Yigal Barkan
email: barkanyigal@gmail.com

Guillaume Paris

Samuel M Webb

Jess F Adkins

Itay Halevy
email: itay.halevy@weizmann.ac.il

Sulfur isotope fractionation between aqueous and carbonate-associated sulfate in abiotic calcite and aragonite

come

Introduction

Sulfate (SO4 2-) substitutes for carbonate (CO3 2-) in all calcium carbonate minerals, in the order of affinity aragonite < calcite < vaterite [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF][START_REF] Arroyo-De Dompablo | Computational investigation of the influence of tetrahedral oxoanions (sulphate, selenate and chromate) on the stability of calcium carbonate polymorphs[END_REF]. The concentration of this carbonate-associated sulfate (CAS) varies between tens parts-permillion (ppm) and a few percent, depending, in addition to mineralogy, on the dissolved SO4 2- to CO3 2-activity ratio (aSO4 2-/aCO3 2-), the precipitation rate, and diagenetic processes [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF][START_REF] Gellatly | Trace sulfate in mid-Proterozoic carbonates and the sulfur isotope record of biospheric evolution[END_REF][START_REF] Gill | Behavior of carbonate-associated sulfate during meteoric diagenesis and implications for the sulfur isotope paleoproxy[END_REF][START_REF] Fichtner | Diagenesis of carbonate associated sulfate[END_REF]. Concentrations of CAS as high as 24,000 and 47,000 ppm occur in natural and synthetic calcite, respectively [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF][START_REF] Staudt | Sulfate Incorporation into Sedimentary Carbonates[END_REF], whereas natural and synthetic aragonite hosts up to 8,200 and 4,500 ppm, respectively (Busenberg and Plummer, 1985, this study). As the sulfate is sourced from the solutions that precipitated the carbonate minerals, the S isotope composition of CAS in marine carbonate rocks is commonly used as a proxy for the S isotope composition of seawater sulfate (e.g., [START_REF] Hurtgen | The sulfur isotopic composition of Neoproterozoic seawater sulfate: implications for a snowball Earth? Earth Planet[END_REF][START_REF] Kampschulte | The sulfur isotopic evolution of Phanerozoic seawater based on the analysis of structurally substituted sulfate in carbonates[END_REF][START_REF] Lyons | Sites of anomalous organic remineralization in the carbonate sediments of South Florida, USA: The sulfur cycle and carbonate-associated sulfate[END_REF][START_REF] Rennie | Cenozoic record of δ 34 S in foraminiferal calcite implies an early Eocene shift to deep-ocean sulfide burial[END_REF]. Although attempts to constrain the S isotope composition of seawater through time have resulted in an increasingly well-sampled geologic record of CAS, the S isotope fractionation associated with sulfate incorporation into CaCO3 has not been systematically constrained in experiments. In this study we perform CaCO3 precipitation experiments to constrain the CAS-SO4 2-S isotope fractionation and its dependence on the precipitation rate and the concentration of aqueous sulfate, in both calcite and aragonite.

Aqueous speciation of S(VI)

In a solution containing S(VI) and metal ions, S(VI) exists in a variety of species, including free ions, such as SO4 2-and HSO4 -, and ion pairs, such as CaSO4 0 and MgSO4 0 . We refer to the sum of all S(VI) species as dissolved inorganic sulfate, or DIS. In contrast with other isotopic systems (e.g., oxygen and carbon), which may include gaseous, liquid, and dissolved species, S(VI) is practically all DIS.

In most natural solutions with neutral to alkaline pH, free DIS consists almost exclusively of aqueous SO4 2-, and in the presence of metal cations a substantial proportion of the DIS is made up of metal ion pairs, depending on the concentration of the cations. For example, in seawater free SO4 2-represents more than half of the DIS, and the rest is distributed evenly between Mg 2+ and Na + ion pairs with more minor contribution from Ca 2+ ions pairs [START_REF] Garrels | A chemical model for sea water at 25 degrees C and one atmosphere total pressure[END_REF]. The DIS chemistry remains relatively invariant over a large range of pH (3-10), unless metal ion concentrations vary with pH due to precipitation/dissolution of other minerals or formation of additional complexes (Figure 1).

Incorporation of sulfate into carbonate minerals

Studies of the mode of sulfate incorporation into CaCO3 minerals suggest that the vast majority of S measured in these minerals is tetrahedral sulfate, which substitutes for the trigonal, planar carbonate ion, despite sulfate's three-dimensional structure and O-O distances that are 8% larger than the carbonate ion [START_REF] Staudt | Surface structural controls on compositional zoning of SO4 2and SeO4 2in synthetic calcite single crystals[END_REF][START_REF] Reeder | Mechanism of SeO4 2substitution in calcite: An XAFS study[END_REF][START_REF] Pingitore | Identification of sulfate in natural carbonates by xray absorption spectroscopy[END_REF][START_REF] Perrin | The coordination of sulfur in synthetic and biogenic Mg calcites: The red coral case[END_REF]. Fluid inclusions [START_REF] Takano | Characterization of sulfate ion in travertine[END_REF], adsorbed sulfate [START_REF] Takano | Characterization of sulfate ion in travertine[END_REF][START_REF] Staudt | Surface structural controls on compositional zoning of SO4 2and SeO4 2in synthetic calcite single crystals[END_REF] and separate sulfate phases [START_REF] Takano | Characterization of sulfate ion in travertine[END_REF][START_REF] Staudt | Surface structural controls on compositional zoning of SO4 2and SeO4 2in synthetic calcite single crystals[END_REF][START_REF] Reeder | Mechanism of SeO4 2substitution in calcite: An XAFS study[END_REF][START_REF] Pingitore | Identification of sulfate in natural carbonates by xray absorption spectroscopy[END_REF] are apparently negligible contributors to the total S in most carbonate rocks. Organic S may coexist in biogenic CaCO3 alongside inorganic CAS, but it is usually minor [START_REF] Takano | Geochemical implications of sulfate in sedimentary carbonates[END_REF][START_REF] Vielzeuf | Distribution of sulphur and magnesium in the red coral[END_REF][START_REF] Nguyen | Distribution of trace element in Japanese red coral Paracorallium japonicum by μ-XRF and sulfur speciation by XANES: Linkage between trace element distribution and growth ring formation[END_REF][START_REF] Tamenori | Identification of the chemical form of sulfur compounds in the Japanese pink coral (Corallium elatius) skeleton using μ-XRF/XAS speciation mapping[END_REF][START_REF] Perrin | The coordination of sulfur in synthetic and biogenic Mg calcites: The red coral case[END_REF], and can be removed during sample preparation (e.g., [START_REF] Wotte | Carbonate-associated sulfate: Experimental comparisons of common extraction methods and recommendations toward a standard analytical protocol[END_REF].

Sulfate incorporation into aragonite and calcite expands the mineral lattice in the direction perpendicular to the planar carbonate groups, as shown by density functional theory (DFT) calculations [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF][START_REF] Arroyo-De Dompablo | Computational investigation of the influence of tetrahedral oxoanions (sulphate, selenate and chromate) on the stability of calcium carbonate polymorphs[END_REF], and X-ray diffraction analyses [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF][START_REF] Kontrec | Incorporation of Inorganic Anions in Calcite[END_REF]. CAS-bearing calcite is less stable than pure calcite, proportionally to its CAS content, as indicated by higher solubility [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF], lower decomposition temperature in differential thermal analysis [START_REF] Kontrec | Incorporation of Inorganic Anions in Calcite[END_REF], and more sluggish kinetics of the transformation from vaterite to calcite when vaterite is a precursor phase [START_REF] Fernández-Díaz | The role of sulfate groups in controlling CaCO3 polymorphism[END_REF]. At low concentrations of aqueous SO4 2-, calcite is the stable CaCO3 polymorph in dilute solutions. At SO4 2-concentrations greater than approximately 8 mM calcite nucleation and precipitation is inhibited, and aragonite precipitates from saturated solutions [START_REF] Kitano | The Behavior of Various Inorganic Ions in the Separation of Calcium Carbonate from a Bicarbonate Solution[END_REF][START_REF] Kitano | Incorporation of sodium, chloride and sulfate with calcium carbonate[END_REF]. A similar stabilization of aragonite relative to calcite is observed at Mg 2+ to Ca 2+ ratios (Mg 2+ /Ca 2+ ) greater than about 2, as in the present "aragonite seas" with Mg 2+ /Ca 2+ = 5.2 [START_REF] Fyfe | The Calcite Aragonite Problem[END_REF][START_REF] Bots | The role of SO4 in the switch from calcite to aragonite seas[END_REF][START_REF] Sun | Nucleation of metastable aragonite CaCO3 in seawater[END_REF].

In addition to increasing the incorporation of CAS and destabilizing calcite, high aqueous SO4 2- activity in the precipitating solution alters the precipitation and dissolution kinetics. At a given saturation state, the precipitation rate is reduced by a factor of a few by an increase of the aqueous SO4 2-concentration from 3 to 50 mmol/kg [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF]. Calcite also dissolves more rapidly in solutions with NaCl or with MgSO4 at high concentrations (>10mM), where the latter strongly promotes etch-pit nucleation. Na2SO4 alone does not promote etch-pit nucleation, but slightly promotes pit spreading rates [START_REF] Ruiz-Agudo | An atomic force microscopy study of calcite dissolution in saline solutions: The role of magnesium ions[END_REF][START_REF] Ruiz-Agudo | The role of background electrolytes on the kinetics and mechanism of calcite dissolution[END_REF].

Existing constraints on CAS-SO4 2-S isotope fractionation

The suggestion that CAS should faithfully record the  34 S a of the seawater from which the carbonate minerals precipitated was originally based on  34 Smeasured in modern foraminifera and mollusca, each collected from two locations (mean 20.6±0.4‰), which were found to fall within analytical uncertainty of the  34 S (20.8±0.4‰) of modern seawater collected at three locations [START_REF] Burdett | A Neogene seawater sulfur isotope age curve from calcareous pelagic microfossils[END_REF]. Subsequent analyses showed that CAS in the skeletons of modern calcifying organisms (collected from natural environments or cultured) exhibits  34 S values both higher and lower than the seawater in which the organisms grew, spanning a range of more than 3.5‰ (Figure 2). In addition to this isotopic variation among biogenic carbonates, variation of up to 20‰ in the  34 S values of different carbonate rock constituents has been reported [START_REF] Present | Large Carbonate Associated Sulfate isotopic variability between brachiopods, micrite, and other sedimentary components in Late Ordovician strata[END_REF], which does not reflect variation in seawater sulfate  34 S values. Deviations towards more negative values are mostly due to oxidation and incorporation of 34 Sdepleted sulfide, whereas deviations towards more positive values probably reflect incorporation of 34 S-enriched sulfate that is residual to microbial sulfate reduction (MSR).

Analytical progress [START_REF] Paris | MC-ICP-MS measurement of δ 34 S and ∆ 33 S in small amounts of dissolved sulfate[END_REF], which allows reliable  34 S measurements in carbonate mineral samples as small as a few tens of milligrams, make it possible to avoid this secondary variability by selection of well-preserved shells (e.g., brachiopods as in [START_REF] Kampschulte | The sulphur isotopic composition of trace sulphates in Carboniferous brachiopods: implications for coeval seawater, correlation with other geochemical cycles and isotope stratigraphy[END_REF][START_REF] Present | Large Carbonate Associated Sulfate isotopic variability between brachiopods, micrite, and other sedimentary components in Late Ordovician strata[END_REF]. Nevertheless, better understanding of the fractionating processes during precipitation of primary and secondary carbonate minerals, including vital effects and abiotic S isotope fractionation, is necessary for robust use of CAS as a proxy for seawater sulfate  34 S values.

Most carbonate mineral precipitation in the modern ocean is skeletal, and this has been the case over the entire Phanerozoic. In this work we studied the effects of CAS incorporation into abiotic calcium carbonate minerals, a choice driven by the recognition that abiotic calibrations, in which the underlying physico-chemical mechanisms may be understood, must serve as a basis and a comparison to any biogenic calibrations. Furthermore, carbonate minerals precipitate abiotically in some marine environments, most notably as cements formed during diagenesis [START_REF] Moore | Carbonate reservoirs : porosity and diagenesis in a sequence stratigraphic framework[END_REF]. In addition, in microbially mediated CaCO3 formation, the precipitation itself is abiotic, and the metabolic activity of the microbes serves to alter environmental conditions in favor of carbonate mineral saturation and precipitation [START_REF] Castanier | Ca-carbonates precipitation and limestone genesisthe microbiogeologist point of view[END_REF]. Finally, the carbonate minerals in the Precambrian geologic record, before the appearance of calcifying organisms, are exclusively abiotic or microbially mediated [START_REF] Sumner | Late Archean Aragonite Precipitation: Petrography, Facies Associations, and Environmental Significance[END_REF][START_REF] Grotzinger | Precambrian Carbonates: Evolution of Understanding[END_REF][START_REF] Schrag | Authigenic carbonate and the history of the global carbon cycle[END_REF]. a  34 S = ( 34 Rs/ 34 Rr -1)×1000, in permil units (‰), where 34 Rs and 34 Rr are 34 S/ 32 S ratios in a sample and a reference material, respectively.

