Juliette Simon

Gabin Guélou

Bhuvanesh Srinivasan

David Berthebaud
email: david.berthebaud@cnrs.fr

Takao Mori

Antoine Maignan
email: antoine.maignan@ensicaen.fr

Exploring the thermoelectric behavior of Spark Plasma Sintered Fe7-xCoxS8 compounds

Keywords: Co-doped Pyrrhotites, Sulfides, SPS, Thermoelectrics, Structural transition, Improved power factor

Sulfide-based materials are emerging as viable alternatives for the current state-of-the-art thermoelectric materials, which usually are composed of toxic, expensive and scarce elements. Here, a systematic study of one such inexpensive and environmentally friendly sulfide-based system, i.e. Fe7-xCoxS8 pyrrhotitetype compounds that were synthesized by solid-state reaction and densified by Spark Plasma Sintering are investigated for their structural and thermoelectric properties. We report that substitution of Co for Fe in pyrrhotites: (i) induces structural transition from monoclinic 4C superstructure to trigonal 3C superstructure; (ii) modifies the magnetic behavior by decreasing the magnetic ordering temperature and magnetization; (iii) alters the type of dominant charge carriers (from p-to n-type) and enhances their electrical transport properties; (iv) mitigates the phonon contribution to the thermal conductivity; and (v) amplifies the thermoelectric figure of merit when compared with that of pristine pyrrhotites.

Introduction

Thermoelectric (TE) materials and devices have drawn increasing interest and attention due to their potential to reversibly convert waste heat into electricity [START_REF] Petsagkourakis | Thermoelectric materials and applications for energy harvesting power generation[END_REF][START_REF] Tritt | Thermoelectric Materials, Phenomena, and Applications: A Bird's Eye View[END_REF][START_REF] Mori | Materials for energy harvesting: At the forefront of a new wave[END_REF][START_REF] Srinivasan | Possible Mechanism for Hole Conductivity in Cu-As-Te Thermoelectric Glasses: A XANES and EXAFS Study[END_REF]. The TE material's efficiency is quantified by a dimensionless figure of merit, zT = S 2 σT/κ where S, σ, T and κ are the Seebeck coefficient, electrical conductivity, absolute temperature and total thermal conductivity (sum of the electronic part, κe, and the lattice part, κlatt), respectively. Industrial applications require large-scale economic and environmentally benign high performance TE materials. However, the current state-of-the-art TE materials are usually composed of expensive, scarce, or toxic heavy elements such as Pb, Te, Bi, Ge, Sb etc [START_REF] Perumal | High performance thermoelectric materials and devices based on GeTe[END_REF][START_REF] Srinivasan | Thermoelectric Properties of Highly-Crystallized Ge-Te-Se Glasses Doped with Cu/Bi[END_REF][START_REF] Biswas | High-performance bulk thermoelectrics with all-scale hierarchical architectures[END_REF][START_REF] Srinivasan | Detrimental Effects of Doping Al and Ba on the Thermoelectric Performance of GeTe[END_REF][START_REF] Snyder | Complex thermoelectric materials[END_REF][START_REF] Srinivasan | Impact of Coinage Metal Insertion on the Thermoelectric Properties of GeTe Solid-State Solutions[END_REF][START_REF] Pei | Convergence of electronic bands for high performance bulk thermoelectrics[END_REF][START_REF] Srinivasan | Enhancement in thermoelectric performance of n-type Pb-deficit Pb-Sb-Te alloys[END_REF]. In the past few years, sulfide materials have gained considerable limelight due to their wide range of potential applications ranging from photovoltaics to thermoelectrics [START_REF] Fan | Energetic I-III-VI2 and I2-II-IV-VI4 nanocrystals: synthesis, photovoltaic and thermoelectric applications[END_REF]. Among those sulfide materials, particular attention has been given to copper-based compounds such as Cu2-xS, chalcopyrites, cubanites, colusites and high-entropy copper sulfides [START_REF] He | High Thermoelectric Performance in Non-Toxic Earth-Abundant Copper Sulfide[END_REF][START_REF] Lefèvre | Thermoelectric properties of the chalcopyrite Cu1-xMxFeS2-y series (M = Mn, Co, Ni)[END_REF][START_REF] Barbier | Structural and thermoelectric properties of n-type isocubanite CuFe2S3[END_REF][START_REF] Bourgès | High-Performance Thermoelectric Bulk Colusite by Process Controlled Structural Disordering[END_REF][START_REF] Zhang | Data-Driven Design of Ecofriendly Thermoelectric High-Entropy Sulfides[END_REF]. However, not much information is available on the Cu-free sulfides for TE application. In this work, one such Cu-free sulfide is explored, i.e. pyrrhotite-type Fe7S8 compounds have been looked at, as both Fe and S are inexpensive, non-toxic and are more abundant in earth's crust. The cobalt substitution for iron, i.e. bringing more electrons, is also investigated in this present work. The choice of this material system also stems from their interesting superstructure formations and magnetic structural transitions [START_REF] Powell | Structure and magnetism in synthetic pyrrhotite Fe7S8: A powder neutron-diffraction study[END_REF][START_REF] Baranov | Layer-preferential substitutions and magnetic properties of pyrrhotite-type Fe7-yMyX8 chalcogenides (X= S, Se; M= Ti, Co)[END_REF], which could play a role in their electrical and thermal transport properties. Magnetic enhancement of TE properties has previously been reported in some systems [START_REF] Vaney | Magnetism-mediated thermoelectric performance of the Cr-doped bismuth telluride tetradymite[END_REF][START_REF] Tsujii | Observation of enhanced thermopower due to spin fluctuation in weak itinerant ferromagnet[END_REF]. Although magnetic and structural properties of these pyrrhotite compounds have been widely studied, their TE behavior has never been explored, especially on the cobalt-doped pyrrhotites, which this work aims to shed some light on.

Materials & Methods

The samples of Fe7-xCoxS8 (0 ≤ x ≤ 7) were prepared by a two-step process: firstly, the ingots were obtained by the vacuum sealed-tube melting process (heated at 1223 K for 24 h), and secondly, the obtained ingots were crushed into powders and consolidated by Spark Plasma Sintering (SPS-1080 -SPS Syntex Inc.) at 773 K (heating rate ~ 60 K/min) for 15 mins (holding time) under an axial pressure of 75 MPa in Ar atmosphere. The sintered discs were then cut and polished to the required shapes and dimensions for various thermoelectric measurements.

Powder X-ray diffraction

Powder X-ray diffraction (PXRD) patterns were recorded at room temperature in the 2θ range of 10 o -90 o in 1 hour using a PANalytical X'Pert Pro diffractometer (Cu Kα1/ Kα2 radiation, λ = 1.540598 Å, 1.544426 Å, PIXcel 1D detector). Le bail fitting was performed using FullProf program [START_REF] Rodríguez-Carvajal | Recent advances in magnetic structure determination by neutron powder diffraction[END_REF] included in the WinPLOTR software.

Electrical and thermal transport measurements

The electrical resistivity and Seebeck coefficient were measured simultaneously using a commercial instrument (ZEM-2, ADVANCE RIKO Inc.) under the partial pressure of He on ~ 2 × 2 × 6 mm 3 bars.

The temperature dependent thermal diffusivity, D, was measured using the laser flash diffusivity method in LFA-467 Hyperflash (Netzsch) on disk-shaped samples of 10 mm diameter and ~ 2 mm thickness. The temperature dependent heat capacity, Cp, was derived using a standard sample (pyroceram) in LFA-467, which is in good agreement with the Dulong-Petit Cp value. The total thermal conductivity was calculated using the formula, κ = DCpρ, where ρ is the density of the sample (measured using Archimedes' principle). To better understand the thermal transport properties, the contributions from electronic and lattice parts were calculated. The lattice thermal conductivity (latt) was estimated from  by subtracting the electronic contribution (e) via Wiedemann-Franz law, as in the following equation,

𝜅 𝑒 = 𝐿𝜎𝑇
where e is the electronic thermal conductivity and L is the Lorenz number computed by the condensed version of Single Parabolic Band model with acoustic phonon scattering (SPB-APS), as in the following equation,

𝐿 = 1.5 + exp [- |𝑆| 116 ]
where Seebeck coefficient (S) is in µVK -1 and Lorenz number (L) is in 10 -8 WΩK -2 .

The uncertainty in the results for the values of electrical and thermal transport properties was 5% and 7%, respectively and for the overall zT was  12%. Error bars are not shown in the figures to increase readability.

Differential scanning calorimetry (DSC) analysis was performed using Thermo-plus EVO (Rigaku Co.) on a small piece of the bulk sample (~ 30 mg).

Magnetic measurements

The magnetization, M was measured as a function of temperature, T (at a constant H = 100 Oe) and as a function of external field, H (at a constant T = 2.5 K) using the Magnetic Properties Measurement System (MPMS, Quantum Design). ZFC mode during heating cycle (4 K -300 K) and FCC mode during cooling cycle (300 K -4 K). A small piece of the sample (~ 20 mg) was loaded into a gelatin capsule for the magnetic measurements.

