Kinetic fractionation of carbon and oxygen isotopes during BaCO₃ precipitation

Abstract

Disequilibrium isotopic compositions in carbonate minerals often reflect the integration of several different kinetic isotope effects (KIEs), whose relative contribution to the overall composition depends on the specific mineral formation process and environment. Thus, potential environmental reconstructions from disequilibrium compositions in natural carbonates require (i) quantification of KIEs associated with reactions involved in mineral formation, and (ii) a theoretical framework linking physical properties of natural environments to the expression and preservation of these KIEs in carbonates.

To constrain KIEs associated with carbonate mineral precipitation reactions, we performed a series of rapid witherite (BaCO₃) precipitation experiments over a range of pH (8.7–13.0), temperature (15–40 °C) and fractional yield of the dissolved inorganic carbon (DIC; a few percent to quantitative precipitation). Our experiments extend the range of pH and temperature explored in previous studies, and include measurements of both carbon and oxygen isotopes. We developed a dynamic model of the DIC system, with which we simulated the experiments. The model results identify isotopic distillation due to formation of aqueous CO₂ and mineral precipitation by either CO₃^2– or HCO₃^– as the main determinants of the carbon and oxygen isotopic evolution of the solid and of the solution.

We estimate that the carbon kinetic fractionation factor (KFF) associated with unidirectional precipitation of witherite via CO₃^2–, $1000\mathrm{l}\mathrm{n}{}^{13}{\mathrm{\alpha }}_{\mathrm{C}{\mathrm{O}}_3^{2-}\to \mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{O}}_3}^{k_{+1}}$, is 0.5 ± 0.1‰ (15–40 °C), whereas the oxygen KFF, $1000\mathrm{l}\mathrm{n}{}^{18}{\mathrm{\alpha }}_{\mathrm{C}{\mathrm{O}}_3^{2-}\to \mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{O}}_3}^{k_{+1}}$, is –1.0 ± 0.3‰ (15 °C) and –0.5 ± 0.2‰ (25–40 °C). The carbon KFF associated with unidirectional HCO₃^– precipitation pathways, $1000\mathrm{l}\mathrm{n}{}^{13}{\mathrm{\alpha }}_{\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}\to \mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{O}}_3}^{k_{+2,+3}}$, is –0.2 ± 1.0‰ (15–40 °C), whereas the oxygen KFF, $1000\mathrm{l}\mathrm{n}{}^{18}{\mathrm{\alpha }}_{\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}\to \mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{O}}_3}^{k_{+2,+3}}$, is –6.7 ± 1.1‰ (15 °C), –4.5 ± 1.1‰ (25 °C) and –4.0 ± 1.1‰ (40 °C). Our oxygen KFF of witherite precipitation from CO₃^2– agrees well with the available literature estimates at 25 °C. In addition, our carbon and oxygen KFFs are comparable to literature KFFs associated with calcite precipitation, possibly suggesting a similarity of precipitation KFFs among carbonate minerals. Importantly, the relative magnitudes and uncertainties of the precipitation KFFs and the equilibrium fractionation between CO₃^2– and HCO₃^–, leads to the expectation that in many natural settings, the isotopic composition of carbonate minerals be an insensitive probe of the precipitation pathway.