Despite the important contribution of abiotic carbonate rocks to the sedimentary record, experimental constraints on S isotope fractionation between aqueous sulfate and CAS in abiotic CaCO3 minerals do not exist. Theoretical constraints do exist, and reduced partition function ratios (𝛽 values) of aqueous sulfate [START_REF] Otake | Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems[END_REF][START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF] and of CAS in calcite, aragonite and vaterite [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF] have been calculated by DFT. Calculations using 𝛽 values from [START_REF] Otake | Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems[END_REF] and [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF] yield 1000 ln α CAS-SO 4 2-eq at 25°C of 3.6, 4.5 and 4.0 ‰, in calcite, aragonite and vaterite, respectively. Fractionations are 0.4‰ larger when using SO4 2-(aq) 𝛽 values from [START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF]. Considerations of computational expense do not allow calculations over the range of naturally occurring CAS concentrations. Consequently, the CAS concentrations in the calculations of [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF] are equivalent to 59,000, 30,000 and 52,000 ppm, in calcite, aragonite and vaterite, respectively, higher than the most CAS-rich samples documented (Figure 2). Furthermore, the calculated S isotope fractionations are at least 2‰ larger than those measured in natural (albeit biogenic) samples (Figure 2).

To better understand the factors determining CAS  34 S values in marine carbonate rocks, we performed CaCO3 precipitation experiments from solutions with variable SO4 2-concentrations, and at variable precipitation rate, and measured the S isotope fractionation between CAS and the SO4 2-in solution. We found that the CAS-SO4 2-S isotope fractionation in aragonite is independent of the concentration of aqueous SO4 2-. On the other hand, in calcite the CAS-SO4 2- S isotope fractionation covaries strongly with the concentration of aqueous SO4 2-, and weakly with precipitation rate. We explored possible explanations for these dependences, and suggest that the appreciable sulfate impurity in calcite affects the carbonate mineral's energetic state and modulates the equilibrium CAS-SO4 2 S isotope fractionation, with possible implications for other isotopic systems.

Methods

Precipitation methods

We employed two CaCO3 precipitation methods, "CO2 degassing" and "constant addition". In the CO2 degassing experiments, we tested the impact of aqueous sulfate concentration on the CAS concentration and S isotope composition in both calcite and aragonite. In the constant addition experiments, we tested the effect of precipitation rate on the concentration and S isotope composition of CAS in calcite. We briefly describe the precipitation methods below, and provide a detailed description of the methods, pH measurements, calculation of precipitation rates, and geochemical parameters in Appendix I.

In the constant addition method, a mixture of 1:1 NaHCO3-Na2SO4-NaCl and CaCl2-Na2SO4-NaCl stock solutions, referred to hereafter as DIC and Ca 2+ solutions, respectively, was injected at various rates into a reactor maintained at a temperature of 25.0±0.1°C. Solution injection rates and the mass of the nucleation seeds added were varied to facilitate a range of precipitation rates, spanning over more than 2 orders of magnitude.

In the CO2 degassing method, we varied pCO2 in a 0.3 m 3 Plexiglas glove box (GB) containing multiple 2-liter solutions in glass bottles, to allow for dissolution of a CaCO3 reagent and its reprecipitation as calcite in solutions with no added Mg 2+ , or as aragonite in solutions where Mg 2+ was added. The Na2SO4 concentration was varied to facilitate a range of sulfate concentrations spanning more than 3 orders of magnitude. During the precipitation, the temperature was 30.1±0.4 and 30.7±0.4°C in the aragonite-and calcite-precipitating sets, respectively.

Measurements of sulfate concentrations and  34 S

Powder samples of ~10 mg were dissolved in triplicate and split into aliquots for sulfate concentration and δ 34 S analysis. Sulfate concentrations were measured by ion chromatography on a Dionex ICS-2000 with an AS-19 column and 20 mM KOH eluent at the Caltech Environmental Analysis Center. Sulfur isotope ratios were measured by MC-ICP-MS on a Thermo Fischer Scientific Neptune Plus, coupled to a Cetac Aridus heated spray chamber in the Division of Geological and Planetary Sciences at Caltech. Prior to S isotope measurement, Ca 2+ was removed from the remaining dissolved carbonate by ion exchange chromatography, and the isotopic measurements were made on aqueous sodium sulfate solutions [START_REF] Paris | MC-ICP-MS measurement of δ 34 S and ∆ 33 S in small amounts of dissolved sulfate[END_REF][START_REF] Paris | Experimental determination of carbonate-associated sulfate δ 34 S in planktonic foraminifera shells[END_REF]. Specimens were prepared in a clean room with high-purity acids (Seastar) and deionized water, and analyzed in sets of up to 20 samples, along with 2-4 procedural blanks, 2 replicates of an in-house dissolved deep-sea coral consistency standard, and 2 replicates of seawater. The powder pretreatment process for natural samples described in [START_REF] Paris | MC-ICP-MS measurement of δ 34 S and ∆ 33 S in small amounts of dissolved sulfate[END_REF] was applied to some samples, and the results yielded no difference from untreated samples. The results were corrected for insoluble residues and for the CAS concentration and  34 S of the nucleation seeds, whenever seeds were added. The S isotope fractionation factor ( was calculated between the samples and the Na2SO4 reagent used and is reported against the Vienna Canyon Diablo Troilite (VCDT) standard:

Mineral identification

The mineralogy of the precipitates was determined by powder X-ray diffraction (XRD) on a Bruker D2 PHASER equipped with Cu Ktube (30 kV, 10 mA) and a 1D Lynxeye detector, in a Bragg-Brentano configuration. Acquisition was in 2 steps of 0.025°, for 1.5 seconds per step at =40 rpm. The diffractogram background was removed using the BEADS method [START_REF] Duval | BEADS: Baseline Estimation And Denoising w/ Sparsity (chromatogram signals)[END_REF], and the abundances of calcite, aragonite and vaterite were then quantified following [START_REF] Kontoyannis | Calcium carbonate phase analysis using XRD and FT-Raman spectroscopy[END_REF] and factors described therein. Most samples consisted of pure phases (>98% pure).

X-ray absorption spectroscopy

X-ray absorption near edge spectra (XANES) were collected at the Stanford Synchrotron Radiation Lightsource (SSRL), using beam line 14-3 on the Stanford Positron Electron Accelerating Ring (SPEAR), run with 500 mA and 3.0 GeV. The energy of incident X-rays was set using a Si (111) double crystal monochromator and calibrated to the thiol peak of a sodium thiosulfate powder at 2472.02 eV. Intensities of incident X-rays were measured with a heliumfilled ion chamber, and the sulfur fluorescence measured with 4-element Si drift detector (Hitachi) using Xspress3 pulse processing electronics (Quantum Detectors). The sulfur K-edge was measured at a variable energy resolution of 0.2 eV at 2460-2480 eV, 0.05 eV at 2480-2484 eV, 0.2 eV at 2484-2500 eV, and 2 eV at 2500-2536 eV. Spectra were averaged using SIXPack [START_REF] Webb | SIXPack a Graphical User Interface for XAS Analysis Using IFEFFIT[END_REF] and then detrended and fit using a MATLAB program of our own development.

The fit was composed of a combination of one step-function for the post-edge plateau, and four Voight line shapes for the main features of the sulfur K-edge spectra (Figure 3). The line shapes were chosen solely to fit the spectra and not with any known S-species in mind. We calculated Voigt line shapes using a publicly available program [START_REF] Abrarov | The Voigt/complex error function[END_REF][START_REF] Ruzi | Voigt line shape fit[END_REF]. Poor fits to the spectra (r 2 <0.9), due to low [CAS] and consequently low signal-to-noise ratios (Appendix I), are not discussed further.

Results

The experiments produced the expected CaCO3 polymorphs with two exceptions. At the highest injection rates in the constant addition experiments (CCL samples, log(J)=-4.3 mol/m 2 /s) 31-48% vaterite precipitated along with calcite (Table A1), and in the CO2 degassing experiments at 8 mM Na2SO4 (no added MgCl2), 52% aragonite precipitated along with calcite (Table A2).

Only pure (>98%) samples will be described and discussed in the following sections. As discussed in Section 1.1, in solutions where ion pairs are abundant, the activity of free sulfate, rather than the total DIS concentration, is a more meaningful quantity. Additionally, during the precipitation of CaCO3 minerals and incorporation of CAS, aqueous sulfate competes with the carbonate ion for available kink sites for anion attachment [START_REF] Vavouraki | An Atomic Force Microscopy study of the growth of calcite in the presence of sodium sulfate[END_REF]. We therefore adopt the activity ratio of sulfate to carbonate (aSO4 2-/aCO3 2-) as the relevant measure of the abundance of DIS.

CAS concentrations

The concentrations of CAS ([CAS]) from the two experimental methods are in agreement for corresponding values of log(J) and aSO4 2-/aCO3 2-(Figure 4). The concentration of CAS in both aragonite and calcite from the CO2 degassing experiments increases linearly with sulfate concentration. Calcite and aragonite show a ~160-fold and ~170-fold increase in [CAS] over a ~170-fold and ~220-fold increase in aSO4 2-/aCO3 2-, respectively.

The dependence of [CAS] in calcite on precipitation rate (Figure 4b), as determined in the constant addition experiments, is much weaker than on aSO4 2-/aCO3 2-. An increase of a factor of ~170 in precipitation rate only leads to approximately a doubling of [CAS] in calcite, whereas a ~170-fold increase in aSO4 2-/aCO3 2-leads to a ~160-fold increase in [CAS].

CAS-SO4 2-S isotope fractionation in aragonite and calcite

The CAS-SO4 2-S isotope fractionation (1000lnα CAS-Na 2 SO 4 ) of the aragonitic samples over the entire range of aSO4 2-/aCO3 2-(Table 1, Figure 5a) falls within error of an average value of 1.0±0.3 ‰ (RMSn=12). This value of 1000lnα CAS-Na 2 SO 4 is smaller than all of the values measured in the calcite samples (see below). The samples precipitated at low aSO4 2-/aCO3 2- (which have low CAS concentrations) display the largest error on 1000lnα CAS-Na 2 SO 4 . Repeated analysis suggests that this error is the result of sample heterogeneity rather than an analytical artifact.

The 1000lnα CAS-Na 2 SO 4 values for calcite are all positive over the entire range of aSO4 2-/aCO3 2- , and decrease with increasing aSO4 2-/aCO3 2-, from 2.9±0.5‰ (RMS, n=2) at aSO4 2-/aCO3 2-of ~7 to 1.9±0.1‰ (RMS, n=3) at aSO4 2-/aCO3 2-of ~1,200 (Table 1, Figure 5a). It is unclear whether 1000lnα CAS-Na 2 SO 4 values continue to decrease in calcite at higher aSO4 2-/aCO3 2-, though pure calcite is unlikely to precipitate under these conditions. As in the case of aragonite, the calcite samples precipitated at low aSO4 2-/aCO3 2-show the largest error on 1000lnα CAS-Na 2 SO 4 , which is the result of heterogeneity among the samples.

The 1000lnα CAS-Na 2 SO 4 values for calcite decrease with increasing precipitation rate, from 1.7±0.2‰ (n=2) at log(J) of ~-7.5 to 1.3±0.1‰ (n=3) at log(J) of ~-5.3 (Table 1, Figure 5b). The 1000lnα CAS-Na 2 SO 4 values from the two experimental methods at the corresponding log(J) and aSO4 2-/aCO3 2-do not fall within error like the CAS concentration values, but are offset by ~0.3‰. * Uncertainty is given by the larger of the root mean square error and 1 standard deviation of external replicates. ** Samples with 31-48% vaterite precipitated along with calcite (Table A2).

Sulfur K-edge XANES

Spectra of CAS in calcite and aragonite differ subtly from each other (Figure 6; see discussion), but the spectra of CAS within each individual CaCO3 polymorph differ from each other mostly in fluorescence intensity and in the signal-to-noise ratios, which depend on [CAS] (Appendix I). The fit to the spectra included four Voigt lines (V1…4), each with a peak location (EVi in eV), an intensity (IVi in arbitrary units) and a full width at half maximum height (FWHMVi in eV). The IV1-4 strongly correlate with [CAS] (Figure 6c, Appendix III), and the FWHMV1 also show a correlation with [CAS], albeit more scattered (Figure 6d).

We find no correlation between the EV1-4 and [CAS] (Figure 6b). All EV1 correspond to a typical sulfate pre-edge energy, as previously reported [START_REF] Pingitore | Identification of sulfate in natural carbonates by xray absorption spectroscopy[END_REF][START_REF] Fleet | XANES spectroscopy of sulfur in earth materials[END_REF]. Furthermore, except for the two aragonite samples with the highest [CAS], EV1 is shifted by 0.1 eV to lower energy in aragonite (2482.6±0.0 eV, 1n=7), relative to calcite (2482.7±0.0 eV, 1n=11) (Figure 6a-b).

The EV1 of 2,482.6 and 2,482.7 eV found in this study for aragonite and calcite, respectively, are within the range found in previous studies, but the observed shift of 0.1 eV in EV1 between these CaCO3 polymorphs has not been previously described.