Results and discussion

Highly densified samples of Fe7-xCoxS8 (x = 0, 2.8, 4.2, 5, 6, 6.5, 7) were obtained after SPS processing. The density of the sintered disks was found to be ~ 97% of the theoretical density. It must be noted that it is a unique highlight from this work, as such compounds have never been processed by SPS in the past. So far, such Fe7S8 based pyrrhotite-type compounds that were presented in the literature were usually synthesized by the conventional (one-step process) sealed-tube melting route [START_REF] Powell | Structure and magnetism in synthetic pyrrhotite Fe7S8: A powder neutron-diffraction study[END_REF][START_REF] Baranov | Layer-preferential substitutions and magnetic properties of pyrrhotite-type Fe7-yMyX8 chalcogenides (X= S, Se; M= Ti, Co)[END_REF]. The rational for employing this 2-step process via SPS is that, it has been proved time and again that SPS processing can control the grain growth [START_REF] Guillon | Field-Assisted Sintering Technology/Spark Plasma Sintering: Mechanisms, Materials, and Technology Developments[END_REF] and can induce nanoscale defects and precipitates, thus scattering a wide spectrum of heat carrying phonons (panoscopic approach [START_REF] Zhao | The panoscopic approach to high performance thermoelectrics[END_REF][START_REF] He | High performance bulk thermoelectrics via a panoscopic approach[END_REF]) when compared to the conventional melt processing (one-step process) route [START_REF] Biswas | High-performance bulk thermoelectrics with all-scale hierarchical architectures[END_REF][START_REF] Srinivasan | Effect of the Processing Route on the Thermoelectric Performance of Nanostructured CuPb18SbTe20[END_REF][START_REF] Srinivasan | Thermoelectric performance of codoped (Bi, In)-GeTe and (Ag, In, Sb)-SnTe materials processed by Spark Plasma Sintering[END_REF][START_REF] Srinivasan | Realizing a stable high thermoelectric zT ∼ 2 over a broad temperature range in Ge1-x-yGaxSbyTe via band engineering and hybrid flash-SPS processing[END_REF]. Importantly, PXRD pattern did not show evidence of any structural change after SPS processing (Supporting Info -SI, Figure S1). Only peak sharpness was slightly increased due to an increased crystallinity through SPS processing. Similar to the work of Baranov et al. [START_REF] Baranov | Layer-preferential substitutions and magnetic properties of pyrrhotite-type Fe7-yMyX8 chalcogenides (X= S, Se; M= Ti, Co)[END_REF], our pristine Fe7S8 compound was found to crystallize in the monoclinic 4C superstructure (space group C2/c) with parameters a = 11.931(3) Å, b = 6.886(6) Å, c = 12.891(1) Å and β = 117.20(1)°. Cobalt substituted samples were found to crystallize in the trigonal 3C superstructure (space group P3121, SI, Figure S2). In the Fe7-xCoxS8 series, for the values of x > 5, secondary phases that could not be indexed with the existing databases were present. Hence, in the forthcoming sections of this paper, the discussion is limited to the solubility or solid-solution limit (x ≤ 5). Our results show that the Co for Fe substitution in the Fe7-xCoxS8 system leads to changes in the crystal structure with the formation of a different NiAs superstructure. According to Baranov et al. [START_REF] Baranov | Layer-preferential substitutions and magnetic properties of pyrrhotite-type Fe7-yMyX8 chalcogenides (X= S, Se; M= Ti, Co)[END_REF], such Fe7-xCoxS8 compounds have a layered crystal structure of the NiAs-type and can be characterized by the lattice parameters a0 and c0 of the primitive NiAs-type unit cell. The evolution of the calculated lattice parameters a0 and c0 is presented in Figure 1. The decreasing trend of c0 stipulates at the decrease of the inter-layer distances with the substitution of Co for Fe. In other words, addition of Co leads to the contraction of the crystal lattice, which is in agreement with the previous reports [START_REF] Baranov | Layer-preferential substitutions and magnetic properties of pyrrhotite-type Fe7-yMyX8 chalcogenides (X= S, Se; M= Ti, Co)[END_REF][START_REF] Sato | Magnetic properties and anisotropy of (Fe1-xCox)7Se8[END_REF]. The a0 parameter is rather constant with Co substitution (contrary to the c0 parameter), implicating a substantially different compressibility of the crystal lattice perpendicular and parallel to the layers. Interestingly, the cobalt substitution enhances the electrical conductivity by about 2 orders of magnitude (Figure 2a) when compared to that of pristine pyrrhotite. Moreover, substitution of Fe by Co induces a sign change of the room temperature Seebeck coefficient from positive to negative (Figure 2b). This suggests that the transport turns from p-type in pristine sample to n-type as cobalt adds electrons in the pyrrhotite. Even in this pristine pyrrhotite, the n-type charge carriers begin to dominate the transport at temperatures above 525 K, which is discussed based on their electronic band structure in the following section. Both the increase in the electrical conductivity and the modification in Seebeck behavior (p-to n-type) with cobalt substitution can be attributed to the increase of the charge carrier concentration as the electrons begin to fill the conduction band when Co is substituted for Fe. The cation Co 2+ has one more electron in its valence shell than Fe 2+ . Due to the changes in σ and S, the thermoelectric factor (PF = S 2 σ) is significantly improved with cobalt substitution (Figure 2c). The σ increase with cobalt substitution impacts the total thermal conductivity (Figure 2d), mainly through the higher contribution from the electronic part, κe (SI, Figure S3(c)). More interestingly, it must be noted that the lattice part of the thermal conductivity, κlatt is also significantly reduced with the Co substitution (Figure 2e), possibly due to reasons such as local defects (segregation of 3C defects in the 4C), role of magnons, and micro/nano-scale artifacts formed during the SPS processing. The cumulative effect of noted improvement in the electrical transport and a considerable suppression of the thermal transport (phonon) with cobalt doping is obviously enhancing the zT (Figure 2f). The Co substituted sample with the composition of x = 0.05 exhibited the highest zT ~ 0.004 at 573 K, which is few orders of magnitude greater than that of related pristine pyrite that was reported very recently [START_REF] Zuñiga-Puelles | Structural stability and thermoelectric performance of high quality synthetic and natural pyrites (FeS2)[END_REF]. However, it must be noted that these zT values are too low for any potential industrial application. The temperature dependent specific heat (Cp) data obtained from the differential scanning calorimetry (DSC) analysis evidences some potential structural transition happening in the pristine pyrrhotite at ~ 590 K (Figure 3). Based on their magnetic measurements, Powell et al. [START_REF] Powell | Structure and magnetism in synthetic pyrrhotite Fe7S8: A powder neutron-diffraction study[END_REF] suggested a phase transition from monoclinic 4C magnetically ordered state to a hexagonal NiAs cation deficient state (1C) at 598 K for the pristine Fe7S8. The sharp bump at ~ 590 K from our DSC data for the pristine sample supports their phase transition (from 4C to 1C) claim, which was based on their magnetic measurement data. In the ferrimagnetic state (below TC ≈ 600K), the electronic band structure of Fe7S8 differs considerably from that of the paramagnetic state owing to the large exchange splitting (~ 3.2 eV) of the 3d states of each Fe-site, and in the non-magnetic state, the Fermi level lies at the higher energy side of the electronic density of states in the non-bonding part of the hybridized bands composed of Fe 3d and S 3p orbitals [START_REF] Shirai | Electronic band structure and photoemission spectra of Fe7S8[END_REF]. This explains the p-to n-type transport change with temperature for the pristine pyrrhotite. From Cp, no such phase transition (in relation with the 3C structural ordering) was observed for the cobalt doped samples in this measurement range from K to 673 K. The substitution of Co for Fe reduced the magnetization, as can be referred from Figure 4a, which displays the M versus H dependences on the Fe7-xCoxS8 (0 ≤ x ≤ 5) compounds at T = 2.5 K. The magnetic ordering temperature was also observed to decrease with Co content, as can be referred from the temperature dependences of the magnetization measured at H = 100 Oe (Figure 4b). The magnetic behavior of these compounds is found to be consistent with the previously reported work [START_REF] Baranov | Layer-preferential substitutions and magnetic properties of pyrrhotite-type Fe7-yMyX8 chalcogenides (X= S, Se; M= Ti, Co)[END_REF], despite the differences in their synthesis methodology. Magnetic enhancement has been reported for some systems [START_REF] Vaney | Magnetism-mediated thermoelectric performance of the Cr-doped bismuth telluride tetradymite[END_REF][START_REF] Tsujii | Observation of enhanced thermopower due to spin fluctuation in weak itinerant ferromagnet[END_REF], however, in this case, the improvement in the thermoelectric properties appear to be driven by the changes in the charge carriers.

Conclusion

Highly dense samples of Fe7-xCoxS8 (0 ≤ x ≤5) compounds were successfully synthesized by a two-step process (melt-processing followed by SPS). Substitution of Co for Fe in pyrrhotites was found to induce some following changes: (i) modification of the crystal structure and to the formation of different superstructure derived from NiAs (from monoclinic 4C to trigonal 3C); (ii) increasing the charge carrier density, and altering the type of majority charge carriers from p-to n-type, thus resulting in a notable enhancement in the electrical transport (i.e., improved thermoelectric power factor); (iii) considerable suppression of the phonon contribution to the thermal conductivity; (iv) significant boost in the thermoelectric figure of merit (albeit not much significant for a practical application); and (v) reduction in their magnetic ordering temperature and the magnetization. In addition, the pristine Fe7S8 compound was found to undergo a phase transition from monoclinic 4C magnetically ordered state to a hexagonal NiAs cation deficient state at ~ 590 K, which fits to the TC values reported for that iron sulfide. This outlines the strong interplay between structure, magnetism and electronic transport in the Fe7-xCoxS8 compounds.

Figure 1 .

 1 Figure 1. Lattice parameters a0 and c0 as function of cobalt content in the Fe7-xCoxS8 (0 ≤ x ≤ 5) series.

Figure 2 .

