Vasileios Mavromatis
email: vasileios.mavromatis@get.omp.eu

Βασίλειος Μαυρομάτης

Jean-Michel Brazier

Katja E Goetschl

Controls of temperature and mineral growth rate on Mg incorporation in aragonite

Keywords: Mg distribution, aragonite, growth rate, temperature effect, defect sites

The incorporation of Mg in aragonite was experimentally investigated as a function of mineral growth rate at 5, 15 and 25 o C using the constant addition technique. Aragonite growth rate was found to be the major parameter affecting the Mg partitioning coefficient (i.e. 𝐷 𝑀𝑔 = ( 𝑀𝑔 𝐶𝑎 ) 𝑠𝑜𝑙𝑖𝑑 ( 𝑀𝑔 𝐶𝑎 ) 𝑓𝑙𝑢𝑖𝑑

) between aragonite and fluid, whereas the effect of temperature is smaller but measurable. At similar surface normalized growth rates, DMg values decrease as temperature increases from 5 to 25 o C. The magnitude of decrease as a function of temperature is similar for all the experiments of this study where growth rate varied in the range 10 -8.6 ≤ rp ≤ 10 -7.1 (mol/m 2 /s). The combined effect of aragonite growth rate and temperature on DMg can be described by the linear equation:

Log DMg = 0.583(±0.020) Log rp -0.026(±0.001) T + 0.863(±0.153); R 2 = 0.97 where T is the temperature in degrees Celsius.

The increase of DMg values at decreasing temperatures in experiments conducted at similar growth rates is consistent with the increase of fluid supersaturation with respect to aragonite. Thus, it can be inferred that increased Mg incorporation at higher supersaturation is associated with the greater presence of defect sites on the growing mineral surface, similar to the incorporation of other incompatible ions in carbonate minerals. Overall, the relationship between Mg content of aragonite with the degree of saturation of the fluid with respect to this mineral phase suggests that DMg values or Mg/Ca ratio in natural aragonites can be used as a proxy for saturation degree of the formation fluid with respect to CaCO3 minerals.

Introduction

The presence of foreign ions in calcite and aragonite of marine and terrestrial origin in the geological record, provides a means for the reconstruction of the environmental conditions that occurred at the time of mineral formation. Owing to its high concentration in oceanic waters and its presence in naturally occurring calcites, the controls Mg exerts on CaCO3 mineral formation have been extensively studied over the last five decades. For example, it is well-known that during abiotic CaCO3 mineral formation, the presence of Mg in the aqueous fluid controls the mineralogy of the forming phase (e.g. [START_REF] Plummer | The solubilities of calcite, aragonite and vaterite in CO2 -H2O solutions between 0 and 90 o C, and an evaluation of the aqueous model for the system CaCO3-CO2-H2O. Geochim[END_REF][START_REF] Morse | Influences of temperature and Mg:Ca ratio on CaCO3 precipitates from seawater[END_REF][START_REF] Goetschl | Effect of sulfate on magnesium incorporation in low-magnesium calcite[END_REF]. Additionally, Mg is incorporated as a trace/impurity in the structure of the forming mineral phase. Actually, the presence of Mg in naturally occurring calcite and aragonite is of great importance for paleo environmental reconstruction studies, because its ratio to other cations in these mineral phases (e.g. Mg/Ca, Mg/Li) has been associated with important environmental parameters such as temperature (e.g. Nürnberg et al., 1996;[START_REF] Raddatz | Stable Sr-isotope, Sr/Ca, Mg/Ca, Li/Ca and Mg/Li ratios in the scleractinian cold-water coral Lophelia pertusa[END_REF][START_REF] Montagna | Li/Mg systematics in scleractinian corals: Calibration of the thermometer[END_REF][START_REF] Marchitto | A simple biomineralization model to explain Li, Mg, and Sr incorporation into aragonitic foraminifera and corals[END_REF]. The replacement of Ca for Mg in the calcite structure results in concentrations that vary from a few mmol/mol to several mol%, with concentrations of a few mmol/mol recorded in speleothems forming from a Mg depleted fluid [START_REF] Huang | Partitioning of Sr 2+ and Mg 2+ into calcite under karstanalogue experimental conditions[END_REF] and Mg concentrations exceeding 20 mol% in marine authigenic high Mg-calcite [START_REF] Mucci | The incorporation of Mg 2+ and Sr 2+ into calcite overgrowths; influences of growth rate and solution composition[END_REF]. In contrast the replacement of Ca for Mg in aragonite structure is less favourable to occur owing to the lack of solid-solution formation in the aragonitemagnesite system. Yet the presence of Mg in natural aragonites provides an intriguing question of the parameters controlling its presence in this mineral phase.

Although aragonite is a major geological archive particularly for marine environments where it occurs as coralline exoskeletons, our understanding of the mechanisms controlling the incorporation of traces/impurities in this mineral phase is rather limited. The earlier work by [START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF] proposed the use of Mg distribution in aragonite as a temperature proxy tool. These authors, however, did not consider the effect of mineral growth rate which has more recently been shown to affect Mg content in aragonite [START_REF] Gabitov | Experimental determination of growth rate effect on U 6+ and Mg 2+ partitioning between aragonite and fluid at elevated U 6+ concentration[END_REF]2011). Note here that mineral formation at increasing growth rates leads to deviations from the elemental ratios that would be expected under thermodynamic equilibrium conditions (e.g. [START_REF] Rimstidt | Distribution of trace elements between carbonate minerals and aqueous solutions[END_REF]. This observation is not only valid for divalent cations (i.e. Me 2+ ) that ideally replace Ca 2+ in the structure of calcite and aragonite (e.g. [START_REF] Lorens | Sr, Cd, Mn and Co distribution coefficients in calcite as a function of calcite precipitation rate[END_REF][START_REF] Mucci | The incorporation of Mg 2+ and Sr 2+ into calcite overgrowths; influences of growth rate and solution composition[END_REF][START_REF] Mucci | The solubility of calcite and aragonite in sulfate-free seawater and the seeded growth-kinetics and composition of the precipitates at 25 o C[END_REF][START_REF] Dromgoole | Iron and manganese incorporation into calciteeffects of growth-kinetics, temperature and solution chemistry[END_REF][START_REF] Tesoriero | Solid solution partitioning of Sr 2+ , Ba 2+ , and Cd 2+ to calcite[END_REF]Lakstanov and Stipp, 2007;[START_REF] Mavromatis | Barium partitioning in calcite and aragonite as a function of growth rate[END_REF], but also for incompatible elements such as Li, B or rare earth elements (REE 3+ ) that are not ideally substituting for Ca 2+ or CO3 2-in the CaCO3 mineral lattice (e.g. [START_REF] Mavromatis | Characterization of boron incorporation and speciation in calcite and aragonite from co-precipitation experiments under controlled pH, temperature and precipitation rate[END_REF][START_REF] Uchikawa | Experimental evidence for kinetic effects on B/Ca in synthetic calcite: Implications for potential B(OH)4and B(OH)3 incorporation[END_REF]2017;[START_REF] Voigt | The experimental determination of REE partition coefficients in the water-calcite system[END_REF][START_REF] Füger | Effect of growth rate and pH on lithium incorporation in calcite[END_REF]. Proper use of traces/impurities in aragonite as proxies for environmental conditions calls for decoupling of the effects of temperature from that of mineral growth rate because both these parameters affect the trace metal concentration in the forming CaCO3 mineral. This prerequisite provides a fundamental step towards understanding the mechanisms controlling the presence of Mg in aragonite and for developing paleo-proxy tools.

