Isotope exchange rates in dissolved inorganic carbon between 40 °C and 90 °C

Journal Pre-proofs Isotope exchange rates in dissolved inorganic carbon between 40°C and 90°C Andreas Weise, Tobias Kluge PII: DOI: Reference:

S0016-7037(19)30610-6 https://doi.org/10.1016/j.gca.2019.09.032 GCA 11456

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Geochimica et Cosmochimica Acta

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30 November 2018 13 September 2019 18 September 2019

Please cite this article as: Weise, A., Kluge, T., Isotope exchange rates in dissolved inorganic carbon between 40°C and 90°C, Geochimica et Cosmochimica Acta (2019), doi: https://doi.org/10.1016/j.gca.2019.09.032

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Isotope exchange rates in dissolved inorganic carbon between 40°C and 90°C Andreas Weisea, Tobias Klugea,b,* a Institute

of Environmental Physics, Heidelberg University, Im Neuenheimer Feld 229, 69120

Heidelberg, Germany b Heidelberg

Graduate School of Fundamental Physics, Heidelberg University, Im

Neuenheimer Feld 227, 69126 Heidelberg, Germany

submitted to Geochimica et Cosmochimica Acta 30.11. 2018

Running head: Isotope exchange rates in dissolved inorganic carbon Keywords: clumped isotopes, oxygen isotope ratios, re-equilibration, rate constants, DIC, exchange time

1

Abstract Carbonate minerals are normally closely related to the stable and clumped isotope composition of the parent solution and are often assumed to record the equilibrium conditions in these proxies. Variations in e.g., temperature, pH or salinity lead to changes in the dissolved inorganic carbon (DIC) composition and to temporary deviations from expected isotopic equilibrium values. The exchange rate, at which the new equilibrium of stable and clumped isotopes is reached, has only been assessed experimentally for clumped isotopes between 5°C and 25°C and for δ18O up to 40°C. In this study the δ18O and Δ47 evolution in the DIC pool of 0.1 molar sodium bicarbonate solutions at pH 8 and various temperatures (40°C, 55°C, 70°C, 90°C) was examined. At time intervals corresponding to the evolution of the DIC, a quantitative and instantaneous precipitation of the DIC was accomplished by adding strontium chloride and sodium hydroxide solutions. As the δ13C of the SrCO3 precipitates was constant and no significant non-first order trend was observed in Δ47, δ18O and Δ47 values could be simply fitted with an exponential approach to isotopic equilibrium. The temperature dependence of the rate constants was evaluated with the Arrhenius equation. The resulting rate constant based on the combined data points from δ18O and Δ47 follows as

(

k (T) [𝑚𝑖𝑛 ―1] = exp ( ― 1.00 ± 0.15)•104 ∗

)

1 + (29 ± 4) 𝑇

The inferred exchange rate constants for Δ47 are of the same order of magnitude as those of the oxygen isotopes and show a similar temperature dependence in the investigated temperature range. Our experimental results suggest that the isotopic equilibration of DIC in a solution with pH<10 and elevated temperatures is rapid (at 70°C: 4.5 min, at 90°C: 36 s for 99% equilibrium) and that even in the case of short-term disturbances an equilibrated DIC

2

composition is very likely for solutions in the diagenetic temperature range above 100°C. In contrast, it is important to consider the generally long equilibration times at low temperatures (e.g., 2-6 days at pH 8.0-8.5 and 0°C) and, in particular, at higher pH (e.g., >100 days at pH 11 and 0°C).

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1. Introduction Mineral formation has the ability to archive the chemical and physical condition of the parent solution. For example, carbonate minerals that form in inorganic processes or are precipitated as supporting structure of living organisms can give valuable information about temperature, pH and salinity of the past ocean (e.g., Emiliani and Edwards, 1953; Palmer et al., 1998; Veizer et al., 1999) or about paleo-climatic changes on the Earth surface (e.g., Winograd et al., 1992; Wang et al., 2008). An implicit requirement is that the physical and chemical information of the parent solution is transferred in a reconstructable way into the mineral. Partitioning of trace elements or fractionation of isotopes with respect to carbonates is relatively well investigated (e.g., Fairchild and Treble, 2009; Watkins et al., 2014) and understood in case of equilibrium or near-equilibrium mineral formation. However, it is inherently difficult to extract quantitative and reliable data from minerals that formed under disequilibrium conditions. Examples are carbonates in the alkaline milieu or in the cave environment where isotopic equilibrium is sometimes not achieved prior to mineral formation (e.g., Kluge and Affek, 2012; Falk et al., 2016). For example, drip water in caves degasses within seconds and is directly initiating super-saturation and speleothem formation, whereas isotopic equilibration in the DIC takes several orders of magnitude longer (depending on pH and cave temperature; e.g.; Dreybrodt and Scholz, 2011; Dreybrodt et al., 2016). Similarly, CO2 enters rapidly alkaline solutions with pH >10 causing almost instantaneous formation of carbonate. However, the equilibration in the DIC-H2O system acts in this pH range on time scales on the order of 100 min (pH 10, 40°C) to ~106 min (pH 12, 0°C) (Uchikawa and Zeebe, 2012), leading to disequilibrium signals in rapidly formed carbonate minerals. Rate constants and equilibration times have been determined in particular relation to isotope exchange reactions during hydration and hydroxylation (see section 2.1). Exemplary equilibration times were determined e.g., by Beck et al. (2005) who investigated the isotope

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fractionation in the carbonic acid system at 15, 25 and 40°C and found time scales of 1440, 540 and 120 min, respectively, for HCO3- dominated solutions at pH 8.0-8.7; ~6.6•104 min (25°C) and ~1.6•104 min (40°C) for CO32- dominated solutions at pH>11. Based on these studies the isotope exchange time scale for δ18O can be calculated, however, direct experimental confirmation is limited to a narrow temperature range of up to 40°C. Little is known about the equilibration behavior at higher temperatures, which is implicitly necessary for meaningful laboratory experiments e.g., related to high-precision calibration studies or for the correct interpretation of natural samples at the elevated temperature range. The emergence of novel proxies, such as carbonate clumped isotopes (e.g., Eiler, 2011), also require an assessment of proxy-related reaction rates and equilibration times of the DIC with the solution and within the DIC, following changes in the controlling conditions (e.g., solution temperature). Carbonate clumped isotopes refer to carbonate molecules that contain both 13C and 18O (Eiler, 2007). Their abundance relative to a pure stochastic distribution is almost completely governed by temperature in the case of equilibrium mineral formation and is mass-spectrometrically quantified as Δ47 (Wang et al., 2004; Cao and Lio, 2012). The Δ47 value increases with decreasing temperature and has a temperature sensitivity of about 0.003 ‰/°C at Earth surface conditions. If the reactivity of 18O bound to 13C is significantly influenced by the heavier 13C (relative to the normally dominating 12C), longer equilibration times for clumped isotopes and lower reaction rate constants are to be expected. So far, no difference was observed for clumped isotopes in CO2 (Affek, 2013; Clog et al., 2015). First indications for a slightly different, kinetically driven behavior of both isotope proxies was found during equilibration of DIC solutions due to a temporal decoupling of related δ18O and Δ47 values on the equilibration path (Staudigel and Swart, 2018). The Δ47 values transiently deviated in their study from the unidirectional approach towards

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equilibrium and proceeded to an opposite direction towards even stronger disequilibrium during the early equilibration phase. The difference in equilibration rates of δ18O and Δ47 was limited and observed to be less than 2% despite this significant non-first order temporal evolution. In the following we investigate in detail the exchange rate for δ18O and Δ47 equilibration in DIC using bicarbonate solutions that were driven out of an initial thermal, isotopic and chemical equilibrium state by increasing the temperature of the solution almost instantaneously to a new steady state value (between 40°C and 90°C). The solution was sampled at adequate time steps by rapid and quantitative precipitation of the DIC as SrCO3, which were analyzed for oxygen and clumped isotopes. We compare our new experimental data with existing equilibration rates for δ18O in carbonates and the model of Uchikawa and Zeebe (2012).

