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Oxygen isotope fractionation in double carbonates a

Yong-Fei Zheng & Michael E. Böttcher

b

a

CAS Key Laboratory of Crust–Mantle Materials and Environments, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, People's Republic of China b

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Geochemistry and Stable Isotope Geochemistry Group, Department of Marine Geology, Leibniz Institute for Baltic Sea Research (IOW), Warnemünde, Germany Published online: 13 Nov 2014.

To cite this article: Yong-Fei Zheng & Michael E. Böttcher (2014): Oxygen isotope fractionation in double carbonates, Isotopes in Environmental and Health Studies, DOI: 10.1080/10256016.2014.977278 To link to this article: http://dx.doi.org/10.1080/10256016.2014.977278

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Isotopes in Environmental and Health Studies, 2014 http://dx.doi.org/10.1080/10256016.2014.977278

Oxygen isotope fractionation in double carbonates Yong-Fei Zhenga∗ and Michael E. Böttcherb∗

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a CAS

Key Laboratory of Crust–Mantle Materials and Environments, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, People’s Republic of China; b Geochemistry and Stable Isotope Geochemistry Group, Department of Marine Geology, Leibniz Institute for Baltic Sea Research (IOW), Warnemünde, Germany (Received 23 April 2014; accepted 1 September 2014)

Dedicated to Professor Dr Jochen Hoefs on the occasion of his 75th birthday Oxygen isotope fractionations in double carbonates of different crystal structures were calculated by the increment method. Synthesis experiments were performed at 60 °C and 100 °C to determine oxygen and carbon isotope fractionations involving PbMg[CO3 ]2 . The calculations suggest that the double carbonates of calcite structure are systematically enriched in 18 O relative to those of aragonite and mixture structures. Internally consistent oxygen isotope fractionation factors are obtained for these minerals with respect to quartz, calcite and water at a temperature range of 0–1200 °C. The calculated fractionation factors for double carbonate–water systems are generally consistent with the data available from laboratory experiments. The experimentally determined fractionation factors for PbMg[CO3 ]2 , BaMg[CO3 ]2 and CaMg[CO3 ]2 against H2 O not only fall between fractionation factors involving pure carbonate endmembers but are also close to the calculated fractionation factors. In contrast, experimentally determined carbon isotope fractionation factors between PbMg[CO3 ]2 and CO2 are much closer to theoretical predictions for the cerussite–CO2 system than for the magnesite–CO2 system, similar to the fractionation behavior for BaMg[CO3 ]2 . Therefore, the combined theoretical and experimental results provide insights into the effects of crystal structure and exchange kinetics on oxygen isotope partitioning in double carbonates. Keywords: carbon isotopes; crystal structure; double carbonate; isotope exchange; isotope fractionation; oxygen isotopes; temperature dependence

1.

Introduction

Double carbonates commonly occur in nature as dolomite CaMg[CO3 ]2 and norsethite BaMg[CO3 ]2 . Their formation conditions in surface environments are still not completely understood. The stable oxygen and carbon isotope compositions of carbonate minerals may be used to determine these conditions, but this requires knowledge of their fractionation factors and their relationship to chemical composition and crystal structure. Many studies of experimental synthesis and oxygen isotope fractionation have been devoted to dolomite [1–6] and norsethite [2,7–12]. However, less attention has been paid so far to other double carbonates that have been reported from natural observations and laboratory experiments. These *Corresponding authors. Emails: [email protected]; [email protected] This article was originally published with errors. This version has been corrected. Please see Erratum (http://dx.doi.org/ 10.1080/10256016.2014.994854). © 2014 Taylor & Francis

