# Strontium isotope fractionation during strontianite (SrCO3) dissolution, precipitation and at equilibrium

Vasileios Mavromatis, Anna L. Harrison, Anton Eisenhauer, Martin Dietzel

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Vasileios Mavromatis, Anna L. Harrison, Anton Eisenhauer, Martin Dietzel. Strontium isotope fractionation during strontianite (SrCO3) dissolution, precipitation and at equilibrium. Geochimica et Cosmochimica Acta, 2017, 218, pp.201-214. 10.1016/j.gca.2017.08.039. insu-03661355

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1 Strontium isotope fractionation during strontianite (SrCO$_3$)

2 dissolution, precipitation and at equilibrium

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4 Vasileios Mavromatis¹,²,*Anna L. Harrison², Anton Eisenhauer³, Martin Dietzel¹

5

6 ¹Institute of Applied Geosciences, Graz University of Technology, Rechbauerstr. 12, A-8010

7 Graz, Austria

8 ²Géosciences Environnement Toulouse (GET), CNRS, UMR5563, 14 Avenue Edouard Belin,

9 31400, Toulouse, France

10 ³GEOMAR Helmholtz Centre for Ocean Research Kiel, Wischhofstr. 1-3, D-24148 Kiel,

11 Germany

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13 *Corresponding author Email: mavromatis@tugraz.at

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15 Abstract

16 In this study we examine the behavior of stable Sr isotopes between strontianite [SrCO₃] and
17 reactive fluid during mineral dissolution, precipitation, and at chemical equilibrium.

18 Experiments were performed in batch reactors at 25°C in 0.01 M NaCl solutions wherein the
19 pH was adjusted by bubbling of a water saturated gas phase of pure CO₂ or atmospheric air.

20 The equilibrium Sr isotope fractionation between strontianite and fluid after dissolution of the
21 solid under 1 atm CO₂ atmosphere was estimated as Δ⁸⁸/⁸⁶Sr<sub>SrCO3-fluid</sub> = δ⁸⁸/⁸⁶Sr<sub>SrCO3</sub> -
22 δ⁸⁸/⁸⁶Sr<sub>fluid</sub> = -0.05±0.01‰. On the other hand, during strontianite precipitation, an enrichment
23 of the fluid phase in ⁸⁸Sr, the heavy isotopomer, was observed. The evolution of the
24 δ⁸⁸/⁸⁶Sr<sub>fluid</sub> during strontianite precipitation can be modeled using a Rayleigh distillation
25 approach and the estimated, kinetically driven, fractionation factor α<sub>SrCO3-fluid</sub> between solid
26 and fluid is calculated to be 0.99985±0.00003 corresponding to Δ⁸⁸/⁸⁶Sr<sub>SrCO3-fluid</sub> = -0.15‰.

27 The obtained results further support that under chemical equilibrium conditions between solid
28 and fluid a continuous exchange of isotopes occurs until the system approaches isotopic
29 equilibrium. This isotopic exchange is not limited to the outer surface layer of the strontianite
30 crystal, but extends to ~7-8 unit cells below the crystal surface. The behavior of Sr isotopes in
31 this study is in excellent agreement with the concept of dynamic equilibrium and it suggests
32 that the time needed for achievement of chemical equilibrium is generally shorter compared to
33 that for isotopic equilibrium. Thus it is suggested that in natural Sr-bearing carbonates an
34 isotopic change may still occur close to thermodynamic equilibrium, despite no observable
35 change in aqueous elemental concentrations. As such, a secondary and ongoing change of Sr
36 isotope signals in carbonate minerals caused by isotopic re-equilibration with fluids has to be
37 considered in order to use Sr isotopes as environmental proxies in aquatic environments.

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# 1. Introduction

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The ability to routinely measure the isotopic composition of a plethora of elements in geological material with very high precision marked a new era for geochemistry. Today, stable isotopes of major and trace elements are used to reconstruct paleo-environmental conditions (e.g., Rollion-Bard et al., 2011; Böhm et al., 2012; Shirokova et al., 2013; Geske et al., 2015; Vigier et al., 2015; Noireaux et al., 2015), to understand weathering processes (e.g., Mavromatis et al., 2014; 2016a; Pokrovsky et al., 2011; Beinlich et al., 2014), to study diagenetic alteration (e.g., Riechelmann et al., 2016; Rollion-Bard et al., 2016), and to trace anthropogenic activity (e.g., Dietzel et al., 2016; Heuser and Eisenhauer, 2010). The use of stable isotope compositions of secondary minerals, however, demands knowledge of whether mineral formation occurred close to or far from chemical equilibrium. This is because at low temperatures kinetic isotope fractionation effects that usually occur during precipitation at far from equilibrium conditions, can generate isotopic compositions of carbonate minerals that differ significantly from isotope equilibrium compositions (Tang et al., 2008a; Mavromatis et al., 2017a). In contrast at higher temperatures kinetic isotope effects occurring during mineral growth would be erased as chemical and isotopic equilibrium between solid and fluid is achieved rather fast (Pearce et al., 2012; Beinlich et al., 2014).

To date it has been well established in a large number of experimental studies that mineral growth rate is one of the parameters that strongly affects isotopic fractionation (e.g., Skulan et al., 2002; Tang et al., 2008a; Eisenhauer et al., 2009, Immenhauser et al., 2010). When it comes to carbonate minerals, that are regularly used by the scientific community to track environmental conditions in the geological past, the number of experimental studies mapping kinetic isotope effects are a minority in the isotope literature (Li et al., 2012; Tang et al., 2008a, 2012; Böhm et al., 2012; Immenhauser et al., 2010; Fruchter et al., 2016). Even smaller is the number of experimental works studying isotope fractionation under near to thermodynamic equilibrium conditions in carbonates at low temperature (Mavromatis et al.,
2013; 2017a; 2017b; Li et al., 2011; 2014; 2015). On the other hand, the improved capability of computational calculations in recent years, has allowed for an increase in the number of studies that estimate isotopic fractionation at equilibrium based on theoretical calculations (Schauble, 2011; Rustad et al., 2010; Meheut et al., 2007; Pinilla et al., 2015; Schott et al., 2016). Comparison of these modelling results with the outcome of experimental studies, however, suggests that a significant discrepancy between measurements and theoretical calculations persists. A good example is the Mg isotopic fractionation between magnesite and fluid (Pearce et al., 2012; Schauble, 2011; Rustad et al., 2010), Mg-calcite and fluid (Mavromatis et al., 2013; Pinilla et al., 2015), and brucite and fluid (Li et al., 2014; Schott et al., 2016). For example the measured Mg isotope fractionation between magnesite and reactive fluid at 200°C reported by Pearce et al. (2012) to be -0.88‰, whereas that predicted by ab-initio calculations varies between -0.50‰ (Rustad et al., 2010) and -1.75‰ (Schauble, 2011).

Knowledge of both the isotopic equilibrium and the effect of mineral growth kinetics on isotope fractionation factors is essential in order to use the stable isotope composition of secondary minerals for (paleo)environmental or forensic tasks. This holds true not only for the stable isotopes of the constituting elements of readily forming Ca- and Mg-bearing carbonate minerals in Earth's surface environments, but also for the stable isotopes of divalent metal cations ($Me^{2+}$) that are commonly incorporated into the Ca-bearing carbonates. Such elements form individual carbonate minerals (e.g., $BaCO_3$, $SrCO_3$, $ZnCO_3$) under specific ambient environmental conditions but are also common constituents of solid-solutions with $CaCO_3$ minerals. The experimental investigation of the isotopic fractionation behavior between these minerals and an aqueous fluid (i) provides the basis for further development and/or validation of theoretical calculations, (ii) gives insights into the isotope behavior during the formation of solid-solutions, and (iii) sheds light on the mechanisms controlling isotopic fractionation during both formation of endmember $Me^{2+}$ carbonate minerals and incorporation of the $Me^{2+}$
91 in carbonate mineral solid-solutions (e.g. the strontianite-aragonite solid-solution series;
92 Plummer and Busenberg, 1987; Plummer et al., 1992).