 2 Figure 2. Temperature dependent transport properties for Fe7-xCoxS8 series (0 ≤ x ≤ 5) -(a) electrical conductivity, σ, (b) Seebeck coefficient, S, (c) Power factor, PF, (d) Total thermal conductivity, κ, (e) Lattice thermal conductivity, κlatt, and (f) figure of merit, zT. The uncertainty in the results for the values of electrical and thermal transport properties was 5% and 7%, respectively and for the overall zT was  12%. Error bars are not shown in the figures to increase readability.

Figure 3 .

 3 Figure 3. Temperature dependent specific heat, Cp obtained from DSC analysis for Fe7-xCoxS8 (0 ≤ x ≤ 5) compounds.

Figure 4 .

 4 Figure 4. Magnetic behavior of Fe7-xCoxS8 (0 ≤ x ≤ 5) compounds -(a) field dependences of the magnetization measured at T = 2.5 K, (b) temperature dependences of the magnetization measured at a fixed magnetic field of 100 Oe.

Acknowledgement

B.S, T.M thank JSPS postdoctoral Fellowship P19720, KAKENHI 19F19720, JST CREST JPMJCR15Q6, JPMJCR19Q.


Vasileios Mavromatis

Kirsten Van Zuilen

Marc Blanchard

Mark Van Zuilen

Martin Dietzel

Jacques Schott

Experimental and theoretical modelling of kinetic and equilibrium Ba isotope fractionation during calcite and aragonite precipitation

Keywords: Ba isotope fractionation, calcite, aragonite, growth rate, first-principles calculations

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

Introduction

Several tools used in paleo-environmental reconstruction studies are based on the incorporation of traces / impurities in the crystal lattice of carbonate minerals grown from natural fluids. Among these exchange reactions the most well studied is the replacement of Ca 2+ in CaCO 3 minerals calcite and aragonite by other divalent cations and most commonly the alkaline earth metals Mg 2+ , Sr 2+ and Ba 2+ [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]Tesoriero and Pankow,1996;[START_REF] Dietzel | Co-precipitation of Sr 2+ and Ba 2+ with aragonite by membrane diffusion of CO 2 between 10 and 50 o C[END_REF]Tang et al., 2008b;[START_REF] Goetschl | Effect of sulfate on magnesium incorporation in low-magnesium calcite[END_REF]. The ability over the last two decades to accurately measure the isotopic composition of these elements in natural geomaterials provides now a new set of tools for the exploration of the environmental conditions in the geological past. Among the divalent metals (i.e. Me 2+ ) that have been widely studied are Ca and Mg as they are both highly concentrated in seawater, and also constituting major elements of calcite, Mg-calcites and dolomite. As such, their isotopic variations in natural waters and carbonate samples account for several dozen published studies as shown by the recent reviews of [START_REF] Gussone | Calcium isotope fractionation during mineral precipitation from aqueous solution[END_REF] and [START_REF] Teng | Magnesium Isotope Geochemistry[END_REF], for Ca and Mg respectively. The isotopic variations of other divalent alkaline earth and transition metals such as Sr 2+ , Ba 2+ , Ni 2+ and Zn 2+ in natural carbonate archives have also been studied but to a lesser extent, likely because the mechanisms controlling these isotopic variations are not yet thoroughly explored.

Recently the stable isotope composition of barium in minerals including carbonates and sulphates has been proposed as a novel tracer of the barium cycle [START_REF] Horner | Pelagic barite precipitation at micromolar ambient sulfate[END_REF][START_REF] Liu | Annually-resolved coral skeletal delta Ba-138/134 records: A new proxy for oceanic Ba cycling[END_REF]. This is because barium occurs in seawater at trace level concentrations and it obeys a nutrient-like distribution that follows that of dissolved Si and alkalinity [START_REF] Chow | On the marine geochemistry of barium[END_REF][START_REF] Wolgemuth | Barium in sea water[END_REF][START_REF] Jeandel | Longitudinal distributions of dissolved barium, silica and alkalinity in the western and southern Indian Ocean[END_REF]. The barium oceanic chemistry is almost exclusively regulated by the solubility of barite (i.e. BaSO 4 ; [START_REF] Monnin | The solubility of celestite and barite in electrolyte-solutions and natural-waters at 25 o C a thermodynamic study[END_REF][START_REF] Hemsing | Barium isotopes in cold-water corals[END_REF]. Actually recent studies on Ba isotope composition of natural barites provide essential information for the use of this isotopic system as a proxy for Ba input and output in the ocean as well as on the formation conditions of barite [START_REF] Horner | Barium-isotopic fractionation in seawater mediated by barite cycling and oceanic circulation[END_REF][START_REF] Teng | Magnesium Isotope Geochemistry[END_REF].

Although Ba is incorporated only in trace amounts in CaCO 3 minerals calcite and aragonite (Pingitore and Eastman, 1985;[START_REF] Böttcher | Metal-ion partitioning during low-temperature precipitation and dissolution of anhydrous carbonates and sulfates[END_REF], this alkaline earth is a good candidate for a detailed study of its isotopic behaviour during carbonate-fluid interactions because the Ba/Ca ratios of carbonates precipitated from seawater is commonly used as indicator of oceanic circulation and/or freshwater runoff (e.g. [START_REF] Shen | Determination of lead, cadmium and other trace-metals in annually-banded corals[END_REF][START_REF] Hall | Ba/Ca in benthic foraminifera: thermocline and middepth circulation in the North Atlantic during the last glaciation[END_REF][START_REF] Montaggioni | Coral barium/calcium record of mid-Holocene upwelling activity in New Caledonia, South-West Pacific[END_REF]. In order to elucidate however the processes that may affect the Ba isotope composition of natural CaCO 3 minerals, experimental studies are necessary. This is because, as it has been observed in other isotopic systems, processes like mineral growth kinetics (Tang et al., 2008a;[START_REF] Boehm | Strontium isotope fractionation of planktic foraminifera and inorganic calcite[END_REF], temperature [START_REF] Li | Magnesium isotope fractionation during precipitation of inorganic calcite under laboratory conditions[END_REF], aqueous complexation [START_REF] Mavromatis | Zinc isotope fractionation during the inorganic precipitation of calcite -Towards a new pH proxy[END_REF]Füger et al., 2019b) or surface complexation (Füger et al., 2019a) may control the isotopic composition of the solid.

To date Ba isotope measurements in carbonate minerals are relatively scarce. Barium isotope fractionation between solutions and BaCO 3 (witherite) and the double carbonate BaMn[CO 3 ] 2 has been investigated experimentally at ambient temperature [START_REF] Von Allmen | Barium isotope fractionation in the global barium cycle: First evidence from barium minerals and precipitation experiments[END_REF][START_REF] Böttcher | Barium isotope fractionation during experimental formation of the double carbonate BaMn[CO 3 ] 2 at ambient temperature[END_REF]2018a;2018b;[START_REF] Mavromatis | Barium isotope fractionation during witherite (BaCO 3 ) dissolution, precipitation and at equilibrium[END_REF]. These studies suggest that the forming carbonates are slightly enriched in the lighter Ba isotope, a feature that is also observed for Ca, Mg and Sr (Tang et al., 2008a;[START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF]Mavromatis et al;2016;2017a). The isotopic compositions of Ba in terrestrial carbonates and as trace in coralline aragonite have been measured by von [START_REF] Von Allmen | Barium isotope fractionation in the global barium cycle: First evidence from barium minerals and precipitation experiments[END_REF], [START_REF] Pretet | Constraints on barium isotope fractionation during aragonite precipitation by corals[END_REF] and more recently by [START_REF] Hemsing | Barium isotopes in cold-water corals[END_REF] and [START_REF] Liu | Annually-resolved coral skeletal delta Ba-138/134 records: A new proxy for oceanic Ba cycling[END_REF], and in coralline high Mg-calcite by [START_REF] Geyman | Barium in deep-sea bamboo corals: Phase associations, barium stable isotopes, & prospects for paleoceanography[END_REF], with all studies reporting enrichment of the lighter isotopes in the solid phase.

In this study, continuing our efforts to deciphering the mechanisms controlling the isotopic fractionation of major and trace elements/impurities in carbonate minerals (e.g. Schott et al., 2016;[START_REF] Mavromatis | Magnesium isotope fractionation during hydrous magnesium carbonate precipitation with and without cyanobacteria[END_REF]2017c;[START_REF] Oelkers | The temporal evolution of magnesium isotope fractionation during hydromagnesite dissolution, precipitation, and at equilibrium[END_REF][START_REF] Saldi | Boron isotopic fractionation during adsorption by calcite -Implication for the seawater pH proxy[END_REF][START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Tang | Sr 2+ /Ca 2+ and 44 Ca/ 40 Ca fractionation during inorganic calcite formation: III. Impact of salinity/ionic strength[END_REF][START_REF] Shirokova | Using Mg Isotopes to Trace Cyanobacterially Mediated Magnesium Carbonate Precipitation in Alkaline Lakes[END_REF], we examine the effect of mineral growth kinetics on Ba isotope fractionation between calcite and aragonite and their forming aqueous solutions. This experimental approach is complemented by first-principles calculations of Ba isotope fractionation at equilibrium. Considering that Ba isotopes in CaCO 3 minerals can be used as a proxy tool for their formation in aquatic environments, this study allows for a systematic assessment of the Ba isotopic fractionation in natural carbonates and provides insights on the role of precipitation rates.