Discussion

CAS concentrations in aragonite and calcite

Higher [CAS] in calcite than in aragonite has been reported in both natural and synthetic samples (e.g., [START_REF] Kitano | Incorporation of sodium, chloride and sulfate with calcium carbonate[END_REF][START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF] and is supported by molecular modeling (Section 1). Concentrations of CAS as high as 4,500 ppm in synthetic aragonite have not been reported previously to this study. Concentrations of CAS as high as 8,200 ppm were previously measured in modern aragonitic corals, and if the corals display a [CAS]-aSO4 2-/aCO3 2-relationship similar to the synthetic aragonite, this implies aSO4 2- /aCO3 2-of 2,500 in the precipitating fluid. This aSO4 2-/aCO3 2-is much higher than in modern seawater (~315), which is thought to be the source of the calcifying fluid (McConnaughey, 1989a;1989b;[START_REF] Adkins | Stable isotopes in deep-sea corals and a new mechanism for "vital effects[END_REF][START_REF] Erez | Calcification in hermatypic corals is based on direct seawater supply to the biomineralization site[END_REF][START_REF] Gagnon | Sr/Ca and Mg/Ca vital effects correlated with skeletal architecture in a scleractinian deep-sea coral and the role of Rayleigh fractionation[END_REF]2012;[START_REF] Tambutté | Coral biomineralization: From the gene to the environment[END_REF]. Without pumping protons out of, or Ca 2+ into the calcifying fluid, quantitative precipitation of aragonite from seawater may only lead to aSO4 2-/aCO3 2-of ~1,300. In other words, the mineral will precipitate from a solution with an average aSO4 2-/aCO3 2-between ~315, as in seawater, and ~1,300. The high aSO4 2-/aCO3 2-of 2,500 suggested by coralline aragonite [CAS] may, therefore, imply either the existence of such proton or Ca 2+ pumps or that coralline aragonite displays a different [CAS]-aSO4 2-/aCO3 2-relationship than abiotic aragonite.

A positive correlation between [CAS] and aSO4 2-/aCO3 2-has been previously shown for synthetic calcite [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF][START_REF] Fernández-Díaz | The role of sulfate groups in controlling CaCO3 polymorphism[END_REF]. The ratio of the mole fractions (X, mol) of sulfate and carbonate ions in CaCO3, are related to the molar concertation (M, mol/L) in solution by Kd, the partition coefficient:

2)

XSO 4 2- XCO 3 2-= K d ( MSO 4 2- MCO 3 2-) .
The mole fraction is related to [CAS] by the molar weight (Mw, g/mol),

XSO 4 2- XCO 3 2-= [CAS] 10 6 × M w CaCO 3 M w SO 4 2- .
Using the measured [CAS] (in ppm) in the calcite and aragonite precipitated in the CO2 degassing experiments and a few constant addition samples with similar log(J) (CCJA-CCJC), the corresponding values of Kd for calcite and aragonite are 16±6×10 -6 and 8±4×10 -6 , respectively.

Taking the logarithm of equation 2 and expressing aqueous concentrations in terms of activities and activity coefficients yields

3) log ( XSO 4 2- XCO 3 2-) = C×log ( aSO 4 2- aCO 3 2-) + log (K d × γCO 3 2- γSO 4 2-
). a linear regression through the logarithm of the data yields the relations:

4) log ( XSO 4 2- XCO 3 2-) calcite = 1.03 (±0.05) × log ( aSO 4 2- aCO 3 2-) -4.87 (±0.10) R 2 = 0.995, 5) log ( XSO 4 2- XCO 3 2-) aragonite = 0.91 (±0.09) × log ( aSO 4 2- aCO 3 2-) -5.20 (±0.19) R 2 = 0.981.
According to the Berthelot-Nernst distribution law, the slope of the regression line (C) should be equal to unity at equilibrium when Kd and [START_REF] Mcintire | Trace element partition coefficients-a review of theory and applications to geology[END_REF][START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF]. In the experiments of [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF], hereafter B&P, log([CAS]) was linearly proportional to log(aSO4 2-/aCO3 2-), with slopes between 0.6 and 0.8, which were interpreted to reflect a kinetic control of sulfate incorporation, while in our experiments slopes of the regression lines are within error of unity. In B&P, the calculated value of Kd was linearly proportional to the precipitation rate, which was itself proportional to . Based on the pH measurements and thermodynamic calculations (Section 6.4), the weighted average precipitation rate in all of our CO2 degassing experiments was lower than the rates in B&P, and the near-unity slopes of log([CAS]) versus log(aSO4 2-/aCO3 2-) in our experiments suggests near-equilibrium sulfate incorporation. The calcite Kd value derived from the experiments in this study (16±6×10 -6 ) is slightly smaller than, but within error of the value from the least supersaturated (= 2.5), slowest to precipitate (J ≤ 3 mg g -1 min -1 ) experiments of B&P (Kd = 19±8×10 -6 ).

γCO 3 2- γSO 4 2-are constant (McIntire

Sulfur K-edge XANES

In XANES spectroscopy the energy at which the absorption edge is located is sensitive to the valence of the element and to the electronic influence of bonds with neighboring atoms. In sulfate compounds, the distinct white line pre-edge feature results from a transition from the 1s orbital to the unoccupied t2 * anti-bonding orbital [START_REF] Pin | Combined Sulfur K-Edge XANES-EXAFS Study of the Effect of Protonation on the Sulfate Tetrahedron in Solids and Solutions[END_REF]. This feature typically peaks at 2482-2483 eV [START_REF] Cuif | XANES mapping of organic sulfate in three scleractinian coral skeletons[END_REF][START_REF] Fleet | XANES spectroscopy of sulfur in earth materials[END_REF][START_REF] Frisia | Variations in atmospheric sulphate recorded in stalagmites by synchrotron micro-XRF and XANES analyses[END_REF][START_REF] Yoshimura | Element profile and chemical environment of sulfur in a giant clam shell: Insights from μ-XRF and X-ray absorption near-edge structure[END_REF][START_REF] Perrin | The coordination of sulfur in synthetic and biogenic Mg calcites: The red coral case[END_REF]. Post-edge features are distinctive for different sulfate minerals (e.g., anhydrite, thenardite) and for CAS in the different carbonate minerals [START_REF] Pingitore | Identification of sulfate in natural carbonates by xray absorption spectroscopy[END_REF][START_REF] Fleet | XANES spectroscopy of sulfur in earth materials[END_REF][START_REF] Yoshimura | Element profile and chemical environment of sulfur in a giant clam shell: Insights from μ-XRF and X-ray absorption near-edge structure[END_REF].

The energy of EV1 suggests that sulfur occurs as sulfate in all samples. The EV1 of 2,482.6 and 2,482.7 eV found in this study for aragonite and calcite, respectively, is within the range found in previous studies. However, the observed shift of 0.1 eV in EV1 between calcite and aragonite has not been previously described. The observed increase in FWHMV1 with increasing [CAS] is not associated with a change in the peak center energy, EV1. A narrow FWHMV1 is expected when the geometry of sulfate is close to tetrahedral and the S-O bonds are nearly identical for O1 through O4 (e.g., as in dissolved sulfate). An increase in FWHMV1 suggests a larger variety of S-O bonding configurations, each with a slightly different X-ray absorption energy [START_REF] Pin | Combined Sulfur K-Edge XANES-EXAFS Study of the Effect of Protonation on the Sulfate Tetrahedron in Solids and Solutions[END_REF]. More specifically, distorting the Td tetrahedral geometry of the sulfate ion, as in CAS, causes the degeneracy of the unoccupied anti-bonding orbitals to collapse, providing a distribution of unoccupied states for the pre-edge transition to occupy. This suggests a slightly different coordination environment of the sulfate in CAS between the carbonate polymorphs.

CAS-SO4 2-S isotope fractionation in calcite

The experimental conditions of the constant addition and the CO2 degassing experiments differed in the pH range, the overlying pCO2, the introduction method of dissolved Ca and inorganic C, the salt concentration and corresponding ionic activity and ionic strength, the presence of carbonic anhydrase, the presence of nucleation seeds, and temperature. The similarity of the dependence of [CAS] and 1000lnα CAS-Na 2 SO 4 on aSO4 2-/aCO3 2-from these very different experimental conditions highlights the dominant influence of aSO4 2-/aCO3 2-on sulfate incorporation as CAS and on the associated S isotope fractionation. It is difficult to confidently ascribe the ~0.3‰ difference in 1000lnα CAS-Na 2 SO 4 values at aSO4 2-/aCO3 2-of ~500 and log(J) of ~-6 in the two experimental sets to one of the many differences between them. Temperature differences can be precluded, however, as theoretical calculations suggest decreasing isotope fractionation with increasing temperature [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF][START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF]. The higher temperature of the CO2 degassing experiments (by 5.7±0.4°C) would thus lead to smaller S isotope fractionation (by ~0.1‰), which is opposite to what we observe.

The dependence of CAS-SO4 2-S isotope fractionation on calcite precipitation rate

The fractionation of S isotopes between CAS in calcite and aqueous sulfate decreases with increasing precipitation rate (Figure 5b). Isotopic effects associated with diffusion (e.g., [START_REF] Lemarchand | Rate-controlled calcium isotope fractionation in synthetic calcite[END_REF]) may be ruled out, as the stirring rate in our experiments implies a diffusional boundary layer about 30 times thinner than the critical boundary layer. Under such conditions, surface reactions, not diffusion from the bulk solution, are expected to control the fractionation of isotopes [START_REF] Depaolo | Surface kinetic model for isotopic and trace element fractionation during precipitation of calcite from aqueous solutions[END_REF]. Next, we discuss possible explanations for the precipitation rate-dependent CAS-SO4 2-S isotope fractionation.

The net isotope fractionation (α net ) expressed in a reaction depends on the ratio between the rate of formation of reactant from product (dissolution or backward flux, J b ) and the rate of product formation from reactant (precipitation or forward flux, J f ). The incorporation of sulfate into a carbonate mineral is analogous to precipitation and the release back into solution is analogous to dissolution. This ratio of sulfate release to incorporation is the reversibility (f) and is related to the Gibbs free energy of the reaction, ΔG r ,

6) f = J b J f = e
ΔG r RT [START_REF] Beard | Relationship between Thermodynamic Driving Force and One-Way Fluxes in Reversible Processes[END_REF],

where R is the gas constant and T the absolute temperature. The equilibrium isotope fractionation (α eq ) will be expressed during nearly fully reversible precipitation (f → 1), while the forward kinetic isotope fractionation (α f ) will be expressed during far-from-equilibrium precipitation (f → 0). The net isotope fractionation is then:

7) α net = α f 1+f ( α f α eq -1)
, [START_REF] Depaolo | Surface kinetic model for isotopic and trace element fractionation during precipitation of calcite from aqueous solutions[END_REF].

Equation 7 has been shown to apply to atomic ratios (e.g., Sr/Ca) as well as to isotopic ratios (e.g., 44 Ca/ 40 Ca). The net precipitation (J p = J f -J b ), in units of moles per surface area per time, is related to f by 8)

J p J b = 1 f -1 .
The inflection point in the transition of α net between the equilibrium and kinetic end members will be observable when J p ≈ J b or f ≈ 0.5, if no fractionating processes other than precipitation are expressed, if the equilibrium and kinetic end members are distinguishable analytically (α eq -α f > σ), and if the experimental range of precipitation rate covers this transition.

Modeling of elemental (Sr/Ca) and isotopic compositions (Ca and O at pH values of 7-8) of experimentally precipitated calcite suggests that the inflection point (J p ≈ J b ) lies at Jp between 10 -7.5 and 10 -5.5 mole m -2 s -1 (DePaolo, 2011; [START_REF] Watkins | The influence of kinetics on the oxygen isotope composition of calcium carbonate[END_REF], similar to our experimental range of precipitation rates. In the Sr/Ca and Ca isotope systems equilibration among aqueous species is rapid, as is equilibration of O isotopes in the CaCO3-H2O system in the presence of carbonic anhydrase. Hence, in the absence of diffusive effects, the main isotope fractionation expressed in such cases is expected to be due to precipitation. We expect similar behavior (i.e., rapid DIS equilibration and isotope fractionation predominantly associated with precipitation) during CAS incorporation in our experiments. Assuming that attachment and detachment rates, among other essential surface reaction parameters, are not dramatically different between CO3 2- , HCO3 -and SO4 2-, we may also expect the transition between the equilibrium and kinetic endmember isotope fractionations in the case of CAS incorporation into calcite to occur over a similar range of Jp. If this is true, then our experimental range of precipitation rates (10 -7.5 to 10 -5.3 mole m -2 s -1 ) should include the inflection point (scenario 1, Figure 7a). In this case, the difference between α eq and α f is on the order of tenths of a permil; 1000lnα eq is ~1.7‰, and 1000lnα f is ~1.3‰, and we should expect natural calcites to exhibit CAS-SO4 2-S isotope fractionation of 1.5±0.2‰ (1, n=11, Table 1), which is only weakly dependent on their precipitation rate.

The near-unity slope of log([CAS]) versus log(aSO4 2-/aCO3 2-) in our CO2 degassing experiments suggests sulfate incorporation close to chemical equilibrium at precipitation rates of about 10 -6 mole m -2 s -1 . This, in combination with rapid DIS equilibration, may result in near-equilibrium CAS-SO4 2-S isotope fractionation in most of our constant addition samples (J<10 -6 mole m -2 s -1 ), rather than a transition from α eq to α f . In this case, the range of experimental Jp does not cover the entire transition (scenario 2, Figure 7b), α eq is constrained to be approximately 1.7±0.2‰ (1, n=2) at aSO4 2-/aCO3 2-of ~500 (left of Figure 5b), and α f cannot be constrained.

We note that the values for the equilibrium end-member S isotope fractionation were obtained at aSO4 2-/aCO3 2-of ~500, and that the measured CAS-SO4 2-S isotope fractionation in calcite depends strongly on aSO4 2-/aCO3 2-(discussed in Section 4.3.2). In modern seawater, where aSO4 2-/aCO3 2-is ~315, the inferred isotope fractionations would be higher by a few tenths of a permil.