93 In the present study we examine the fractionation of stable Sr isotopes between
94 strontianite [SrCO3] and reactive fluid. Strontium is an impurity in calcite and usually present
95 in natural aragonites at high concentrations, owing to the isostructural crystallization of
96 aragonite and strontianite and the formation of an ideal solid-solution at the aragonite
97 endpoint (Speer, 1983). Stable strontium isotope fractionation has been investigated during
98 calcite (Böhm et al., 2012; AlKhatib and Eisenhauer, 2017a) and aragonite growth (Fruchter
99 et al., 2016; AlKhatib and Eisenhauer, 2017b) in laboratory studies. Herein we focus on the
100 formation of pure SrCO3 following the previous works on MgCO3 (Pearce et al., 2012) and
101 BaCO3 (Mavromatis et al., 2016b) in an effort to expand the existing knowledge on the
102 behavior of stable isotope fractionation of divalent cations of their pure Me-carbonate mineral
103 phase during dissolution, precipitation, and at equilibrium. In this study, the Sr isotopic
104 evolution of the reactive solution during strontianite dissolution and precipitation was
105 measured, with particular attention paid to the isotopic evolution following attainment of
106 chemical equilibrium of the reactive fluid with respect to strontianite. The experimental
107 results are discussed in the context of isotope (dis-) equilibrium phenomena, the potential
108 secondary resetting of the Sr isotope signal in the Sr-endmember carbonate mineral
109 strontianite, and the utility of Sr isotopes as an environmental proxy.
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## 2. Materials and Methods

112 2.1 Experimental materials

113 The methodology followed for strontianite synthesis is similar to that reported
114 previously by Mavromatis et al. (2016b) for synthesis of witherite (BaCO3). Briefly, pure
115 strontianite seeds were produced by mixing equimolar SrCl2 and Na2CO3 solutions prepared
116 from analytical grade chemicals (Sigma-Aldrich) in deionized water, and placing the slurry
into a stirred titanium Parr reactor (series 4560). The reactor was sealed and the temperature and pCO2 adjusted to 200°C and 15 bars, respectively. The solids were recovered after 30 days of reaction time, rinsed in deionized water, and dried at room temperature. The synthesis of seed crystals with this technique provides chemical and isotopic homogeneity in the precipitated carbonate, as is evident from the amount of Sr remaining in the aqueous phase, at < 0.1 % of the total mass of Sr introduced initially. This is further supported by the δ<sup>88/86</sup>Sr isotopic composition of the bulk strontianite (i.e., δ<sup>88/86</sup>Sr = 0.145±0.003), which is identical to that of the initial SrCl<sub>2</sub> solution (i.e., δ<sup>88/86</sup>Sr = 0.154±0.013) within analytical error (Table 1). Note here that Skulan et al. (2002) postulated achievement of equilibrium in Fe isotopes between hematite and fluid at 98°C after ~40 days of incubation time, suggesting that the method followed for the formation of strontianite likely results to an isotopic homogeneous solid.

The synthesized strontianite consisted of 0.1-2.0 µm euhedral crystals (Fig. 1). The mineralogy of these crystals was confirmed by X-ray diffraction (XRD) analysis. The specific surface area of the synthetic strontianite powder determined by multi-point krypton adsorption BET method (Brunauer et al., 1938) using a Quantachrome Autosorb-1MP, was 1.1±0.1 m²/g.

## 2.2 Dissolution/Precipitation experiments

The experimental set up for strontianite dissolution and precipitation makes use of the pH dependent solubility of carbonate minerals to induce dissolution and precipitation in separate steps within the same reactor, and is described in detail by Mavromatis et al. (2016b). The pH of the aqueous fluid was controlled by continuous bubbling of a water-saturated gas phase through the reactors throughout the experimental runs. The experimental set up can be seen in Fig. 2. At the onset of the experimental run, approximately 5 g of synthetic strontianite were placed in a 1.2 L Nalgene batch reactor containing ~1.1 L of a 10⁻² M NaCl
aqueous solution (refer to Electronic Supplementary Material-ESM Table 1). Within this study, two identical experiments were performed in order to control the reproducibility of the reaction mechanisms and kinetics of the experimental runs. Reactors were equipped with a floating stir bar rotating at 300 rpm (Fig. 2). The experimental setup was placed in a room with a constant temperature of 25±1 °C. Strontianite dissolution during phase I of the experimental runs was initiated by bubbling pure CO₂ (1 atm) through the reactor. This kept the pH of the fluid at a quasi-constant value of about six. A subsequent change of the bubbling gas phase from pure CO₂ to atmospheric air marked the onset of phase II and resulted in the fluid becoming oversaturated with respect to strontianite due to CO₂ degassing and an increase in pH. This initiated strontianite precipitation until a second chemical equilibrium was attained according to the reaction:

$$Sr^{2+} + CO_3^{2-} \rightleftharpoons SrCO_3 \quad (K_{\text{strontianite}}: 10^{-9.27}; \text{Busenberg et al., 1984}) \quad (1)$$

This new chemical equilibrium was achieved at a pH value of approximately 8 (Fig. 2). In order to minimize evaporation, gases were bubbled through a 10⁻² M NaCl solution prior to their introduction in the reaction vessel (Fig. 2). Fluid samples of known quantity were taken at regular time intervals throughout the experiment using a syringe. Stirring of the fluid was stopped shortly prior to sampling to allow the strontianite to settle. In this way solid removal was minimized and the solid-to-solution ratio was precisely monitored during the course of each experiment. This protocol provided precise knowledge of Sr mass distribution (i.e., between fluid phase, solid phase and retrieved sample). At the end of phase I and prior to change of the gas phase, a few grains of the strontianite present in the reactors were removed for isotopic analysis. The removal of this material did not significantly alter the mass of solid present in the reactor and is not considered in the calculations presented hereafter.

Immediately after sampling, the fluid was filtered through a 0.2 µm cellulose acetate membrane syringe filter and a sub-sample was acidified for Sr concentration and isotopic measurements. Reactive fluid carbonate alkalinity was determined in a second sub-sample,
and fluid pH was measured *in situ* in the reactors. At the end of the experimental run, the entire reactive fluid was vacuum filtered through a 0.2 µm membrane (Sartorius, cellulose acetate). The solids were rinsed with MilliQ water and dried at room temperature.

## 2.3 Solid and fluid phase characterization

Strontium concentrations were measured by inductively-coupled plasma optical emission spectrometry (ICP-OES) using a Perkin Elmer Optima ICP-OES 4300. The statistical uncertainty is reported as two standard deviations (2σ) in the concentration range of 0.01 – 0.17 x10⁻³ M corresponding to ±3%. The total alkalinity of the reactive fluids was determined by a Schott TitroLine alpha plus titrator with an uncertainty of ±2% and a detection limit of 5 x10⁻⁶ M. Fluid pH was measured with a Schott Blueline 28 combined electrode, calibrated with NIST standard buffers at pH of 4.01, 7.00 and 10.00, and with an uncertainty of ± 0.03 pH units. The calibration of the pH-meter took place shortly prior to each sample collection and pH measurements performed in-situ.