Material and methods

Seed materials

The calcite powder used in this study, purchased from Sigma-Aldrich, was pure calcite and contained about 20 µg kg -1 Ba. The size of calcite crystals ranged between 2 and 10 µm and their specific area, as determined by the BET method [START_REF] Brunauer | Adsorption of Gasses in Multimolecular layers[END_REF] using krypton and 11 measured adsorption points, was equal to 0.16 m 2 g -1 . Aragonite seeds were synthesized at 80 ±2°C by the dropwise addition of 80 mL of a 1.25 M Na 2 CO 3 solution into a 2 L borosilicate reactor containing 1.5 L of a 0.1 M CaCl 2 , 0.1 M MgCl 2 and 0.43 M NaCl solution, which was stirred at 240 rpm. The precipitated solids were rinsed with ultrapure water and dried in an oven at 40°C overnight. X-ray diffraction of the synthesized solids showed only the presence of aragonite; the solids Ba content as determined by wet chemical analysis of digested solid using an Inductive Coupled Plasma Optical Emission Spectrometer (PerkinElmer Optima ICP-OES 8300 DV) was equal to ∼ 3.5 mg kg -1 . Aragonite crystals, 5-20 µm in size, showed characteristic acicular forms. The specific surface area of the synthetic aragonite powder was 0.7 m 2 g -1 .

Experimental set up

Barium co-precipitation experiments with calcite and aragonite were performed using mixed flow reactors as described in [START_REF] Mavromatis | Barium partitioning in calcite and aragonite as a function of growth rate[END_REF]. Briefly, mineral overgrowth on CaCO 3 seeds under 1 bar pCO 2 was induced by the simultaneous addition of two solutions in a thermally-controlled 1L polypropylene reactor containing the seed material and a background electrolyte of known concentration. The first inlet solution contained CaCl 2 , BaCl 2 , and, in experiments conducted in the presence of aragonite seeds, 0.05M MgCl 2 , whereas the second inlet solution contained Na 2 CO 3 in a concentration equal to that of CaCl 2 in the first inlet solution. These inlet solutions were added with the aid of a peristaltic pump at equal rates in a reactor containing 0.5 L of a solution that was pre-equilibrated with calcite or aragonite at 1 atm pCO 2 . The reactor was equipped with a Teflon floating stir bar rotating at 350 rpm. Shortly prior to each experimental run a small amount of a BaCl 2 stock solution (~0.5 mL) was added together with a known amount of seed material in the reactor solution to bring its concentration to ~0.1 mM Ba. In experiments conducted in the presence of calcite, the background electrolyte was 300 mM NaCl, whereas in experiments conducted in the presence of aragonite the background electrolyte consisted of 250 mM NaCl and 25 mM MgCl 2 . In all experimental runs Ba in both the inlet and reactor solutions originated from a single source of 0.2 M BaCl 2 stock solution. The pH of the reactive solution was controlled by the continuous bubbling of a water saturated 1 bar pCO 2 gas and the measured pH value during the whole course of an experiment was 6.3 ±0.1. In order to minimize evaporation, for all runs CO 2 gas was bubbled in a 300 mM NaCl solution prior to its introduction into the reaction vessel. During the course of a run, the introduction of the two inlet solutions induced an increase of the volume of the reactive solution. Thus, every 24 hours, a volume of reactive fluid, equal to the sum of the volumes of the inlet solutions added in 24 h by the peristaltic pump, was sampled from the reactor so that the fluid volume in the reactor remained constant to within ± 4%. Stirring was stopped shortly prior to sampling to allow the solid material to settle. In this way solid removal was minimized and the solid/fluid ratio was kept quasi constant during the course of an experiment. 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 solution was vacuum filtered through a 0.2 µm membrane filter (Sartorius, cellulose acetate). The solids were rinsed with deionized water and dried at room temperature.

Chemical and mineralogical analyses

The concentrations of cations in the sampled fluids were measured by Inductive Coupled Plasma Optical Emission Spectrometry (PerkinElmer Optima ICP-OES 8300 DV) with an analytical precision of ± 3% (2sd) determined based on replicate analyses of NIST 1640a and seawater standards. The alkalinity was determined by standard acid titration with an uncertainty of ± 2% using an automated Schott TitroLine alpha plus titrator together with a 10 mM HCl solution. The pH was measured with a Schott Blueline 28 combined electrode, calibrated with standard buffers at pH of 4.01, 7.00 and 10.00 (25°C) with an uncertainty of ±0.03 units.

Seed materials and recovered solids were characterized for their X-ray powder diffraction (XRD) patterns. Those were recorded on a PANalytical X´Pert PRO diffractometer using Co-Kα-radiation (40mA, 40kV) at a 2θ range from 4° to 85° and a scan speed of 0.03° s -1 .

Additionally, selected precipitates were gold-coated and imaged using a ZEISS DSM 982 Gemini scanning electron microscope (SEM) operated at 5 kV accelerating voltage. Specific surface area of seed materials and solids at the end of the experimental runs were determined by the BET method. The bulk chemical composition of the solids at the end of every experimental run was defined after digestion using 3M HNO 3 (Suprapur) and subsequent solution analysis as described above. Finally aqueous speciation of the reactive solutions was calculated using the PHREEQC software together with its MINTEQ.V4 database [START_REF] Parkhurst | User's guide to PHREEQC (Version 2)-a computer program for speciation, bath-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF].

Barium isotope analyses

Barium isotope analyses were conducted at the Institut de Physique du Globe de Paris.

Between about 2 and 100 mg of solid samples were weighted and dissolved in 3 M HCl to obtain at least 1 µg Ba per sample. An adequate amount of 130 Ba-135 Ba double spike [START_REF] Van Zuilen | Barium Isotopic Compositions of Geological Reference Materials[END_REF]) was added to the dissolved samples. For solution samples, aliquots of around 150 µl were directly mixed with the double spike. All samples were taken to dryness and re-dissolved in 3 M HCl for ion-exchange chromatography. The chromatographic protocol is based on the one by van Zuilen et al. (2016), but acid strengths were adapted to 3 M HCl for matrix removal (7 ml in total) and 6 M HCl for Ba collection (6 ml). Total procedure blanks were below 0.2 ng.

Isotope measurements were done on a Thermo Scientific Neptune Plus MC-ICP-MS. The dried samples were diluted in 0.5 M HNO 3 to 300 µg kg -1 natural Ba. Solutions were introduced into the mass spectrometer via a quartz dual cyclonic spray chamber. Typical 137 Ba + signals were ~3.5 V (using a 10 11 Ω resistor). Data acquisition was performed in low-resolution mode and consisted of 100 cycles of 4 s integration time. Signals of all seven Ba isotopes were detected simultaneously with 129 Xe + and 131 Xe + to correct for isobaric interferences on 130 Ba, 132 Ba, 134 Ba and 136 Ba. All isotope data are given relative to the reference material NIST SRM 3104a in the δ 137/134 Ba notation (in ‰):

δ 137/134 Ba = !"# Ba /!"# Ba ) sample !"# Ba /!"# Ba ) SRM 3104a -1 ×1000 (
! ! = ! ! !! ! ! ! ! !!! ! ! !! ! !!! , (2)
where n i is the number of repeated measurements of each sample i and s i 2 their variance, to be ±0.039 ‰ (n=53). Sample data are reported with either the 2s p uncertainty or the 2 standard deviation (2sd) of the repeated analyses (Table 1) if the latter is larger than 0.039 ‰. Analytical accuracy was assessed by repeated analyses of the in-house standards BaBe12 (-1.130 ± 0.045 ‰, n = 3) and BaBe27 (-0.610 ± 0.034 ‰, n = 10), which are in good agreement with literature values [START_REF] Van Zuilen | Barium Isotopic Compositions of Geological Reference Materials[END_REF].

Description of isotope fractionation as a function of the reaction rate within the framework of Transition State Theory

For a slow elementary reaction to proceed, the reactant species have to pass a potential energy barrier which is a configuration roughly midway between that of the reactants and the products.

Transition state theory (TST) originally developed by [START_REF] Eyring | The activated complex in chemical reactions[END_REF] provides the means to characterize the path of reactants over this energy barrier and their configuration, often termed the activated complex, in the neighborhood of this energy maximum. According to TST, the rate of an elementary reaction depends on the number of reactants that cross the energy barrier and the time needed for these complexes to yield products. Within this concept the rate of a forward elementary reaction R f can be written:

R f = k* [AC*] (3)
where k* refers to a rate constant and [AC*] stands for the concentration of the activated complex. The same approach can be applied to a reversible chemical reaction leading to the formation of component XYZ from reactants X and YZ

X + YZ ⇌ XYZ , K (4)
where K stands for the equilibrium constant of reaction (4). Element X contains two isotopes, heavy h X and light l X. Therefore the potential energy barrier the reactants have to pass for forming light l XYZ is lower than that for heavy h XYZ. The forward formation reaction of l XYZ can be described by

l X + YZ ⇌ l XYZ* , l K f * (5) l XYZ* → l XYZ
where the activated complex l XYZ* is assumed to be in equilibrium with l X and YZ, and l K f * is its formation constant. The rate of reaction ( 5), l R f , can be expressed as

l R f = l k f * [ l XYZ*] = l k f * l K f * [ l X].[YZ] = l k f [ l X].[YZ] (6)
and the rate of the backward reaction

l XYZ → l X+ YZ (7) is given by l R b = l k b * [ l XYZ*] = l k b * l K b * [ l XYZ] = l k b [ l XYZ] (8)
with l k f / l k b = l K, where l K is the formation constant of l XYZ and l R net = l R f -l R b is the overall rate of formation of l XYZ. An equation similar to eq. ( 8) can be written for the formation of heavy h XYZ. The two kinetic isotopic fractionation factors associated with the forward and backward reactions are given by α f = h k f / l k f and α b = h k b / l k b whereas the equilibrium fractionation factor is

α eq = α f /α b = h K/ l K.
Introducing the Gibbs free energy change for the formation reaction, yields the following relation for the overall rate of formation of l XYZ and h XYZ

l R net = l k f (1 -exp( l ΔG/RT)) (9) h R net = h k f (1 -exp( h ΔG/RT)) (10)
whereas the overall rate of reaction ( 4) is given by

R net = l R net + h R net = k f (1 -exp(ΔG/RT)) (11)
where k f and ∆! stand for the forward rate constant and Gibbs free energy change.