The aim of this study is to investigate the effect of mineral growth rate and formation temperature on the incorporation of Mg in aragonite. For this, we used the constant addition technique to grow aragonite on seed material at 5, 15 and 25 o C as a function of mineral growth rate. Our results examine systematically the mechanisms controlling Mg uptake in aragonite and aim to ameliorate interpretation of paleoenvironmental reconstruction studies that commonly use Mg/Ca ratio in aragonite as a proxy tool.

2.Methods

Precipitation experiments

The incorporation of Mg in aragonite has been studied using the mixed flow reactor experimental setup that has previously been described in [START_REF] Gautier | Hydromagnesite solubility product and growth kinetics in aqueous solution from 25 to 75 °C[END_REF] and [START_REF] Mavromatis | Characterization of boron incorporation and speciation in calcite and aragonite from co-precipitation experiments under controlled pH, temperature and precipitation rate[END_REF]. In this study, overgrowth experiments were performed on synthetic aragonite seeds at 5, 15 and 25 o C under continuous bubbling of atmospheric air, using the experimental setup that is illustrated in Fig. 1. Aragonite growth was induced by continuous pumping at similar rates of two separate inlet solutions into the reactor using a peristaltic pump. The pumping rates of the inlet solution in this study varied among runs between 9.2 and 23.1 mL/24h. One inlet solution contained CaCl2, MgCl2, and LiCl, and the second contained Na2CO3 and NaCl. The concentrations of Mg, Li and Na in the inlet solutions were double compared to those present in the reactor in order to avoid changes in concentrations of the reactive fluid due to dilution. In all experimental runs, the background electrolyte concentration was kept the same at ~10 mM LiCl, ~25 mM MgCl2 and ~270 mM NaCl. The concentrations of CaCl2 and Na2CO3 in the inlet solutions varied between 40 and 240 mM and in combination with variation in the pumping rates and the amount of the seed material, experimental work could be conducted over a wide range of aragonite growth rate. All reacting solutions were prepared using analytical grade chemicals and high purity deionized water (Millipore Integral 3: 18.2 MΩ cm -1 ). The reactor was placed into a temperature cabinet prior to the runs to equilibrate at the experiment temperature. In the temperature cabinets the temperature of the experimental solutions remained constant throughout the experimental runs. Shortly before the onset of each run a known amount of aragonite seeds was added to the reactor. The pH of the reactive fluid (i.e. 8.1 ≤ pH ≤ 8.4) was controlled by the continuous bubbling of atmospheric air through the reactive fluid. In order to minimize evaporation during the experimental runs, air was bubbled in a 300 mM NaCl solution prior to its introduction into the reactors. Each reactor contained 500 mL of solution and was equipped with a Teflon floating stir bar rotating at 240 rpm. During the course of a run, introduction of inlet solutions induced an increase of the volume of the reactive fluid. Thus, every 12 or 24 h, a volume of reactive fluid, equal to the sum of the volumes of the inlet solutions added in the previous 12 or 24 h respectively, by the peristaltic pump, was sampled from the reactor so that the variations of the volume of the reactive fluid would remain roughly constant to within ±4 %. In order to reduce aragonite removal from the reactor during sampling and to keep the solid/fluid ratio quasi constant during the course of an experiment, stirring was stopped shortly prior to sampling to allow the aragonite to settle.

Immediately after sampling, the fluid was filtered through a 0.2 μm VWR cellulose acetate membrane filter and a sub-sample was acidified for cation concentration analyses. Reactive fluid carbonate alkalinity was determined in a second sub-sample, whereas the fluid pH was measured in-situ. At the end of the experimental run, the entire reactive fluid was vacuum filtered through a 0.2 μm membrane filter (Sartorius, cellulose acetate). The solids were rinsed with deionized water and dried at 40 °C.

Chemical and mineralogical analyses

Sodium elemental concentrations of the inlet solutions and the reactive fluids were measured using a Perkin Elmer Optima 8300 DV inductively coupled plasma optical emission spectrometer (ICP-OES) with an analytical precision of <±3 % (RSD), whereas Ca and Mg concentrations were determined by Inductively Coupled Plasma Mass Spectrometer (ICP-MS; Agilent 7500CX) with an analytical precision better than 2 % (RSD). The alkalinity of fluid samples was measured by standard HCl titration using an automatic Schott TitroLine alpha plus titrator with an uncertainty of ±2 %. The pH was measured using a SenTix ® 945 pH gel electrode from WTW, calibrated against NIST standard buffers.

Aqueous speciation, ion activities and saturation states of the reactive fluids with respect to aragonite (i.e. Ωaragonite) were calculated using PHREEQC software together with its MINTEQ.V4 database [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] after the addition of the solubility products of magnesite (Benezeth et al., 2011), hydromagnesite [START_REF] Gautier | Hydromagnesite solubility product and growth kinetics in aqueous solution from 25 to 75 °C[END_REF] and nesquehonite [START_REF] Harrison | Solubility of the hydrated Mg-carbonates nesquehonite and dypingite from 5 to 35 ο C: Implications for CO2 storage and the relative stability of Mg-carbonates[END_REF].