We cannot conclusively distinguish between the two scenarios suggested above, though inferences may be made about CAS-SO4 2-S isotope fractionation in natural calcite. Abiotic rates of natural CaCO3 precipitation are, on average, orders of magnitude slower than experimental precipitation rates (e.g., [START_REF] Coplen | Calibration of the calcite-water oxygen-isotope geothermometer at Devils Hole, Nevada, a natural laboratory[END_REF][START_REF] Fantle | Ca isotopes in carbonate sediment and pore fluid from ODP Site 807A: The Ca 2+ (aq)-calcite equilibrium fractionation factor and calcite recrystallization rates in Pleistocene sediments[END_REF]. Therefore, CAS-SO4 2-S isotope fractionation in most natural abiotic calcite is expected to be ≥1.7±0.2‰ (1, n=2) at aSO4 2-/aCO3 2-of ~500, the value measured at our lowest precipitation rates. For biogenic CaCO3, we cannot rule out the possibility that average precipitation rates reflect brief pulses of rapid growth separated by periods of no growth. In such cases, the majority of mineral mass may be precipitated under kinetic control, and if scenario 2 is correct, CAS-SO4 2-S isotope fractionation lower than the lowest values measured in our experiments is expected. It is interesting to note that almost all CAS-SO4 2-S isotope fractionations measured in biogenic CaCO3 are lower than the lowest S isotope fractionations measured in this study (Figure 8). For S isotopes in CAS, might relatively rapid biotic rates of precipitation be an explanation for these "vital effects" (discussed in Section 4.5)?

4.3.2 The dependence of CAS-SO4 2-S isotope fractionation on aSO4 2-/aCO3 2-in calcite

Next, we discuss possible mechanisms for the decreasing S isotope fractionation with increasing aSO4 2-/aCO3 2-in the calcite samples. In both experimental methods, sulfate was removed from the system only by incorporation into the growing CaCO3 from a single reservoir, the dissolved Na2SO4. Thus, any isotopic fractionation between the sulfate in solution and CAS is due to the processes involved in the transport of sulfate to the precipitation surface or due to the incorporation itself. In both the CO2 degassing and constant addition methods, solutions were well stirred suggesting that diffusion-driven isotope fractionation should be insignificant, as discussed above. Differing degrees of Rayleigh distillation as a function of the initial sulfate concentration (and, therefore, aSO4 2-/aCO3 2-) may also be ruled out due to the small fraction of aqueous sulfate that was incorporated from all experimental solutions into the minerals (<0.5%). The absence of measurable deviation in the  34 S values of sulfate remaining in the solutions after CaCO3 precipitation in preliminary experiments supports the inference that Rayleigh distillation cannot explain the dependence on aSO4 2-/aCO3 2-. We note that the aSO4 2- /aCO3 2-did not affect the S isotope fractionation in the aragonite samples, suggesting a mechanism for the dependence of isotope fractionation on aSO4 2-/aCO3 2-that is specific to calcite. In the next sections we discuss other mechanisms that may lead to a relationship between CAS-SO4 2-S isotope fractionation and aSO4 2-/aCO3 2-, which required a more elaborate treatment.

Competition between entrapment and exchange of CAS cannot explain the trend

It is possible that at the precipitation rates of the CO2 degassing experiments, the growing mineral entrapped sulfate ions that had not isotopically equilibrated with aqueous sulfate in the solution. We discuss this possibility in detail in Appendix II, and only briefly summarize the resulting insight below. In this mechanism, the decrease in bulk precipitation rate with increasing aSO4 2-, which has been demonstrated experimentally [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF][START_REF] Vavouraki | An Atomic Force Microscopy study of the growth of calcite in the presence of sodium sulfate[END_REF][START_REF] Nielsen | Inhibition of Calcite Growth: Combined Effects of Mg 2+ and SO4 2[END_REF], would manifest as a dependence on aSO4 2- /aCO3 2-of the competition between S isotope exchange and entrapment by the growing crystal.

A high aSO4 2-/aCO3 2-would result in a lower precipitation rate, allowing for longer S isotope exchange times between surface-attached and aqueous sulfate, and promoting S isotope fractionations closer to isotopic equilibrium. If this were correct, the small CAS-SO4 2-S isotope fractionation exhibited at high aSO4 2-/aCO3 2-should represent a value closer to the equilibrium S isotope fractionation. In other words, the equilibrium S isotope fractionation associated with sulfate incorporation into calcite is expected to be smaller than the kinetic S isotope fractionation (i.e., α eq <α f ) in this scenario. However, the results of our constant addition experiments clearly demonstrate that the equilibrium S isotope fractionation associated with sulfate incorporation into calcite is larger than the forward kinetic S isotope fractionation. This makes competition between entrapment and exchange of sulfate at the carbonate mineral's surface an unlikely explanation for the dependence of the CAS-SO4 2-S isotope fractionation on aSO4 2-/aCO3 2-.

Internal isotopic distribution among S(VI) species requires implausibly large S isotope fractionations to explain the trend

In a solution with Ca 2+ , Mg 2+ and Na + , such as our CO2 degassing solutions, S(VI) rapidly forms a variety of aqueous species (e.g., SO4 2-, HSO4 -, CaSO4 0 , CaHSO4 + , MgSO4 0 , MgHSO4 + , NaSO4 -). These aqueous species of DIS may be fractionated from each other in S isotopes as in other isotopic systems [START_REF] Zeebe | CO2 in seawater: equilibrium, kinetics[END_REF][START_REF] Beck | Experimental studies of oxygen isotope fractionation in the carbonic acid system at 15°, 25°, and 40°C[END_REF]. If the pool from which CAS forms (e.g., SO4 2-or CaSO4 0 ) is fractionated relative to the DIS, and the proportion of the different species changes with the total DIS concentration, then the CAS-SO4 2-S isotope fractionation may vary with aSO4 2-/aCO3 2-. Although we found no work constraining sulfur isotopic fractionation among the different DIS species, it is possible to determine the speciation in thermodynamic calculations (here using PHREEQC, see Section 6.4), and evaluate the isotope fractionation among DIS species that would explain our data. As the speciation changes slightly during the CO2 degassing experiments, the mole percentages given below represent CaCO3 precipitated mass-weighted averages (as, e.g., our calculations of the precipitation rate, see Section 6.4).

We find that free sulfate (SO4 2-) constitutes about 87% of the total DIS in all the CO2 degassing calcite precipitation experiments. The rest of the pool is composed of ion pairs, so that CaSO4 0 makes up 13.3 and 8.7% of the total DIS in the low-and high-aSO4 2-/aCO3 2-experiments, respectively, and NaSO4 -makes up 0.02 and 3.7% in the low-and high-aSO4 2-/aCO3 2- experiments, respectively. HSO4 -and CaHSO4 + together make up less than 0.0005%. To first order, we may approximate the DIS pool in the calcite-precipitating experiments as being composed of SO4 2-and CaSO4 0 . We were able to reproduce the CAS-SO4 2-S isotope fractionation trend observed in calcite (Figure 9) if SO4 2-is the source of CAS, and CaSO4 0 is 34 S-depleted relative to SO4 2-by ~20‰. We could not reproduce the data with other combinations of S isotope distributions among DIS species. In the aragonite-precipitating CO2 degassing experiments, MgSO4 0 comprises 42 and 31% of the DIS in the low-and high-aSO4 2- /aCO3 2-experiments, and CaSO4 0 comprises only a minor fraction. Consequently, assuming the same SO4 2--CaSO4 0 isotope fractionation of ~20‰ as for the calcite experiments, and MgSO4 0 isotopically unfractionated from SO4 2-, it is possible to reproduce the relatively invariant CAS-SO4 2-isotope fractionation in aragonite (Figure 9). Despite the ability to explain the CAS-SO4 2-S isotope fractionation trends with aSO4 2-/aCO3 2- in calcite and aragonite, we find an explanation by aqueous DIS speciation implausible for two reasons. First, this explanation requires that: (1) CaSO4 0 be 34 S-depleted relative to SO4 2-by ~20‰, and (2) that MgSO4 0 be essentially unfractionated from SO4 2-. Because MgSO4 0 constitutes a major fraction of the DIS in the aragonite-precipitating experiments, the solution is extremely sensitive to the MgSO4 0 -SO4 2-S isotope fractionation, and the second requirement is quite strict. Considering that MgCl2 was found to be the only one out of a few common chloride salts to have an influence on carbon isotope fractionation among dissolved inorganic carbon species (Thode et al., 1965), a SO4 2--CaSO4 0 isotope fractionation of ~20‰ alongside a negligible SO4 2--MgSO4 0 isotope fractionation seems unlikely. In addition, the gypsum-SO4 2- S isotope fractionation is thought to be small and positive [START_REF] Thode | Sulfur-isotope geochemistry of petroleum, evaporites, and ancient seas[END_REF][START_REF] Raab | Sulfur isotopic variations during seawater evaporation with fractional crystallization[END_REF][START_REF] Van Driessche | Unraveling the Sulfate Sources of (Giant) Gypsum Crystals Using Gypsum Isotope Fractionation Factors[END_REF] and it seems unlikely that an aqueous complex of Ca 2+ and SO4 2-(with less stiff bonds than gypsum) discriminate against 34 S (at isotopic equilibrium) so much more strongly than the mineral.

The identity of the calcite or aragonite precursor is unlikely to affect the CAS-SO4 2-S isotope fractionation

The common CaCO3 polymorphs, calcite and aragonite, often form via amorphous calcium carbonate (ACC) or vaterite precursors, which have been previously observed in biological precipitation as well as in abiotic experiments [START_REF] Politi | Structural Characterization of the Transient Amorphous Calcium Carbonate Precursor Phase in Sea Urchin Embryos[END_REF][START_REF] Bots | Mechanistic Insights into the Crystallization of Amorphous Calcium Carbonate (ACC)[END_REF][START_REF] Nielsen | In situ TEM imaging of CaCO3 nucleation reveals coexistence of direct and indirect pathways[END_REF]. Under most conditions, vaterite and ACC transform to the stable polymorphs, calcite and aragonite, within minutes to hours [START_REF] Fernández-Díaz | The role of sulfate groups in controlling CaCO3 polymorphism[END_REF][START_REF] Bots | Mechanistic Insights into the Crystallization of Amorphous Calcium Carbonate (ACC)[END_REF][START_REF] Nielsen | In situ TEM imaging of CaCO3 nucleation reveals coexistence of direct and indirect pathways[END_REF]. Several organic and inorganic compounds are known to stabilize vaterite or ACC, slowing down or altogether preventing its transformation to calcite or aragonite [START_REF] Kato | Effects of macromolecules on the crystallization of CaCO3 the Formation of Organic/Inorganic Composites[END_REF][START_REF] Fujikawa | Vaterite Stabilization in CaCO3 Crystal Growth by Amino Acid[END_REF][START_REF] Raz | The Transient Phase of Amorphous Calcium Carbonate in Sea Urchin Larval Spicules: The Involvement of Proteins and Magnesium Ions in Its Formation and Stabilization[END_REF][START_REF] Halevy | Sulfur dioxide inhibits calcium carbonate precipitation: Implications for early Mars and Earth[END_REF][START_REF] Bentov | Stabilization of amorphous calcium carbonate by phosphate rich organic matrix proteins and by single phosphoamino acids[END_REF][START_REF] Fernández-Díaz | The role of sulfate groups in controlling CaCO3 polymorphism[END_REF][START_REF] Bots | Mechanistic Insights into the Crystallization of Amorphous Calcium Carbonate (ACC)[END_REF]. The transformation between the precursors and the stable minerals is suggested to occur through dissolution-recrystallization (e.g., [START_REF] Nielsen | In situ TEM imaging of CaCO3 nucleation reveals coexistence of direct and indirect pathways[END_REF] or through solid-state transformation (e.g., [START_REF] Nakahara | Properties of Calcium Carbonate Prepared by Interfacial Reaction Method[END_REF][START_REF] Walker | Solid-State Transformation of Amorphous Calcium Carbonate to Aragonite Captured by CryoTEM[END_REF]. The latter involves dehydration of the precursor phase, and is likely to capture some of the impurities in the precursor. In the case of CAS, for example, solid-state transformation is expected to conserve the initial isotopic fractionation, whereas dissolution-recrystallization involves incorporation of sulfate from solution, with a S isotope fractionation that should reflect the ultimate stable polymorph rather than the precursor.

We considered the possibility that the relative abundance of metastable precursors and/or the mechanism of transformation to the stable CaCO3 polymorphs change with increasing aSO4 2- /aCO3 2-, and that this may explain the dependence of calcite CAS-SO4 2-S isotope fractionation on aSO4 2-/aCO3 2-. The XRD results do not support an increase in the relative abundance of vaterite with increasing aSO4 2-/aCO3 2-. Nevertheless, it is possible that more vaterite formed and then transformed into calcite, and that this influenced the final CAS-SO4 2-S isotope fractionation. However, the only experiments in which vaterite inadvertently formed and was detected by XRD (CCLB, CCLC, CCLD) suggest that the CAS-SO4 2-S isotope fractionation in vaterite is larger than in calcite, not smaller (Table 1). Therefore, an increasing abundance of vaterite with increasing aSO4 2-/aCO3 2-, as would be expected given existing knowledge on the effects of Na2SO4 on CaCO3 polymorph stability [START_REF] Fernández-Díaz | The role of sulfate groups in controlling CaCO3 polymorphism[END_REF], would lead to increasing calcite CAS-SO4 2-S isotope fractionation with increasing aSO4 2-/aCO3 2-, which is opposite to the trend observed in our experiments.