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Y.-F. Zheng and M.E. Böttcher

include the trimorphs of BaCa[CO3 ]2 (alstonite, barytocalcite and paralstonite) [13,14], kutnahorite CaMn[CO3 ]2 [15,16], minrecordite CaZn[CO3 ]2 [17,18], olekminskite SrCa[CO3 ]2 [19], PbMg[CO3 ]2 [4,20,21], SrMg[CO3 ]2 [22] and BaMn[CO3 ]2 [23–25]. Although the formation of BaFe[CO3 ]2 has not been observed, its possible existence has been hypothesized from thermodynamic modeling (Peters and Böttcher, unpublished results). All of these double carbonates can form under specific environmental conditions and thus are of fundamental importance to our understanding of different paleoenvironments and the general principles of stable isotope fractionation in minerals. The basis of stable isotope geochemistry is an accurate knowledge of the isotope partitioning between two different compounds at thermodynamic equilibrium. The theoretical basis for calculating isotope fractionation factors by first principles was formulated in the 1940s [26,27] and has successfully been utilized to make theoretical predictions since then [28,29]. However, quantitative calculations using this classical theory are only feasible to molecules in the gas phase but fail to provide accurate predictions for crystalline phases and dissolved compounds in water [30,31]. Because the calculation of stable isotope fractionation factors is fundamental to practical applications in geochemistry, a variety of modifications have been applied to the classical theory [29,31,32]. The determination of oxygen isotope fractionation factors for abiogenic and biogenic minerals of geochemical interest has been one of the most important tasks in stable isotope geochemistry during the past decades [33]. In doing so, calculations are a useful approach when experimental or empirical calibrations are difficult to assess [34]. Systematic calculations for various minerals of geochemical interest have been made by Zheng [35–41] using the increment method. This study presents a systematic calculation of oxygen isotope fractionation in double carbonates that have different structures of crystallography. In addition, oxygen and carbon isotope fractionations involving PbMg[CO3 ]2 were experimentally determined. The calculated and experimental results are compared with known data for norsethite BaMg[CO3 ]2 from both theoretical calculations and laboratory experiments, providing insights into the effects of crystal structure and exchange kinetics on oxygen isotope partitioning in double carbonates.

2. 2.1.

Methods Theoretical calculations

The present calculations follow the increment method developed by Zheng [35–41]. The increment method was originally developed by Schütze [42] for semi-quantitative evaluation of oxygen isotope fractionations among silicate minerals. It focuses on individual bonds, the relative strengths of which are given by integrated variables such as ionic charge and bond length (determined from ionic radii). Cation mass is included in a form appropriate for diatomic molecules. Because the effects of both bond strength and cation mass on isotope substitution have been taken into account, oxygen isotope fractionation in crystalline minerals can be calculated as it moves away in increments from a reference mineral. By taking into account the effects of both crystal structure and chemical composition, Zheng [35–37] established the physical formulae for the calculation of oxygen isotope fractionation in various minerals as a function of temperature. In doing so, experimental and empirical data available at that time were utilized as constraints on modifications based on the consideration of quantum mechanics. Afterwards, the increment method was developed as an independent approach for the calculation of oxygen isotope fractionation in minerals [31]. There are two critical steps in the increment method when calculating oxygen isotope fractionation factors (103 ln α) for minerals. The first is to determine the degree of 18 O-enrichment in a