Introducing r r = [ h X]/[ l X] and r p = [ h XYZ]/[ l XYZ], the isotope ratio in the reactant and product, respectively, two equations can be derived from eqs ( 6) and ( 8) that relate the two isotope-forward and backward reaction rates:

h R f = α f. r r . l R f (12) and h R b = (α f /α eq )r p . l R b ( 13
)
The expression of the fractionation factor between the products and the reactants at a given time can be derived from eqs ( 12) and ( 13):

! = ! !" ! !. ! ! ! ! ! !. ! ! ! ! (14)
At steady-state, which corresponds to a constant isotope composition of XYZ as a function of time, it can be shown that !

! = ! !"# ! ! !"# !
. Substitution of eqs ( 12) and ( 13) into this relation leads after some algebraic handling to the following expression of the isotope fractionation factor at steady-state:

! !! = ! ! !! ! ! ! ! ! ! ! ! ! !" !! = ! ! !! ! ! ! ! !"# ! ! ! ! ! ! ! ! !" !! (15) At equilibrium, ! !! = ! !" and ! ! ! ! ! ! = ! ! ! ! = 1. At kinetically controlled conditions with R net > R b and ! !! ∼ ! ! , the ratios ! ! ! ! ! ! and ! ! ! !
can be considered to be equal because for most geochemical reaction ! !" and ! ! differ only by a few per mil. As such eq. ( 15) simplifies to

! !! = ! ! !! ! ! ! !"# !! ! ! ! ! !" !! (16)
Equation ( 16) is identical to the eq. ( 11) derived by DePaolo (2011) to describe the steady-state calcium isotope fractionation during calcite precipitation, assuming the precipitation of this mineral follows the first order TST rate law. In this equation R b and R net stand for calcite backward dissolution rate and net precipitation rate, respectively, whereas ! ! represents the kinetic isotope fractionation factor associated with calcite precipitation. Eq. ( 16) can be also applied to describe the isotope fractionation of a trace metal like barium during its steady-state coprecipitation with calcite or aragonite. Indeed, considering that the substitution of a trace metal for Ca in CaCO 3 leads to the formation of a true Ca 1-x Me x CO 3 solid solution, it should be noted that at steady-state precipitation the chemical composition of the precipitating solid does not change with time and therefore the precipitation rate of Me x CO 3 is equal to that of the Ca 1- x Me x CO 3 solid solution. The above TST rate laws have been derived for an element containing only two isotopes. It should be noted, however, that eq. ( 16), that describes the fractionation factor at steady-state conditions, can be as well applied to an element like Ba containing several isotopes to account for the steady-state behaviour of any stable isotope couple like 137/134 Ba or 138/134 Ba. In the following, eq. ( 16) has been therefore used to describe the value of ! !! for 137/134 Ba as a function of calcite or aragonite net precipitation rate (R net ) during the steady-state co-precipitation of barium with calcite or aragonite.

First-principles calculation of equilibrium Ba isotope fractionation

The investigated models of Ba-bearing calcite and aragonite are based on the 2 × 2 × 2 rhombohedral calcite supercell and the 2 × 1 × 2 orthorhombic aragonite supercell in which one Ba atom is substituted for one Ca atom. Both supercells contain a total of 80 atoms. The Ba atom is separated from its periodic images by ~ 8 Å in the shortest direction of the aragonite model and by at least 10 Å in the calcite model. We can thus consider the Ba atom as isolated and models as representative of the dilute samples studied here. The pure barium carbonate (witherite, BaCO 3 ) was also modeled. In order to approach the structure of an Ba aquo ion, we took the crystal structure of barium hydroxide octahydrate (Ba(H 2 0) 8 (OH) 2 ) described by [START_REF] Persson | Structure of the solvated strontium and barium ions in aqueous, dimethyl-sulfoxide and pyridine solution, and crystal-structure of strontium and barium hydroxide octahydrate[END_REF]. This approach was chosen because modeling of Ba aquo ion using ab initio molecular dynamic simulations is not expected to change significantly the results and such approach would represent an extensive theoretical study on its own. According to [START_REF] Bigeleisen | Calculation of equilibrium constants for isotopic exchange reactions[END_REF], the equilibrium isotopic fractionation factor (α) between two phases (a and b) can be determined from the reduced partition function ratios (β):

! !, ! = !(!) !(!) (17)
more conveniently expressed in ‰ with the following logarithmic relation:

1000!"# !, ! = 1000!"# ! -1000!"# ! (18)
Since the equilibrium mass-dependent isotopic fractionation arises mainly from the change in vibrational energy induced by the isotopic substitution, the β-factor can be calculated from the harmonic vibrational frequencies as follows (e.g. [START_REF] Blanchard | Equilibrium fractionation of non-traditional isotopes: A molecular modelling perspective[END_REF]:

! = ! !,! * ! !,! ! !!! !,! * !!" !!! !!! !,! * !" ! !! !" !!! !!! !!! !,! !" ! !!! !,! !!" ! !! ! (19)
where ! !,! and ! !,! * are the frequencies of the vibrational mode defined by indexes i (i=1,3N at ) and wavevector q for the two isotopically distinct systems. N at is the total number of atoms in the simulation cell, N q the number of wavevectors, n the number of isotopically exchanged sites (1 for calcite and aragonite, 4 for witherite and the hydrate), h Planck's constant, k Boltzmann's constant, T the temperature. The second product is performed on a sufficiently large grid of N q wavevectors in the Brillouin zone.

The structural relaxations (i.e. optimization of atomic positions and cell parameters) followed by the vibrational frequency calculations were carried out from first-principles calculations based on density functional theory, using the PWscf and PHonon codes of the Quantum ESPRESSO package [START_REF] Giannozzi | Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials[END_REF]; http://www.quantum-espresso.org). The computational parameters used here are similar to the ones used in previous works on sulfatebearing calcium carbonates [START_REF] Balan | First principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF], on Mg-bearing carbonates [START_REF] Pinilla | Equilibrium magnesium isotope fractionation between aqueous Mg 2+ and carbonate minerals: Insights from path integral molecular dynamics[END_REF], and on boron-bearing carbonates [START_REF] Balan | Firstprinciples study of boron speciation in calcite and aragonite[END_REF]2018). Namely, we used the generalized gradient approximation (GGA) to the exchange-correlation functional with the Perdew-Burke-Ernzerhof (PBE) parametrization [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. The ionic cores of all elements (Ba, Ca, C, O, H) were described by ultrasoft pseudopotentials from the GBRV library [START_REF] Garrity | Pseudopotentials for high-throughput DFT calculations[END_REF]. The electronic wave functions and charge density were expanded using finite basis sets of plane-waves with 60 and 300 Ry cutoffs respectively. Electronic integration is performed by sampling the Brillouin zone according to the Monkhorst-Pack scheme [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF]) with a 3 × 2 × 3 shifted k-point grid for witherite, and a 2 × 2 × 2 shifted k-point grid for the three other phases (calcite, aragonite and barium hydroxyl hydrate). These values lead to a convergence of the total energy better than 0.5 mRy/atom. Structural relaxations were performed until the residual forces on atoms were less than 5.10 -5 Ry/a.u., before computing the harmonic frequencies on a 2 × 1 × 2 shifted grid of wavevectors for witherite, and on a single shifted wavevector for the three other phases.

Results

Composition and precipitation rates of CaCO 3 overgrowths.

As mentioned earlier by [START_REF] Mavromatis | Barium partitioning in calcite and aragonite as a function of growth rate[END_REF], the XRD patterns of collected solids are indicative of calcite or aragonite and they do not exhibit differences with those of the seed material. It is worth noting, however, that three experiments reported in this study exhibit peaks of both calcite and aragonite despite the fact that the seed material was aragonite. Based on Rietveld refinement analyses using the PANalytical X'Pert HighScore Plus software coupled with the PDF-2 database, the abundance of aragonite in the bulk precipitate of experiments CaBa38, CaBa39 and CaBa40 was 37.2, 26.5 and 15.4 wt.%, respectively (Table 1). In these experiments growth rate estimation is not straightforward as nucleation of calcite in the reactive fluid produces material with specific surface different than that of aragonite. As such herein we estimated steady-state growth rate as in previous studies (e.g. [START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]2015;2017b) based on the number of moles of Ca added to the reactor per time unit corrected for the number of moles of Ca removed from the reactor via sampling:

! p = ! Ca(add) ! ! Ca(rem) !",!"" /! (20)
where 86,400 is the number of seconds in time unit (i.e. 24 h), S is the total surface area of CaCO 3 in m 2 and R p is expressed in mol/m 2 /s. Similar to the experiments presented in [START_REF] Mavromatis | Barium partitioning in calcite and aragonite as a function of growth rate[END_REF], the total surface area of experiments CaBa38, CaBa39 and CaBa40 has been corrected for the amount of precipitated CaCO 3 mineral phase based on steady-state aqueous concentration of Ca. We note however that rate estimation for those three experiments using eq. ( 20) is based on the assumption that calcite has the same specific surface area as aragonite.