X-ray diffraction analyses of synthetic strontianite was performed using a PANalytical X'Pert PRO diffractometer equipped with a Scientific X'Celerator detector and a Co-target tube operated at 40 kV and 40 mA. The 2θ angle range was set to 4 to 85° using a step size of 0.008° 2θ and a count time of 40 s/step. Scanning Electron Microscopy (SEM) observations of solids were performed after gold-coating using a ZEISS DSM 982 Gemini microscope operating at 5 kV accelerating voltage.

Aqueous speciation and the saturation state ($\Omega_{\text{strontianite}} = \text{IAP}/K_{\text{sp,strontianite}}$) of the reacting fluids with respect to strontianite were calculated using the PHREEQC software together with its MINTEQ V4 database (Parkhurst and Appelo, 1999).

## 2.4 Strontium isotope analyses
Stable strontium isotope (δ<sup>88/86</sup>Sr) measurements of liquid and selected solid samples were measured on a Finnigan Triton Thermal Ionization Mass Spectrometer (TIMS) at GEOMAR mass-spectrometer facilities in Kiel using the <sup>87</sup>Sr/<sup>84</sup>Sr double spike method (Krabbenhöft et al., 2009). Each sample was separated into two aliquots. The double spike was added to one aliquot (spiked) and the other aliquot was left unspiked. Sr was separated from the matrix solution of each aliquot using the strontium-selective chromatographic resin Eichrom Sr-spec (50–100 mesh) that is loaded in a 650 ll BIO-RAD column tube. The recovery for Sr separation was better than 90%. In each batch of carbonate sample measurements, the JCp-1 standard was also prepared and analyzed repeatedly (δ<sup>88/86</sup>Sr = 0.20 ± 0.02‰, 2SD, n = 10) using the same protocol as used for the unknown samples. The IAPSO Seawater Standard (batch ID. P152) was measured in batches of seawater sample measurements (δ<sup>88/86</sup>Sr = 0.39 ± 0.02‰, 2SD, n = 4). No blank correction was needed since the total procedural Sr blanks were about 0.04 ng, which is insignificant compared to the amount of Sr in the measured samples (300–700 ng). Sr isotopic values are presented in the standard δ-notation relative to SRM987 as the standard (at value of <sup>88</sup>Sr/<sup>86</sup>Sr = 8.375209).

$$ \delta^{88/86}Sr = \left( \frac{^{88}Sr \cdot ^{86}Sr_{sample}}{^{88}Sr \cdot ^{86}Sr_{SRM987}} - 1 \right) \times 1000 \quad (2) $$

The δ<sup>88/86</sup>Sr is presented with an uncertainty of two standard deviations (2σ), as obtained from the external long-term reproducibility of measurements of the JCp-1 coral standard, all seawater samples (of approximately constant <sup>88</sup>Sr/<sup>86</sup>Sr composition), and the IAPSO standard. The measurements of both JCp-1 and seawater (including the IAPSO seawater standard), yielded an identical external reproducibility of 0.02‰ (2SD).

# 3. Results

## 3.1 Strontianite dissolution and precipitation
The measured concentrations of Sr and alkalinity in the reactive fluid during the experimental runs are reported in Table 1 and ESM Table 2 for both replicate experiments. In Fig. 3 the temporal evolution of Sr concentration is plotted together with the evolution of aqueous pH. The observed behavior during phase I of the experimental runs is consistent with the initial dissolution of strontianite and the achievement of chemical equilibrium between strontianite and fluid. The achievement of chemical equilibrium at the onset of phase I, when pure CO₂ was bubbled through the reactors, occurred before the first sample was removed at 1500 min. During these first 1500 min ~16% of the strontianite initially introduced in the reactor was dissolved. The achievement of equilibrium was confirmed by the quasi-constant aqueous Sr and alkalinity concentrations in duplicate experiments during phase I (Table 1). Conversely, at the beginning of phase II, precipitation was induced via bubbling of atmospheric air, which drove an increase in fluid pH and thus the saturation state with respect to strontianite (Table 1). Strontianite precipitation rapidly removed Sr from solution and reduced alkalinity (Fig. 3). A second chemical equilibrium between strontianite and fluid was then achieved within ~420 min (Table 1), as evidenced by near constant pH and Sr concentrations (Fig. 3).

The temporal evolution of strontianite growth rate, $r_p$, during its precipitation can be assessed by aqueous Sr mass balance in the system and is described by:

$$r_p = \frac{n_{Sr,t_i} - n_{Sr,t_{i-1}}}{t_i - t_{i-1}} / S \qquad (3)$$

where $n_{Sr,t_i}$ are the moles of Sr in the fluid at time $t_i$, and S refers to the total surface area of strontianite in m², which was calculated based on the mass of strontianite present in the reactor and the BET surface area of the strontianite. Thus, $r_p$ is expressed in mol/m²/s. Rates were calculated between sampling points. The total surface area, S, was corrected for the amount of strontianite dissolved or precipitated during the experimental runs and assuming surface area increased proportionally to the mass change and BET measured surface area.
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Details on Sr mass balance in the reactor and evolution of the reactive surface can be found in Table ESM 1. The strontianite growth rate during its precipitation exhibits an initial increase of ~3 orders of magnitude in the range of $10^{-11} < r_p < 10^{-8}$ mol/m²/s (Table 1) which is followed by a decrease after 13020 min elapsed time as chemical equilibrium is approached.

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## 3.2 Sr isotopic composition of fluids and solids

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The measured $\delta^{88/86}$Sr<sub>fluid</sub> values are given in Table 1 and illustrated in Fig. 4. The strontianite seed crystals ($\delta^{88/86}$Sr<sub>seed</sub> = 0.145±0.003 ‰), the SrCl<sub>2</sub> solution from which the seed crystals were synthesized ($\delta^{88/86}$Sr<sub>SrCl2</sub> = 0.154 ± 0.013 ‰) and the strontianite collected at the end of the experimental run ($\delta^{88/86}$Sr<sub>SrCO3-end</sub> = 0.154 ± 0.002 ‰) have the same isotopic composition within analytical error. The radiogenic ($^{87}$Sr/<sup>86</sup>Sr) isotope composition of all material used in this study exhibit the same composition as shown in Table 1. The stable isotope composition of strontianite that remained in the reactor during phase I and collected at 12540 min of reaction time exhibits an enrichment in <sup>88</sup>Sr ($\delta^{88/86}$Sr<sub>strontianite-phI</sub> = 0.167 ± 0.004 ‰). The isotopic composition of the reactive fluid during phase I of the experiment was constant within analytical uncertainty, and exhibited a value of $\delta^{88/86}$Sr<sub>fluid</sub>=0.194 ± 0.006 ‰ (n=5), indicative of isotopic steady state in the strontianite-fluid system. After the end of phase I, strontianite precipitation occurred between 12660 and 13400 min, causing a significant increase in $\delta^{88/86}$Sr<sub>fluid</sub> from 0.194 ‰ to 0.622 ‰ (Fig. 4). This is attributed to the preferential incorporation of <sup>86</sup>Sr in the precipitating strontianite, which effectively enriches the fluid in <sup>88</sup>Sr. After the pH-jump, both the pH of the reactive fluid and the aqueous Sr concentration are quasi-constant at ~8.0 and 0.18 mM, respectively within ~420 min (see Fig. 3). Yet, the $\delta^{88/86}$Sr<sub>fluid</sub> value is progressively evolving towards lower values up to ~22500 min of reaction time (Fig. 4). This continuing $\delta^{88/86}$Sr<sub>fluid</sub> change in the fluid phase indicates that there is ongoing isotopic exchange between the solid and the aqueous phase, despite the achievement of chemical equilibrium.