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3

mineral based on calculated 18 O-increments for each type of cation–oxygen bond (ict−o ) in the crystal structure of the mineral. For this purpose, the cation valence, the mass and coordination number of both cation and oxygen and the corresponding ionic radii in a given mineral must be known exactly. The bonds with a higher 18 O-increment are preferentially enriched in heavy oxygen isotopes. The 18 O-increments for all types of the bonds in the mineral are normalized relative to a reference cation–oxygen bond in a given reference mineral. The normalized 18 O-increments (ict−o ) are then weighted in terms of cation valence and the number of oxygen atoms, yielding an oxygen isotope index for the mineral (I–18 O). This relative 18 O-enrichment scale is tied to an absolute scale for the reference mineral, whose reduced partition function ratios (103 ln β) are determined by independent approaches. The second is the choice of the reference mineral and its reduced partition function ratios. Two series of reference minerals have been used for the calculations: (1) the Si–O bond in quartz is used to normalize the 18 O-increment of all cation–oxygen bonds in one series of silicate, metal oxide and hydroxide minerals [35–37,39,40]; (2) the C–O and Ca–O bonds in calcite are taken as reference bonds, respectively, for cation–oxygen bonds inside a chemically complexed unit, and cation–oxygen bonds outside the complexed unit for the other series of carbonate, sulfate and phosphate minerals [38,41]. Similarities in crystal structure between the reference mineral and the minerals in question warrant the accuracy of the calculated oxygen isotope indices. Correspondingly, the reduced partition function ratios of quartz and calcite calculated originally by Kieffer [43] and then corrected by Clayton et al. [44] have been used as the reference values to calculate the thermodynamic oxygen isotope factors (equivalent to 103 ln β) for the minerals of quartz and calcite series, respectively. The present calculations deal with double carbonates with the chemical formula XY[CO3 ]2 , where X and Y denote the divalent cations such as Ca2+ , Mg2+ , Mn2+ , Fe2+ , Zn2+ , Sr2+ , Ba2+ and Pb2+ . All crystalline carbonates are structurally composed of the layers of triangular CO3 groups alternating with layers of divalent cations in different coordinated sites [45,46]. The calcite-group single carbonates are structurally composed of the layers in which the same divalent cations occupy sixfold coordinated sites (VI), whereas the same divalent cations in the aragonite-group single carbonates occupy the ninefold coordinated sites (IX). Vaterite represents a transitional structure in which Ca2+ occupies the eightfold coordinated sites. Double carbonates contain two kinds of divalent cations X and Y with intervals of [CO3 ]2− in the crystal structure, which is composed of an X layer, a [CO3 ]2− layer, a Y layer, another [CO3 ]2− layer and so forth. However, there are a series of differences in their cation occupation [46]. According to the property of cation coordination, the crystal structures of double carbonates can be classified into three types: (1) the calcite type with a structural form of VI XVI YIII C2 III O6 , in which the divalent cations X and Y alternatively occupy the sixfold coordinated sites with the intervals of [CO3 ]2− layers. This is typical for dolomite VI CaVI Mg[CO3 ]2 and norsethite VI BaVI Mg[CO3 ]2 ; (2) the aragonite type with a structural form of IX XIX YIII C2 III O6 , in which the divalent cations X and Y alternatively occupy the ninefold coordinated sites with the intervals of [CO3 ]2− layers. This is typical for alstonite IX BaIX Ca[CO3 ]2 ; (3) the mixture type with various mixed structures, in which the divalent cations X and Y alternatively occur between the [CO3 ]2− layers, but X may occupy the 6-fold to 12-fold coordinated sites and Y may occupy the sixfold or ninefold coordinated sites. This is common for barytocalcite XII BaVI Ca[CO3 ]2 and paralstonite VI BaIX Ca[CO3 ]2 . The crystallographic parameters of all carbonates are generally following those presented by Jaffe [47] and Smyth and Bish [48]. The calculation of 18 O-increments for cation–oxygen bonds in the double carbonates is essentially the same as that presented by Zheng [41] for single carbonates. The only difference lies in the choice of ionic radii, where the present calculations refer to Muller and Roy [45]. The calculated 18 O-increments are listed in Table 1. The I-18 O index of calcite is defined as unity (1.0000) for the carbonate minerals [41]. As such, the reduced partition function ratios of calcite

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Y.-F. Zheng and M.E. Böttcher

Table 1.