2. Re-equilibration experiments 2.1. Theoretical background Clog et al. (2015) found that the δ18O and Δ47 values of dissolved CO2 have similar equilibration rates during the exchange of liquid water and CO2. This only relates to the gaseous and dissolved CO2, but the equilibration rates for δ18O and Δ47 in the DIC system could also be similar if no additional rate limiting steps or kinetic processes were important. In a recent study, Staudigel and Swart (2018) observed a non-first order behavior of clumped isotopes during the equilibration process. A kinetic difference between oxygen bound to 12C relative to 13C is proposed as an explanation for the non-first order behavior. Nonetheless, Staudigel and Swart (2018) expect the difference in equilibration rates to be minor (below 2%). For a theoretical assessment we start with the model of Uchikawa and Zeebe (2012) for δ18O. The model describes the equilibration of 18O via the CO2 hydration and CO2 6

hydroxylation (e.g. Zeebe and Wolf-Gladrow, 2001) and can be summarized in the following equations: the temporal evolution of 18ε(DIC-H2O) 18ε(t)=18

ε eq + (18 ε initial-18 ε eq)* exp(-t/τ)

(1)

with 1 𝜏

= 0.5 ∗ (𝑘 +2 + 𝑘 +4 ∗ [𝑂𝐻 ]) ∗ (1 + ―

𝐶𝑂2

𝐶𝑂2

𝐶𝑂2 2 1/2

[ ] ― {1 + ∗ [ ] + ( 2 3

𝑆

𝑆

𝑆

)}

)

(2)

k+2 is the rate constant for the hydration (CO2 + H2O ↔ H2CO3; k+2), k+4 for the hydroxylation (CO2 + OH- ↔ HCO3-; k+4), S is the sum of H2CO3, HCO3- and CO32-, τ refers to the equilibration time constant. For the following discussion we define the isotope equilibration time τ99 as time period where 99% equilibrium is achieved in the DIC (τ99=-ln(0.01)*τ) and refer to this parameter when not indicated otherwise. Note that both rate constants k+2 and k+4 were experimentally determined at relatively low temperatures of 0-38°C and 0-40°C, respectively (Pinsent et al., 1956). Whereas k+4 showed a temperature-dependent change consistent with the Arrhenius equation, potentially allowing for limited extrapolation to higher temperatures, k+2 diverges from a simple Arrhenius relationship (Pinsent et al., 1956) restricting interpretations beyond previous experimental temperatures. In contrast to Uchikawa and Zeebe (2012) we calculated the DIC speciation and the equilibration time τ using the values of the different DIC fractions of Millero et al. (2007) as they cover a broader temperature and salinity range. The rate constants k+2 and k+4 were calculated according to Pinsent et al. (1956). Model-based values for τ99 (the time period for reaching 99% equilibrium) were determined for pH 4-12 and temperatures ranging from 0 to 110°C (Fig. 1). τ99 reflects a generally fast equilibration at low pH values given higher concentrations of CO2,aq that can be converted to HCO3- via hydration and hydroxylation - and much slower equilibration at higher pH values, where the CO2,aq fraction is very small or negligible. Importantly, patterns also shift with temperature (at fixed salinity, Fig.1). 7

Extrapolating to high temperatures, τ99 has rather constant values at 80°C over a large pH range from 4 and 10. At 100°C and higher (that could be achieved under pressurized conditions, e.g. in subsurface diagenetic fluids) τ99 appears to be apparently smaller in the pH range 6-10 compared to pH<6 following equation (2). This inversion with apparently faster equilibration at pH 6-10 compared to lower pH at temperatures above 100°C illustrate the problem that currently existing data do not allow for reliable extrapolation of Eq.2 to high temperatures. Furthermore, the divergence of k+2 from the Arrhenius relationship calls for very cautious application of eq. (2), whereas the Uchikawa and Zeebe model (2012) is independent of the experimental data. Beyond investigating equilibration rate constants at higher temperatures, the knowledge of the rate constants over a larger temperature interval could help in improving the precision of the current data set and for assessing potential differences between values determined only for δ18O and those of clumped isotope Δ47. Although we only assessed the influence of temperature on the equilibration rate constant, it has to be kept in mind that salinity changes can have substantial influence on equilibration times (Fig. 2). For example, at pH 8 and 20°C the equilibration time τ99 varies by a factor of 3 between zero salinity and ~60 PSU (practical salinity units). This is due to a shift in the DIC speciation with changing salinity, e.g., leading to an increased CO32- fraction at the same pH but elevated salinity. 2.2 Experimental methods The experimental setup consists of a well-controlled heated aluminum plate that hosts the reaction vessels and of a N2-flushed glove bag in which the whole experiment is placed (Fig. 3). The experimental approach (flow chart in Fig. 4) has been designed similar to the experiments of Uchikawa and Zeebe (2012) and Beck et al. (2005). In the first step all chemicals (SrCl2 , NaHCO3 and NaOH, masses see Table 1) were weighed and stored in 2 ml Eppendorf vessels, SrCl2 in 10 ml glass containers sealed with polypropylene lids. The

8

chemicals were transferred as dry powder into the glove bag. In addition, a glass beaker containing de-ionized water filled to a height of approximately 1.5 cm was positioned inside the glove bag. This shallow water level was selected to allow reasonably fast degassing of atmospheric gases (other than N2), in particular, residual CO2. The glove bag was then purged with N2 and at least 5 times renewed within 2 days to ensure an almost pure N2 atmosphere (with only minor traces of water vapour and CO2). The water in the beaker was passively degassed during these two days to ensure that the water was free of residual CO2. Using the equation of Carslaw and Jaeger (1959) for the exponential time constant td of the diffusive exchange in a water body (D is the diffusion constant, calculated after Rutten, 1992 and d the water depth) td=(2d)2/(π2 D)