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### 4.1 Sr isotope fractionation during strontianite dissolution and precipitation

#### 4.1.1 Strontianite dissolution

The $\delta^{88/86}\text{Sr}_{\text{fluid}}$ values during the chemical equilibrium achieved in phase I are ~0.05 ‰ higher compared to that of the strontianite seed material (Fig. 4). The observed difference between $\delta^{88/86}\text{Sr}_{\text{fluid}}$ and $\delta^{88/86}\text{Sr}_{\text{strontianite}}$ can be attributed to achievement of isotopic equilibrium in the strontianite-fluid system during phase I of the experimental run. The first measurement of the fluid occurred after chemical equilibrium was already achieved; therefore detailed information regarding Sr fractionation during strontianite dissolution cannot be extracted from this dataset. The rather fast achievement of isotopic equilibrium following dissolution, however, is consistent with the behaviour of Ba isotopes in the witherite-fluid system at 25°C (Mavromatis et al., 2016b). This is also expected due to the fast exchange of water molecules between the Sr hydration sphere and the bulk fluid (i.e., $10^9 \text{s}^{-1}$; Lincoln and Merbach, 1995), a parameter that is suggested to control isotopic fractionation between mineral and fluid (Gussone et al. 2003, Pearce et al., 2012; Mavromatis et al., 2013). The preferential enrichment of the fluid phase in $^{88}\text{Sr}$ versus the solid that was observed during phase I of the experimental run is consistent with the shorter Sr-O bond length observed in strontianite (2.61 Å; O'Day et al., 2000) compared to that in the aqueous phase (i.e. 2.60 Å; D'Angelo et al., 2016). The small but measureable stable Sr isotope fractionation observed between strontianite and reactive fluid that averages at -0.05 ‰ is comparable to that observed for Mg isotopes during magnesite dissolution and subsequent chemical equilibrium demonstrated by Pearce et al. (2012) in experiments performed at 120 and 150°C. In contrast, in the witherite-fluid system, investigated by Mavromatis et al. (2016b), no significant stable Ba isotope fractionation was observed during the achievement of chemical and isotopic equilibrium. In this latter case it was argued that the absence of measureable fractionation of
stable Ba isotopes between witherite and fluid at chemical equilibrium might stem from the small difference in the Ba-O bond length between witherite (i.e. 2.80 Å; Holl et al., 2000) and the aqueous Ba octahedron (i.e 2.79 Å; Persson et al., 1995). Indeed the Me-O bond lengths in strontianite and magnesite are longer compared to the respective aqueous Me²⁺ species, which may lead to observed greater degree of fractionation.

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### 4.1.2 Strontianite precipitation

Strontianite precipitation occurred between 12500 and 13000 min of elapsed time when aqueous pH increased from ~6 to ~8 as seen in Fig. 3. This pH increase was driven by changing the supplied gas from pure CO₂ to laboratory atmosphere (~0.05%), and resulted in an increase of the supersaturation of the reactive fluid with respect to strontianite (Ω ≈ 2.7; Table 1), and significant removal of Sr from the fluid phase to the solid. The invoked pH-jump forced the system to attain a second chemical equilibrium (phase II). Unlike phase I, however, measurable changes in the δ⁸⁸/⁸⁶Srₜₐₗₐₜ were observed throughout phase II (Fig. 4). The fluid became significantly enriched in ⁸⁸Sr (Fig. 4), indicating a preferential uptake of the lighter ⁸⁶Sr into the precipitating strontianite. Owing to the closed system behavior of Sr in this experimental setup, the extent of stable Sr isotope fractionation during strontianite precipitation can be estimated using a Rayleigh-type equation (Criss, 1999) where the fractionation factor α between strontianite and reactive fluid is defined as:

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$$ \alpha_{\text{strontianite-fluid}} = \frac{\log\left(\frac{1000 + \delta^{88/86} \text{Sr}_{\text{inst}}}{1000 + \delta^{88/86} \text{Sr}_{\text{init}}}\right)}{\log F} + 1 \quad (4) $$

where δ⁸⁸/⁸⁶Srₜₐₗₐₜ and δ⁸⁸/⁸⁶Srₜₐₗₐₜ are the Sr isotope composition of the reactive fluid during phase I (average δ⁸⁸/⁸⁶Srₜₐₗₐₜ = 0.194±0.006‰; n=5) and throughout the precipitation period (i.e. ~12500 – 13000 min, 0.2 > δ⁸⁸/⁸⁶Srₜₐₗₐₜ > 0.62; Fig. 4), respectively. F is the molar fraction of Sr remaining in the reactive fluid. At F = 0.052 (see ESM Table 1) δ⁸⁸/⁸⁶Srₜₐₗₐₜ is

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0.62 ‰, representing the $\delta^{88/86}\text{Sr}_{\text{fluid}}$ at the beginning of phase II and at the end of the pH-jump. A fractionation factor $\alpha_{\text{strontianite-fluid}}$ at this point in the experiment is estimated to be 0.99987, which corresponds to $\Delta^{88/86}\text{Sr}_{\text{strontianite-fluid}} \approx -0.13$ ‰. The mass of Sr removed via sampling compared to that in the reactive fluid is ~3 orders of magnitude lower (ESM Table 1), and thus does not affect the results of Eq. 4. Note here that the estimated $\alpha$ value using Eq. (4) refers to strontianite precipitation between 12540 and 13380 min elapsed time. The $\Delta^{88/86}\text{Sr}_{\text{strontianite-fluid}}$ value, however, can also be estimated by fitting all the measured data for the aqueous fluid in phase I and during strontianite precipitation, as is illustrated in Fig. 5. Indeed the Rayleigh curve fitted in Fig. 5 provides an $\alpha_{\text{strontianite-fluid}}$ value of 0.99985 (or $\Delta^{88/86}\text{Sr}_{\text{strontianite-fluid}} \approx -0.15$‰). Likely this slight difference in calculated $\alpha$ values occurs due to statistical treatment of the data, as in the case of Eq. (4), only two measured values at 12540 min and 13380 min were taken into account during the calculation, whereas for the Rayleigh-type fractionation fit all data points during phase I and during strontianite precipitation ($t = 1500-13380$ min; $n = 10$) were considered. The observed enrichment of strontianite in the lighter $^{86}\text{Sr}$ isotopomer is overall in good agreement with the behavior of alkali earth metals during the precipitation of pure metal-carbonate phases (e.g., Böttcher et al., 2012; Pearce et al., 2012; Tang et al., 2008b; Eisenhauer et al., 2009, Mavromatis et al., 2012a; 2016b; Shirokova et al., 2013; Li et al., 2015). Similar is the case for the incorporation of alkaline earths in $\text{CaCO}_3$ minerals as traces or impurities (e.g., Li et al., 2012; Mavromatis et al., 2013; 2017a; 2017b; Böhm et al., 2012; Immenhauser et al., 2010; Fruchter et al., 2016)