The mineralogy of seed material and collected solids was defined using X-ray powder diffraction (XRD) patterns that were recorded using a PANalytical X´Pert PRO diffractometer and Co-Kα-radiation (40 mA, 40 kV) in the 2θ range from 15 o to 60 o and with scan speed of 0.03 o s -1 . The qualitative characterization of crystalline products conducted using the PANalytical HighScore Plus software together with the ICSD database (aragonite: [START_REF] De | Crystal structures of aragonite, strontianite, and witherite[END_REF]calcite: Markgraf and Reeder, 1985) and the mineral phases were quantified by Rietveld refinement. Analytical uncertainty of this quantification was better than 1 wt.%. The precipitates were gold-coated and imaged using a ZEISS DSM 982 Gemini scanning electron microscope (SEM) equipped with a field emission gun operating at 5 kV accelerating voltage. The specific surface area of selected solids was measured with 11-point Kr isotherm using a Micromeritics TristarII plus surface area analyzer [START_REF] Brunauer | Adsorption of Gasses in Multimolecular layers[END_REF]. The Ca and Mg concentrations of the solids were determined using an Agilent 7500CX ICP-MS with an analytical precision better than 2% (RSD). Instrumental drift was corrected by using a mixture of Sc, Se, and Ge internal standard normalization, while the accuracy of the measurements was ensured by repeated measurement of SPS-SW1 reference material, XXI multi-element standard solution (Merck) and of an in-house artificial solution.

For the analysis ~80 mg of solid sample was digested in concentrated bi-distilled HNO3. The digestions were performed in duplicates to avoid potential heterogeneity of the powder and thus ensure the repeatability of the measurements.

Seed material

The aragonite seeds used in this study were synthesized prior to the experimental work. The majority of aragonite synthesis protocols use Mg as background electrolyte owing to the fact that this element inhibits calcite nucleation or growth (e.g., [START_REF] Bischoff | Catalysis, inhibition, and the calcite-aragonite problem; [Part] 2, The vaterite-aragonite transformation[END_REF][START_REF] Zhang | Influence of Mg 2+ on the kinetics of calcite precipitation and calcite crystal morphology[END_REF]. In order to reduce the presence of Mg in the synthesized aragonite, in the protocol developed in this study, aragonite seeds were synthesized in the absence of Mg. During synthesis, ~130 mL of a 1.52 M CaCl2 solution were titrated into a borosilicate reactor containing 1.5 L of a 0.066 M Na2CO3 solution, with the aid of a peristaltic pump operating at a flow rate of 0.6 mL/min. The temperature of the reactive solution was kept constant at 80±2 °C using a heating mantle system (series WMO TM , Mohr & Co) and it was continuously stirred at 300 rpm. The solution was filtered using a 0.2 µm cellulose acetate filter to recover the precipitates. After filtration, solids were rinsed three times with 200 mL of deionized water to remove NaCl residue and then dried at 80 °C for at least 24 h. The synthesized solid was aragonite with traces of calcite (<2 wt.%) as determined by X-ray diffraction analysis.

Scanning Electron Microscopy (SEM) images of the synthetic aragonite seeds revealed needle shaped aragonite crystals of 20-100 µm in length and 2-10 µm diameter (Fig. 2A).

The specific surface area of the seed material was 0.38 m 2 /g, whereas wet chemical analyses revealed that the seed contained ~0.5 µmol/g (i.e. ~13 ppm) Mg. The source of Mg can be assigned to impurities in the CaCl2 salts used during synthesis.

Results

Mineralogy and chemical composition of the precipitated solids

The XRD patterns of all the solid samples in this study are indicative of aragonite with trace amounts of calcite. Note here that the proportion of calcite in the bulk solids was lower than that measured in the seed material (i.e. < 2 wt. %) consistent with overgrowth of only aragonite in the experimental runs. X-ray diffraction patterns of selected samples can be seen in Fig. S1 of the Electronic Supplement. The synthesized aragonite seeds exhibit needlelike structure typical of this mineral phase (Fig. 2A). The solid materials recovered from the reactors at the end of each run exhibit surface features indicative of mineral overgrowth on seed material. As it can be seen in Figs. 2B-2F, the aragonite precipitates exhibit surface features typical for mineral overgrowth, including surface roughness, presence of steps and surface porosity and are noticeably different in surface morphology than the seed material displayed in Fig. 2A which appears to have a smooth surface. Note here that in experiments conducted at 5 o C SEM microphotographs depict aggregates of a few 10s of nm in size present on the precipitates (e.g. Fig. 2E and2F). The presence of these features is not associated with aragonite growth rate as can be deduced from a comparison of Fig. 2E and2F displaying experiments LiAr-23 (rp=10 -7.6 mol/m 2 /s) and LiAr-28 (rp=10 -7.2 mol/m 2 /s), respectively. Note here that such features were not observed in experiments conducted at 15 and 25 o C at similar growth rates. Moreover, their presence did not increase the reactive surface area of the precipitate. In fact, as can be seen in Table S1 of the Electronic Supplement, the reactive surface for samples LiAr-23 (Fig. 2E) and LiAr-28 (Fig. 2F) are 0.41 and 0.34 m 2 /g, respectively, and within error identical to the seed material (i.e. 0.38 m 2 /g).

The amount of aragonite overgrowth has been estimated based on mass balance considerations using the concentration of Ca in the inlet solutions and the reactive fluid under steady-state conditions. The mole fraction of Mg in aragonite overgrowths has been estimated using the measured Mg concentration of bulk sample corrected for the moles of Mg in the seed material. This calculation assumes that overgrowth consists only of aragonite, consistent with the reduction of calcite presence in the bulk solid as defined by XRD techniques. The Mg concentration of the bulk precipitate in each run can be found in Table 1. In the aragonite overgrowths, Mg concentrations achieve minimum values of 0.10, 0.16 and 0.27 mmol/mol for experiments performed at 25, 15 and 5 o C, respectively. The maximum Mg concentrations of the overgrowths achieve values of 0.69, 0.97 and 1.47 mmol/mol for experiments performed at 25, 15 and 5 o C, respectively. This observation suggests an inverse correlation of Mg content in the precipitated aragonite with increase in the growth temperature.

Chemical composition of the reactive fluids and growth rate calculations

An example of the temporal evolution of Ca and Mg concentrations and the prevailing pH of the reactive fluid can be seen in Fig. 3 for experiment LiAr-20. Chemical steady-state conditions with respect to aqueous Ca and Mg concentration occur in the total duration of the experimental runs. At these chemical steady-state conditions aragonite growth rate can be estimated based on mass balance considerations. The amount of aragonite precipitated can be approximated by the moles of Ca introduced in the reactor per time unit corrected for the moles of Ca removed from the reactor during sampling similar to [START_REF] Mavromatis | Zinc isotope fractionation during the inorganic precipitation of calcite -Towards a new pH proxy[END_REF] as:

𝑟 𝑝 = 𝑛 𝐶𝑎(𝑎𝑑𝑑) -𝑛 𝐶𝑎(𝑟𝑒𝑚) 86,400 /𝑆 (1)
where S is the reactive surface of aragonite in m 2 and 86,400 is the number of seconds per time unit (i.e. 24 h). In Eq. ( 1) rp is expressed in mol/m 2 /s and the estimated uncertainty is ~0.1 log units. The reactive surface S has been corrected for the mass of aragonite overgrowths precipitated during the course of each run based on mass balance considerations using the mass of the overgrowth and the reactive surface of the bulk sum of overgrowth and seed (see Table S1). In cases that the reactive surface area was not measured, it was assumed to be equal to that of the seed material (i.e. 0.38 m 2 /g). In addition, Eq. ( 1) does not consider the amount of Mg present in the solid phase, due to its low concentration in aragonite overgrowths. As can be seen in Table 1, aragonite growth rate in the experiments conducted in this study varies about 1.5 orders of magnitude within the range 10 -8.6 ≤ rp ≤ 10 -7.1

(mol/m 2 /s).