Introduction

Offsets from isotopic equilibrium are widely observed in natural and synthetic carbonate minerals (e.g., Hendy, 1971, Wefer and Berger, 1991, Clark and Lauriol, 1992, Clark et al., 1992, Watkins et al., 2013, Watkins et al., 2014, Dreybrodt et al., 2016, Hansen et al., 2017, Hansen et al., 2019, Thaler et al., 2017). These offsets are related to physical processes (e.g., evaporation, diffusion), biological activity (“vital effects”, e.g., metabolism), reservoir (Rayleigh) distillation, and expression of kinetic isotope effects (KIEs) during chemical reactions in which the light and heavy isotopologues react at different rates. A KIE is associated with the mechanism of a specific unidirectional reaction (Mariotti et al., 1981, Sade and Halevy, 2017), and it has a characteristic magnitude, which is often dependent on environmental parameters such as pressure and temperature (Bigeleisen and Wolfsberg, 1958, Lasaga, 1998). The magnitude of a fully expressed KIE is here referred to as the kinetic fractionation factor, or KFF. Importantly, the degree to which a KIE is expressed as an isotopic fractionation depends on the reversibility of reaction. When a reaction is unidirectional (i.e., no back reaction), the KIE is fully expressed and the net fractionation is identical to the KFF. However, when an isotopic reaction is fully reversible (i.e., at isotopic equilibrium), KIEs associated with the forward and reverse reactions lead to a specific distribution of isotopes among the reactants and products. This distribution defines the equilibrium isotopic fractionation (DePaolo, 2011, Wing and Halevy, 2014). In these two end-member scenarios, as well as anywhere in the range between them, KIEs are always present, but variably expressed.

In addition to mineral precipitation and dissolution, reactions involved in carbonate mineral formation commonly include dissolved inorganic carbon (DIC) speciation and CO₂ degassing and ingassing. Specifying the contribution of KIEs associated with these reactions to the observed isotopic composition of natural carbonate minerals bears the potential to unlock currently inaccessible paleoclimatic and paleohydrological information.

Synthetic precipitation of witherite (BaCO₃) is common in investigations of both equilibrium and kinetic isotope effects in the carbonate system (Kim and O’Neil, 1997, Beck et al., 2005, Kim et al., 2006, Uchikawa and Zeebe, 2012, Uchikawa and Zeebe, 2013, Kim et al., 2014). The main advantage over more geologically relevant carbonate minerals (e.g., CaCO₃) is that solutions bearing Ba²⁺ and dissolved inorganic carbon (DIC) tend to precipitate witherite only. Rapid precipitation of CaCO₃, on the other hand, results in a mixture of several polymorphs (calcite, aragonite and vaterite), as well as amorphous calcium carbonate. Formation of multi-phase samples complicates both isotopic analysis by the conventional acid digestion method (Kim et al., 2006, Uchikawa and Zeebe, 2012), and interpretations of their disequilibrium isotopic compositions, because in theory, a different KIE may be associated with precipitation of each of the solid phases in the mixture. The experimental advantages of witherite, alongside similarities with calcite and aragonite in precipitation and dissolution kinetics (Chou et al., 1989), and in the temperature dependence of equilibrium isotope fractionations (Kim and O’Neil, 1997), suggest kinetic investigations of BaCO₃ formation and associated isotope effects as a means of improving our understanding of these effects in the formation of CaCO₃ minerals as well.

Witherite precipitation/dissolution may proceed via CO₃^2– or HCO₃^–, following several suggested stoichiometries (Chou et al., 1989):

$$\mathrm{B}{\mathrm{a}}^{2+}+\mathrm{C}{\mathrm{O}}_3^{2-}\underset{k_{-1}}{\overset{k_{+1}}{\rightleftarrows }}\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{O}}_3,$$

$$\mathrm{B}{\mathrm{a}}^{2+}+2\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}\underset{k_{-2}}{\overset{k_{+2}}{\rightleftarrows }}\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{O}}_3+{\mathrm{H}}_2\mathrm{C}{\mathrm{O}}_3^{\ast },$$

$$\mathrm{B}{\mathrm{a}}^{2+}+\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}\underset{k_{-3}}{\overset{k_{+3}}{\rightleftarrows }}\mathrm{B}\mathrm{a}\mathrm{C}{\mathrm{O}}_3+{\mathrm{H}}^{+},$$

where H₂CO₃* represents the sum of carbonic acid (H₂CO₃) and aqueous CO₂.