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Bond C−O Ca−O Mg−O Mn−O Fe−O Zn−O Sr−O Ba−O Pb−O Sr−O Pb−O Ca−O Mn−O Fe−O Zn−O Sr−O Ba−O Pb−O Ba−O Ba−O

The 18 O-increment of cation − oxygen bonds in double carbonates. V ct

CNct

mct

rct

ro

rct + ro

Wct–o

C ct–o

ict–o

ict−o

4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

3 6 6 6 6 6 6 6 6 8 8 9 9 9 9 9 9 9 11 12

12.01 40.08 24.31 54.94 55.85 65.37 87.62 137.34 207.19 87.62 207.19 40.08 54.94 55.85 65.37 87.62 137.34 207.19 137.34 137.34

0.06 1.14 0.88 0.97 0.92 0.89 1.27 1.50 1.32 1.39 1.45 1.32 1.11 1.02 1.06 1.42 1.57 1.46 1.66 1.74

1.22 1.22 1.22 1.22 1.22 1.22 1.22 1.22 1.22 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24

1.28 2.36 2.10 2.19 2.14 2.11 2.49 2.72 2.54 2.63 2.69 2.53 2.35 2.26 2.28 2.64 2.81 2.70 1.90 1.98

1.02471 1.04224 1.03529 1.04602 1.04620 1.04786 1.05057 1.05381 1.05594 1.05057 1.05594 1.04224 1.04602 1.04620 1.04786 1.05057 1.05381 1.05594 1.05381 1.05381

1.04085 0.14124 0.15858 0.15221 0.15547 0.15798 0.13387 0.12255 0.13123 0.095057 0.092937 0.08790 0.09456 0.09833 0.09747 0.08430 0.07917 0.08246 0.095694 0.084175

0.02540 0.00584 0.00550 0.00685 0.00702 0.00739 0.00660 0.00642 0.00714 0.00469 0.00506 0.00364 0.00425 0.00444 0.00456 0.00416 0.00415 0.00449 0.00502 0.00441

0.9998 1.0000 0.9701 1.0825 1.0962 1.1243 1.0631 1.0484 1.1056 0.8958 0.9304 0.7889 0.8533 0.8718 0.8831 0.8436 0.8427 0.8764 0.9265 0.8689

calculated originally by Kieffer [43] and then corrected by Clayton et al. [44] are used as the reference system to calculate the thermodynamic oxygen isotope factors (equivalent to 103 ln β) for the double carbonates. For the fractionations involving water, the 103 ln β data listed by Hattori and Halas [49] are applied, which were based on the theoretical calculations of Richet et al.[28] These reference 103 ln β values are regressed in the function of 103 ln β = A × 106 /T 2 + B × 103 /T + C, where T is the temperature in K. This makes the calculated fractionation factors for the target minerals (Table 2) sufficiently precise at both high and low temperatures [33]. Zheng [35,37] has estimated uncertainties contributed to the fractionation factors by using the modified increment method. The following error sources have been taken into account: (1) assignment in the parameters of crystal structure; (2) assumption of the coupling coefficients; (3) accuracy of the thermodynamic oxygen isotope factors for the reference system and (4) the use of polynomial approximations. According to his estimates, errors in the results from the fractionation equations in Table 2 are within ± 5 % of the factor values (i.e. 10 ± 0.5 ‰ or 2 ± 0.1 ‰). 2.2.

Laboratory experiments

The present experiments focus on oxygen isotope fractionation between PbMg[CO3 ]2 and H2 O at two selected temperatures, using an approach following that described by Böttcher [12] for studying stable isotope fractionation in norsethite BaMg[CO3 ]2 . PbMg[CO3 ]2 was synthesized at 60 °C and 100 °C, respectively, in closed-vessel batch-type reactors by using procedures described by Böttcher et al. [21]. Briefly summarized, aliquots of artificial anhydrous PbCO3 and nesquehonite (MgCO3 ·3H2 O) were reacted in aqueous solutions of NaHCO3 as modified after an approach originally applied by Lippmann [3,20] for low temperature conditions. The reactions were performed in sealed 316ss autoclaves (40 ccm) which were continuously rotated at about 38 rpm in a modified drying oven (Heraeus). As documented by Böttcher [12], nearequilibrium fractionation was observed upon the slow transformation of an end-member into norsethite BaMg[CO3 ]2 . All chemicals used were of p.a. grade quality (Merck, Riedel de Häen). The artificial nesquihonite was prepared at 20 °C as described by Böttcher et al. [11]. At high

Isotopes in Environmental and Health Studies Table 2. C).