Magnesium partitioning between aragonite and the reactive fluid

The Mg distribution coefficient between formed aragonite and reactive fluid at chemical steady-state conditions can be estimated from the bulk Mg content of aragonite overgrowths and the molarities of aqueous Ca and Mg concentrations at chemical steady state conditions using the expression:

𝐷 𝑀𝑔 = ( 𝑀𝑔 𝐶𝑎 ) 𝑠𝑜𝑙𝑖𝑑 ( 𝑀𝑔 𝐶𝑎 ) 𝑓𝑙𝑢𝑖𝑑 (2)
where the subscript fluid denotes steady-state concentrations in the reactive fluid. Note here that the use of Eq. ( 2) is based on the assumptions that the presence of Mg in aragonite can be described as a diluted solid-solution that assumes random distribution of Mg in aragonite structure. Although XAFS data of Mg in coralline aragonite suggest that the latter is rather unlikely to occur and Mg is likely accommodated in nanodomains [START_REF] Finch | Mg structural state in coral aragonite and implications for the paleoenvironmental proxy[END_REF], the use of Eq. ( 2) allows for a systematic treatment of bulk Mg composition in aragonite and direct comparison with other divalent cation (i.e. Me 2+ ) replacement reactions in CaCO3 minerals where solid-solutions form. Additionally, the estimation of the Mg distribution coefficient in aragonite using Eq. ( 2) and the activities of free ions in the reactive fluid (i.e.

Ca 2+ and Mg 2+ ), produces DMg* values that are within error identical to those estimated with bulk concentrations (i.e. DMg) as can be seen in Table 1. The estimation of DMg* assumes that only free ions are incorporated in the growing mineral phase as is dictated by the classical mineral growth model [START_REF] Burton | The Growth of Crystals and the Equilibrium Structure of their Surfaces[END_REF] Overall, the dependence of Mg distribution coefficient on growth rate, described with Eqs (3a-3c), comes in agreement with the general behavior of incompatible Me 2+ during their incorporation in CaCO3 minerals for which an increase in DMe value can be observed at increasing growth rate (e.g. [START_REF] Zhong | Calcite and aragonite precipitation from seawater solutions of various salinities; precipitation rates and overgrowth compositions[END_REF][START_REF] Tesoriero | Solid solution partitioning of Sr 2+ , Ba 2+ , and Cd 2+ to calcite[END_REF][START_REF] Mavromatis | Barium partitioning in calcite and aragonite as a function of growth rate[END_REF][START_REF] Goetschl | Effect of sulfate on magnesium incorporation in low-magnesium calcite[END_REF].

Finally, regression analysis of the obtained results (least squares method) allows for the development of a numerical expression that combines the effects of temperature and growth rate on DMg and can be described by the linear equation:

Log DMg = 0.583(±0.020) Log rp -0.026(±0.001) T + 0.863(±0.153); R 2 = 0.97 (4)

where T is the temperature in degrees Celsius. Note here that Eq. ( 4) is only valid for the temperature and growth rate ranges of this study, and any application to other systems should be handled with caution.

Discussion

The role of growth rate in Mg incorporation in aragonite

The results of this study suggest that mineral growth rate is likely the major parameter controlling the incorporation of Mg in aragonite overgrowths. As can be seen in Table 1, for experiments conducted at 25 o C, an increase of rp from 10 -8.6 to 10 -7.1 (mol/m 2 /s) results in an increase in DMg values of about an order of magnitude from 1. DMe>1 at near equilibrium conditions such as Fe 2+ , Mn 2+ in calcite and Sr 2+ in aragonite (e.g. [START_REF] Lorens | Sr, Cd, Mn and Co distribution coefficients in calcite as a function of calcite precipitation rate[END_REF][START_REF] Dromgoole | Iron and manganese incorporation into calciteeffects of growth-kinetics, temperature and solution chemistry[END_REF]. In contrast an increase in DMe is observed during the incorporation of incompatible ions that are characterized by DMe<1 at near equilibrium conditions such as Ba 2+ and Sr 2+ in calcite and Ba 2+ in aragonite (e.g. [START_REF] Tesoriero | Solid solution partitioning of Sr 2+ , Ba 2+ , and Cd 2+ to calcite[END_REF][START_REF] Tang | Sr 2+ /Ca 2+ and 44 Ca/ 40 Ca fractionation during inorganic calcite formation: I. Sr incorporation[END_REF][START_REF] Mavromatis | Barium partitioning in calcite and aragonite as a function of growth rate[END_REF]. This dependence of DMe on growth rate suggests that at increasing growth rate the composition of the growing mineral is not controlled by thermodynamic principles and tends to achieve a composition similar to that of the forming fluid. Similar to other Me 2+ , the presence of Mg 2+ in calcite is also affected by mineral growth kinetics [START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]. Interestingly however, the dependence of Mg partitioning in calcite on mineral growth rate is significantly weaker compared to that observed in this study for Mg incorporation in aragonite. The incorporation of Mg in calcite exhibits an increase of roughly half an order of magnitude in DMg,calcite for an order of magnitude increase in growth rate [START_REF] Goetschl | Effect of sulfate on magnesium incorporation in low-magnesium calcite[END_REF]. The absolute value of DMg,calcite reported in the literature at 25 o C however, at similar surface normalized growth rates to those measured in this study for aragonite (i.e. 1.69 x 10 -5 ≤ DMg,aragonite ≤ 4.12 x 10 -4 , see Table 1), is 2-3 orders of magnitude larger (i.e. 0.01≤ DMg,calcite ≤ 0.04; [START_REF] Oomori | Distribution coefficient of Mg 2+ ions between calcite and solution at 10-50 °C[END_REF][START_REF] Mucci | Influence of temperature on the composition of magnesian calcite overgrowths precipitated from seawater[END_REF][START_REF] Howson | Synthesis and distribution coefficient of low-magnesium calcites[END_REF][START_REF] Burton | The effects of pCO2 and temperature on magnesium incorporation in calcite in seawater and MgCl2 -CaCl2 solutions[END_REF][START_REF] Hartley | The influence of pCO2 on the partitioning of magnesium in calcite overgrowths precipitated from artificial seawater at 25 o C and 1 atm total pressure[END_REF][START_REF] Huang | Partitioning of Sr 2+ and Mg 2+ into calcite under karstanalogue experimental conditions[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]2017).