(3)

we obtain a decay time of around 13 hours at room temperature for the glass beaker with 1.5 cm of pure water. After degassing of the deionized (DI) water for at least two days the NaHCO3 solution was prepared by adding two milliliters of the degassed water to the NaHCO3 powder. The NaHCO3 solution was then stored another two days in closed Eppendorf vessels to establish internal isotope equilibrium at room temperature (23°C). In the next step a 0.1 molar NaOH solution was produced using the degassed de-ionized water. Two milliliters of this NaOH solution was then added to the SrCl2 powder. The aluminum frame on the heat plate was heated to the specific experiment temperature prior to insertion of the solution. The used heat plate (Neolab D-6010) provides a temperature stability of ± 2°C. Once the temperature was reached, the NaHCO3-filled Eppendorf vessels were placed in the aluminum block, equilibrated for pre-determined time periods, and sampled accordingly. The pH value of the solution was only measured before the equilibration process (pH ~8) and not controlled afterwards. A small shift to lower pH values was expected during the experiment (to a maximum of 0.5 pH units at 90°C) due to

9

temperature-driven changes in the CO2 dissociation constants that influence DIC speciation and pH. The lower pH was taken into account in the theoretical assessment, but has been disregarded in the experimental evaluation. More frequent pH analyses were abandoned to avoid a reduction in the temporal resolution. Note that the equilibration times at higher temperature are on the order of only a few tens of seconds. After selected equilibration time steps the NaHCO3 solution was quickly removed from the aluminum block and immediately poured into the SrCl2 + NaOH solution inside the glove bag, leading to an instantaneous precipitation of SrCO3. The SrCO3 was then vacuum filtrated from the solution using a waterjet-pump attached to the filter setup and filter paper with 0.6 µm pore size. After filtration the filter papers were air dried for one to two days. Filters were dried outside the glove bag, as preliminary tests did not reveal any differences between the drying procedure within or outside the glove bag. 2.3. Sample treatment for carbonate clumped isotope analysis The sample treatment follows the method described in Kluge et al. (2015). Due to the higher molar mass of strontium compared to calcium, more carbonate powder (50-100% more) was used as compared to pure calcite. SrCO3 samples of 3-5 mg were inserted into a reaction vessel that allowed to store 105% phosphoric acid (~ 1 ml per sample) separate from the carbonate sample. The reaction vessels were evacuated for 20 min and heated to 90°C in a temperature-controlled aluminum frame on a heat plate. Before acid digestion, the pressure reached 10-1-10-2 mbar that is slightly above the baseline pressure of the empty extraction line of 10-3 mbar. This slightly increased pressure relative to the baseline was caused by water vapour desorbing from the reaction vessel walls and connectors and/or due to degassing of water vapour and residual atmospheric gases from the phosphoric acid. The SrCO3 aliquots were reacted with ortho-phosphoric acid for 10 min at 90°C in a stirred reaction vessel. The emerging CO2 was continuously collected with a liquid-N2 cooled trap. The product CO2 was

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cleaned using a procedure initially described by Dennis and Schrag (2010). Volatile gases were then cryo-distilled from this trap at liquid nitrogen temperature. Subsequently, water was separated from the remaining gas using a dry-ice ethanol cooled glass trap. The water-free CO2 gas was then passively passed through silver wool and another trap densely packed with Porapak Q (filled length: 13 cm, inner diameter: ~8 mm) held at -35 °C. The cleaned CO2 gas was directly transferred to the dual inlet system of the mass spectrometer and was analyzed immediately or within a few hours. 2.4. Mass spectrometric analysis Mass spectrometric measurements were performed on a Thermo Scientific MAT 253 Plus with a baseline monitoring cup on m/z 47.5 and 1013Ω resistors on m/z 47-49. The analysis protocol followed the procedures described by Huntington et al. (2009) and Dennis et al. (2011) (8 acquisitions with 10 cycles each, integration time for each cycle: 26 s). Each acquisition included a peak centre, background measurements and an automatic bellows pressure adjustment aimed at a 6 V signal at mass 44. The first acquisition additionally included a recording of the sample m/z 18 (water vapour residual) and m/z 40 signal (Ar – indicator for air remainder). For each cycle the baseline signal on m/z 47.5 was measured simultaneously to the actual sample and reference gas analysis on m/z 44-49. For pressurebaseline correction high-voltage peak scans were manually taken at the beginning and/or end of a measurement run (integration time 0.5 s, step size 0.0005 kV). The sample gas was measured against an in-house reference gas standard (Oberlahnstein: δ13C = - 4.42 ‰ VPDB, δ18O = -9.79 ‰ VPDB). For establishing an absolute reference frame and for interlaboratory comparability we regularly analyzed community-wide distributed carbonates (ETH1-4, Meckler et al., 2014), Carrara Marble, NBS 19, as well as equilibrated (5°C, 90°C) and heated gases (~1000°C). 2.5. Data evaluation

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All data, with the exception of one sample, were evaluated with the Easotop software of John and Bowen (2016) and manually cross-checked. In Easotop a non-linearity correction (e.g., Huntington et al., 2009) was applied based on standards with varying δ47 but constant Δ47 values (e.g., ETH1 and ETH2, Meckler et al. 2014; four in-house laboratory precipitates). One sample (Sr40-11) could not be evaluated with Easotop due to a short reference period not allowing for non-linearity correction and was only evaluated manually. For manual data evaluation a PBL correction was applied that takes into account that the signal on m/z 47 is additionally influenced by a negative background potentially induced by secondary electrons and broadening of the m/z 44 peak (He et al., 2012; Bernasconi et al., 2013; Fiebig et al., 2015). The background was determined via high-voltage scans and adjusting the m/z 44 signal by increasing or decreasing the bellows pressure. The working pressure for the measurement run was typically about 22 mbar for a m/z 44 signal of 6000 mV. As the δ47 values only varied slightly between the SrCO3 samples of one equilibration experiment and to a limited degree amongst all samples (maximum: 5‰ from the mean) and as the slope of the applied non-linearity correction was mostly in the range of 10-4 to 10-3, the observed Δ47 values and the differences between them are at best marginally influenced by the method of evaluation. The empirical transfer function (ETF) was determined based on the non-linearity corrected Δ47 values and uses carbonate standards, heated and equilibrated gases with agreed Δ47 values as reference (Dennis et al., 2011). For establishing an equilibrated gas reference frame heated gases (~1000 °C) and water-equilibrated gases (5 °C, 25°C, 90°C) were prepared and measured. Carbonate standards (In house marble “Richter”, NBS 19, ETH1ETH4, laboratory precipitates at 19.8°C and varying bulk composition) were measured regularly for inter-laboratory comparability and standardisation (Meckler et al., 2014; Müller et al., 2017).

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For both, Easotop and the manual evaluation, updated isotope parameters following Brand et al. (2010) were used for the Δ47 calculation which have been found to reduce scatter and increase consistency (Daëron et al., 2016; Schauer et al., 2016).