In contrast to divalent cation isotope fractionation at equilibrium that can be estimated by thermodynamic considerations of the solid structure and the aqueous species in the fluid phase (Schauble 2011; Rustad et al., 2010; Schott et al., 2016; Pinilla et al., 2015), isotopic fractionation during mineral growth at far from equilibrium conditions is neither well understood nor adequately modeled. There are two models designed to simulate isotopic fractionation during calcite growth; 1) the growth entrapment model (GEM), and 2) the
surface reaction kinetic model (SRKM). The growth entrapment model, developed by Watson and coworkers (Watson and Liang, 1995; Watson, 1996; 2004), suggests the presence of a chemically and isotopically distinct surface layer that is in contact with the reactive fluid and can be either enriched or depleted in an isotopomer or a trace element. The GEM assumes that this reactive layer at the calcite surface is approximately 0.5 nm thick. The GEM has previously been applied to simulate uptake of elements and/or their isotopes in a number of experimental studies (e.g., Mavromatis et al., 2013; 2015b; Noireaux et al., 2015; Gabitov et al., 2008; 2012; Tang et al., 2008a; 200b; 2012). Alternatively, DePaolo (2011) developed the surface reaction kinetic model (SRKM) using the principle of transition state theory (TST) to simulate elemental and isotopic fractionation during calcite growth. This model has been further extended recently (Nielsen et al., 2012, 2013; Watkins et al., 2013), and suggests a continuous change of the fractionation factor during mineral growth. This is not consistent with the mono-directional Rayleigh model used herein to estimate the fractionation factor during mineral growth, though it is worth noting that Druhan et al. (2013) suggested that a coupled ion-by-ion and reactive transport model is a better approach to a Rayleigh model in the studied groundwater system. Note also here that to date the SRKM model has been only applied to the formation of calcite in natural systems or in laboratory studies. The application of the SRKM model to elements that their masses is not limited only to two isotopomers as in the case of Ca (see Druhan et al., 2013) requires extension with respect to the system of equations that has to be solved.

In addition to growth kinetics, there are other parameters that have been shown to control isotopic fractionation during mineral growth. These include ionic strength and temperature (Watson, 1996; 2004; Dietzel et al., 2004; Tang et al., 2012), crystal structure (Mavromatis et al., 2012b, Gussone et al., 2003), as well as aqueous complexation (AlKhatib and Eisenhauer, 2016; 2017a; 2017b, Schott et al., 2016; Fujii et al., 2013; 2014; Mavromatis et al., 2017a; 2017b). Aqueous complexation effects together with the dehydration of aqueous
371 Me²⁺ ions have been shown to control fractionation between Mg-bearing carbonates and reactive fluids (Schott et al., 2016). In fact, dehydration of aqueous Mg²⁺ has been suggested to control both rate of crystal growth (Saldi et al., 2009; Gautier et al., 2014; 2016) and Mg isotope fractionation for a variety of Mg-carbonate minerals (Pearce et al., 2012; Mavromatis et al., 2013; 2017a, b; Immenhauser et al., 2010). In the case of aqueous Sr, however, dehydration of the 9-coordinated aquo-ion, occurs rather fast (10⁹ s⁻¹) compared to Mg (10⁵ s⁻¹; Lincoln and Merbach, 1995), thus dehydration may not be of great significance for isotope fractionation between aqueous Sr and strontianite. Thus the observed Sr isotope fractionation during strontianite precipitation can be attributed to growth kinetics in our experiments.

380

381 4.2 Sr isotope fractionation during chemical equilibrium

382 The pH increase induced by the change from pure to atmospheric CO₂ bubbling promoted rapid precipitation of strontianite, the rate of which was effectively dependent on the rate of CO₂ degassing. As such, the decrease in aqueous Sr concentration closely tracked the temporal evolution of pH, and near steady conditions with respect to both aqueous Sr concentration and pH occurred simultaneously after ~12500 minutes as soon as chemical equilibrium was achieved (Fig. 3). Yet, the δ⁸⁸/⁸⁶Srfluid during phase II continued to evolve well past the achievement of chemical equilibrium (Fig. 4). This suggests the continuous exchange of Sr between strontianite and the reactive fluid at chemical equilibrium that is marked by a preferential release of light ⁸⁶Sr from the solid to the fluid phase. The continued evolution of the isotopic composition of the fluid after the attainment of chemical equilibrium has previously been observed for stable Ba isotopes in the witherite-fluid system (see Mavromatis et al., 2016b) and stable Mg isotopes in the magnesite-fluid system (Pearce et al. 2012). These observations are consistent with the concept of dynamic thermodynamic chemical equilibrium. Under equilibrium conditions in a mineral-fluid system, both forward- (i.e., precipitation) and back- (i.e., mineral dissolution) reactions occur, but at equal rates.

383

384

385

386

387

388

389

390

391

392

393

394

395

396
Thus the net reaction rate is zero, which results in no measurable change in elemental fluid composition. The concept of thermodynamic chemical equilibrium has been widely used to describe fluid-mineral reactions under the formulation of the transition state theory (Lasaga, 1981; Aagaard and Helgeson, 1982; Oelkers, 2001; Schott et al., 2009). In accordance with the witherite-fluid and the magnesite-fluid systems, the obtained results presented herein suggest that isotopic fractionation, in this case for Sr, is induced during mineral precipitation when the aqueous Sr is transferred to the precipitating strontianite. This results in the rapid enrichment of the fluid in ⁸⁸Sr observed between ~12000 and 13800 min (Fig. 4) due to the preferential uptake of ⁸⁶Sr into the precipitating strontianite. Near and at chemical equilibrium the rate of precipitation approaches or becomes equal to that of dissolution, which provokes the enrichment of the fluid with the lighter ⁸⁶Sr due to re-equilibration. At the end of the experimental run, the δ⁸⁸/⁸⁶Srₜₐₗ does not approach that of phase I (i.e. 0.194 ‰) but is somewhat heavier, averaging at 0.400 ‰ (n=4) between 20100 and 25860 min of elapsed time (Fig. 4).

After the chemical equilibrium achieved in phase II, the δ⁸⁸/⁸⁶Srₜₐₗ values exhibit an exponential decline that can be expressed using a relaxation curve. Similar relaxation curves have been used previously in order to estimate fluid composition changes that have been induced by jumps in experimental conditions, such as temperature-jumps (Prabhananda et al., 1987; Castaing et al., 1991), pressure-jumps (Dangles et al., 1994), and pH-jumps (Pines and Huppert, 1983; Benezeth et al., 2008). More recently we used a similar approach to explain the temporal evolution of Ba isotopes after witherite precipitation (see Mavromatis et al., 2016b). Similar to this latter study, the temporal evolution of δ⁸⁸/⁸⁶Srₜₐₗ during phase II of the experimental run can be written as:

$$ \delta^{88/86} \text{Sr}_{\text{fluid}} = y_o + A e^{-x/\tau} \qquad (5) $$

where y₀ and A are constants and equal to 0.339 (±0.064) and 2.368 (±2.051) respectively, x is the reaction time (in minutes) from the onset of the experimental run and τ denotes the
relaxation time. For the experimental data shown here, $\tau$ takes the value 6233 (±3017). Note here that the use of Eq. 5 provides the means to quantify the observed isotope trend during phase II, it cannot however provide insights to the individual reaction mechanisms controlling isotope exchange. On the other hand, relaxation curves have been earlier used to define the order of reaction.

At the end of phase II, mass balance calculations suggest that the mass of strontianite remaining in the reactor was ~4.9 g, with a final measured specific area of 1.1 m²/g, similar to that of the seed material. Considering that there are 4 atoms of Sr in each unit cell of this mineral phase, the amount of Sr in the outer surface of the strontianite present in the reactor at the end of the experiment is equal to ~0.08 mmol. Note here that for this calculation a cubic unit cell was assumed with volume equal to that of the strontianite unit cell (i.e. 259 Å³) and an edge dimension of ~6.4 Å. This cubic unit cell has been used in all the calculations presented below.