The observed dependence of DMg on growth rate that can be seen in Fig. 4, comes in excellent agreement with the earlier observations by [START_REF] Gabitov | Experimental determination of growth rate effect on U 6+ and Mg 2+ partitioning between aragonite and fluid at elevated U 6+ concentration[END_REF]. These authors conducted experiments of nucleation and growth of aragonite crystals using the ammonium carbonate diffusion technique and reported increasing DMg values as a function of growth rate. The DMg values reported by [START_REF] Gabitov | Experimental determination of growth rate effect on U 6+ and Mg 2+ partitioning between aragonite and fluid at elevated U 6+ concentration[END_REF] lay in the range 1.9-7.5 x 10 -5 and are in good agreement with the results of this study. In contrast to the growth rate dependence of DMg values observed in this study and by [START_REF] Gabitov | Experimental determination of growth rate effect on U 6+ and Mg 2+ partitioning between aragonite and fluid at elevated U 6+ concentration[END_REF], the earlier work by [START_REF] Zhong | Calcite and aragonite precipitation from seawater solutions of various salinities; precipitation rates and overgrowth compositions[END_REF] found no growth rate effects on DMg values. Using a chemo-stat technique, similar to that used in this study, [START_REF] Zhong | Calcite and aragonite precipitation from seawater solutions of various salinities; precipitation rates and overgrowth compositions[END_REF] estimated an average DMg value of 6.9±1.3 x 10 -4 . The rather high DMg value was assigned by these authors to the presence of calcite in the aragonite seed and/or to differences in the analytical techniques used for the estimation of Mg in the solid [START_REF] Gabitov | Experimental determination of growth rate effect on U 6+ and Mg 2+ partitioning between aragonite and fluid at elevated U 6+ concentration[END_REF]. Additionally, it is likely that the higher DMg values reported by [START_REF] Zhong | Calcite and aragonite precipitation from seawater solutions of various salinities; precipitation rates and overgrowth compositions[END_REF] are to some extent also controlled by the composition of the background electrolyte, which in their experiments was artificial seawater of various salinities. For example, [START_REF] Bots | The role of SO4 in the switch from calcite to aragonite seas[END_REF] reported that the presence of sulphate in aragonite impacts its Mg content.

Although Mg is commonly present in natural aragonites such as corals, its presence in the crystal structure of this mineral phase is not favored according to thermodynamic considerations. The major limitation stems from the inability of Mg to increase its coordination from 6 in the Mg 2+ (aq) ion to 9 in this mineral phase that would lead to an ideal positioning in the Ca site in the crystal lattice. Indeed, molecular dynamic simulations have shown that at thermodynamic equilibrium, Mg presence in the surface of aragonite is energetically favored, however the replacement of Ca for Mg in the bulk solid is energetically less favored [START_REF] Ruiz-Hernandez | Mg/Ca Partitioning Between Aqueous Solution and Aragonite Mineral: A Molecular Dynamics Study[END_REF][START_REF] Kawano | Incorporation of Mg 2+ in surface Ca 2+ sites of aragonite: an ab initio study[END_REF].

The high sensitivity of DMg values to growth rate (Fig. 4) suggests that the incorporation of Mg in aragonite likely occurs at defect sites on the growing mineral surface.

Such behavior is common for incompatible ion incorporation in carbonate minerals (e.g., Li + , Na + , BO4 - , SO4 2-). For example, [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF] suggested that the incorporation of Na + in calcite depends on the density of crystal surface defects, which increases with the degree of saturation of the forming fluid with respect to the precipitating phase [START_REF] Teng | Kinetics of calcite growth; surface processes and relationships to macroscopic rate laws[END_REF]. As such, Na content in calcite has been observed to increase with increasing growth rate [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF][START_REF] Mucci | Manganese uptake during calcite precipitation from seawater -conditions leading to the formation of a pseudokutnahorite[END_REF][START_REF] Füger | Effect of growth rate and pH on lithium incorporation in calcite[END_REF]. As can be seen in Fig. 5, DMg values exhibit a positive dependence to the saturation degree in the forming fluid, with the latter parameter to control mineral growth. Indeed, as has been shown

by [START_REF] Teng | Kinetics of calcite growth; surface processes and relationships to macroscopic rate laws[END_REF] for calcite, at low supersaturation degrees, attachment of solutes mainly occurs at surface defect sites (i.e., dislocations, surface imperfections, grain boundaries) leading to spiral growth mechanism, whereas at increasing supersaturation mineral growth can also proceed by surface nucleation processes. Thus, it can be suggested that the increasing supersaturation of the fluid with respect to aragonite promotes the presence of defect sites on crystal surface and subsequently augments the concentration of Mg in the solid phase.

Mechanistically the elevated concentration of Mg in aragonite at higher growth rates can be explained by the growth entrapment model (GEM) [START_REF] Watson | A simple model for sector zoning in slowly grown crystals: Implications for growth rate and lattice diffusion, with emphasis on accessory minerals in crustal rocks[END_REF][START_REF] Watson | Surface enrichment and trace-element uptaking during crystal growth[END_REF][START_REF] Watson | A conceptual model for near-surface kinetic controls on the traceelement and stable isotope composition of abiogenic calcite crystals[END_REF]. The GEM proposes that trace elements/impurities that are incompatible with the mineral structure are enriched in the surface layer of the growing crystal. This implies that despite the lack of a diluted solid-solution formation in the magnesite-aragonite system, Mg concentration in the crystal lattice, would increase at elevated growth rates. The GEM has been successfully applied to describe the incorporation of both cations and anions between carbonate minerals and fluids in earlier studies [START_REF] Gabitov | Partitioning of strontium between calcite and fluid[END_REF][START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF][START_REF] Tang | Sr 2+ /Ca 2+ and 44 Ca/ 40 Ca fractionation during inorganic calcite formation: I. Sr incorporation[END_REF]. Interestingly, [START_REF] Gabitov | Experimental determination of growth rate effect on U 6+ and Mg 2+ partitioning between aragonite and fluid at elevated U 6+ concentration[END_REF]2011) applied the GEM and found that at ∼100% Mg entrapment in growing aragonite DMg should achieve a value up to 7.5 ±1.7 x10 -5 . This value is roughly half compared to the maximum value measured at 25 o C in this study (i.e. 1.33 x10 -4 ; exp LiAr-17), suggesting that greater Mg entrapment in aragonite, similar to what is observed in natural samples (e.g. [START_REF] Montagna | Li/Mg systematics in scleractinian corals: Calibration of the thermometer[END_REF][START_REF] Rollion-Bard | Possible controls on Li, Na, and Mg incorporation into aragonite coral skeletons[END_REF], is likely possible.