The carbonate minerals precipitated in our experiments were not sampled and analyzed shortly after precipitation, and we cannot rule out the formation of an ACC precursor. However, both in-situ TEM observations [START_REF] Nielsen | In situ TEM imaging of CaCO3 nucleation reveals coexistence of direct and indirect pathways[END_REF] and the evolving Ca and Mg isotope composition during transformation of ACC to calcite [START_REF] Giuffre | Isotopic tracer evidence for the amorphous calcium carbonate to calcite transformation by dissolution-reprecipitation[END_REF] suggest that the transformation occurs by dissolution-reprecipitation, rather than in the solid state. In an experimental system such as ours, which was well mixed and in which the abundance of sulfate in solution was much greater than in the precipitated solid, dissolution of ACC and reprecipitation of calcite would lead to incorporation of sulfate from solution rather than an inheritance of the isotopic composition of CAS in the precursor ACC. Thus, it appears that neither inheritance from vaterite nor from ACC can explain the observed decreasing CAS-SO4 2- S isotope fractionation with increasing aSO4 2-/aCO3 2-.

Does the sulfate "impurity" affect lattice energy and the equilibrium S isotope fractionation?

Although CAS is not one of the main building blocks of CaCO3, it occurs at much higher concentrations than most impurities, and may thus have a non-negligible effect on the lattice energy. Distortion of the mineral structure, and changes to cell parameters, solubility, and stability of calcite correlate with [CAS] and aSO4 2-/aCO3 2-in solution (Section 1.2). These effects of CAS on the properties of calcite support an effect of [CAS] on the lattice energy. Indeed, Fernández-Díaz et al. ( 2010) calculated an increase in lattice energy of 1.6 and 4.2 kJ/mol for every 10,000 ppm CAS added to calcite and aragonite, respectively.

Equilibrium isotope fractionation associated with mineral precipitation is related to the energetic difference between isotopic species of a solvated ion relative to the energetic difference between isotopic species of the ion in the solid. In the schematic isotope exchange reaction: ) + (∆G M,34 -∆G M,32 ).

The third term on the right-hand side of the resulting expression for ∆Gr depends on [CAS], and so the equilibrium CAS-SO4 2-S isotope fractionation is also expected to depend on [CAS], as we observe. Equation 13illustrates how a sulfate impurity may affect the equilibrium CAS-SO4 2-S isotope fractionation.

An influence of a minor component on the isotopic composition of carbonate minerals is observed in the effect of Mg on the calcite-water O isotope fractionation. The O isotope fractionation between synthetic magnesian calcites and water at 25°C changes by 0.06 to 0.17 ‰ for every 1 mole % of MgCO3 [START_REF] Tarutani | The effect of polymorphism and magnesium substitution on oxygen isotope fractionation between calcium carbonate and water[END_REF][START_REF] Jiménez-López | Oxygen isotope fractionation in synthetic magnesian calcite[END_REF]. Additionally, DFT calculations suggest a change in the Mg and Ca isotopic compositions of calcite-type minerals, which arises from a change in bond lengths with changes in the proportion of MgCO3 and CaCO3 in the solid [START_REF] Qin | Concentration effect on equilibrium fractionation of Mg-Ca isotopes in carbonate minerals: Insights from first-principles calculations[END_REF]. It is not unexpected, therefore, that a change in [CAS] may be associated with a change in S isotope fractionation, as well as the fractionation of isotopes of the other elements in the mineral lattice, namely O, C and Ca.

Support for the hypothesis of a change in the energetics of the CaCO3 lattice (and the sulfate in it), and an associated change in the equilibrium CAS-SO4 2-S isotope fractionation, may come from the XANES results. The correlation observed between the FWHMV1 and [CAS] (Figure 6d) may arise from an increase in the available electronic states due to the breaking of the symmetry (and the anti-bonding degeneracy) of the SO4 2-tetrahedron. The resulting heterogeneity in the S-O bonding environment should manifest as a change in vibrational frequencies and the associated chemical and isotopic equilibrium constants. Interestingly, other than the two aragonite samples with the highest [CAS], which appear to display anomalous behavior relative to the other aragonite samples (Figure 6), the FWHMV1 of the aragonite precipitated in this study do not show a clear correlation with [CAS] (Figure 6d). In contrast, all calcite samples with high signal-to-noise ratios display FWHMV1 values that clearly correlate with [CAS]. This observation is consistent with the dependence of the CAS-SO4 2-S isotope fractionation on aSO4 2-/aCO3 2-in calcite, but not in aragonite (Figure 5).

If the change in equilibrium CAS-SO4 2-S isotope fractionation arises from distortion of the lattice due to sulfate incorporation, a physical-chemical model of sulfate in a calcium carbonate mineral lattice, such as the one developed by [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF], should capture this phenomenon. However, the results from that study suggest a S isotope fractionation of approximately 4‰ between CAS in calcite and aqueous sulfate, at a very high [CAS] (set by practical computational cost), where our data suggest CAS-SO4 2-S isotope fractionation should be small at comparable CAS concentrations.

CAS-SO4 2-S isotope fractionation in aragonite

The fractionation of S isotopes between sulfate in aragonite and aqueous sulfate does not show a dependence on [CAS] over the range of aSO4 2-/aCO3 2-explored in this study (6 to ~1300; Figure 5a). This is unexpected if the explanation for [CAS]-dependent CAS-SO4 2-S isotope fractionation is an effect of the sulfate impurity on lattice energy and the equilibrium fractionation, as the lattice energy change calculated for aragonite is almost 3 times that calculated for calcite (Fernandez-Diez et al., 2010). First, it is possible that CAS-SO4 2-S isotope fractionation in aragonite is as sensitive to [CAS] as the S isotope fractionation in calcite, but due to the smaller partition coefficients of sulfate into aragonite (and the lower [CAS]), the trend is not resolved. Alternatively, it is possible that the molecular model does not capture all of the relevant processes involved in incorporation of sulfate into aragonite at an appropriate accuracy. In this case, aragonite would be less sensitive to substitution of sulfate for the carbonate ion, an inference that is supported also by the XANES data. Similar insensitivity has been observed for O isotope fractionation between aragonite and water in past studies. For example, experimental aragonite-water O isotope fractionation shows little or no response to variation in the Mg 2+ concentration, precipitation method and rate [START_REF] Kim | Oxygen isotope fractionation between synthetic aragonite and water: Influence of temperature and Mg 2+ concentration[END_REF].

Finally, "coupled" incorporation of SO4 2-and Mg 2+ into the aragonite precipitated in our experiments may have resulted in [CAS]-independent CAS-SO4 2-S isotope fractionation. A possible reason is the compensating effect of incorporation of the oversized (relative to CO3 2-) SO4 2-ion, and the undersized (relative to Ca 2+ ) Mg 2+ ion. Sulfate incorporation expands the dspacing and cell size (Section 1.2), while Mg 2+ decreases d-spacing leading to shorter bond lengths [START_REF] Goldsmith | Lattice constants of the calcium-magnesium carbonates[END_REF][START_REF] Finch | Coordination of Sr and Mg in calcite and aragonite[END_REF]. To the best of our knowledge, similar effects in aragonite have not been studied systematically, but may exist. In this case, aragonite formation in the CO2 degassing experiments, which was promoted by Mg 2+ /Ca 2+ of 5, is expected to be accompanied by a [CAS]-insensitive CAS-SO4 2-S isotope fractionation.

We expect S isotope fractionation similar to our experiments in the majority of marine environments in either case. The concentration of Mg 2+ in seawater is thought to have been at least ~30 mmol kg -1 through Phanerozoic time [START_REF] Horita | Chemical evolution of seawater during the Phanerozoic[END_REF], and was unlikely much lower than ~10 mmol kg -1 over the majority of Earth history [START_REF] Halevy | The geologic history of seawater pH[END_REF]. Thus, if co-substitution of Mg 2+ and SO4 2-is responsible for the insensitivity of CAS-SO4 2-S isotope fractionation to [CAS], this is expected in natural abiotic aragonite as well. Alternatively, if the low [CAS] is responsible for the insensitivity, then this is also expected in most abiotic inorganic aragonites, which would incorporate low [CAS], especially in the Precambrian ocean, in which aqueous sulfate concentrations are thought to have been much lower than today.

Support for the values of the aragonite CAS-SO4 2-S isotope fractionation determined in our experiments comes from natural aragonite ooids precipitated abiotically in the Bahamas. These ooids contain CAS, which is fractionated from the aqueous sulfate in seawater by 0.7±0.3‰ [START_REF] Trower | Active Ooid Growth Driven By Sediment Transport in a High-Energy Shoal, Little Ambergris Cay, Turks and Caicos Islands[END_REF], in agreement with the 1.0±0.3‰ we find experimentally, both at ~30°C. Note that both the experiments and natural samples suggest that the S isotope fractionation is much closer to the 1-2‰ gypsum-SO4 2-S isotope fractionation [START_REF] Thode | Sulphur isotope geochemistry[END_REF][START_REF] Raab | Sulfur isotopic variations during seawater evaporation with fractional crystallization[END_REF][START_REF] Van Driessche | Unraveling the Sulfate Sources of (Giant) Gypsum Crystals Using Gypsum Isotope Fractionation Factors[END_REF], than the DFT calculations, which suggested 4.5‰ for the CAS-SO4 2-S isotope fractionation in aragonite at 30°C. The agreement between CAS-SO4 2- S isotope fractionations observed in experimental and natural abiotic aragonite provides confidence in the use of CAS in abiogenic aragonite to reconstruct paleo- 34 S values in ancient seawater.

4.5 Implications for natural samples 4.5.1 Effects on CAS-SO4 2-S isotope fractionation in abiotic and biogenic primary carbonate minerals

The experimental results in this study apply to the primary carbonate minerals precipitated from Precambrian seawater (if well preserved, see discussion below), all of which were abiotic or microbially-mediated [START_REF] Sumner | Late Archean Aragonite Precipitation: Petrography, Facies Associations, and Environmental Significance[END_REF][START_REF] Grotzinger | Precambrian Carbonates: Evolution of Understanding[END_REF][START_REF] Schrag | Authigenic carbonate and the history of the global carbon cycle[END_REF]. The experimental results also apply to abundant abiotic precipitates, such as ooids [START_REF] Trower | Active Ooid Growth Driven By Sediment Transport in a High-Energy Shoal, Little Ambergris Cay, Turks and Caicos Islands[END_REF]. Phanerozoic carbonate minerals, however, are mostly biogenic. All but one of the CAS-SO4 2-S isotope fractionations observed in modern calcifying organisms (Figure 2, 8) are smaller positive values (or even small negative values) than the experimental CAS-SO4 2-S isotope fractionation in aragonite, and all are smaller than CAS-SO4 2-isotope fractionation in calcite. As mentioned in section 4.3.1, variation in precipitation rate (0.4±0.2‰) cannot explain the large variation in CAS-SO4 2-S isotope fractionation observed in the skeletons of calcifying organisms, and especially not negative fractionation. It is possible that a variety of yet uncharacterized biological processes shift the isotopic fractionation down from the experimental values. The existence of such "vital effects" suggests that the use of CAS in biogenic carbonate minerals to constrain paleo- 34 S values in Phanerozoic seawater requires calibration of species-specific CAS-SO4 2-S isotope fractionations in controlled experiments. Such calibrations of CAS-SO4 2-S isotope fractionation have been performed for a few species [START_REF] Paris | Experimental determination of carbonate-associated sulfate δ 34 S in planktonic foraminifera shells[END_REF][START_REF] Rennie | Cenozoic record of δ 34 S in foraminiferal calcite implies an early Eocene shift to deep-ocean sulfide burial[END_REF], and are performed routinely for other isotopic systems, such as O isotopes in carbonate minerals (e.g., [START_REF] Wefer | Isotope paleontology: growth and composition of extant calcareous species[END_REF]. Future focus on testing the dependence of CAS-SO4 2-S isotope fractionation in biogenic calcite on aSO4 2-/aCO3 2- would provide confidence in the use of CAS in biogenic carbonate minerals to reconstruct seawater sulfate S isotopes.

With the caveats to the interpretation of CAS  34 S values discussed below in mind, it is important to note that according to several proxies (sulfate evaporites, barite and CAS), seawater sulfate  34 S values have varied between 0‰ and 50‰ VCDT throughout Earth history [START_REF] Kampschulte | The sulfur isotopic evolution of Phanerozoic seawater based on the analysis of structurally substituted sulfate in carbonates[END_REF][START_REF] Paytan | Seawater sulfur isotope fluctuations in the Cretaceous[END_REF][START_REF] Fike | Rethinking the Ancient Sulfur Cycle[END_REF]. Perhaps with the exception of diagenetic carbonate formation in MSR-influenced sediments, the proposed mechanisms below alter (mostly increase) CAS  34 S values by only a few permil relative to the original CAS. Therefore, CAS  34 S values in primary, well preserved carbonate samples should capture the major changes in seawater  34 S values.