3. Results 3.1. Re-equilibration experiments – δ13C values The experimental results for δ13C, δ18O and Δ47 are summarized in Table 2 with raw data, ETFs, correction intervals, etc. provided in the supplementary data file. Displaying the δ13C value against time for every experiment shows that the δ13C value is constant and has no temporal evolution during any experiment (Fig.5). As there are no significant temporal δ13C variations, the Δ47 evolution with time is largely driven by oxygen isotope exchange between DIC and H2O.. Slightly differing kinetic constants of 16O12C18O and 16O13C18O may nevertheless lead to subtle differences between the evolution of δ18O and Δ47. In addition to the temporal constancy, δ13C values show no dependence on the mass of the precipitated SrCO3 (Fig.6), despite an estimated precipitation efficiency of about 50% and slightly higher yields in later experiments. An examination for δ18O and Δ47 relative to the precipitated mass also shows no correlation (Supplementary Fig. S1). The medium precipitation efficiency can mainly be explained by the filtration method. Sample powder could have been partially lost during the filtration process related to vacuum pumping. A change of the filtration process (reduced vacuum, lower pressure gradient) and the use of finer filters provided an overall increase in the recovery efficiency in the last experiments. The δ13C values of the precipitated SrCO3 can also be compared to the measured δ13C of the pure NaHCO3, which was used for preparing the DIC solutions (-5.2±0.4 ‰, Fig.6). The δ13C values of the individual SrCO3 experiments scatter around this starting value. The majority lies within the 2 σ-area of the expected value. A slight overrepresentation of more

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positive δ13C values can be observed which could be explained by limited degassing effects. A contamination with ambient air can be excluded as it would tend towards more negative values. The atmospheric δ13C value has decreased in the past decades due to fossil fuel combustion, is now below -8 ‰ (e.g., Keeling et al., 2005) and continues to decrease. 3.2. Re-equilibration experiments – δ18O and Δ47 values The δ18O and Δ47 values generally show a clear temporal evolution towards an equilibrium value (Figs. 7 and 8) which were fitted as follows: δ18O(t) = δ18Oeq + (δ18Oini-δ18Oeq) e-kt

(4)

Δ47(t) = Δ47,eq + (Δ47ini-Δ47,eq) e-kt

(5)

These equations describe a limited exponential decay, where δ18Oini and Δ47,ini are the isotopic starting points, δ18Oeq and Δ47,eq the equilibrium values and k the rate constant [1/min]. The measured δ18O and Δ47 data for the different temperatures are given in Table 2. The fit parameters related to equations (4) and (5) and R2 values are given in Table 3 and 4. One should note that the first measurement points in the equilibration runs, which were taken before the solution was heated, do not represent room temperature (~23°C) in Δ47. We assumed SrCO3 to have an acid fractionation factor similar to calcite of 0.069 ‰ and with that measured a starting Δ47 value of 0.75 ± 0.01‰ (n=17). This corresponds to a temperature of ~ 8 ± 3°C using the calibration of Kluge et al. (2015). A certain fraction of CO2 that may have been still dissolved in the initial solution could lead to a higher apparent Δ47 value and consequently lower temperature. Water-equilibrated gasphase CO2 has a much higher Δ47 value compared to the Δ47 value of CO2 produced by acid-reaction from carbonate minerals that formed at the same temperature (e.g., at 20°C 0.951 ‰ vs. 0.712 ‰ for carbonate; Wang et al., 2004; Kluge et al., 2015). However, the good agreement between the δ13C value of NaHCO3 and SrCO3 (Fig.6) suggests a minor contribution of residual CO2 and points toward 14

rapid mineral formation as main reason for the observed offset. Rapid mineral formation is expected to cause positive offsets in Δ47 relative to the equilibrium calcite on the order of 0.01 ‰ at pH 8 (Hill et al., 2015; Watkins and Hunt, 2015), explaining at least partially the too low apparent Δ47-based temperature of the initial solution. The reaction vessel and the solution need a certain time period to heat to the experimental temperature. In relation to this heat-up time we applied an experimentally determined correction for setting the starting point t=0 s, at which the solution reached the experimental temperature. The thermal inertia of the used thermometer and the thermal inertia of the solution-filled Eppendorf vessels were measured for different temperatures (exemplary process shown in Fig. 9). The thermal inertia of the thermometer was then subtracted from the inertia of the solution. Together with the temperature uncertainty of the heating plate (±2°C), we obtained a time lag of the solution in the Eppendorf vessels relative to the insertion into the aluminum block of 2.5-3 minutes. The zero point of the sample evaluation was shifted by 2.5 min for 40°C and 55°C, and 3 min for 70°C and 90°C. Samples with resulting negative times were ignored in the following evaluation and discussion. The end point of each experiment approaches the expected Δ47 value of carbonates for the examined temperature following Kluge et al. (2015) (section 4.1). Therefore, we can conclude that the equilibrium was reached for each experiment.

4. Discussion 4.1. Δ47 temperature relationship of SrCO3 The final data point at each experimental temperature very likely reflects mineral formation from an equilibrated solution. Both δ18O and Δ47 values were generally constant between the last and the preceding sample (Figs. 7, 8). Following eq. (2) the last sample taken corresponds in all cases to sampling times that were multiple times longer than the necessary 15

time for 99% re-equilibration (τ99), confirming a very high likelihood of achieved equilibrium conditions in the solution. Note that the mineral formation proceeded close to the kinetic limit (see e.g., Watkins and Hunt, 2015) due to the rapid SrCO3 precipitation. We assessed the Δ47T relationship and the fractionation factor α(SrCO3-H2O) within the investigated temperature range up to 90°C and the related narrow pH range (8±0.5) relative to the predictions of Watkins and Hunt (2015) for the difference between very slow and rapid mineral formation. We added two temperature reference points (two samples at 5°C and three samples at 23°C) (Table 5) that correspond to SrCO3 precipitation of equilibrated 5°C and 23°C solutions. The 5 and 23°C samples are related to precipitation of degassed commercially available and bottled sparkling water of regional origin. The sparkling water was stored at the two different temperatures for a time span long enough to allow isotopic equilibration and then either degassed using thin film water flow on an inclined plane or sampled directly (details in Weise, 2018). The DIC of the 5 °C and 23°C samples was precipitated by pipetting small ml aliquots of the equilibrated water into a solution of NaOH and SrCl2 sealed in polypropylene bags (Weise, 2018). Shaking of the solution bag caused fast mineral formation which was assumed to be quantitative as only small ml aliquots were added. Subsequent filtration and sample treatment for carbonate clumped isotope analysis followed the same procedures as outlined in section 2. Comparison of the acid-correction free Δ47 values of the strontium carbonates of this study with recent calibration lines (Fig. 10) shows that most samples yield Δ47 values above the calibration lines. Relative to the inorganic Δ47-T relationship of Kluge et al. (2015) the difference is positive and on the order of 0.02‰ (mean: 0.024 ± 0.002 ‰, 1σ) up to 55°C and, including all data points, of 0.014 ± 0.016 ‰ (1σ). The overall difference is not significant, but corresponds well to the predictions of Hill et al. (2014) and Watkins and Hunt (2015) for fast grown calcites at pH 8. Note that mineral growth rate as well as the solution pH is expected to influence the oxygen isotope fractionation 18α(CaCO3-H2O) as well as the Δ47