The role of temperature in Mg incorporation in aragonite

As can be seen in Fig. 4, at similar surface normalized growth rates, DMg values appear systematically lower as aragonite formation temperature increases. This observation is likely to be associated to the higher supersaturation of the reactive fluid with respect to aragonite at decreasing temperatures (Fig. 5), although surface normalized growth rates are similar among the three temperatures at which experiments were conducted in this study.

Note here that in all the runs of this study the availability of ions in the reactive fluid is controlled by the titration of the inlet solutions which was kept similar for all the three temperatures explored. Thus, the difference in the saturation of the fluid with respect to the aragonite among the three temperatures explored can be assigned to the retrograde solubility of aragonite [START_REF] Plummer | The solubilities of calcite, aragonite and vaterite in CO2 -H2O solutions between 0 and 90 o C, and an evaluation of the aqueous model for the system CaCO3-CO2-H2O. Geochim[END_REF]. For example, in experiments LiAr-18, LiAr-36 and LiAr-30 conducted at 25, 15 and 5 o C, respectively the measured surface-normalized growth rate was the same for all the three runs (i.e. ~10 -7.1 mol/m 2 /s). Yet, in these three runs Ωaragonite was 3.98, 4.66 and 5.29, respectively, exhibiting a systematic increase as formation temperature decreases. As has been observed earlier, a direct link occurs between supersaturation of the fluid from which carbonate mineral form and the presence of defect sites (e.g. [START_REF] Mcdermott | Holocene climate variability in Europe: Evidence from delta O-18, textural and extension-rate variations in three speleothems[END_REF][START_REF] Frisia | Calcite fabrics, growth mechanisms, and environments of formation in speleothems from the Italian Alps and southwestern Ireland[END_REF][START_REF] Wynn | Sulphate partitioning into calcite: Experimental verification of pH control and application to seasonality in speleothems[END_REF]. The presence of these defect sites promotes incorporates of incompatible ions in carbonate minerals (e.g. [START_REF] Pingitore | The coprecipitation of Sr 2+ with calcite at 25 o C and 1 atm[END_REF][START_REF] Uchikawa | Influence of solution chemistry on the boron content in inorganic calcite grown in artificial seawater[END_REF][START_REF] Wynn | Sulphate partitioning into calcite: Experimental verification of pH control and application to seasonality in speleothems[END_REF]. Thus, it can be inferred that the elevated supersaturation of the fluid with respect to aragonite observed in this study for experiments conducted at similar growth rates but different temperatures, promotes the incorporation of Mg in this mineral phase. This likely occurs as a result of the greater presence of surface defects promoted by the higher Ωaragonite values that occur at lower temperatures. similar correlation between DMg values and temperature was reported earlier by [START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF] in aragonite nucleation experiments. Actually, [START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF] proposed an exponential relationship between DMg and temperature in the range between 15 and 75 o C, suggesting a significant impact of temperature on Mg incorporation in aragonite.

Interestingly, differences in

We note here that overall the DMg values reported in [START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF] are about an order of magnitude higher than the maximum value measured in this study at 25 o C and about two orders of magnitude higher for experiments conducted at 5 o C. Likely the observed discrepancies in absolute DMg values can be assigned to differences in the experimental design. In this study, aragonite precipitation occurred via overgrowth on seed material at relatively low Ωaragonite (~1 to 5), whereas in [START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF] mineral formation occurred at Ωaragonite >25. The relatively high Ωaragonite values in the experiments of [START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF] were induced by the titration of a carbonate-bearing solution in the forming fluid that promoted an increased entrapment of traces/impurities in the initial nucleating and later growing aragonite crystals. Despite differences in experimental design impacting the magnitude of the estimated DMg values, the temperature trends observed in this study and [START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF] are consistent. A similar discrepancy in the magnitude of distribution coefficients due to differences in experimental setups has been observed in the Ba content of aragonite nucleated by [START_REF] Dietzel | Co-precipitation of Sr 2+ and Ba 2+ with aragonite by membrane diffusion of CO2 between 10 and 50 o C[END_REF] and [START_REF] Gaetani | Element partitioning during precipitation of aragonite from seawater: A framework for understanding paleoproxies[END_REF] compared to overgrowth experiments of [START_REF] Mavromatis | Barium partitioning in calcite and aragonite as a function of growth rate[END_REF]. Alternatively, the high supersaturation degrees of CaCO3 formation in these earlier studies likely led to mineral formation through an amorphous precursor, which could impact the extent of Me incorporation [START_REF] Purgstaller | Transformation of Mg-bearing amorphous calcium carbonate to Mg-calcite -In situ monitoring[END_REF]2017).

4.3 Implications for the modelling of trace metal incorporation in CaCO3 minerals and the use of Mg content in natural aragonites

The incorporation of Me 2+ in CaCO3 minerals is commonly modelled based on the assumption that an ideal solid-solution occurs between the pure Me-carbonate mineral and the CaCO3 phase (e.g. [START_REF] Sverjensky | Prediction of Gibbs free-energies of calcite-type carbonates and the equilibrium distribution of trace-elements between carbonates and aqueous-solutions[END_REF][START_REF] Sverjensky | The distribution of divalent trace-elements between sulfides, oxides, silicates and hydrothermal solutions .1. Thermodynamic basis[END_REF][START_REF] Rimstidt | Distribution of trace elements between carbonate minerals and aqueous solutions[END_REF][START_REF] Wang | Prediction of trace metal partitioning between minerals and aqueous solutions: A linear free energy correlation approach[END_REF].