The observed deviation from the Rayleigh curve at high $F_{Sr-precipitated}$, illustrated in Fig. 5, suggests a continuous exchange of Sr between the ⁸⁶Sr enriched strontianite and the ⁸⁸Sr enriched fluid. The amount of Sr released from strontianite to the fluid in order to produce its observed reduction in $\delta^{88/86}\text{Sr}_{\text{fluid}}$ can be estimated by mass balance calculations. At the chemical equilibrium that describes the strontianite-fluid system during phase II, the mass balance can be written as:

$$ \delta^{88/86}\text{Sr}_{\text{fluid-final}} = \delta^{88/86}\text{Sr}_{\text{fluid}} \times (1 - f_{\text{strontianite}}) + \delta^{88/86}\text{Sr}_{\text{strontianite}} \times f_{\text{strontianite}} \quad (6) $$

where $\delta^{88/86}\text{Sr}_{\text{fluid-final}}$ and $\delta^{88/86}\text{Sr}_{\text{fluid}}$ are the final isotopic compositions of the fluid during phase II of the experiment (i.e., 0.40‰, n=4) and after the end of strontianite precipitation due to pH jump at t = 13,380 min (i.e., 0.62‰), respectively. The fraction of Sr in the aqueous phase that must be derived from exchange with strontianite after the end of precipitation is represented in Eq. (6) as $f_{\text{strontianite}}$. At the end of the experimental run, the analyzed strontianite solid had a $\delta^{88/86}\text{Sr}_{\text{strontianite}}$ of 0.154‰ (Table 1). From Eq. (6) it is calculated that to produce
the measured Sr stable isotopic composition of the fluid, ~47% of the Sr in the fluid phase at the end of the experiment must have been derived from strontianite, despite a lack of strontianite dissolution. During phase II chemical equilibrium, the average Sr in the fluid was 0.15 mmol, indicating that 0.08 mmol or 0.2% of the total mass of Sr present in strontianite (i.e., 33.02 mmol) were exchanged with the fluid by the end of the experiment. The problem with this calculation, however, is the assumption that the bulk isotopic composition of the solid at the end of the experiment represents the isotopic composition of the freshly precipitated strontianite. Bulk δ⁸⁸/⁸⁶Srₐₜₚₐₜₚₐₒₐ₆ is consistent with the large amount of aqueous Sr removed from the reactive fluid as SrCO₃ (see Fig. 5), which simply denotes that the bulk composition of the solid at the end of the pH jump should be similar to that of the initial fluid. On the other hand, the temporal evolution of the δ⁸⁸/⁸⁶Srₐₜₚₐ₅ during precipitation (Fig. 4) suggests an isotopic zoning of the precipitated solid with a relative enrichment of ⁸⁶Sr in the early precipitating layers and a progressive depletion towards the surface of the crystals. The evolution of the δ⁸⁸/⁸⁶Srₐₜₚₐₜₚₐ₅ as a function of Sr precipitated as strontianite that is illustrated in Fig. 5 suggests that at the time the δ⁸⁸/⁸⁶Srₐₜₚₐ₅ takes its maximum value of 0.62 ‰, which would equate to an instantaneous value of δ⁸⁸/⁸⁶Srₐₜₚₐ₅,ₐₘ₅ for strontianite of 0.48‰. The decline of the δ⁸⁸/⁸⁶Srₐₜₚₐ₅ far below this value during phase II suggests that the observed isotopic exchange cannot be limited to a single surface layer, but is rather extended below it. The isotopic gradient in the solid invoked by the Rayleigh distillation process makes the estimation of the Srₐ₅,ₐₘ₅ involved in the exchange not a straight forward process. As a first approach we assume that at isotopic equilibrium during phase II the fractionation factor between strontianite and fluid should be similar to that measured for phase I, i.e. Δ⁸⁸/⁸⁶Srₐ₅,ₐₘ₅,ₐ₅ = -0.05‰. Thus the isotopic composition of the solid should be ~0.35‰ considering that the measured δ⁸⁸/⁸⁶Srₐₜₚₐ₅ is 0.40‰ (Fig. 4), and assuming that this latter value represents isotopic equilibrium. As calculated from the evolution of the δ⁸⁸/⁸⁶Srₐₜₚₐ₅,ₐₘ₅ value (Fig. 5), the amount of Sr precipitated as strontianite is 0.55 mmol. This number is ~8 times larger than
all Sr present in the external strontianite surfaces in the reactor which is calculated to be ~0.08 mmol, based on a cubic unit cell as described previously. In other words, this simplified calculation suggests that 7-8 unit cells (or ~4 nm) below the freshly precipitated strontianite surface must participate in isotopic exchange to produce the observed evolution of fluid chemistry. Note here however that this calculation assumes that all the surface sites are active, thus corresponds to the maximum moles of Sr that actually exchange with the fluid phase. As mentioned previously, these calculations include some analytical uncertainties, mainly due to the isotopic zoning in the freshly precipitated strontianite, but they nevertheless confirm that isotope exchange associated with sorption/desorption processes on the outer surface layer alone cannot explain the observed temporal evolution of the reactive fluid during phase II. Rather, it is suggested that a significant proportion (0.2 %) of the solid mass is participating in the observed isotopic exchange that takes place in phase II of the experiment.

The participation of such a large mass of the strontianite crystal suggests a mechanism of exchange with the crystal interior, rather than just the surface. The implication is that Sr is transported within the freshly precipitated crystal, either as an aqueous species within the pore space of the crystal or in the solid state, or that the outer 4 nm of the sample is dissolved and re-precipitated in place (e.g., Putnis and Mezger, 2004; Putnis, 2015). Solid-state diffusion of cations ($Cd^{2+}$, $Ca^{2+}$) has been documented to occur in calcite at 25°C at a rate on the order of nanometers in weeks (Stipp et al., 1992; Lahav and Bolt, 1964). Lahav and Bolt (1964) estimate a diffusion coefficient of $8 \times 10^{-24} \text{ m}^2/\text{s}$ of $Ca^{2+}$ in calcite at 25°C. If the same diffusion coefficient is assumed for $Sr^{2+}$ transport in strontianite and we apply the simplified diffusion equation of Stipp et al. (1992; Equation 7), which neglects particle shape, a diffusion distance of 2 nm within 8520 min is calculated (i.e., the time span over which $\delta^{88/86}$Sr is observed to stabilize during phase II) as:

$$t = d^2/D \qquad (7)$$
where *t* is time, *d* is distance, and *D* is the diffusion coefficient. On the other hand, if the diffusion coefficient determined by Cherniak (1997) for Sr²⁺ in calcite between 440 and 800°C is extrapolated to 25°C using the activation energy (1.57 × 10⁻³⁶ m²/s), a diffusion distance of only 9 × 10⁻⁷ nm is calculated. The disagreement with the Cherniak (1997) diffusion coefficient may be due to error in extrapolation from high to low temperature (e.g., Gorski and Fantle, 2017). Although it is unknown whether Sr²⁺ in strontianite exhibits a similar rate of diffusion as Ca²⁺ in calcite, the better agreement between the diffusion distance calculated with the Lahav and Bolt (1964) diffusion coefficient and our experimentally calculated 4 nm thickness of isotopic alteration is permissive of a solid-state diffusion process as an explanation for the observed isotopic exchange. It should be noted that the Lahav and Bolt (1964) diffusion coefficient was determined in heterogeneous aqueous-solid systems at low temperature, suggesting it may combine aqueous and solid-state diffusion or dissolution/re-precipitation, compared to the Cherniak (1997) diffusion coefficient, which was measured under anhydrous conditions. As such, the Lahav and Bolt (1964) diffusion coefficient may better represent the conditions of our experiments.