16

value (Watkins and Hunt, 2015; Daëron et al., 2019), even if the DIC in the solution was in equilibrium. 4.2. Oxygen isotope fractionation between HCO3- and H2O The DIC in our experiments was dominated by HCO3- (contributing 97-98% to the total DIC) due to a solution pH value of ~8. Therefore, we can assess the oxygen isotope fractionation between HCO3- and the DI water that was used to prepare the solutions (δ18Owater: -8.5±0.2‰ VSMOW). For an assessment of the oxygen isotope fractionation potential influences of the relatively long degassing and equilibration periods of the original solutions and potential oxygen isotope exchange with atmospheric water vapor has to be kept in mind. Nevertheless, using the oxygen isotope fractionation factors of O’Neil et al. (1969) or of Zheng (1999) for SrCO3-water and the acid fractionation factor of Sharma and Sharma (1969) (8.8 ‰ at 90°C) yields recalculated water δ18O values of the individual experiments that are within 0.5 ‰ of the average of all equilibrated samples (Table 3). This suggests that the solution preparation only yielded a small or even negligible effect on the water δ18O values and, if at all, affected all experiments in a comparable way. Following the approach of Beck et al. (2005, eq.6 therein) we calculated the oxygen isotope fractionation 18α(HCO3--H2O) by separating the measured fractionation 18α(SrCO3H2O) into the contribution of the different DIC species and the related fractionation factors α. For 18α(CO32--H2O) and 18α(CO2,aq-H2O) we used the values of Beck et al. (2005) and disregarded the small fraction related to 18α(OH--H2O) (contributes <0.5%). Calculated 18α(HCO --H O) 3 2

values yield a relationship with temperature that corresponds well to the

extrapolation of the Beck et al. (2015) data towards higher temperatures up to 90°C (Fig. 11). Small deviations e.g. for 55°C or 90°C could be due to minor variations in the fluid δ18O values during NaHCO3 solution preparation The average deviation of our data from the

17

extrapolated Beck et al. fractionation factor α(HCO3--H2O) (T) is -0.1±0.5‰ and therefore statistically insignificant. 4.3. Equilibration rate constants The determination of equilibration rate constants in this study is based on the assumption of first order (exponential) kinetics for δ18O and Δ47 (eqs. 4, 5). Recently, Staudigel and Swart (2018) discovered a non-first order kinetic evolution of Δ47 in a system where both δ18O and δ13C changed with time. Changes of δ13C are up to 2.5-3 ‰ in the experiments of Staudigel and Swart (2018), whereas they are mostly within uncertainty of the average with no temporal evolution in our experiments (Fig. 5). Maximum differences between the lowest and the highest δ13C data points in the individual experiments are 0.5 ‰ in the 40 and 70°C experiment. Thus, due to the very limited δ13C variations in our experiments we do not expect a non-first order behavior related to δ13C. However, potential transient deviations of Δ47 along the isotopic equilibration path also depend on the specific initial and final δ18O and Δ47 values (Staudigel and Swart, 2018). Even without temperature change (i.e. same initial and final Δ47 value) temporal deviations of the Δ47 value from equilibrium are possible given δ18O values change significantly from an initial value towards equilibrium (e.g., about 20 ‰ in the study of Staudigel and Swart, 2018). δ18O variations were small in our study with 3-5 ‰ within the equilibration time interval, strongly limiting non-first order deviations. Furthermore, applying the model of Staudigel and Swart (2018) to our data also confirms simple first order exponential kinetics for both δ18O and Δ47 and verifies that no transient deviation to more disequilibrium is expected in our study. The 90°C data could not be fitted meaningfully with the model (uncertainty relative to data range too high). In contrast to the experiments of Staudigel and Swart, the scatter of the δ18O and Δ47 values around the first-order exponential curve in the early and intermediate equilibration phase in our study is likely unrelated to the kinetic difference between oxygen bound to 13C 18

instead of 12C. The variability in the intermediate time interval of each experiment may rather be due to small changes related to subtle shifts in pH and DIC speciation following on heating up the solution to the equilibration temperature. An indication for this effect is the timing at which minimum δ18O values are found. It decreases exponentially with increasing experimental temperature. A small contribution of this kind affected both the temporal δ18O and Δ47 evolution in the intermediate time interval and has been considered by removing obviously influenced data points from fitting (see Fig. 8). The equilibration rate constants of Δ47 and δ18O were determined for each temperature separately following eqs. (4) and (5). Both isotope proxies exhibit a change in the rate constant with temperature that follows the Arrhenius equation, i.e. significantly larger k at higher temperatures (Fig. 12). We observed a good agreement between the measured δ18O values and theoretically expected data (Fig. 12) following the model of Uchikawa and Zeebe (2012). In detail, experimental re-equilibration times τ99 are within the range of predicted values for 40- 70°C and are slightly higher at 90°C (Fig.1). The rate constants based on the experimental data suggest a slightly lower temperature dependence compared to the model of Uchikawa and Zeebe (Fig.12). However, the lower experimental slope is mainly influenced by the 90°C data point. All other data points correspond within uncertainty to the predictions. Note that the predicted temporal evolution of δ18O following Uchikawa and Zeebe (2012) is also within uncertainty of the individual measurement points of the 90°C experiment (Fig. 7). The experimental slope of the rate constants versus 1/T should therefore not be overinterpreted and mainly discussed in the context of the determined order of magnitude. For Δ47 the data imply a similar temperature dependence, but due to comparatively large uncertainties in kΔ47 as a result of considerable spread of the individual Δ47 data points as function of time, predicted differences between the rate constants of Δ47 and δ18O on the low % range can hardly be resolved. The high uncertainty of the rate constants at 90°C is partially 19

based on the small difference between starting and end value for Δ47 and δ18O. The finite duration of the heating period (from room temperature to the experiment temperature) of the test solution in the heat block with increasingly faster re-equilibration of both Δ47 and δ18O values make it progressively harder to determine precise values for the rate constants at elevated experiment temperatures. The fits in Fig. 12 yield the following equations and show that at least up to 90°C δ18O and Δ47 have a similar temperature dependence that closely approaches predictions of Uchikawa and Zeebe (2012; kTheory): log10(kΔ47)

= (10.9 ± 2.7) + (-3852 ± 922) * 1/T (R² = 0.8971)

(6)

log10(kδ18O)

= (12.5 ± 0.5) + (-4327 ± 178) * 1/T (R² = 0.9966)

(7)

log10(kTheory) = (15.5 ± 0.4) + (-5306 ± 126) * 1/T (R² = 0.9988)

(8)

In summary, our measured reaction rates do not contradict the model by Uchikawa and Zeebe (2012) and its extrapolation to higher temperature up to 90°C. Therefore, it could be used to determine whether a solution is in equilibrium or not regarding Δ47 and the δ18O. Note that the equations (6-8) are only valid for the used pH value of ~8 and the same low salinity (see Fig.2). 4.4. Implications 4.4.1 Similarity of Δ47 and δ18O rate constants The similarity of the experimentally determined rate constants for Δ47 and δ18O (eq. 6 and 7) corresponds well to comparable observations in DIC at lower temperatures (5-25°C, Staudigel and Swart, 2018) and to gas phase CO2 that has been equilibrated with the aid of traces of water (Affek, 2013; Clog et al., 2015). Even over a larger temperature range from 5°C to 150°C, no significant differences in the equilibration behavior of gaseous CO2 and related rate constants of both isotope proxies are evident (Kalb, 2017). The corresponding observations in both gas phase CO2 and in DIC suggest that the additional 20