For example, the model of [START_REF] Rimstidt | Distribution of trace elements between carbonate minerals and aqueous solutions[END_REF] correlates the solubility products of pure end-member carbonates with partitioning of traces in calcite, it ignores however, that crystal structure is an important parameter that affects incorporation, as for example that of Ba and Sr in calcite. Indeed, witherite (BaCO3) and strontianite (SrCO3) crystallize in the orthorhombic system at ambient temperatures and thus are not isostructural to rhombohedral calcite making the modelling of their replacement somewhat complex. This complication was pointed out by [START_REF] Böttcher | Solid solution partitioning of Sr 2+ , Ba 2+ , and Cd 2+ to calcite -Comment[END_REF] for the experimental work of [START_REF] Tesoriero | Solid solution partitioning of Sr 2+ , Ba 2+ , and Cd 2+ to calcite[END_REF] on the incorporation of Ba and Sr in calcite. In an effort to resolve the issue of mineral structure, [START_REF] Sverjensky | Prediction of Gibbs free-energies of calcite-type carbonates and the equilibrium distribution of trace-elements between carbonates and aqueous-solutions[END_REF][START_REF] Sverjensky | The distribution of divalent trace-elements between sulfides, oxides, silicates and hydrothermal solutions .1. Thermodynamic basis[END_REF] correlated metal partitioning with the Gibbs free energy of the formation of end-member metal carbonates. Even for this theoretical consideration however, when the Gibbs free energy of formation is used for the orthorhombic magnesite-aragonite solid-solution [START_REF] Sverjensky | A linear free-energy relationship for crystalline solids and aqueous ions[END_REF] a rather elevated DMg value of 10 -2.93 at 25 o C can be estimated, which is ~2 orders of magnitude higher than the DMg value closest to equilibrium measured in this study at 25 o C (i.e 10 -4.76 in experiment LiAr-1; Table 1).

Although the theoretical modeling of Me 2+ incorporation in CaCO3 minerals may deviate from experimental studies or natural analogues, the ideal replacement of Ca 2+ for Me 2+ has been shown for a large number of elements present in calcite (e.g., Ba, Co, Mg, Zn; [START_REF] Reeder | XAFS study of the coordination and local relaxation around Co 2+ , Zn 2+ , Pb 2+ , and Ba 2+ trace elements[END_REF][START_REF] Finch | Coordination of Sr and Mg in calcite and aragonite[END_REF] [START_REF] Montagna | Li/Mg systematics in scleractinian corals: Calibration of the thermometer[END_REF]. For corals, the correlation between Mg/Ca and the calcification rates has been reported for a number of specimens grown in cultures (e.g. [START_REF] Inoue | Empirical assessment of coral Sr/Ca and Mg/Ca ratios as climate proxies using colonies grown at different temperatures[END_REF][START_REF] Reynaud | Light and temperature effects on Sr/Ca and Mg/Ca ratios in the scleractinian coral Acropora sp[END_REF]. In bio-induced carbonates however, a number of processes have been shown to affect Mg content that includes the presence of organic layers (e.g. [START_REF] Foster | Seawater pH, pCO2 and CO3 2variations in the Caribbean Sea over the last 130 kyr: A boron isotope and B/Ca study of planktic forminifera[END_REF], pH variations in the calcifying fluid (e.g. [START_REF] Holcomb | Compositional and morphological features of aragonite precipitated experimentally from seawater and biogenically by corals[END_REF], compartmentalized precipitation (e.g. [START_REF] Rollion-Bard | Boron isotopes as pH proxy: A new look at boron speciation in deep-sea corals using 11 B MAS NMR and EELS[END_REF][START_REF] Rollion-Bard | Possible controls on Li, Na, and Mg incorporation into aragonite coral skeletons[END_REF] and formation via an amorphous precursor phase (e.g. [START_REF] Rollion-Bard | Boron isotopes as pH proxy: A new look at boron speciation in deep-sea corals using 11 B MAS NMR and EELS[END_REF][START_REF] Mass | Amorphous calcium carbonate particles form coral skeletons[END_REF]. Thus, the rate effect described in Eqs (3a-3c)

Rollion

may not be directly applicable in natural samples.

The results of the present study indicate that if properly calibrated, Mg in aragonite may provide pertinent information on the formation conditions of natural aragonites. As can be seen in Fig. 5 These relations suggest that if the temperature of formation is known or can be estimated (e.g., δ 18 Ο compositions of the samples), the Mg content of aragonite can provide insights for the degree of supersaturation of the forming fluid and/or the carbonate ion concentration if the chemical composition of the forming fluid can be hypothesized (e.g., seawater). Such correlation between Mg/Ca ratio and carbonate ion concentration has been earlier shown in the aragonitic foraminifera species Hoeglundina elegans [START_REF] Rosenthal | Temperature and carbonate ion effects on Mg/Ca and Sr/Ca ratios in benthic foraminifera: Aragonitic species Hoeglundina elegans[END_REF]. Note however that the range of Ωaragonite is not the same among the three temperatures groups explored (see Table 1) thus the use of Eqs. (5a-5c) may require further calibration that reflect conditions met in natural systems. Overall, the relationship between Mg content of aragonite with the degree of saturation of the fluid with respect to this mineral phase suggest that in the case of proper calibration (e.g., for seawater-like fluids), DMg or Mg/Ca ratio in the forming solid can be used as a proxy for saturation degree of the fluid with respect to CaCO3 minerals.

Conclusions

The experimental work performed in this study documents that the presence of Mg in

  . Owing to the similar values of DMg* and DMg in all the runs only the latter parameter is discussed below. The minimum DMg values estimated in this study at 25, 15 and 5 o C are 1.69 x10 -5 , 2.52 x10 -5 and 5.47 x10 -5 , respectively, whereas the maximum DMg values at the same temperatures were 1.33 x10 -4 , 2.20 x10 -4 , and 4.12 x10 -4 , respectively. Similar to the Mg content of aragonite overgrowths, the lowest DMg values are observed at the highest overgrowth temperature in this study (i.e. at 25 o C). The dependence of DMg on aragonite growth rate as it has been calculated with Eq. (2) for experiments at 25, 15 and 5 o C respectively, can be numerically described with the aid of the linear equations: Log DMg,25 = 0.586 (±0.029) Log rp +0.231 (±0.225); R 2 =0.96 (3a) Log DMg,15 = 0.578 (±0.041) Log rp +0.438 (±0.312); R 2 =0.95 (3b) Log DMg,5 = 0.584 (±0.039) Log rp +0.738 (±0.302); R 2 =0.95 (3c) and are valid for aragonite growth rate of 10 -8.6 ≤ rp ≤ 10 -7.1 (mol/m 2 /s). The obtained results of the co-precipitation experiments conducted in this study are plotted as a function of aragonite growth rate in Fig. 4. These trends suggest that the temperature dependence of DMg values is the same within error for all of the temperatures examined in this study.