Post-depositional processes

Post-depositional recrystallization of the original carbonate minerals and precipitation of diagenetic carbonate minerals may affect the  34 S values preserved in CAS in several ways. Recrystallization rates in some marine sediments are tens of percent per million years [START_REF] Walter | Dissolution and recrystallization in modern shelf carbonates: evidence from pore water and solid phase chemistry[END_REF][START_REF] Fantle | Ca isotopes in carbonate sediment and pore fluid from ODP Site 807A: The Ca 2+ (aq)-calcite equilibrium fractionation factor and calcite recrystallization rates in Pleistocene sediments[END_REF], and diagenetic carbonate minerals, both recrystallized and new void-filling cements, may contribute a substantial fraction of the total carbonate rock mass preserved in some environments [START_REF] Schrag | Authigenic carbonate and the history of the global carbon cycle[END_REF][START_REF] Sun | Significant contribution of authigenic carbonate to marine carbon burial[END_REF]. If these processes occur in good communication with seawater sulfate (i.e., the sulfate incorporated into the diagenetic or recrystallized carbonate minerals is similar in isotopic composition to seawater sulfate), they will shift bulk  34 SCAS values upwards as abiotic carbonate minerals are added to or replace the original biogenic minerals. For example, in the Phanerozoic, when aSO4 2-/aCO3 2- in the oceans mostly stayed within the range of 220 to 2530, abiotic calcite CAS concentrations are expected to be between 3,100 and 38,400 ppm (Equation 4; gray rectangle, Figure 8). At such CAS concentrations the minimal fractionation we measured will be expressed, which averages to 1.7±0.3‰ (1, n=20). Thus, recrystallization or diagenetic carbonate mineral formation in good communication with aqueous sulfate in the overlying seawater is expected to shift CAS-SO4 2-isotope fractionation from a biogenic value of approximately -1‰ to an abiotic value of +1-2‰ (Figure 8). In a study of diagenesis of Key Largo carbonates, [START_REF] Gill | Behavior of carbonate-associated sulfate during meteoric diagenesis and implications for the sulfur isotope paleoproxy[END_REF] interpreted a 1‰ enrichment in  34 S of secondary calcite relative to the primary aragonite to reflect local microbial sulfate reduction, which enriched pore-water sulfate in 34 S (see discussion below). Because the difference in CAS-SO4 2-S isotope fractionation between calcite and aragonite is 0.5-2‰, a 34 S enrichment of 1‰ in calcite is also consistent with aragonite dissolution and calcite precipitation in contact with seawater-like solutions. In Precambrian sediments, all carbonate minerals are abiotic, and less of an isotopic difference is expected between CAS in primary and diagenetic or recrystallized carbonate minerals. Nevertheless, mineralogical transformations, for example, from primary aragonite to calcite or dolomite, may shift the preserved S isotope composition.

In the case of poor communication with the overlying seawater (i.e., near-closed-system conditions), the original isotopic composition of the CAS may be retained in the recrystallized or diagenetic carbonate minerals. However, such near-closed-system conditions are often associated with the drawdown of sulfate within the sediments by MSR. Anaerobic respiration of organic matter (e.g., MSR) often involves an increase in porewater alkalinity and in carbonate mineral saturation state [START_REF] Higgins | Oxygenation of the ocean and sediments: Consequences for the seafloor carbonate factory[END_REF], and promotes diagenetic carbonate mineral formation. The S isotope composition of CAS in MSR-influenced minerals may be altered from the original values in several ways. First, the drawdown of sulfate and the production of alkalinity depresses aSO4 2-/aCO3 2-, and consequently, the CAS concentration in the diagenetic minerals. Our experiments suggest that the CAS-SO4 2-isotope fractionation under such conditions should be larger in calcite, approaching +3‰ (compared to between +1 and +2‰ for abiotic calcite and between -1 and +1‰ in biogenic carbonate minerals formed in seawater), and ~1‰ in aragonite. The sulfate preserved in the diagenetic or recrystallized carbonate minerals may thus be between 1 and 4‰ enriched in 34 S relative to the original carbonate. Perhaps more importantly, isotopic fractionation during MSR leads to production of 34 S-depeleted sulfide and gradual 34 S enrichment of the residual sulfate (e.g., [START_REF] Harrison | Mechanism of the bacterial reduction of sulphate from isotope fractionation studies[END_REF][START_REF] Canfield | The evolution of the Earth surface sulfur reservoir[END_REF]. Thus, carbonate minerals formed due to MSR-driven production of alkalinity in sediment porewater are expected to incorporate 34 S-enriched sulfate, sometimes by several percent relative to seawater [START_REF] Rennie | The preservation of and in carbonate-associated sulfate during marine diagenesis: A 25 Myr test case using marine sediments[END_REF][START_REF] Present | Large Carbonate Associated Sulfate isotopic variability between brachiopods, micrite, and other sedimentary components in Late Ordovician strata[END_REF]. In combination with larger CAS-SO4 2-isotope fractionation expected as sulfate is utilized by MSR, CAS in diagenetic or recrystallized carbonate minerals is expected to be enriched in 34 S relative to primary marine carbonates. Seawater sulfate  34 S values inferred from measured  34 SCAS values may, therefore, be erroneously high if care is not taken in avoiding recrystallized or diagenetic carbonate minerals.

Conclusions

The fractionation of S isotopes between CAS and aqueous sulfate was observed experimentally to be positive and significant both in calcite and aragonite, in contrast with the common assumption of negligible CAS-SO4 2-S isotope fractionation. The magnitude of the CAS-SO4 2- S isotope fractionation at high CAS concentrations (~1‰ in aragonite, ~2‰ in calcite) is also inconsistent with the large isotope fractionations (>4‰) suggested by DFT modeling. Our results reveal a different response of aragonite and calcite to the aSO4 2-/aCO3 2-in aqueous solutions. The CAS-SO4 2-S isotope fractionation in synthetic aragonite is in agreement with the isotope fractionation observed in natural abiotic aragonite ooids, and we suggest a constant value of 1.0±0.3‰ (at ~30°C) for this isotope fractionation, which is independent of aSO4 2- /aCO3 2-. The CAS-SO4 2-S isotope fractionation in calcite, on the other hand, varies between 3.1±0.6 and 1.7±0.4‰ (at ~30°C) at low and high aSO4 2-/aCO3 2-, respectively. While precipitation rate inversely correlates with the CAS-SO4 2-S isotope fractionation, its effect is too small and cannot explain the stronger inverse correlation of S isotope fractionation with aSO4 2-/aCO3 2-. This correlation is probably due to a change in the equilibrium S isotope fractionation caused by the effect of CAS incorporation on the lattice energy of calcite, but not of aragonite. Such an effect is consistent with the change in the S K-edge X-ray absorption spectra, which we observe in calcite but not in aragonite, and which is presumably caused by a change in the distorted tetrahedral symmetry of sulfate.

The majority of CAS-SO4 2-S isotope fractionations observed in our aragonite and calcite samples are larger, sometimes by several permil, than those displayed by modern calcifying organisms. These differences cannot be explained by the effects of aSO4 2-/aCO3 2-on the CAS-SO4 2-S isotope fractionation observed in our abiotic samples. As our experiments cannot constrain the kinetic fractionation of S isotopes upon incorporation of sulfate into carbonate minerals, we cannot rule out much higher, "pulsed" rates of biogenic precipitation as the cause for the smaller positive and even small negative CAS-SO4 2-S isotope fractionation in biogenic carbonate minerals. Alternatively, other isotope fractionation mechanisms upon sulfate incorporation into biogenic carbonate minerals may exist, and calibrations of CAS-SO4 2- isotope fractionation in specific skeletal carbonates may be inevitable.

The dependence of CAS-SO4 2-S isotope fractionation on aSO4 2-/aCO3 2-described here, and the effects of other aqueous species on carbonate mineral thermodynamics and kinetics documented in previous studies, suggest that the chemistry of carbonate mineral-forming solutions may affect CAS-SO4 2-S isotope fractionation in other ways as well. This highlights not only the importance of experimental constraints on the effects of solution chemistry on CAS-SO4 2-S isotope fractionation, but also of constraints on the chemical composition of geologic carbonate mineral-forming solutions, which are often difficult to obtain. Furthermore, the perspective on isotope-fractionating processes in the presence of impurities that emerges from this study calls for an investigation of such effects on other isotopic systems (e.g., C and O isotopes in carbonate minerals) and for impurities other than sulfate.

Appendix I 6.1 Constant addition

The constant addition experiments consisted of two main steps: I. reaching a steady state, and II. precipitation at a stable rate and headspace pCO2 (Figure A1). In step I, 50 mL each of the Ca 2+ and DIC solutions was added. In step II, 200 mL of each of these solutions was added, for a total accumulation of mL of solution in steps I and II. The conditions of the constant addition experiments are in Table A1. During solution injection, the solutions were held under a constant flow of compressed air to reduce accumulation in the headspace of CO2 released during CaCO3 precipitation. The compressed air cylinders contained between 370 and 630 ppm CO2, and the air was pre-moistened via a dual gas dispersion tube (GDT) system with deionized water (18.2 MΩ cm) to avoid loss of water vapor from the reaction vessel. In both steps I and II, two solutions were used: i) a Ca 2+ stock solution with 0.2 mol/kg CaCl2×2H2O (99% ACS, Sigma Aldrich), 1 mmol/kg Na2SO4 (99.9955%, Alfa Aesar) and 0.169 mol/kg NaCl (ACS, J.T.Baker), and ii), a DIC stock solution to which 0.1 mol/kg NaHCO3 (99.7, ACS, Sigma Aldrich) was added along with 1 mmol/kg Na2SO4 and 0.683 mol/kg NaCl. The NaCl was added to achieve an ionic strength of ~0.7 in the stock solutions. According to calculation, the DIC stock solution would have to degas 65% of the DIC to reach equilibrium with the pCO2 of the compressed air, leaving 63-67 mmol/kg DIC at a pH value of 9.3-9.4 (depending on cylinder pCO2). To expedite degassing, N2 was bubbled via a GDT into the DIC stock solution until the target pH was reached, which took 2-3 days. Lyophilized carbonic anhydrase (CA) powder was added to the stock solutions to catalyze chemical equilibrium in the carbonate system. To prevent biological contamination, reaction vessels and tubing were sterilized prior to the experiments, and all solutions and gases were passed through 0.2-m filters.

Step I started upon solution injection and air flow into a 250-mL bottle, stirred with a magnetic stir bar, at room temperature. pH was measured periodically. Precipitation commenced upon mixing of the two stock solutions, and when pH values stabilized and a mixed solution volume of more than 100 mL was accumulated, the mixed solution was quickly filtered.

Step II started when 100 mL of filtrate was poured into the main 500-mL double-jacketed temperaturecontrolled glass reactor, which contained 100 or 200 mg of calcite nucleation seeds. In step II, solution injection and airflow rates remained unchanged from step I, but an overhead Teflon stirring rod at 400 RPM replaced the magnetic stir bar, the jacketed reactor replaced the 250-mL bottle, and a temperature of 25.0±0.1°C was maintained. The precipitation rates (J) during the experiments were 10 -7.5 , 10 -6.8 , 10 -6.2 , 10 -5.3 and 10 -4.3 mol/m 2 /s and will be expressed hereafter as the logarithm of J for simplification.

The remaining 200 mL of both DIC and Ca 2+ solutions were added dropwise via 1/8" PTFE tubing into the mixed solution at a rate of 5 to 5000 L/min using an Atlas Syringe Pump (Syrris), in dual dose mode or in continuous mode (for log(J)=-4.3 experiments only). Addition of 200 mL of the DIC and Ca 2+ solutions resulted in precipitation of ~900 mg of calcite. The moistened air was introduced into either the headspace or the solution via a GDT at rates of 23 to 1,000 standard cubic centimeters per minute (SCCM), controlled by a mass flow controller (Alicat Scientific), and forming ~1 mm bubbles when the GDT was submerged. Variations of up to 0.15 pH units were measured in all experiments, and are considered acceptable for the purposes of these experiments. Larger and short-lived pH changes occurred at the onset of step II, in the fastest precipitating experiments, CCK and CCL, where variation of 0.4 pH units over 10 minutes and 0.75 pH units over 100 minutes, respectively, were observed. However, these changes were short enough relative to the duration of the experiments, that the pH standard deviation throughout the experiment duration did not exceed 0.2 units (1).

Upon completion of step II, solids were filtered out of the solution through a 0.2-m nylon filter, washed with deionized water, and left overnight in a vacuum oven at 60°C and 700 mmHg to dry. The mass of the solids precipitated was evaluated gravimetrically by the difference in filter mass with and without the precipitates.

CO2 degassing

The CO2 degassing experiments consisted of three steps: I. acidification (to dissolve the calcite reagent), II. undersaturated diffusive loss of CO2, III. saturated diffusive loss of CO2 and precipitation of CaCO3 (Figure 4). The conditions of the CO2 degassing experiments are in Table A2.

In step I (Figure 4) a calcite reagent (99.997%, Alfa Aesar) was dissolved in a 2-liter solution of deionized water with Na2SO4 (99.9955%, Alfa Aesar) and MgCl2×6H2O (ACS grade, Sigma Aldrich). One bottle with pure deionized water was used as a control. Dissolution was achieved by three cycles of evacuation of the contents of the GB, and replacement by cylinder CO2 (95.7%) at near-atmospheric pressure. The open solutions in the GB were continuously stirred on a multi-point magnetic stirring plate. Subsequent to atmosphere replacement, a constant CO2 flow was maintained to assure a constant pCO2. Acidification of the solution due to the increased pCO2 led to the dissolution of the CaCO3 solid in the following net reaction:

14)

CO 2 (g) + CaCO 3 + H 2 O → Ca 2+ + 2HCO 3 -.

Step I was considered complete when no CaCO3 was visible in the most CaCO3-rich solution and the target pH was reached and remained stable. This step took ~1 day, and an extra day was taken to assure full dissolution. In step II (Figure 4) small threads in the GB with a total area of 3.5 cm 2 were opened, to allow diffusive exchange with the ambient atmosphere (with 400-700 ppm CO2). As pCO2 decreased, the pH increased, until the concentration of CO3 2-was high enough to reach calcite or aragonite saturation at pHsat.

Step III started when a further decrease in pCO2 increased pH (to above pHsat) and the degree of saturation increased enough to lead to nucleation. Precipitates then formed both in solution and on the 2-liter glass bottle walls. When the pH of the deionized water in the control bottle and in the other solutions remained static for a day or so (i.e., GB CO2 reached equilibrium with the atmosphere), the experiment was terminated and the GB was opened. Upon completion of step III, solids were filtered out of solution through a 0.2-m nylon filter, after the bottles were sonicated to remove solids from the bottle walls to maximize yield. The filtrate was washed with deionized water and then with ethanol, and left overnight in a 60°C oven. The mass of the solids precipitated was evaluated gravimetrically by the difference in filter mass with and without precipitates, except for cases in which the filter became clogged and was replaced by one or more additional filters (see dashes in column 'mtot' of Table A2).