With diffusion occurring at this relatively fast rate, it would nevertheless take ~3960 years to entirely re-equilibrate the strontianite crystals (i.e., for the diffusion front to reach the center of a 2 µm crystal). For a different element it has earlier been suggested that the diffusion of carbon in calcite at temperatures between 250-550°C exhibits a depth-dependence, with a higher diffusion coefficient in the outer-most layers due to a higher density of dislocation pipes and defects (Anderson, 1969). In the case of the experiments conducted in this study, mass balance calculations suggest that about 600 unit cells (or 14 % of the Sr initially dissolved from the seed) re-precipitated on the surface of the crystals during the pH-jump. Diffusion in these outer-most layers therefore may not reflect rates of diffusion in the bulk crystal. The relatively rapid exchange observed in the upper 4 nm of the strontianite crystals could be followed by a slower re-equilibration of the bulk of the crystal,
therefore longer timescales than calculated might be required to reset the isotopic composition of the bulk crystal. Longer-term experiments are required to assess the diffusion coefficient and how it may change over time. Interestingly, a relatively slow rate of diffusion of Sr within the bulk crystal structure implies that the isotopic composition of the fluid will be dictated largely by the isotopic composition of the surface layers of the solid, which may lead to an apparent disequilibrium between the bulk solid composition and the fluid, as postulated by Druhan et al (2015). Given the available data, however, it is not possible to clearly distinguish the individual mechanisms of isotopic exchange, as aqueous diffusion and dissolution/reprecipitation cannot be excluded.

535

4.3 Implications for Sr isotope signatures of natural carbonate minerals

537

The obtained results suggest that in the strontianite-fluid system, isotopic exchange between solid and aqueous fluid proceeds at chemical equilibrium. Similar behavior has been previously observed for Ba isotopes in the witherite-fluid system by Mavromatis et al. (2016b) and for Mg isotopes in the magnesite-fluid system at 150 and 200°C (Pearce et al., 2012). Details on the mechanisms related to the observed isotopic exchange cannot be extracted mainly because the above calculations are essentially based on isotopic composition of the reactive fluid. It can however be inferred that the temporal evolution of the $\delta^{88/86}\text{Sr}_{\text{fluid}}$ is not a result of solely a surface process such as adsorption/desorption phenomena that have been earlier observed in some metal oxides and hydroxides (e.g. Barling and Anbar, 2004; Wasylenki et al., 2015). Note here that the $\delta^{88/86}\text{Sr}_{\text{fluid}}$ achieves a value of 0.4‰ at the end of phase II and does not evolve to lower values, although the bulk solid isotopic composition is ~0.15‰, suggesting that a highly porous structure in the freshly precipitated solid cannot explain the isotopic shift of the $\delta^{88/86}\text{Sr}_{\text{fluid}}$ value. Similar to the witherite-fluid system (Mavromatis et al., 2016b), the results of this study are likely explained by ion mobility below

538

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540

541

542

543

544

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548

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551
the crystal surface, as has been measured by Stipp and co-workers for a number of anions and cations ($Cd^{2+}$, $Zn^{2+}$, $Na^{+}$, $K^{+}$ and $Cl^{-}$) near the calcite surface (Stipp et al., 1992; 1996; 1998).

In these studies, ion exchange was assumed to extend up to 10 atomic layers below the crystal surface, which is in accordance with the ~7-8 unit cells that we estimated in this study for strontianite. However, the mechanism by which the ions are transported remains unclear.

Isotopic re-equilibration is well known to occur at high temperatures. It has been documented experimentally for Mg isotopes in magnesite (Pearce et al., 2012), and in biogenic Mg-calcite (Riechelmann et al., 2016). At low temperature, isotopic exchange has been observed in highly reactive hydrous Mg-carbonate minerals (Mavromatis et al., 2012a; 2015a; Shirokova et al. 2013), hydrous Mg-sulphates (Li et al., 2012), calcite (Avrahamov et al., 2013; Mozeto et al., 1984), and redox active Fe-bearing minerals such as goethite, and (Handler et al., 2009). The most important outcome of the present study, however, is the observed continued exchange of Sr that alters the isotopic composition of the strontianite over time. This has also been observed for witherite, and has major implications for the interpretation of growth conditions of carbonates in natural archives, and the use of these archives as paleoproxies. Considering that natural carbonate archives tend to stay in contact with a fluid that differs in composition from the growth fluid from which they precipitated their isotopic signals may be significantly reset over time. This general behavior is of great interest for all carbonates phases, in particular for calcite and aragonite that are the most abundant carbonate minerals, biogenic or abiogenic, in Earth's surface environments.

Accordingly, Fantle and DePaolo (2007) studied Ca isotopes in calcite recovered from an IODP core, where Ca isotope re-equilibration between solid and fluid was postulated. Further experimental work is necessitated in order to unravel the mechanisms and the extent of $Me^{2+}$ isotopic re-equilibration in carbonate minerals at temperatures encountered near the Earth's surface for both constituting elements and traces/impurities. The potential secondary resetting of Sr isotope signals in the Sr-endmember carbonate mineral, strontianite, hints on limitations
for the straightforward use of stable Sr isotopes in carbonate minerals as environmental or
578
forensic proxies. On the other hand, the improved understanding of such a highly dynamic Sr
579
isotope exchange behavior between solid and fluid at chemical equilibrium conditions may
580
open up new proxy approaches for estimating time-resolved re-setting periods and/or
581
explanations for zoning structures of carbonate minerals.
582

583

5. Conclusions
84

585

In this study we examined the behavior of stable Sr isotopes during the interaction of
586
strontianite with an aqueous phase. The obtained results suggest that under isotopic
587
equilibrium conditions the Sr isotope fractionation between strontianite and aqueous fluid is
588
rather small but measurable and close to -0.05 ‰. This finding is in agreement with the
589
relatively smaller Sr-O bond length in the aqueous Sr ion compared to that in strontianite. In
590
contrast, during strontianite precipitation a preferential uptake of the ⁸⁶Sr isotopomer in the
591
solid phase is observed, which is kinetically driven and is in overall agreement with the
592
behaviour of alkali earth metals during their incorporation in carbonate minerals.
593

The obtained results further suggest that at chemical equilibrium conditions, a
594
continuous exchange of Sr isotopes between solid and fluid takes place and affects at least 7-8
595
unit cells below the mineral surface. This observation is consistent with that observed
596
previously for Ba isotopes in the witherite-fluid system and Mg isotopes in the magnesite-
597
fluid system, with isotopic exchange extending up to ~10 unit cells below the crystal surface.
598
If such a process takes place in natural aqueous settings, it likely has major implications for
599
the secondary change of isotopic signatures of natural carbonate minerals, in particular
600
considering that the time scales for a solid-fluid contact are significantly larger compared to
601
the present experimental approach.
602

603
604 Acknowledgments

605 We acknowledge the assistance of Ana Kolevica for chemical preparation of the samples and
606 their measurements at the GEOMAR mass-spectrometer facilities in Kiel, Germany and of
607 Alain Castillo (GET, France) for his support with BET measurements. We are thankful to
608 Bettina Purgstaller and Andre Baldermann for their support with SEM and chemical analyses.

