)	11.0(0.2)	0(0.10)
	Pt/Co/Au	1.65(0.01)	770(30)	-105(10)	635(25)	5.0(0.1)	12.7(0.3)	-0.87(0.09)
	Au/Co/Pt	1.61(0.02)	900(100)	+78(10)	726(80)	4.7(0.3)	13.6(0.8)	0.59(0.08)

ACKNOWLEDGMENTS

We wish to thank J. Sampaio for careful reading of the manuscript.