The two main variables in this experimental set were the concentrations of Na2SO4 and the CaCO3 mineralogy. Some aragonite precipitates alongside calcite in solutions with Mg 2+ /Ca 2+ greater than 2 (e.g., [START_REF] Bots | The role of SO4 in the switch from calcite to aragonite seas[END_REF]. To ensure the precipitation of a pure aragonite phase and to mimic the Mg 2+ /Ca 2+ of the modern ocean (5.2), we chose a Mg 2+ /Ca 2+ of 5 for the experiments. The aCa 2+ /aCO3 2-ratio, which was controlled by the initial mass of dissolved CaCO3 reagent, was ~950 in all of the calcite-forming solutions and ~470 in all of the aragoniteforming solutions. Activity ratios refer to the fully dissolved CaCO3 at the maximal pCO2 reached, as modeled by PHREEQC. The concentrations of Na2SO4 in the calcite-forming solutions were 0.03, 0.1, 0.3, 1, 3 and 8 mM, with the upper sulfate concentration chosen as the expected threshold that still led to calcite (rather than aragonite) precipitation. The concentrations of Na2SO4 in the aragonite-forming solutions were 0.1, 0.3, 1, 3, 10 and 30 mM.

The progress of the experiments was monitored by measuring pH directly in the precipitating solution with the highest initial amount of CaCO3, and in the control bottle with deionized water to monitor pCO2 indirectly, because a pCO2 range of 4 orders of magnitude is difficult to accurately measure directly by one method. The duration of the diffusive loss steps (II+III) was designed to be 1-2 weeks, resulting in log(J) of about -5.9 mol/m 2 /s on average. As the pCO2 within the GB decays exponentially, and due to non-linearity in the dissolved inorganic carbon system, J, aCa 2+ , aCO3 2-and other chemical parameters changed throughout the experiment duration, and were retrieved from the measured quantities (pH in the precipitating solution and pCO2 calculated from the pH measured in the deionized water) by geochemical modeling (Section 6.4).

pH measurements

A combination of 2 types of pH electrode and 2 types of pH meter were used in the 3 experimental methods. In all but the CO2 degassing experiments, where a Syrris pH probe was used for the deionized water measurment, an InLab® 413SG electrode (Mettler-Toledo) was used. A combination of the SevenGo2 meter (Mettler-Toledo) and the built-in pH meter in an Atlas Syringe Pump (Syrris) was used both experiments. Repeated calibration and measurement with each electrode gave practical accuracy and precision of 0.02 pH units for the InLab® 413SG, and an accuracy of 0.1 and a precision of 0.02 pH units for the Syrris pH electrode. The choice of pH meter had no appreciable effect on accuracy or precision. The calibration was done either against disposable buffer sachets (Mettler-Toledo) at pH 4.00, 7.00 and 10.01, or against buffer solutions (Fluka) at pH 4.0, 7.0 and 9.0. The Atlas Syringe Pump failed on rare occasions, leading to loss of some logged pH data.

Calculation of precipitation rates and geochemical parameters

Precipitation rates were calculated as the moles precipitated per surface area available per second (mole/m 2 /s). In the constant addition experiments, the precipitation rate is determined by the surface area of nucleation seeds added, the rate of delivery of the stock solutions and the response of the solution chemistry. We calculate an average precipitation rate using the measured mass of seeds (mseed converted to moles using the molar mass Mw), the measured seed material specific surface area (SSA), the gravimetrically measured mass of total solid (mtot converted to moles using the molar mass) and the experiment duration (t) is:

15) J Cons. Add. = (m tot -m seed ) t × M w × m seed × SSA ,
where the SSA of the 100-200 mg of nucleation seeds was measured on a NOVA 2000e BET surface area analyzer (Quantachrome) using N2 gas. The calcite samples were first placed under vacuum and heated to 60°C and yielded a SSA of 0.60±0.01 m 2 /g (n=8). Processes such as nucleation of new particles, a change in the morphology of the crystals or roughening of the crystal surface could increase the surface area and decrease the per-area precipitation rate.

Calculations accounting for such a change in the surface area are expected to yield lower rates than those in which the surface area is held constant (as in this study), and so the J values we report for the constant addition experiments should be treated as upper limits on the precipitation rates.

Parameters of the CO2 degassing experimental system, including the pH, ion concentrations and precipitation rates, change over the course of an experiment, as pCO2 decreases. To account for these changes, and allow for calculation of mass-weighted average precipitation rates and other parameters (e.g., aSO4 2-/aCO3 2-), we calculated the ion concentrations through time, using the pH measurements as constraints. In order to describe the state of the carbonate system, one needs at least 2 parameters out of 6 (pCO2, CO2(aq), HCO3 -, CO3 2-, pH, AT); [START_REF] Stumm | Aquatic chemistry : chemical equilibria and rates in natural waters[END_REF]. In the case of deionized water under a CO2 atmosphere, AT=0, and it is possible to calculate pCO2(t) in the GB from pH(t) measurements, under an assumption of chemical equilibrium. This value of pCO2(t), which is common to all solutions open to the GB atmosphere, along with the pH(t) measured in the solutions, allows a complete description of the state of the carbonate system (i.e., DIC speciation).

Thermodynamic calculations were carried out using the PHREEQC interactive V3.3.3 software [START_REF] Parkhurst | PHREEQC (Version 3)-A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF], with the default database. The pH measurements in deionized water in two of the 24 precipitating solutions (8KCL2, 30KAR1) were used to calculate the time-dependent pCO2 in the GB. The pCO2 time series was used as input to PHREEQC calculations of time-dependent pH values, ion activities, CaCO3 saturation, and precipitation rates (moles/s) in the 22 solutions for which we did not have pH measurements. This approach assumes equilibrium between the dissolved inorganic carbon in the solutions and the CO2 in the GB atmosphere, which is a reasonable approximation of reality, given the slow rate of decrease in pCO2 and the long duration of the CO2 degassing experiments.

To calculate per-area precipitation rates, and allow comparison between the results of the constant addition and CO2 degassing experiments, we approximated the SSA of CaCO3 precipitated in the CO2 degassing experiments as constant at a value of 0.27 m 2 /g, following observations of stabilization of SSA at 0.27±0.05 m 2 /g in long (>~30 hours) nucleation and precipitation experiments [START_REF] Tang | Sr 2+ /Ca 2+ and 44 Ca/ 40 Ca fractionation during inorganic calcite formation: I. Sr incorporation[END_REF]. The mass-weighted average precipitation rate is then:

16) J CO 2 Degas. = ∑ ( ∆m i m tot × ∆m i ∆t i ×M w ×SSA× ∑ ∆m j i j=0 ) n i=0
, where mtot (moles) is the total amount of CaCO3 precipitated, Mw (g/mole) is the molar weight of CaCO3, and ∆m i (moles) and ∆t i (seconds) are the mass of CaCO3 precipitated in time interval i, and the duration of time interval i, respectively.

In the constant addition experiments aSO4 2-/aCO3 2-was constant, and retrieved from PHREEQC simulations of the experimental solutions. In the CO2 degassing experiments aSO4 2- /aCO3 2-varied over the experiment, and was calculated as a mass-weighted average, similar to the precipitation rate:

17) aSO 4 2-/aCO 3 2- CO 2 Degas. = ∑ ( ∆m i m tot × aSO 4 2-/aCO 3 2- i ) n i=0
.

The precipitation rates and aSO4 2-/aCO3 2-in the CO2 degassing experiments are given in Table A2, including a conservative estimate of uncertainty in their values. This estimate accounts for uncertainty in the pH measurements and small disagreements between the pCO2 calculated from pH measurements in the precipitating solutions (8KCL2, 30KAR1) and the deionized water.

= J A -J D - v L [CAS S ] = k A [SO 4 2-] -k D [CAS s ] - v L [CAS s ] ,
where JA and JD are the sulfate attachment and detachment rates, respectively, [CAS s ] and [SO 4 2-] are the sulfate concentrations in the solid and solution, respectively, v is the onedimensional growth front velocity, and L is the typical growth step height. kA and kD are rate constants, which incorporate the kinetics of attachment and detachment as well as the kinetics of creation and destruction of appropriate kink sites for sulfate (or carbonate) attachment. The latter are thought to be the limiting factor for calcite growth [START_REF] Yoreo | Rethinking classical crystal growth models through molecular scale insights: Consequences of kink-limited kinetics[END_REF]. The change in the isotopic composition of CAS is then described by:

19) d dt [CAS S ]R CAS = k A [SO 4 2-]R SO 4 α f -k D [CAS S ]R CAS α b - v L [CAS S ]R CAS ,
where R is the ratio of 34 S to 32 S and α f and α b are the forward and backward kinetic isotopic fractionation factors. At a steady state (ss), the mass balances in equations 18 and 19 are equal to zero, yielding an expression for the isotopic composition of CAS,

20) R CAS ss = (k D + v L )R SO 4 α f k D α b + v L . When k D ≫ v L
, the expression for R CAS ss reduces to R SO 4 α f /α b , which is the isotopic composition of CAS in isotopic equilibrium with sulfate in solution. When

k D ≪ v L
, the expression for R CAS ss reduces to R SO 4 α f , which is the isotopic composition of CAS irreversibly incorporated into the carbonate and fractionated from the sulfate in solution by the forward kinetic isotope fractionation. Thus, increasing precipitation rate, expressed here by the growth front velocity, v, shifts the isotopic fractionation from α eq to α f (Equations 3,20). The results of the constant addition experiments, in which the CAS-SO4 2-isotope fractionation decreased with an increase in the precipitation rate of ~2 orders of magnitude (at a constant aSO4 2-/aCO3 2-), and suggests that for sulfate incorporation into calcite, α eq > α f .

The fluxes of sulfate attachment and detachment (JA and JD, respectively) onto a growth step are proportional to the sulfate concentration in the solution and solid, respectively (Equation 18). We assume that the associated rate constants, kA and kD, are independent of the aqueous sulfate concentration, supported by a similar independence of the rate constants for Mg 2+ attachment and detachment on the aqueous Mg 2+ concentration [START_REF] Davis | The Role of Mg 2+ as an Impurity in Calcite Growth[END_REF]. With constant kA and kD, an increase in [SO 4 2-], and a consequent increase in [CAS s ], leads to higher rates of both attachment and detachment, or a high sulfate exchange rate between the solution and mineral surface relative to the precipitation rate. However, a larger size of the surface CAS pool at higher [SO 4 2-] means that exchange timescales ([CAS s ]/J D) do not change with increasing aSO4 2-/aCO3 2-. On the other hand, the precipitation rate (v), has been shown to decrease with increasing aSO4 2- [START_REF] Busenberg | Kinetic and thermodynamic factors controlling the distribution of SO4 2and Na + in calcites and selected aragonites[END_REF]. Therefore, with increasing [SO 4 2-] we expect increasingly rapid sulfate exchange relative to CaCO3 precipitation, and a shift towards α eq , which in our case is larger than α f , as discussed above. In other words, exchange-entrapment dynamics lead to the expectation of increasing CAS-SO4 2-isotope fractionation with increasing aSO4 2-/aCO3 2-, which is opposite to the experimental results (Figure 5a).

The competition between sulfate exchange and entrapment may be further explained by the mechanism of calcite growth, which is thought to be limited by the creation of new kink sites [START_REF] Yoreo | Rethinking classical crystal growth models through molecular scale insights: Consequences of kink-limited kinetics[END_REF]. When a new kink forms, attachment of solute molecules (Ca 2+ , CO3 2-, HCO3 -) onto the kink is rapid and the new layer or step advances quickly from the original site of kink formation. Impurities bind to kinks, blocking further growth and generating a hiatus until the next kink is created. Increasing concentrations of the "contaminant" in the solution increase the density of blocked kinks, and result in slow mineral growth [START_REF] Yoreo | Rethinking classical crystal growth models through molecular scale insights: Consequences of kink-limited kinetics[END_REF].

The decrease in bulk precipitation rate with increasing aSO4 2-, as demonstrated experimentally by B&P, has been observed also in studies of nano-scale surface processes at variable aSO4 2- [START_REF] Vavouraki | An Atomic Force Microscopy study of the growth of calcite in the presence of sodium sulfate[END_REF][START_REF] Nielsen | Inhibition of Calcite Growth: Combined Effects of Mg 2+ and SO4 2[END_REF]. Consequently, the time available for the attached sulfate ions to exchange and equilibrate with sulfate ions in solution before the sulfate is entrapped increases. In other words, high aSO4 2-/aCO3 2-should promote isotope fractionations closer to α eq , which in our case is larger than α f . This is inconsistent with the decrease in CAS-SO4 2-isotope fractionation with increasing aSO4 2-/aCO3 2-measured in our experiments.

Appendix III

*Includes only figure A3.

Figure Captions

Figure 1: Speciation of DIS as a function of pH. The results are for a solution containing 10 mM DIS and 10 mM each of Ca 2+ , Mg 2+ , Na + , and K + as chloride salts. Equal concentrations were chosen to show the affinity of sulfate towards the different cations. Na + and K + ion-pair concentrations were negligible. The low fraction of Mg 2+ and Ca 2+ ion pairs at high pH is due to increasing proportions of metal-hydroxide ion pairs.