13C

in the heavy isotopologue

13C18O16O

(as the main constituent of the measured Δ47) has only a small and hardly measurable

influence on the equilibration rate constants relative to that of δ18O, at least with regard to the investigated temperature range and the currently achievable precision. More quantitatively, Staudigel and Swart (2018) calculated a maximum difference below 2% between the rate constants of Δ47 and δ18O using information from the equilibration trajectories. Note that in contrast to the similarity of the Δ47 and δ18O rate constants in various experiments (this study; Affek, 2013; Clog et al., 2015; Staudigel and Swart, 2018), a kinetic influence of

13C

on the specific equilibration path of Δ47 has been observed in the study of

Staudigel and Swart (2018) with an initial change to more disequilibrium prior to a ‘normal’ exponential approach to equilibrium. We deem this non-first order behavior in the study of Staudigel and Swart (2018) to be mainly visible due to the chosen initial and final δ18O values and its large difference relative to the limited Δ47 variation. In all other equilibration experiments that investigated Δ47 rate constants upon equilibration (Affek, 2013; Clog et al., 2015) the Δ47 difference between initial and final conditions was almost one order of magnitude larger (0.8-1 ‰ vs 0.15‰ in the study of Staudigel and Swart, 2018) whereas δ18O changes were generally small (5-10‰). An exception was an experimental series of Clog et al. (2015) with maximum δ18O changes of ~30‰. However, also there only a simple first-order exponential approach to equilibrium was observed, likely due to the still large Δ47 variation relative to the δ18O change. Although the Δ47 variation in our study is below 0.1 ‰ in the equilibration interval, δ18O changes are also limited and < 4 ‰ in the same interval. Therefore, the small variations in δ18O together with the given uncertainty and the data scatter in the intermediate equilibration intervals do not allow for a more detailed investigation of the kinetic isotope fractionation here. Experiments with explicitly large δ18O variations and at best no difference between initial and equilibrated Δ47 values would be optimal for verifying the magnitude of the kinetic isotope effect as described by Staudigel and Swart (2018).

21

4.4.2 Laboratory experiments Based on this DIC equilibration experiment and the study of related rate constants, we resolved a set of conditions that are pivotal for successful DIC investigation using instantaneous precipitation of SrCO3. Residual dissolved CO2 in the solution could cause deviations from expected carbonate isotope values. In our experiments the SrCO3 samples that were used for the rate constant determination were not influenced by residual CO2, because we allowed for two days of degassing of the sample vials (during equilibration to room temperature conditions) in addition to the degassing of the initial solution before every experiment (see section 2.2). Bubbling of the experimental solution with N2 for extended time periods could also safely prevent residual CO2 from influencing the experiment. Furthermore, the SrCO3 precipitation should be made in a CO2-free atmosphere as it can lead to measureable effects due to the temporal shift of the pH to values of ~12 during the mineral precipitation and potential uptake of CO2 from the surrounding. For example, already a 5% CO2 contribution leads to Δ47 values higher by about 0.01-0.015 ‰. A good control for atmospheric contamination can be the analysis of the δ13C values (section 3). The necessary isotopic equilibration times span a very wide range covering several magnitudes following either temperature or pH variations (Fig. 1). We investigated the temperature dependence at ~ pH 7.5-8.5 as this is an important range for many natural samples and as also many laboratory experiments are conducted there. The calibration efforts for isotope proxies such as δ18O and Δ47 may benefit from the precise knowledge of equilibration conditions and rate constants. The exponential increase of the necessary equilibration time with decreasing temperature (Fig.10) demands for correspondingly longer equilibration time periods. For example, at pH 8 and 40°C about 50-100 min are necessary to fully achieve isotopic equilibration if the experimental solutions was taken from a different temperature environment. The time periods are longer at low temperature and can reach several 1000 min for temperatures 22

close to 0°C (Fig.1). If studies are conducted at pH >10 one to two orders of magnitude longer equilibration times are expected. Salinity also has an influence on the equilibration times (Fig. 2), leading for low to moderate salt concentrations to an increase by up to one order of magnitude, in particular at high pH. 4.4.3 Natural samples An expanded knowledge of equilibration times beyond the previously assessed range is beneficial for the understanding and interpretation of signals detected in natural samples. If carbonates precipitate after a significant temperature change, they will be likely out of isotopic equilibrium in case of a high pH solution at low temperature. Examples are alkaline solutions that can form travertine deposits (e.g., Falk et al., 2016). In contrast, subsurface waters are often low in pH (<8) and can exhibit elevated temperatures, in particular in hydrothermal systems. At pH <8 and 90°C the equilibration time τ99 is only about a few minutes or below. Thus, DIC in low pH, warm hydrothermal waters can be assumed to be in isotopic equilibrium concerning δ18O and Δ47 even following relatively fast temperature changes on the order of a few °C per 5 minutes (e.g. during rapid hydrothermal water ascent).

5. Conclusion Solutions at pH 8 and negligible salinity were used to determine the equilibration rate constants for δ18O and Δ47 in DIC at 40°C, 55°C, 70°C and 90°C by quantitatively precipitating the DIC at different time intervals as SrCO3. The equilibration rate constants of δ18O and Δ47 in the DIC at the selected temperatures are consistent with each other and with expected extrapolated values within 1-2 σ. Only at 90°C slightly lower rate constants were measured compared to theoretically expected values. The equilibration time dependency τ99 (= ln(0.01)*τ) on temperature T (in K) in the experimentally assessed range based on the combined data points from δ18O and Δ47 follows as

23

(

τ99 (T) [min] = ― ln (0.01) ∗ 1/exp ( ― 1.00 ± 0.15)•104 ∗

)

1 + (29 ± 4) 𝑇

In general, additional experiments are advisable to determine the accurate temperature dependency under different pH conditions and higher salinities. The equilibration times have to be closely considered for both preparing solutions that are intended for isotopic calibration studies in the laboratory as well as for the interpretation of naturally formed carbonate. At pH 8 the DIC equilibration rate constant varies by about two orders of magnitude between 40°C and 90°C. As a byproduct of the analysis, the Δ47-T relationship for SrCO3 could be assessed on the equilibrated samples. The Δ47-T relationship of SrCO3 resembles closely the published data of Kluge et al. (2015), Kelson et al. (2017) and Bonifacie et al. (2017) in the interval from 590°C and also follows the same temperature relationship as other carbonates. Slightly higher SrCO3 Δ47 values (order of 0.02 ‰) from 5 up to 55°C relative to the equilibrium calcite reference likely reflect kinetic effects during rapid mineral formation.

Acknowledgement We gratefully acknowledge funding by the Heidelberg Graduate School of Fundamental Physics (HGSFP). The authors thank Maximilian Kalb for support in mass spectrometer operation and the members of the research group for fruitful discussions. We acknowledge the support of the N. Frank, M. Schmidt and the team 'physics of environmental archives' to maintain the IRMS instrument that was funded through the grant DFG-INST 35/1270-1 FUGG. We highly appreciate helpful suggestions and comments of Joji Uchikawa and an anonymous reviewer.