The approach to isotopic equilibrium among DIC species depends on the kinetics of DIC speciation reactions (e.g., Zeebe and Wolf-Gladrow, 2001). These include the first and second deprotonations of carbonic acid, specifically the dissociation of H₂CO₃ (protolysis):

$${\mathrm{H}}_2\mathrm{C}{\mathrm{O}}_3\underset{k_{-4}}{\overset{k_{+4}}{\rightleftarrows }}\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}+{\mathrm{H}}^{+},$$

and HCO₃^– (protolysis and hydrolysis):

$$\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}\underset{k_{-5}^{{\mathrm{H}}^{+}}}{\overset{k_{+5}^{{\mathrm{H}}^{+}}}{\rightleftarrows }}\mathrm{C}{\mathrm{O}}_3^{2-}+{\mathrm{H}}^{+},$$

$$\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}+\mathrm{O}{\mathrm{H}}^{-}\underset{k_{-5}^{\mathrm{O}{\mathrm{H}}^{-}}}{\overset{k_{+5}^{\mathrm{O}{\mathrm{H}}^{-}}}{\rightleftarrows }}\mathrm{C}{\mathrm{O}}_3^{2-}+{\mathrm{H}}_2\mathrm{O},$$

CO₂ hydration/H₂CO₃ dehydration, hereafter CO₂ (de)hydration:

$$\mathrm{C}{\mathrm{O}}_{2(\mathrm{a}\mathrm{q})}+{\mathrm{H}}_2\mathrm{O}\underset{k_{-6}}{\overset{k_{+6}}{\rightleftarrows }}{\mathrm{H}}_2{\mathrm{C}\mathrm{O}}_3,$$

and CO₂ hydroxylation/HCO₃^– dehydroxylation, hereafter CO₂ (de)hydroxylation:

$$\mathrm{C}{\mathrm{O}}_{2(\mathrm{a}\mathrm{q})}+\mathrm{O}{\mathrm{H}}^{-}\underset{k_{-7}}{\overset{k_{+7}}{\rightleftarrows }}\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}.$$

Lastly, speciation of water is relevant for oxygen isotope equilibrium between DIC and water,

$${\mathrm{H}}_2\mathrm{O}\underset{k_{-8}}{\overset{k_{+8}}{\rightleftarrows }}{\mathrm{H}}^{+}+\mathrm{O}{\mathrm{H}}^{-}.$$

Fig. 1 shows the pH-dependent DIC speciation (Fig. 1A) and equilibrium fluxes (Fig. 1B, C) in the carbonate system (Reactions (1), (2), (3), (4), (5), (6), (7), (8), (9) at 25 °C, with 20 mM DIC and varying concentrations of Na and BaCl₂). Notably, carbonic acid dissociation reactions are faster, sometimes by several orders of magnitude, than H₂O speciation (Fig. 1B), suggesting effectively instantaneous equilibration of carbon and oxygen isotopes among H₂CO₃, HCO₃^– and CO₃^2– (but not with the H₂O). Due to the much slower (de)hydration and (de)hydroxylation reactions, aqueous CO₂ may be out of equilibrium with the other DIC species, though equilibrium among all DIC species (including CO₂(aq)), but not with the H₂O, is achieved in a matter of seconds to minutes under most conditions. The (de)hydration and (de)hydroxylation reactions are also responsible for the exchange of oxygen between the total DIC and the H₂O, and because the latter is a much larger reservoir of oxygen, even when aqueous CO₂ is in equilibrium with the other DIC species, the total DIC may be out of equilibrium with ambient H₂O. These factors have significant implications for disequilibrium isotopic compositions recorded in carbonate minerals. Close to equilibrium, over much of the examined pH range, the dominant pathway of witherite precipitation involves CO₃^2– (Reaction (1); Fig. 1C). However, at pH values around 8 and lower, HCO₃^– precipitation becomes significant (Reactions (2), (3); HCO₃^– precipitation accounts for 14% and 50% of the total precipitation flux at pH 8.0 and 7.2, respectively).