The barium content of the precipitated overgrowths range between 20-50 mg kg -1 and 1450-3350 mg kg -1 in calcite and aragonite, respectively. The values of corresponding partition coefficients (! !" =

( [!"] [!"] ) !"#$% ( [!"] [!"]
) !"#$%

) which increases with the overgrowth precipitation rates, range between 0.004 ≤ D Ba ≤ 0.009 and 0.22 ≤ D Ba ≤ 0.77 for calcite and aragonite, respectively (Table 1).

In the CaBa38, CaBa39 and CaBa40 runs, which lead to a mixture of aragonite and calcite in the overgrowths, only a small fraction of barium was incorporated in calcite due to the significant higher affinity of barium for aragonite than for calcite. The fractions of Ba in the solid that was incorporated in calcite in runs CaBa38, CaBa39 and CaBa40 have been estimated to range between 1.4 and 4.5 % of the total amount of Ba in the overgrowth.

Barium isotope composition of CaCO 3 overgrowths

The δ 137/134 Ba composition of the stock solution used in all the runs had a value of 0.085±0.039 ‰ (2s p ; see Table 1). This composition is identical to that of the BaCl 2 solution used for the experiments on Ba isotope fractionation between witherite and aqueous solution reported in [START_REF] Mavromatis | Barium isotope fractionation during witherite (BaCO 3 ) dissolution, precipitation and at equilibrium[END_REF]. Over the course of an experimental run, as well as among runs, the isotopic composition of the reactive fluids shows insignificant variations in δ 137/134 Ba composition compared to the stock solution as it can be seen in Table 1 for all experiments either the growing mineral was calcite (CaBa5, CaBa8 and CaBa14) or aragonite (CaBa25, CaBa28 and CaBa29).

The δ 137/134 Ba composition of the six calcite overgrowths analyzed in this study does not exhibit analytically significant variation compared to the BaCl 2 stock solution, however precipitates of experiments CaB12 and CaBa14 may be slightly enriched in light isotopes compared to the other samples (by near 0.05 ‰). In contrast, the δ 137/134 Ba composition of the eleven aragonite overgrowths exhibit significant variations with values ranging from 0.339±0.049 ‰ for experiment CaBa31 to 0.037 ± 0.039 ‰ (2s p ) for experiment CaBa30. The three experiments where the overgrowth was a mixture of calcite with aragonite exhibit δ 137/134 Ba composition that is enriched in the lighter Ba isotopes compared to the stock solution, ranging between 0.032±0.044 ‰ and -0.011±0.068 ‰ (see Table 1).

Barium isotope fractionation between calcium carbonates and the fluid

The Δ 137/134 Ba mineral-fluid values listed in Table 1 have been deduced from the difference between the isotopic composition of the solid and that of the forming fluid (i.e. Δ 137/134 Ba solid-fluid =δ 137/134 Ba solid -δ 137/134 Ba fluid ). This approach has been used because in all runs Ba aqueous concentration in the reactor was the same within uncertainty than that of the inlet solution and δ 137/134 Ba fluid did not exhibit temporal variations and was identical within analytical uncertainties among the various runs (see Table 1). For calcite, Δ 137/134 Ba calcite-fluid has an average value of -0.003 ±0.040 ‰ and does not exhibit a significant variation with calcite growth rate in the range of growth rates investigated (Fig. 1A). In contrast the Δ 137/134 Ba aragonite-fluid values exhibit a systematic decrease as a function of increasing aragonite growth rate (Fig. 1B) that can be described by the following linear trend:

Δ 137/134 Ba aragonite-fluid = -0.1834 (±0.0314) LogRate -1.4843 (±0.2490); R 2 = 0.75,

with this relation to be valid for -9.0 ≤ LogRate ≤ -7.6. Note that samples CaB38, CaB39 and CaB40 have been included in this fit as their isotopic composition could not have been impacted by the very small Ba content of the calcite co-precipitated with aragonite. Eq. ( 21) suggests that aragonite which is formed at low growth rates (≤10 -8.1 mol/m 2 /s) is enriched in the heavier Ba isotopes. In contrast at growth rates ≥ ~10 -8.0 mol/m 2 /s, the forming solid becomes progressively enriched in the lighter Ba isotopes.

Theoretical structural and isotopic properties

The relaxed cell parameters of barium hydroxide octahydrate (a = 9.296 Å, b = 9.288 Å, c = 11.884 Å, β = 99.17) are in good agreement with the experimental structure [START_REF] Persson | Structure of the solvated strontium and barium ions in aqueous, dimethyl-sulfoxide and pyridine solution, and crystal-structure of strontium and barium hydroxide octahydrate[END_REF]; the theoretical volume being only 0.3% larger than the experimental one. In this model, the eight water molecules of the first solvation shell are at an average distance of 2.84 Å from Ba 2+ . Keeping in mind that the first atomic neighbors greatly influence the equilibrium isotopic fractionation, we can expect this hydrate to be a good analogue of an aqueous Ba 2+ ion. Indeed, extended X-ray absorption fine structure (EXAFS) spectroscopy studies of dilute aqueous solutions report a hydration number of about eight (8.1 and 7.8) and average Ba-O bond length of 2.81 and 2.78 Å (Persson et al. 2015 andD'Angelo et al. 1996, respectively) where Ba has a coordination number of 9 (de Villiers, 1971). X-ray absorption spectroscopy measurements on a Ba substituted calcite (~2000 mg kg -1 Ba) give a Ba-O bond length of 2.68 Å with a coordination number of 6 [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]. As for aragonite, there is no available data in either synthetic or natural aragonite (e.g. Ba concentrations in corals are too low for EXAFS analyses; [START_REF] Finch | Ba XAFS in Ba-rich standard minerals and the potential for determining Ba structural state in calcium carbonate[END_REF]. However, it has been found that Sr and Mg are in 9-fold coordination with respect to O in the aragonite lattice [START_REF] Finch | Coordination and local relaxation around Sr and Mg in calcite and aragonite[END_REF].

The temperature dependence of β-factors is shown in Fig. 2 and the corresponding polynomial fits are given in Table 2. Results indicate that at equilibrium, calcite and in particular aragonite will be enriched in the heavy Ba isotopes relative to aqueous barium, whereas no fractionation is expected between witherite and aqueous barium. At 25°C, the theoretical equilibrium fractionation factors 1000lnα mineral-fluid are +0.34‰, +0.17‰ and -0.01‰ for aragonite, calcite and witherite, respectively. This latter value between witherite and aqueous Ba is consistent with the experimentally derived fractionation factor of -0.07 ± 0.04‰ [START_REF] Mavromatis | Barium isotope fractionation during witherite (BaCO 3 ) dissolution, precipitation and at equilibrium[END_REF]. It is noteworthy that in the present case, the relative order of heavy isotope enrichment (Ba hydrate < calcite < aragonite) does not follow the usual anticorrelation with the average bond length (Ba-hydrate with 2.84 Å > aragonite with 2.75 Å > calcite with 2.67 Å).

This observation may be explained by the contrasted Ba local environments in calcite and aragonite (Fig. 3). While there are six carbonate groups around the Ba atom in both minerals, these groups are arranged differently. In calcite, carbonate groups are located in two crystallographic planes and the six Ba-O bonds have the same length. In aragonite, carbonate groups belong to four crystallographic planes and the Ba atom forms one or two bonds with each carbonate group, leading to a coordination number of 9. The effect of this local environment on the barium atom is expressed through the interatomic force constant (Fig. 4). The Ba force constant is 19% larger in aragonite than in calcite, and therefore an aragonite crystal will be enriched in heavy Ba isotopes if in thermodynamic equilibrium with a calcite crystal.

Discussion

The impact of calcite and aragonite growth kinetics on Ba isotope fractionation

During the standard growth mechanism of carbonate minerals involving ion-by-ion attachment to advancing steps, desolvation of the metal ion and thus the rate of exchange of water molecules in its coordination sphere are believed to control the incorporation of the metal in the crystal lattice [START_REF] Pokrovsky | Surface Chemistry and Dissolution Kinetics of Divalent Metal Carbonates[END_REF][START_REF] Hofmann | Ion desolvation as a mechanism for kinetic isotope fractionation in aqueous systems[END_REF]. For instance, it has been found experimentally that (de)solvation processes seem to substantially impact Ba isotope fractionation upon mineral formation (Böttcher et al., 2018a). As water exchange rate in the hydration shell follows an inverse power-law mass dependence [START_REF] Hofmann | Ion desolvation as a mechanism for kinetic isotope fractionation in aqueous systems[END_REF], light isotopes are preferentially incorporated into the precipitating solid and the resulting kinetic fractionation should increase with increasing precipitation rate. Equation ( 16) shows that for steady-state precipitation this kinetic effect is maximum at conditions where the net precipitation rate is much faster than the dissolution rate whereas it is null at chemical equilibrium (equality of the forward and backward reaction rates). This increasing enrichment of the solid in light isotopes with precipitation rate has been observed for calcium in calcite (Tang et al., 2008a), magnesium in magnesite [START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF], barium in witherite [START_REF] Mavromatis | Barium isotope fractionation during witherite (BaCO 3 ) dissolution, precipitation and at equilibrium[END_REF]Böttcher et al., 2018b) and strontium in strontianite (Mavromatis et al., 2017a). It is expected that the isotopic composition of the divalent metals substituted for Ca in the CaCO 3 lattice should follow a similar dependence on growth rate provided that the desolvation rates of these metals are comparable to that of calcium. This is indeed observed for example during the incorporation of Sr in calcite [START_REF] Boehm | Strontium isotope fractionation of planktic foraminifera and inorganic calcite[END_REF] and Ba in aragonite (this study), two alkaline earth metals with water-exchange rates in their coordination sphere (10 -8.9 and 10 -9.2 s -1 , respectively; Lincoln and Merbach, 1995) very close to that for calcium (10 -8.8 s -1 ; [START_REF] Lincoln | Substitution reactions of solvated metal ions[END_REF].