24

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Tables Table 1: Parameters of solutions in the individual Eppendorf vessels used for determining the equilibration rate constants. NaOH and DI water was used for preparing a 0.1 M NaHCO3 solution in the glove bag. 2 ml of the NaHCO3 solution was added to the SrCl2 leading to a pH of ~8. The measurement time step is related to the time span from the start of the experiment (placing the Eppendorf vessel in the heated aluminium block) to the SrCO3 precipitation. The weighing uncertainty is ~0.1 mg. The SrCl2 mass varied as we tried to account for adsorbed water. Sample Sr40-1 Sr40-2 Sr40-3 Sr40-4 Sr40-5 Sr40-6 Sr40-7 Sr40-8 Sr40-9 Sr40-10 Sr40-11 Sr55-1 Sr55-2 Sr55-3 Sr55-4 Sr55-5 Sr55-6 Sr55-7 Sr70-1 Sr70-2 Sr70-3 Sr70-4 Sr70-5 Sr70-6 Sr70-7 Sr70-8 Sr70-9 Sr5to90-1 Sr5to90-2 Sr5to90-3 Sr5to90-4 Sr5to90-5

SrCl2 (mg) 40.1 35.9 36.2 36.4 36.7 36.9 39.5 51.6 49.7 50.4 50.6 36.9 36.0 35.5 36.0 34.7 36.7 38.9 40.9 38 37.8 38.2 37.4 38.1 39.3 48.1 48.2 51.2 49.5 49.1 50.0 51.3

SrCO3 (mg) 10.8 6.4 6.1 7.4 14.7 12.8 10.3 16.7 15.7 19.3 24.1 13.8 10.8 7.6 4.3 8.8 12.4 8 8.7 9.3 13.7 11.4 7.3 8.7 5.4 8.3 3 22.4 21.6 23.1 21.0 20.4 31

Measurement time step (min) 0 2.72 10.9 29 59.77 90.53 325 2.5 40 120 350 0 0.62 2.5 6.63 13.67 20.72 110 0 0.2 0.55 1.53 3.08 6.78 20 4 5 3 3.08 3.166 3.25 3.7

Sr90-X

48.7

22.6

5

Table 2: Isotope ratios and clumped isotope values of the samples used for determining the equilibration rate constants. The uncertainty is for δ13C = ±0.2‰ (1σ), δ18O =±0.3‰ (1σ) and Δ47=±0.02 to ±0.03‰ (1σ, depending on the measurement interval, based on standard replication). δ13C is given in VPDB, δ18O in VSMOW, including a phosphoric acid correction of -8.8 ‰ (Sharma and Sharma, 1969). δ13 C

δ18 O

Δ47

[‰ ]

[‰ ]

[‰ ]

Sr40-1 Sr40-1 Sr40-2 Sr40-3 Sr40-4 Sr40-5 Sr40-5 Sr40-6 Sr40-6 Sr40-7 Sr40-8 Sr40-8 Sr40-9 Sr40-9 Sr40-10 Sr40-10 Sr40-11 Sr40-11

-5.5 -5.2 -5.4 -5.3 -5.1 -5.9 -5.3 -5.4 -5.1 -5.0 -5.2 -5.0 -5.3 -4.9 -5.7 -5.0 -5.5 -5.5

22.3 23.0 22.8 21.1 20.9 19.0 20.5 19.6 20.3 20.7 23.8 23.8 20.6 20.6 20.6 20.4 20.7 20.8

0.77 0.76 0.77 0.72 0.74 0.74 0.71 0.67 0.67 0.70 0.73 0.77 0.67 0.66 0.66 0.66 0.66 0.65

Sr55-1 Sr55-1 Sr55-2 Sr55-2 Sr55-3 Sr55-3 Sr55-4 Sr55-5 Sr55-5 Sr55-6 Sr55-6 Sr55-7 Sr55-7

-4.9 -4.9 -4.6 -4.5 -4.6 -4.5 -4.6 -4.3 -4.3 -4.6 -4.4 -4.8 -4.7

23.8 23.9 24.1 24.0 23.1 23.5 20.6 19.2 19.3 18.5 18.9 19.1 19.2

0.73 0.76 0.71 0.72 0.73 0.72 0.66 0.62 0.65 0.64 0.63 0.64 0.64

Sr70-1 Sr70-1

-4.9 -5.0

23.8 23.7

0.76 0.76

Sample

32

Sr70-2 Sr70-2 Sr70-3 Sr70-3 Sr70-4 Sr70-4 Sr70-4 Sr70-5 Sr70-5 Sr70-6 Sr70-6 Sr70-7 Sr70-8 Sr70-9

-5.1 -5.3 -5.1 -5.0 -4.8 -4.9 -4.8 -5.2 -5.0 -5.0 -4.9 -4.8 -5.1 -5.5

24.3 24.0 23.8 24.4 23.2 23.3 23.4 19.7 20.3 15.9 16.4 16.9 18.1 16.6

0.76 0.73 0.73 0.70 0.78 0.73 0.76 0.70 0.69 0.62 0.61 0.57 0.68 0.71

Sr5to90-1 Sr5to90-1 Sr5to90-2 Sr5to90-2 Sr5to90-3 Sr5to90-3 Sr5to90-4 Sr5to90-4 Sr5to90-4 Sr5to90-5 Sr5to90-5 Sr90-X

-5.0 -5.1 -5.2 -5.3 -5.0 -5.0 -5.0 -5.0 -5.0 -4.9 -5.0 -5.2

14.8 14.9 14.3 14.2 14.0 14.0 13.6 13.9 13.9 13.4 13.3 13.7

0.56 0.58 0.58 0.58 0.56 0.57 0.62 0.58 0.59 0.52 0.56 0.54

Table 3: Equilibration rate constant k for δ18O determined from fitting measured data to equation (4). This equation describes a limited exponential decay, where δ18Oini is the isotopic starting point, δ18Oeq the equilibrium value (both given in VSMOW) and k the rate constant (1/min). δ18Oini and δ18Oeq refer to the acid-corrected value (using a correction of -8.8‰). n gives the number of data points considered in the fit. “Theory” refers to a fit of the experimental data using k of Uchikawa and Zeebe (2012) (Eq. 2).

40°C Fit 40°C Theory 55°C Fit 55°C Theory 70°C Fit 70°C Theory 90°C Fit

k (1/min) 0.13 ± 0.08 0.05 0.24 ± 0.04 0.22 1.0 ± 0.05 1.022 4.7 ± 0.4

δ18Oeq (‰ ) 20.4 ± 0.5 20.2 ± 0.2 18.9. ± 0.2 18.9 ± 0.1 16.4 ± 0.4 16.4 ± 0.3 13.31 ± 0.04

δ18Oin (‰ ) 22.8 ± 0.5 22.4 ± 0.4 23.3 ± 0.3 23.3 ± 0.2 20.1 ± 0.6 20.1 ± 0.5 14.82 ± 0.04 33

R2

n

0.80 0.75 0.99 0.99 0.93 0.93 0.996

9 5 5 6

90°C Theory

7.81

13.44 ± 0.08

14.9 ± 0.1

0.95

Table 4: Equilibration rate constant k for Δ47 determined from fitting the measured data to equation (5). This equation describes a limited exponential decay, where Δ47,ini is the isotopic starting point, Δ47,eq the equilibrium value and k the rate constant (1/min). n gives the number of data points considered in the fit. “Theory” refers to a fit of the experimental data using k of Uchikawa and Zeebe (2012) (Eq. 2).