Kim et al. (2006) studied the mechanism of aragonite precipitation and the expression of oxygen KIEs during aragonite formation. In their study, they “quasi-instantaneously” precipitated fractions of DIC as witherite, an aragonite isomorph, from initially isotopically equilibrated solutions at 25 °C and pH of 8.3, 10.1 and 10.7. Thus, the witherite recorded both KIEs during mineral formation and reservoir (Rayleigh) distillation effects. Kim et al. (2006) noted that in the pH > 10 experiments, at fractional yields smaller than the initial CO₃^2– fraction (CO₃^2– constituted 42–78% of the initial DIC), the δ¹⁸O of the witherite closely represented the δ¹⁸O of the CO₃^2–. They deduced that precipitation via CO₃^2– (Reaction (1)) was preferred at this pH, suggesting that the fractionation of –0.2 to –0.6‰ observed between the smallest fractional yields of the witherite (i.e., minimal Rayleigh distillation of the DIC reservoir) and the initial isotopic composition of the CO₃^2– reflected a KIE during CO₃^2– precipitation (Reaction (1)). Assuming that Reaction (1) dominated the precipitation mechanism in all of their experimental settings, Kim et al. (2006) proposed that witherite precipitated from solutions at an initial pH of 8.3 (97% of the initial DIC is present as HCO₃^–) also recorded a KIE of HCO₃^– deprotonation, in addition to the KIE of CO₃^2– precipitation. That is, HCO₃^– isotopologues depleted in ¹⁸O relative to the bulk HCO₃^–, preferentially deprotonated to CO₃^2– during mineral formation.

Devriendt et al. (2017) reviewed the experimental data of Kim et al. (2006) (Section 4.2.4 in Devriendt et al., 2017), accepting that mineral formation involved two major reactions, precipitation (only) via CO₃^2– and deprotonation of HCO₃^–. To constrain the oxygen KIEs associated with these reactions, Devriendt et al. (2017) solved a sequence of Rayleigh equations, where unidirectional HCO₃^– deprotonation preceded precipitation from CO₃^2–. Their model fit the observations well, suggesting KIE magnitudes of –0.5 ± 0.2‰ during unidirectional CO₃^2– precipitation and –5.0 ± 0.2‰ during unidirectional HCO₃^– deprotonation.

In general, during precipitation of carbonate minerals, alkalinity and DIC concentration decrease at a ratio of 2:1 (Deffeyes, 1965, Zeebe and Wolf-Gladrow, 2001). As a consequence, pH decreases and the speciation of the residual DIC changes. CO₂(aq) is formed (by H₂CO₃ dehydration and/or HCO₃^– dehydroxylation) and bulk CO₃^2– is protonated to HCO₃^–. Overall, it is expected that as an initial DIC pool precipitates (without replenishment of the DIC or the precipitating cation), the degree of mineral (over) saturation decreases, and the importance of precipitation pathways via HCO₃^– (Reactions (2), (3)) increases. Thus, mechanistic models describing carbonate mineral formation, especially from HCO₃^–-dominated solutions, should include mineral precipitation and dissolution reactions via both CO₃^2– and HCO₃^–, reversible HCO₃^– dissociation and CO₂ formation.

In this study, we rapidly precipitated fractional yields of the DIC as witherite, using an experimental protocol similar to Kim et al. (2006). However, in addition to measuring the oxygen isotope ratios in the witherite, we measured the carbon isotope ratios in both the witherite and the residual solutions. Furthermore, we performed the experiments at 15, 25 and 40 °C to explore the dependence of the KIEs on temperature. To analyze the isotopic data and constrain the KIEs during CO₃^2– and HCO₃^– precipitation reactions, we developed a dynamic model of the aqueous DIC system, which includes all of the reactions relevant to mineral formation in the experiments. The outcome is an internally consistent set of kinetic fractionation factors associated with witherite precipitation, as well as a mechanistic understanding of the processes governing DIC chemistry and isotopes during rapid carbonate mineral precipitation.