However, the isotopic composition of Ba during its incorporation in calcite does not exhibit a significant dependence on calcite growth kinetics for the range of precipitation rates investigated in the present study (10 -7.3 -10 -8.0 mol m -2 s -1 ). It is tempting to use eq. ( 16) derived from TST to try to understand the apparent contrasting behaviour of Ba isotope fractionation during calcite and aragonite steady-state precipitation.

The application of eq. ( 16) to Ba isotope fractionation in aragonite is shown in Fig. 5A.

For this calculation, a constant value of aragonite backward dissolution rate, R b = 1×10 -7 mol m -2

s -1 at 25°C and pH = 6.25, is assumed based on the R b value determined in pure water by [START_REF] Chou | Comparative study of the kinetics and mechanisms of dissolution of carbonate minerals[END_REF] corrected for the inhibiting effect of aqueous Mg (25 mM MgCl 2 in the background electrolyte) on aragonite dissolution rate as quantified by [START_REF] Gutjar | Studies of the growth and dissolution kinetics of the CaCO 3 polymorphs calcite and aragonite II. The influence of the divalent additives on the growth and dissolution rates[END_REF]. A good fit of the experimental data is obtained using values of α eq = 1.00027 (Δ 1 37/134 Ba aragonite-fluid (eq) = +0.27±0.06‰) and α f = 0.9980±0.0002 (Δ 1 37/134 Ba aragonite-fluid (kin) = -2.0±0.2‰). For this fit the value of α eq in eq. ( 16) is kept constant and that of α f is allowed to achieve minimum and maximum values in the growth rate range where experimental data occur. It should be noted that the value of the kinetic fractionation factor used is this study is slightly lower than that proposed by [START_REF] Hofmann | Ion desolvation as a mechanism for kinetic isotope fractionation in aqueous systems[END_REF] based on MD simulations (α f = 0.9989). The good fit of Ba isotope data by eq. ( 16) is noteworthy because the selected aragonite R b value is not an adjustable parameter and the α eq value that fits the data best is in excellent agreement with the fractionation measured at the slowest aragonite growth rates (10 -9 mol m -2 s -1 ). This experimental model is also strengthened by the comparison with first-principles calculations. The equilibrium fractionation factor derived here (+0.27±0.06‰) is in good agreement with the theoretical value (+0.34‰). Interestingly the model predicts that significant kinetic fractionation of Ba isotopes (Δ 1 37/134 Ba aragonite-fluid < -1 ‰) should be observed for very fast aragonite growth rate (R p > 10 -7 mol m -2 s -1 ), similar to those met during the growth of biominerals such foraminifera and corals (e.g. [START_REF] Gussone | Calcium isotope fractionation in calcite and aragonite[END_REF][START_REF] Lorrain | Strong kinetic effects on Sr/ Ca ratios in the calcitic bivalve Pecten maximus[END_REF]. Furthermore, the TST kinetic model confirms that, depending on the value of aragonite growth rate, Ba isotope fractionation between aragonite and its forming fluid could be positive at near thermodynamic equilibrium but also negative or equal to zero under mineral formation from an oversaturated fluid with respect to aragonite.

The application of eq. ( 16) to Ba isotope fractionation during steady state calcite precipitation is shown in Fig. 5B. With a value of calcite backward dissolution rate equal to 2×10 -6 mol m -2 s -1 at 25°C and pH = 6.2 [START_REF] Chou | Comparative study of the kinetics and mechanisms of dissolution of carbonate minerals[END_REF]), the dashed line in Fig. 5B is obtained for limiting fractionation factors of α eq = 1.00002 (Δ 1 37/134 Ba calcite-fluid (eq) = +0.02±0.06 ‰) and α f = 0.9982±0.0002 (Δ 1 37/134 Ba calcite-fluid (kin) = -1.8 ± 0.2‰). In contrast with witherite and aragonite, we note for calcite a small but significant discrepancy between experimental and theoretical equilibrium fractionation factors (+0.02‰ against +0.17‰). The model which accurately accounts for the very small Ba isotope fractionation observed also indicates that calcite growth rates investigated in the present study (R p ≤ 5×10 -8 mol m -2 s -1 ) were too slow to induce substantial kinetic isotope fractionation. Fig. 5B shows that kinetic Ba isotope fractionation greater than -1‰ should be observed for calcite growth rates ≥ 10 -6 mol m -2 s -1 which is consistent with available data on Ca and Sr isotopes fractionation during calcite growth which show substantial kinetic fractionation of -1.5‰ (Ca) and -0.3‰ (Sr) for calcite growth rates of ∼3×10 -6 mol m -2 s -1 (Tang et al., 2008a;[START_REF] Boehm | Strontium isotope fractionation of planktic foraminifera and inorganic calcite[END_REF].

4.2 Control of Ba equilibrium isotope fractionation during co-precipitation with aragonite and calcite.

Calcite. The equilibrium value for Δ 137/134 Ba calcite-fluid (eq) determined in this study (+ 0.02‰) suggests that at equilibrium no significant Ba isotope fractionation occurs between calcite and solution. This result is in contradiction with DFT predictions. The Ba isotope composition in calcite measured in this study thus does not seem consistent with the rule governing mass-dependent isotope fractionation stating that, at equilibrium, the heavy isotopes of an element will tend to be concentrated in substances where that element forms the stiffest bonds [START_REF] Schauble | Applying stable isotope fractionation theory to new systems[END_REF][START_REF] Blanchard | Equilibrium fractionation of non-traditional isotopes: A molecular modelling perspective[END_REF]. The apparent discrepancy and the lack of Ba isotope fractionation during Ba co-precipitation with calcite likely originates from the mechanism of incorporation of this element in the growing crystal. In the standard calcite growth under low saturation state conditions, the first step is the ion-by-ion attachment of reacting species, including Ca and Ba aquo ions to the crystal advancing steps. During this sorption step, Ba forms with a calcite surface CO 3 group a monodendate inner sphere complexes in which a CO 3 substitutes for a water molecule of Ba coordination sphere [START_REF] Pokrovsky | Surface speciation of dolomite and calcite in aqueous solutions[END_REF]. This surface complex, in which Ba likely keeps the same coordination (8) and undergoes only subtle change of its first hydration shell (replacement of a H 2 O by a CO 3 ), is not expected to have an isotopic composition which differs significantly from that of the Ba aquo ion [START_REF] Saldi | Boron isotopic fractionation during adsorption by calcite -Implication for the seawater pH proxy[END_REF].

The following Ba incorporation in calcite lattice and substitution for Ca is accompanied by a reduction of Ba coordination number and average Ba-O bond length to 6 and ~2.68 Å, respectively. This structural change must occur without further exchange with Ba in solution as the experiments do not document significant Ba isotope fractionation between calcite and the fluid. Such a mechanism has already been invoked to explain the isotopic composition of boron [START_REF] Sen | Coordination Environments of B-Impurities in Calcite and Aragonite Polymorphs -a B-11 Mas Nmr-Study[END_REF][START_REF] Noireaux | Crystallographic control on the boron isotope paleo-pH proxy[END_REF][START_REF] Balan | Theoretical isotopic fractionation between structural boron in carbonates and aqueous boric acid and borate ion[END_REF] and zinc [START_REF] Mavromatis | Zinc isotope fractionation during the inorganic precipitation of calcite -Towards a new pH proxy[END_REF]) coprecipitated with calcite.

Aragonite. Ba co-precipitation with aragonite is accompanied by a significant enrichment of the solid in 137 Ba at equilibrium with Δ 1 37/134 Ba aragonite-fluid (eq) = +0.27‰. This value is in good agreement with the theoretical one (+0.34‰). The incorporation of the Ba aquo ion in the aragonite lattice does not require a significant change in its coordination number. This positive fractionation is related to the reduction of the average Ba-O bond length (from 2.84 Å in the aqueous ion to 2.75 Å in the aragonite), which is induced by structural constraints imposed by the surrounding CaCO 3 structure. To our knowledge this is the first time that is reported the enrichment of an alkaline earth in heavy isotopes during its incorporation in a carbonate mineral.

All previous experimental studies have reported the enrichment in light isotopes of Ca, Mg, Sr and Ba in carbonate minerals (e.g. Tang et al., 2008a;[START_REF] Oelkers | The rapid resetting of the Ca isotopic signatures of calcite at ambient temperature during its congruent dissolution, precipitation, and at equilibrium[END_REF][START_REF] Boehm | Strontium isotope fractionation of planktic foraminifera and inorganic calcite[END_REF][START_REF] Böttcher | Barium isotope fractionation during experimental formation of the double carbonate BaMn[CO 3 ] 2 at ambient temperature[END_REF]2018a;2018b;[START_REF] Pearce | Isotopic fractionation during congruent dissolution, precipitation and at equilibrium: Evidence from Mg isotopes[END_REF][START_REF] Mavromatis | Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite[END_REF]2016;2017c;[START_REF] Immenhauser | Magnesium-isotope fractionation during low-Mg calcite precipitation in a limestone cave -Field study and experiments[END_REF][START_REF] Li | Magnesium isotope fractionation during precipitation of inorganic calcite under laboratory conditions[END_REF]2015;[START_REF] Von Allmen | Barium isotope fractionation in the global barium cycle: First evidence from barium minerals and precipitation experiments[END_REF].