40°C Fit 40°C Theory 55°C Fit 55°C Theory 70°C Fit 70°C Theory 90°C Fit 90°C Theory

k (1/min) 0.03 ± 0.03 0.053 0.32 ± 0.05 0.22 0.22 ± 0.04 1.022 2.2 ± 1.5 7.81

Δ47,eq (‰ ) 0.67 ± 0.02 0.67 0.637 ± 0.004 0.634 ± 0.003 0.56 ± 0.03 0.5873 0.537 ± 0.009 0.548 ± 0.008

R2

n

0.62 0.52 0.99 0.98 0.90 0.57 0.91 0.64

8

Δ47,ini (‰ ) 0.76 ± 0.03 0.77 ± 0.02 0.721 ± 0.004 0.718 ± 0.006 0.710 ± 0.02 0.72 ± 0.04 0.579 ± 0.006 0.58 ± 0.01

5 4 5

Table 5: Additional isotopically equilibrated SrCO3 samples for Fig.10. The samples marked with e were degassed before initiating the SrCO3 precipitation with a setup designed for degassing water samples to remove excess CO2 (Weise, 2018). The SrCO3 precipitation was carried out at normal atmospheric conditions (not in N2-filled glove bag, see 4.1). Initial pH of the investigated mineral water samples was 5.6. δ18O values include a phosphoric acid correction of -8.8 ‰. δ13 C (VPDB)

δ18 O (VSMOW)

Δ47

[‰ ]

[‰ ]

[‰ ]

[h] / [cm]

MW5e

-31.5

19.5

0.81

<500 / 11.5

FB5e

-30.9

18.9

0.76

45 / 11.5

Mw23e

-28.2

21.0

0.74

72 / 11.5

Mw23e2

-27.8

22.0

0.7

456/ 11.5

Mw23

-5.9

27.0

0.72

72/ 1.5

Sample

34

Degassing time/ Water depth

Figure caption Fig. 1: Model-based calculations of time period τ99 for reaching 99% equilibrium with respect to oxygen isotope fractionation between DIC and water at different temperature and pH values. The calculations are based on eq. (2) and a fixed salinity of 0.007. τ99 is defined here as –ln(0.01)*τ. Individual data points (filled circles) reflect the experimental results of this study. Related uncertainties are smaller than the symbol size where not indicated.

Fig.2: Calculated time period τ99 for reaching 99% equilibrium at different salinities, but constant pH 8 and temperature (20°C). The calculations are based on eq. (2) and pK*i values of Millero et al. (2007).

Fig. 3: Schematic drawing and photo showing the temperature-stabilized aluminum block on a heat plate within the glove bag (grey circle). The cavities (blue) within the aluminum block are used to store the experimental solution within the Eppendorf vessels at the experiment’s temperature. The glove bag was flushed with pure N2 at least 5 times within two days to prepare a CO2-free atmosphere. The photograph at the right shows the setup inside the glove bag.

Fig. 4: Flow-chart of the experimental procedure: solution preparation, isotopic equilibration at room temperature, re-equilibration to the new temperature, quantitative SrCO3 precipitation, and gas preparation for mass spectrometric analysis.

Fig. 5: δ13C values during the individual experiment runs. No significant change with time is observable. The dashed lines refer to the δ13C values of the initial NaHCO3 solution.

35

Fig.6: SrCO3 δ13C values (black squares) vs. sample mass recovered from the individual Eppendorf vessels. The red line refers to the δ13C values of the initial NaHCO3 solution.

Fig. 7: Temporal evolution of the δ18O values during the different experimental runs: A) 40°C, B) 55°C, C) 70°C, D) 90°C. The red line is a fit to the measured data with rate constant and start and end value as free parameters (Table 3). The blue line is a fit to the measured data with the rate constant set to the value given by our calculations (based on Uchikawa and Zeebe 2012) and the start and end value as free parameters (Table 3). For 70°C (C) both curves fall on top of each other.

Fig. 8: Temporal evolution of the Δ47 values during the different equilibration experiments: A) 40°C, B) 55°C, C) 70°C, D) 90°C. The red line is a fit to the measured data with rate constant, start and end value as free parameters (Table 4). The blue line is a fit to the measured data with the rate constant set to the value given by our calculations (based on Uchikawa and Zeebe, 2012) and the start and end value as free parameters. For 40°C and 70°C the end value was also set to the theoretically predicted value (Table 4). The two samples marked by an asterisk were disregarded in the evaluation. Fig. 9: Exemplary temperature evolution of the reaction vessel filled with water (blue) at 70°C (A) and 90°C (B) after insertion into the temperature-stabilized aluminum block. For comparison, the temperature evolution of a thermometer is shown (red points) that was inserted in the same hole of the aluminum block without water and without reaction vessel.

Fig. 10: Δ47-T relationship of SrCO3 precipitated from equilibrated solutions (end-points of the equilibration experiments at 40-90°C, including additional experiments at 5°C and 23°C,

36

section 4.1, Table 5). Values are given without acid reaction correction and reflect the Δ47 value in the CRDS scale for acid reaction at 90°C. Calibration curves of Kluge et al. (2015) for CaCO3 (black, mostly calcite), Kelson et al. (2017) for CaCO3 (blue) and Bonifacie et al. (2017) for dolomite (grey) are given for comparison. All calibration lines were determined for phosphoric reactions at 90°C and are given without addition of an acid fractionation factor. Fig. 11: ε(HCO3--H2O) of this study relative to the experimental data points of Beck et al. (2005) and its extrapolation to higher temperatures (dashed line). ε(HCO3--H2O) was calculated from the measured SrCO3 δ18O value by considering the contributions of CO32- and CO2,aq at pH 8 (see section 4.2). Fig. 12: Isotope exchange rate constant k versus 1/T for Δ47 (A) and δ18O (B) with linearly fitted temperature relationship (black continuous lines) and the predicted relationship (blue dashed line) following Uchikawa and Zeebe (2012). The fit in (A) does not consider the individual uncertainties, because this would particularly over-represent the 70°C data point. The error bars for 55°C and 70°C are the smallest in (A), but the fit at 70°C has the lowest number of measurement points taken into account for the fit, causing a misleadingly low apparent uncertainty. The fits in (B) include the uncertainties of each data point. The uncertainties appear asymmetric due to the logarithmic scale.

37

Supplementary Figures

Fig. S1: δ18O (top) and Δ47 values (bottom) versus mass of the SrCO3 precipitated from the individual Eppendorf vessels.

38