  69 x10 -5 to 1.33 x10 -4 . A similar dependence of DMg on growth rate can be seen also for experiments conducted at 15 and 5 o C as is depicted in Fig. 4. Actually, the slopes of Eqs (3a-3c) are identical within uncertainty, implying that the same mechanism is controlling DMg in the temperature range between 5 and 25 o C. Mineral growth rate is a well-studied parameter controlling the incorporation of Me 2+ in CaCO3 minerals. As has been shown by Rimstid et al. (1998), an increase in growth rate results in a decrease of DMe during the formation of CaCO3 minerals for elements exhibiting

  DMg values are not only associated with differences of Ωaragonite at different formation temperatures, but are also directly controlled by the temperature of aragonite formation. This is observed in experiments conducted at very low growth rate when the degree of supersaturation of the fluid with respect to aragonite is similar among the three formation temperatures. For example, in experiments LiAr-1, LiAr-31 and LiAr-25 conducted at 25, 15 and 5 o C, respectively, the measured Ωaragonite was ~1.1. Despite the similarity in Ωaragonite a significant variation in DMg values occurs with an increase from 10 -4.77 at 25 o C (LiAr-1) to 10 -4.09 at 5 o C (LiAr-25). Thus, at near equilibrium conditions, temperature is directly controlling the Mg incorporation in aragonite, although the exact mechanism promoting the incorporation of this cation in aragonite at lower temperatures requires further investigation. The decrease of DMg values with increasing temperature are consistent with the results of Gabitov et al. (2008), who reported reduced Mg/Ca ratio in aragonite overgrowths formed at 53 o C compared to those formed at 22 o C. Moreover, a

  , there is a linear dependence between DMg values and the degree of aragonite supersaturation in the forming fluid. Those can be numerically described for experiments conducted at 25, 15 and 5 o C, respectively, as: Log DMg,25 = 1.146 (±0.092) LogΩArag -4.803 (±0.036); R 2 =0.94 (5a) Log DMg,15 = 1.339 (±0.144) LogΩArag -4.527 (±0.062); R 2 =0.88 (5b) Log DMg,5 = 1.192 (±0.154) LogΩArag -4.300 (±0.075); R 2 =0.84 (5c)

  aragonite is predominantly affected by mineral growth rate and to a lesser extent by temperature. The strong increase of DMg values at increasing growth rate suggests that Mg in aragonite can be a robust indicator of mineral growth rate, if formation temperature is known.Additionally, the results provide insights on the mechanisms controlling the presence of Mg in aragonite overgrowths. Indeed, the inverse correlation between DMg values and temperature for experiments performed at similar surface normalized growth rates together with the observed higher degree of saturation at lower formation temperatures suggests that incorporation of Mg in this mineral phase might be associated with the presence of surface defect sites. Here the retrograde solubility of aragonite at lower temperatures promotes a larger number of defect sites due to higher saturation of the fluid with respect to the growing mineral at decreasing temperatures. This feature suggests that DMg values and Mg/Ca ratio in natural aragonite have the potential to be used as a proxy of fluid saturation degree with respect to CaCO3 minerals. Finally, and in contrast to the behavior of other divalent cations during their incorporation in CaCO3 minerals, the co-precipitation of Mg with aragonite cannot be modelled as a diluted solid-solution using thermodynamic considerations. Similar to the presence of other incompatible ions in carbonate minerals presence of Mg in aragonite requires empirical calibrations, specific for the background electrolyte composition of the forming fluid.

  and aragonite (e.g., Ba, Sr;[START_REF] Finch | Coordination of Sr and Mg in calcite and aragonite[END_REF] based on spectroscopic techniques. In contrast the experimental results of this study suggest that during its incorporation in aragonite, Mg is behaving as an incompatible element to the mineral structure, exhibiting a high sensitivity to mineral growth rate. Similar dependencies of the distribution coefficients of incompatible ion incorporation in CaCO3 minerals have been earlier shown for Li[START_REF] Füger | Effect of growth rate and pH on lithium incorporation in calcite[END_REF] and B[START_REF] Mavromatis | Characterization of boron incorporation and speciation in calcite and aragonite from co-precipitation experiments under controlled pH, temperature and precipitation rate[END_REF][START_REF] Uchikawa | Experimental evidence for kinetic effects on B/Ca in synthetic calcite: Implications for potential B(OH)4and B(OH)3 incorporation[END_REF]. For these elements the exact position in the crystal lattice is still under debate and as such theoretical modelling has been proven to deviate from experimental calibrations and natural samples. Considering that the obtained relationship between DMg and growth rate is affected by temperature and most likely by background electrolyte composition, it can be suggested that the use of incompatible elements in carbonate minerals, including Mg in aragonite, requires empirical calibrations in order to be applied in biological systems. For example, the high sensitivity of DMg on aragonite growth rate suggests that Mg content in this mineral phase can be used as a tool for mapping growth rate regimes in speleothems that usually form from solution with low degrees of supersaturation with respect to CaCO3 minerals. Actually,[START_REF] Wassenburg | Determination of aragonite trace element distribution coefficients from speleothem calcite-aragonite transitions[END_REF] presented data on speleothem aragonites characterized by an average DMg value of 9.7 x 10 -5 that lays well within the range estimated in this study. Similarly, the reported DMg values ofa number of other aragonitic archives fall well within the range of values measured in this study, including the Manila

	The good correlation between mineral growth rate and DMg values numerically
	described using Eqs (3a-3c) including the effect of temperature (Eq. 4) likely provides the
	means for the potential use of aragonite Mg content or Mg/Ca ratio as a proxy tool in natural
	samples.

clams R. philippinarum (DMg= 4.6 -6.2 x 10 -4 ;

[START_REF] Poulain | An evaluation of Mg/Ca, Sr/Ca, and Ba/Ca ratios as environmental proxies in aragonite bivalve shells[END_REF]

, fresh water mussel shells Lampsilis cardium (DMg= 3 -8 x 10 -4 ;

[START_REF] Geeza | Controls on magnesium, manganese, strontium, and barium concentrations recorded in freshwater mussel shells from Ohio[END_REF]

and scleractinian corals of various species (DMg= 3 -5 x 10 -4 ;

Table 1 :

 1 Temperature, Mg/Ca ratio in aragonite overgrowths, saturation state of the forming fluid with respect to aragonite (i.e. Ωaragonite), aragonite growth rate and distribution coefficient of Mg in aragonite based on concentrations (i.e. DMg) and activities of free ions (i.e. DMg*) in the reactive fluid.

Acknowledgments

For her assistance with ICP-OES, the authors are thankful to Stefanie Eichinger. Anna

Harrison is highly acknowledged for her support with BET analyses and her help with English. We wish to thank Jacques Schott and Michael Böttcher for fruitful discussions. This manuscript benefitted from the insightful comments of three anonymous reviewers. This work was funded by the French National program INSU/LEFE, the FWF project P 31832-N29 and supported by DFG-FWF collaborative research initiative CHARON II (DFG Forschergruppe 1644, FWF-I3028-N29) and NAWI Graz (Central Lab for Water, Minerals and Rocks).