4.3 Implications for the use of Ba isotopes in natural CaCO 3 minerals

The most interesting feature observed in the experimental results of this study is the fact that the Δ 137/134 Ba aragonite-fluid can present both positive and negative values, depending on the growth rate at which aragonite forms. In addition to this observation, the theoretical modelling of the experimental findings suggests that growth rate can induce variations to the fractionation factor between aragonite and fluid as large as -2.0 ‰ (see Fig. 5A). To date the Ba isotope data in natural aragonites are limited to three studies and are derived exclusively from aragonitic corals [START_REF] Pretet | Constraints on barium isotope fractionation during aragonite precipitation by corals[END_REF][START_REF] Hemsing | Barium isotopes in cold-water corals[END_REF][START_REF] Liu | Annually-resolved coral skeletal delta Ba-138/134 records: A new proxy for oceanic Ba cycling[END_REF]. In these studies, the fractionation factors between Ba in the coral and seawater are reported to range between -0.15 and -0.3‰, however the interpretation of these variations when present is assigned to vital effects (see [START_REF] Pretet | Constraints on barium isotope fractionation during aragonite precipitation by corals[END_REF] and is not taking into account growth rate effects. According to the TST fit described in Fig. 5 using eq. ( 16), these fractionation factors can be the result of relatively fast aragonite growth rates ranging from 10 -7.7 to 10 -7.4 mol m -2 s -1 . Such fast aragonite growth rate would as well impact the Ba partition coefficient between aragonite and the fluid [START_REF] Mavromatis | Barium partitioning in calcite and aragonite as a function of growth rate[END_REF] and suggest co-variation in Ba concentration and Ba isotope composition in natural aragonitic samples such as corals. Considering however that vital effects as well as the presence of pure BaCO 3 in the coralline aragonite skeletons [START_REF] Liu | Annually-resolved coral skeletal delta Ba-138/134 records: A new proxy for oceanic Ba cycling[END_REF] can affect their Ba isotope composition, direct use of this isotopic system for growth rate estimates may be challenging. On the other hand, the formation of speleothems commonly occurs at low growth rates. The positive Δ 137/134 Ba aragonite-fluid values at low growth rates of aragonite, and the ability for robust estimation of growth rate in speleothem aragonite suggests that the chemical and isotopic composition of Ba in the solid phase can provide information for the composition of the fluid from which they were formed.

With respect to the application of Ba isotope fractionation in natural aragonitic archives, an interesting implication is the negative relationship of the partition coefficient and isotope fractionation of Ba between aragonite and the precipitating fluid that can be numerically described using the linear equation:

Δ 137/134 Ba aragonite-fluid = -0.5783 × LogD Ba -0.134 (R 2 = 0.84) (22)
and is valid for -0.11 ≤ LogD Ba ≤ -0.66. As it can be seen in Fig. 6, at near chemical and isotopic equilibrium conditions, Δ 137/134 Ba aragonite-fluid attains its maximum value of about +0.3‰, whereas D Ba approaches its minimum value of ~ 10 -0.7 . The advantage of the relationship between Ba chemical partitioning and isotopic fractionation that is described with eq. ( 22) is that it is independent of the precipitation rate of aragonite, thus it can be used as a multiproxy approach to decipher variations of chemical and isotopic composition of the forming fluid. Similar approach has been used earlier based on Sr incorporation and Ca isotope fractionation during calcite formation (Tang et al., 2008a). In the case of Ba in aragonite, if the (Ba/Ca) aq ratio of the aragonite forming fluid is known and can be considered to be constant during mineral growth, the D Ba,aragonite value is determined by analysing the Ba content of the precipitated aragonite. This D Ba,aragonite value is defining the Δ 137/134 Ba aragonite-fluid with the aid of eq. ( 22). Thus, the obtained Finally, another important finding of this study is the absence of significant Ba isotope fractionation during calcite standard inorganic growth mechanism at near equilibrium conditions despite Ba coordination number and Ba-O bond lengths are notably reduced in calcite compared to the Ba aquo ion. This likely arises because the structural change accompanying adsorbed Ba incorporation in the crystal lattice occurs without exchange between aqueous and solid barium.

Conclusions

Based on laboratory experiments and first-principles calculations, we have investigated the Ba isotope fractionation between the anhydrous CaCO 3 minerals, calcite and aragonite, and reactive fluids. In the case of calcite, experimental results show an almost insignificant Ba isotope fractionation (Δ 137/134 Ba calcite-fluid = +0.02±0.06‰) and indicate a weak impact of growth rate on the Δ 137/134 Ba calcite-fluid within the range of mineral growth rates investigated (i.e. 10 -8.0 mol m -2 s -1 ≤ R p(calcite) ≤ 10 -7.3 mol m -2 s -1 ). In contrast, in the case of aragonite mineral growth rate significantly affects the isotopic composition of the precipitated solid. The Δ 137/134 Ba aragonite-fluid

shows positive values up to + 0.27±0.06‰ at aragonite growth rates ≤ 10 -8.0 mol m -2 s -1 but negative values when growth rates are faster than this threshold value. This behaviour can be well explained using the surface reaction kinetic model derived from The variation in the isotopic composition of the precipitated aragonite as a function of growth rate has a potential to be used as a proxy tool for estimation of growth rate or, in the case of speleothems where growth rate can be established with other techniques, the chemical and isotopic composition of Ba in the solid phase can be used to estimate the composition of the forming fluids. Likely the same can be said for coralline aragonites that are generally grown at higher rates, however other parameters such as speciation and vital effects have here to be considered.

863

Table 2: Polynomial fits of β-factor for the four phases (10 3 lnβ = b.10 6 /T 2 with T in K) and α fractionation factor between each mineral and Ba-

Δ

  137/134 Ba aragonite-fluid values can be used for the reconstruction of the Ba isotopic composition of the fluid present during aragonite formation by analyzing the Ba isotopes of the aragonite, regardless of precipitation rates. However, further systematic experiments are required to get distinct insight into the impact of decisive environmental factors, like ionic strength, Mg/Ca ratio, temperature and Ba speciation in the fluid phase on Ba distribution and isotope fractionation during aragonite formation.

*

  If the 2sd is smaller than ±0.039 ‰, the pooled 2 standard deviation of the sample set (±0.039 ‰) is used.

Figure 1 :

 1 Figure 1: Ba isotope fractionation between calcite (A), aragonite (B) and fluid as a function of growth rate. Black and white symbols correspond to samples CaB38, CaB39 and CaB40, containing both calcite and aragonite overgrowths.

Figure 2 :

 2 Figure 2: Theoretical temperature dependence of Ba isotope β-factor for aragonite, calcite, witherite and barium hydrate.

Figure 3 :

 3 Figure 3: Local structure around Ba atom in calcite (A) and aragonite (B), from firstprinciples calculations. Numbers correspond to relaxed Ba-O bond lengths (in Å). Ba, O and C atoms are represented in green, red and brown, respectively.

Figure 4 :

 4 Figure 4: Theoretical Ba isotope β-factor at 25°C as a function of the Ba interatomic force constant.

Figure 5 :

 5 Figure 5: Best-fit line of the TST model to the experimental data for A) aragonite and B) calcite. The grey dashed lines denote the equilibrium and the maximum kinetic isotope fractionation that can be theoretical observed based on the model. The dotted line illustrates the equilibrium isotope fractionation predicted by first-principles simulations. The uncertainty of the best-fit line is ±0.2 ‰.This uncertainty has been approximated as the square root of the sum of the squares of the analytical uncertainty for the α eq (i.e. ±0.06‰) and α f (i.e ±0.2‰).

Figure 6 :

 6 Figure 6: Barium partition coefficient of synthetic aragonite samples plotted as a function of Ba isotope fractionation between solid and fluid. The linear trend represents Eq. (19).

  Transition State theory and already used by DePaolo (2011) and Druhan et al. (2013) to describe Ca isotopes fractionation during calcite precipitation. Additionally, this model predicts that Δ 137/134 Ba aragonite-fluid can take values as low as -2.0‰. The equilibrium experimental and theoretical Δ 137/134 Ba aragonite-fluid values determined in this study (+0.27±0.06 and +0.34 ‰, respectively) are in excellent agreement whereas the lack of Ba isotope fractionation between calcite and the fluid contrasts with the positive theoretical value (Δ 137/134 Ba calcite-fluid = +0.17‰). This likely suggests that the coordination reduction required for the incorporation in the lattice of Ba adsorbed at calcite growing sites proceeds without isotope fractionation.

Table 1 :

 1 Mineralogy, growth rate, pH, partition coefficient, saturation state of the fluid with respect to forming CaCO 3 mineral, isotopic 859 composition of the solid phase and selected fluids and Ba isotope fractionation between carbonate solids and fluid in the experiments performed 860 in this study. All the δ 137/134 Ba values express the average of duplicate analyses.

Acknowledgments

For their assistance with XRD and BET analyses we are thankful to Katja E. Goetschl and Alain Castillo, respectively. DFT calculations were performed using HPC resources from CALMIP (grant 2019-P1037). This work has benefitted from the insightful comments of two anonymous reviewers and those by the AE Chen Zhu. The study has been supported by DFG Forschergruppe 1644 (DFG reference IM44/10-1), the French national programme LEFE/INSU and the European Research Council under the European Union's Horizon 2020 research and innovation program (grant agreement 646894).