Figure 2: Compilation of CAS concentrations and CAS-SO4 2-S isotope fractionations b measured in modern calcifying organisms [START_REF] Burdett | A Neogene seawater sulfur isotope age curve from calcareous pelagic microfossils[END_REF][START_REF] Kampschulte | The sulphur isotopic composition of trace sulphates in Carboniferous brachiopods: implications for coeval seawater, correlation with other geochemical cycles and isotope stratigraphy[END_REF][START_REF] Lyons | Sites of anomalous organic remineralization in the carbonate sediments of South Florida, USA: The sulfur cycle and carbonate-associated sulfate[END_REF][START_REF] Paris | Experimental determination of carbonate-associated sulfate δ 34 S in planktonic foraminifera shells[END_REF][START_REF] Present | Large Carbonate Associated Sulfate isotopic variability between brachiopods, micrite, and other sedimentary components in Late Ordovician strata[END_REF][START_REF] Rennie | Cenozoic record of δ 34 S in foraminiferal calcite implies an early Eocene shift to deep-ocean sulfide burial[END_REF]. DFT calculations are based on CAS  values (reduced partition function ratios) at 25°C, calculated in calcite and aragonite by [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF], and  values for SO4 2-(aq) calculated by [START_REF] Otake | Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems[END_REF] and [START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF].  values from [START_REF] Eldridge | Theoretical estimates of equilibrium sulfur isotope effects in aqueous sulfur systems: Highlighting the role of isomers in the sulfite and sulfoxylate systems[END_REF] yield the larger isotope fractionation. dependent DIS speciation. Simulated and measured S isotope fractionations are in agreement, but this scenario seems improbable (see text). Figure A3: Normalized S K-edge X-ray absorption near-edge spectra (XANES). The spectra are shown by blue and yellow dots, for calcite and aragonite, respectively, together with a 5point moving average, which was applied to smooth the spectra (black lines). Samples with poor fits to the spectra (r2<0.9) are marked with a star.

Figure 3 :

 3 Figure 3: Example of a fit to a S K-edge spectrum. The detrended XANES data (blue dots) is fit (black line) as a sum of one step-function (Sfn) and four Voight line shapes (V1…4, gray lines).

Figure 4 :

 4 Figure4: CAS concentrations of all calcite (blue) and aragonite (yellow) samples versus (a) aSO4 2-/aCO3 2-and (b) log(J). The[CAS] in calcite from the two experimental methods are in agreement for corresponding values of log(J) and aSO4 2-/aCO3 2-. The dependence of[CAS] in calcite on precipitation rate is much weaker than on aSO4 2-/aCO3 2-.

Figure 5 :

 5 Figure 5: 1000lnα CAS-Na 2 SO 4 in the calcite (blue) and aragonite (yellow) samples versus (a) aSO4 2-/aCO3 2-and (b) log(J). The vertical error bars represent error on the measurements, which is the larger of the root mean square error and 1 standard deviation of external replicates.

Figure 6 :

 6 Figure 6: Representative XANES spectra and fit results. Left: Representative spectra of calcite (3KCL1 in blue) and aragonite (30KAR1 in yellow, shifted upwards) and the difference in energy of the sulfate pre-edge peak (inset). A 5-point moving average was applied to smooth the spectra. Right: EV1, IV1 and FWHMV1 against [CAS] in panels b-d, respectively. The two aragonite samples with highest [CAS] mentioned in the text are denoted by circles with no outline.

Figure 7 :

 7 Figure 7: Schematic illustration of 2 possible scenarios to explain the S isotope results from calcite precipitation at various precipitation rates and constant aSO4 2-/aCO3 2-. The kinetic forward and equilibrium S isotope fractionation factors are represented by α f and α eq , respectively, where superscripts (s1, s2) indicate the specific scenario (see text).

Figure 8 :

 8 Figure8: CAS-SO4 2-S isotope fractionation vs. CAS concentration in computational, abiotic experimental and modern carbonate samples. See Figure2for computational and modern clacifier data sources. The gray area indicates the CAS concentrations expected over the range of Phanerozoic aSO4 2-/aCO3 2-, and the yellow area indicates the CAS-SO4 2-isotope fractionation range in natural modern aragonite ooids. The range of S isotope fractionation from variation in precipitation rate over ~2.5 orders of magnitude (Figure5) is shown for reference.

Figure 9 :

 9 Figure 9: Experimental (Exp.) and simulated (Sim.) CAS-SO4 2-S isotope fractionations for the case of a large (20.4‰) isotope fractionation between SO4 2-and CaSO4 0 and aSO4 2-/aCO3 2--

Figure A1 :

 A1 Figure A1: Schematic illustration of the components and steps in the constant addition method. Lines represent tubing, where the thick gray line is for airflow. Solid lines indicate flow in step I and broken lines in step II.

Figure A2 :

 A2 FigureA2: Schematic illustration of the steps in the CO2 degassing method (top), the evolution of pCO2 in the glove box (bottom, blue) and pH in an experiment bottle(bottom, black). See text for details of steps I-III.

Table 1 -

 1 CAS concentrations and S isotope fractionation in all samples.

	Name	CAS conc.	1000lnα CAS-Na 2 SO 4 *
		(ppm)	(‰)
	30CL1	87(±7)	2.7±0.4
	30CL2	11(±2)×10 1	3.1±0.6
	100CL1	25(±6)×10 1	2.8±0.2
	100CL2	32(±3)×10 1	2.9±0.3
	300CL1	82(±3)×10 1	2.5±0.2
	300CL2	11(±1)×10 2	2.6±0.1
	1KCL1	34(±2)×10 2	2.2±0.1
	1KCL2	35(±2)×10 2	2.2±0.1
	3KCL1	7(±1)×10 3	2.0±0.1
	3KCL2	95(±8)×10 2	1.9±0.1
	8KCL2	16(±3)×10 3	1.8±0.1
	100AR1	33(±8)	1.0±0.4
	100AR2	18(±2)	1.0±0.7
	300AR1	9(±2)×10 1	1.1±0.3
	300AR2	9(±3)×10 1	0.9±0.2
	1KAR1	22(±2)×10 1	1.1±0.3
	1KAR2	38(±1)×10 1	1.0±0.2
	3KAR1	72(±5)×10 1	1.0±0.1
	3KAR2	5(±1)×10 2	1.2±0.2
	10KAR1	14(±1)×10 2	1.1±0.1
	10KAR2	141(±7)×10 1	1.0±0.1
	30KAR1	44(±2)×10 2	1.0±0.4
	30KAR2	43(±3)×10 2	1.0±0.1
	CCHA	71(±1)×10 2	1.7±0.2
	CCHB	71(±1)×10 2	1.7±0.3
	CCIA	82(±2)×10 2	1.8±0.1
	CCIB	75(±1)×10 2	1.6±0.1
	CCIC	107(±2)×10 2	1.5±0.1
	CCJA	101(±2)×10 2	1.5±0.1
	CCJB	96(±2)×10 2	1.5±0.1
	CCJC	105(±2)×10 2	1.6±0.1
	CCKC	146(±6)×10 2	1.4±0.1
	CCKD	138(±5)×10 2	1.3±0.1
	CCKE	134(±2)×10 2	1.3±0.1
	CCLB**	90(±1)×10 2	1.4±0.1
	CCLC**	131(±2)×10 2	1.5±0.2
	CCLD**	122(±2)×10 2	1.7±0.2

  Gibbs free energies of formation of a single CaCO3, Ca 32 SO4 and Ca 34 SO4 subunit, respectively, and ∆G M,32 and ∆G M,34 are the Gibbs free energies of mixing a single subunit of Ca 32 SO4 and Ca 34 SO4, respectively, together with (N -1) subunits of CaCO3. The Gibbs free energy of reaction 16, which is related to the equilibrium S isotope fractionation between the CAS and the sulfate, is:

	12)		∆G r = ∆G * Ca 34 SO 4 o	+ ∆G 32 SO 4 2-o	-∆G * Ca 32 SO 4 o	-∆G 34 SO 4 2-o	.
	Substituting equations 10 and 11 into equation 12:
	13)	∆G r = (∆G Ca 34 SO 4 o	-∆G Ca 32 SO 4 o	) -(∆G 34 SO 4 2-o	-∆G 32 SO 4 2-o
	9)		* Ca	32 SO 4 + 34 SO 4 2-⇌ * Ca	34 SO 4 + 32 SO 4 2-,
	* Ca	32 SO 4 and * Ca	34 SO 4 are a calcite or aragonite unit containing exactly one sulfate molecule
	(with 32 S and 34 S, respectively) and many carbonate molecules, with the exact number of
	carbonate molecules depending on the overall [CAS]. According to solid-solution
	thermodynamics (e.g., Matschei et al., 2007), the Gibbs free energy of these solids may be
	expressed as follows:
	10)		∆G * Ca 32 SO 4 o	= (N -1)∆G CaCO 3 o	+ ∆G Ca 32 SO 4 o	+ ∆G M,32 ,
	11)		∆G * Ca 34 SO 4 o	= (N -1)∆G CaCO 3 o	+ ∆G Ca 34 SO 4
	∆G Ca 32 SO 4 o	and ∆G Ca 34 SO 4		o CaCO 3	,

o + ∆G M,34 , where N is the sum of CaCO3 and CaSO4 subunits within the calcite or aragonite unit. ∆G o are the

Table A2 -

 A2 Experimental conditions for the CO2 degassing experiments. Competition between entrapment and exchange of CAS While a complete growth-entrapment model is beyond the scope of this study, a simplified version suffices to explore this possibility. The change in sulfate concentration at the surface of a growing crystal can be described by the following mass balance:

	7. Appendix II
	7.1 18)	Name	Na2SO4 (mM) d[CAS s ] dt	Solution pH	aSO 4 2-aCO 3 2-	CaCO3 mtot cal|arg|vat (mg/2L) (mg) minitial (%)	log(J) (mole/m 2 /s)
		30CL1	0.03	7.35 -0.05 +0.05	5±2	498	283	100|0|0	-5.89 -0.21 +0.14
		30CL2	0.03	7.35 -0.05 +0.05	5±2	501	260	100|0|0	-5.89 -0.21 +0.14
		100CL1	0.1	7.34 -0.05 +0.05	17±7	505	249	100|0|0	-5.89 -0.21 +0.14
		100CL2	0.1	7.34 -0.05 +0.05	17±7	506	239	100|0|0	-5.89 -0.21 +0.14
		300CL1	0.3	7.34 -0.05 +0.05	51±21	522	268	100|0|0	-5.91 -0.21 +0.14
		300CL2	0.3	7.34 -0.05 +0.05	51±21	520	281	100|0|0	-5.91 -0.21 +0.14
		1KCL1	1	7.32 -0.05 +0.05	159±67	566	307	100|0|0	-5.93 -0.21 +0.14
		1KCL2	1	7.32 -0.05 +0.05	159±67	565	336	100|0|0	-5.93 -0.21 +0.14
		3KCL1	3	7.28 -0.05 +0.05	422±176	680	398	100|0|0	-6.04 -0.22 +0.14
		3KCL2	3	7.28 -0.05 +0.05	422±176	681	404	100|0|0	-6.04 -0.22 +0.14
		8KCL1	8	7.22 -0.05 +0.05	923±386	893	590	47|52|0	-6.17 -0.22 +0.15
		8KCL2	8	7.22 -0.05 +0.05	923±386	895	-	100|0|0	-6.17 -0.22 +0.15
		100AR1	0.1	7.47 -0.12 +0.02	7±2	652	436	0|100|0	-5.97 -0.1 +0.08
		100AR2	0.1	7.47 -0.12 +0.02	7±2	650	427	0|100|0	-5.97 -0.1 +0.08
		300AR1	0.3	7.47 -0.12 +0.02	22±6	655	447	0|100|0	-5.97 -0.1 +0.08
		300AR2	0.3	7.47 -0.12 +0.02	22±6	655	439	0|100|0	-5.97 -0.1 +0.08
		1KAR1	1	7.47 -0.12 +0.02	73±20	670	451	0|100|0	-5.96 -0.1 +0.08
		1KAR2	1	7.47 -0.12 +0.02	73±20	670	459	0|100|0	-5.96 -0.1 +0.08
		3KAR1	3	7.45 -0.11 +0.02	213±58	713	490	0|100|0	-5.96 -0.1 +0.08
		3KAR2	3	7.45 -0.11 +0.02	213±58	713	484	0|100|0	-5.96 -0.1 +0.08
		10KAR1	10	7.41 -0.11 +0.02	669±182	846	598	0|99|1	-5.96 -0.1 +0.08
		10KAR2	10	7.41 -0.11 +0.02	669±182	845	582	0|99|1	-5.96 -0.1 +0.08
		30KAR1	30	7.35 -0.11 +0.02	1717±467	1150	-	0|100|0	-5.94 -0.09 +0.08
		30KAR2	30	7.35 -0.11 +0.02	1717±467	1150	-	0|99|1	-5.94 -0.09 +0.08
	aSO4 2-/aCO3 2-, pH and log(J) were calculated as a mass-weighted average (Section 6.4).
	The abbreviations cal, arg, and vat refers to percentage of calcite, aragonite and vaterite in a sample.
	Unavailable mtot due to use of multiple filters is marked in dashes (see Section 6.2).

Acknowledgments

We thank Ziv Sade and Nir Galili for discussions. I.H. acknowledges support from a European Research Council Starting Grant (No. 337183). This work was supported by the Tellus program from CNRS/INSU. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515.

Na2SO4 concentration in all experiment was 1 mM. The abbreviations cal, arg, and vat refers to percentage of calcite, aragonite and vaterite in a sample. Superscript d and s indicate whether the gas dispersion tube was dry or submerged in solution, respectively. aSO4 2-/aCO3 2-was calculated based on the pH range.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

None