609 For their illuminating comments during the preparation of this manuscript we wish to thank
610 our colleagues Florian Konrad and Cyrill Grengg. This work benefited from the constructive
611 comments of Christopher R. Pearce and two anonymous reviewers. This study was financially
612 supported by DFG Forschungsgruppe 1644, CHARON (IM44/10-1) and NAWI Graz.

613

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<table><caption>Table 1: Strontium concentration, Sr isotope composition, pH and saturation degree with respect to strontianite in fluid samples and stable Sr isotope composition of solids and reference materials analyzed in this study for experiment 1. $r_p$: growth rate of strontianite calculated according to equation (3). The sample $SrCl_2$ – synthesis refers to composition of the fluid used for the synthesis of strontianite.</caption><thead><tr><th>Elapsed Time (min)</th><th>Sr (mM)</th><th>pH</th><th>Ω<sub>strontianite</sub></th><th>Alkalinity (mM)</th><th>R<sub>p</sub> (mol/m<sup>2</sup>/s)</th><th>δ<sup>88/86</sup>Sr (%)</th><th>2sd</th><th><sup>87/86</sup>Sr</th></tr></thead><tbody><tr><td>0</td><td></td><td>6.00</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1500</td><td>5.08</td><td>5.90</td><td>1.16</td><td>7.51</td><td></td><td>0.191</td><td>0.005</td><td>0.708541</td></tr><tr><td>2880</td><td>5.08</td><td>5.88</td><td>1.12</td><td>7.59</td><td></td><td></td><td></td><td></td></tr><tr><td>4260</td><td>4.86</td><td>5.94</td><td>1.20</td><td>7.33</td><td></td><td>0.200</td><td>0.003</td><td>0.708548</td></tr><tr><td>5820</td><td>4.96</td><td>5.92</td><td>1.20</td><td>7.54</td><td></td><td></td><td></td><td></td></tr><tr><td>7140</td><td>4.89</td><td>5.91</td><td>1.12</td><td>7.32</td><td></td><td>0.193</td><td>0.008</td><td>0.708537</td></tr><tr><td>8700</td><td>4.87</td><td>5.91</td><td>1.15</td><td>7.53</td><td></td><td>0.198</td><td>0.004</td><td>0.708546</td></tr><tr><td>10080</td><td>4.72</td><td>5.96</td><td>1.24</td><td>7.47</td><td></td><td></td><td></td><td></td></tr><tr><td>11580</td><td>4.87</td><td>5.94</td><td>1.23</td><td>7.54</td><td></td><td></td><td></td><td></td></tr><tr><td>12540</td><td>4.76</td><td>5.93</td><td>1.18</td><td>7.58</td><td></td><td>0.187</td><td>0.011</td><td>0.708538</td></tr><tr><td>12660</td><td>4.29</td><td>6.15</td><td>1.55</td><td>6.43</td><td>1.5E-09</td><td>0.167</td><td>0.004</td><td>0.708544</td></tr><tr><td>12780</td><td>3.27</td><td>6.35</td><td>1.41</td><td>4.57</td><td>3.0E-09</td><td>0.202</td><td>0.005</td><td>0.708543</td></tr><tr><td>12840</td><td>2.27</td><td>6.81</td><td>2.07</td><td>3.17</td><td>5.5E-09</td><td>0.227</td><td>0.002</td><td>0.708540</td></tr><tr><td>12930</td><td>0.76</td><td>7.50</td><td>2.71</td><td>2.41</td><td>5.1E-09</td><td>0.298</td><td>0.010</td><td>0.708540</td></tr><tr><td>13020</td><td>0.47</td><td>7.64</td><td>2.22</td><td>2.28</td><td>9.5E-10</td><td>0.508</td><td>0.003</td><td>0.708540</td></tr><tr><td>13380</td><td>0.27</td><td>7.84</td><td>1.83</td><td>2.08</td><td>1.7E-10</td><td>0.590</td><td>0.004</td><td>0.708540</td></tr><tr><td>14340</td><td>0.21</td><td>7.96</td><td>1.59</td><td>1.71</td><td>1.8E-11</td><td>0.622</td><td>0.003</td><td>0.708547</td></tr><tr><td>15960</td><td>0.17</td><td>8.00</td><td>1.13</td><td>1.36</td><td>7.7E-12</td><td>0.597</td><td>0.004</td><td>0.708541</td></tr><tr><td>17280</td><td>0.17</td><td>8.05</td><td>1.16</td><td>1.21</td><td>7.8E-14</td><td>0.527</td><td>0.002</td><td>0.708744</td></tr><tr><td>18720</td><td>0.18</td><td>7.93</td><td>0.93</td><td>1.22</td><td></td><td>0.538</td><td>0.007</td><td>0.708539</td></tr><tr><td>20100</td><td>0.23</td><td>7.91</td><td>1.07</td><td>1.16</td><td></td><td>0.475</td><td>0.009</td><td>0.708704</td></tr><tr><td>21540</td><td>0.22</td><td>7.89</td><td>1.05</td><td>1.26</td><td></td><td>0.428</td><td>0.008</td><td>0.708534</td></tr><tr><td>24420</td><td>0.19</td><td>7.98</td><td>1.04</td><td>1.15</td><td></td><td>0.369</td><td>0.003</td><td>0.708545</td></tr><tr><td>25860</td><td>0.14</td><td>8.10</td><td>1.02</td><td>1.14</td><td></td><td>0.387</td><td>0.006</td><td>0.708699</td></tr><tr><td>Strontianite seed</td><td></td><td></td><td></td><td></td><td></td><td>0.145</td><td>0.003</td><td>0.708542</td></tr><tr><td>Strontianite after dissolution</td><td></td><td></td><td></td><td></td><td></td><td>0.167</td><td>0.004</td><td>0.708542</td></tr><tr><td>Strontianite final</td><td></td><td></td><td></td><td></td><td></td><td>0.154</td><td>0.002</td><td>0.708542</td></tr><tr><td>SrCl<sub>2</sub> - synthesis</td><td></td><td></td><td></td><td></td><td></td><td>0.154</td><td>0.013</td><td>0.708543</td></tr></tbody></table>

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<figure><img src="image_2.png" /></figure>

902

903 Figure 1: Scanning electron microscopy images of strontianite seeds (A) and strontianite

904 collected at the end of the experimental run (B). No significant changes in the shape and

905 surface texture of strontianite occurred during the course of the experiment.

906
<figure><img src="image_3.png" /></figure>
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Figure 3

<figure><img src="image_4.png" /><figcaption>Fig. 3: Temporal evolution of Sr concentration (closed symbols) and pH (open symbols) in the two replicate experimental runs. The dashed gray line indicates the transition in bubbling from CO₂ to atmospheric air. Analytical uncertainty is smaller than symbol size.</figcaption></figure>

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921 Figure 4

922

<figure><img src="image_5.png" /><figcaption>Figure 4: Temporal evolution of δ<sup>88/86</sup>Sr values of Sr ions in the reactive fluid. The white points represent the δ<sup>88/86</sup>Sr value of the strontianite in the reactor. Analytical uncertainty is included in the symbol size.</figcaption></figure>

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<figure><img src="image_6.png" /></figure>

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937
938

Figure 5: $\delta^{88/86}\text{Sr}_{\text{fluid}}$ values (■) plotted as a function of the molar fraction of Sr precipitated as strontianite. (□): $\delta^{88/86}\text{Sr}_{\text{SrCO}_3}$ values of the solid phase. The dashed lines indicate the theoretical evolution of the isotopic composition of the cumulated solid phase, whereas the dotted line indicates the instant isotopic composition of the precipitating solid. The fractionation factor used for both models, Rayleigh and closed system, is $\alpha = 0.99985$.