Calculated oxygen isotope fractionation in double carbonates (103 ln α = A × 106 /T 2 + B × 103 /T +

Mineral#

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5

103 ln α Quartz–Mineral

103 ln α Calcite–Mineral

103 ln α Mineral–Water

A

A

C

A

B

C

M Min

I–18 O

0.90977

1.0022

0.452 − 0.125

0.01

− 0.014 − 0.024

0.01

4.027

− 4.640

1.70

0.92178

1.0078

0.418 − 0.183

0.04

− 0.048 − 0.082

0.04

4.061

− 4.582

1.70

0.92208

1.0097

0.406 − 0.203

0.05

− 0.060 − 0.102

0.05

4.073

− 4.562

1.69

0.92517 0.92713

1.0110 0.9939

0.398 − 0.217 0.05 0.504 − 0.037 − 0.03

− 0.068 − 0.116 0.05 0.038 0.064 − 0.03

4.081 3.975

− 4.548 − 4.728

1.69 1.71

0.93934 0.95090

0.9786 0.9759

0.599 0.616

0.124 − 0.10 0.152 − 0.12

0.133 0.150

0.225 − 0.10 0.253 − 0.12

3.880 3.863

− 4.889 − 4.917

1.73 1.74

Aragonite structure Alstonite IX BaIX Ca[CO ] 0.94240 3 2

0.9127

1.008

0.816 − 0.42

0.542

0.917 − 0.42

3.471

− 5.581

1.82

0.94240

0.9605

0.711

0.314 − 0.19

0.245

0.415 − 0.19

3.768

− 5.079

1.76

0.94240

0.9460

0.801

0.466 − 0.26

0.335

0.567 − 0.26

3.678

− 5.231

1.77

0.93150 0.95090 0.92713 0.93934 0.94516 0.94501

0.9595 0.9477 0.9663 0.9494 0.9597 0.9576

0.717 0.791 0.675 0.780 0.716 0.729

0.324 0.448 0.253 0.430 0.322 0.344

− 0.19 − 0.25 − 0.16 − 0.24 − 0.19 − 0.20

0.251 0.325 0.209 0.314 0.250 0.263

0.425 0.549 0.354 0.531 0.423 0.445

− 0.19 − 0.25 − 0.16 − 0.24 − 0.19 − 0.20

3.762 3.688 3.804 3.699 3.763 3.750

− 5.089 − 5.213 − 5.018 − 5.195 − 5.087 − 5.109

1.76 1.77 1.75 1.77 1.76 1.76

Calcite structure Dolomite VI CaVI Mg[CO ] 3 2 Kutnahorite VI CaVI Mn[CO ] 3 2 Ankerite VI CaVI Fe[CO ] 3 2 Minrecordite VI CaVI Zn[CO ] 3 2 VI SrVI Mg[CO ] 3 2 Norsethite VI BaVI Mg[CO ] 3 2 VI PbVI Mg[CO ] 3 2

Mixture structure Barytocalcite XI BaVI Ca[CO ] 3 2 Paralstonite VI BaIX Ca[CO ] 3 2 Olekminskite VI SrIX Ca[CO ] 3 2 VIII PbVI Mg[CO ] 3 2 VIII SrVI Mg[CO ] 3 2 XII BaVI Mg[CO ] 3 2 IX BaVI Fe[CO ] 3 2 IX BaVI Mn[CO ] 3 2

B

C

B

Note: Roman number at the left superscript of divalent cations in the structural form denotes their coordination number in double carbonates.

temperatures and pressures, the double carbonate SrMg[CO3 ]2 was also synthesized succesfully by Froese [22]. Our attempt to synthesize this double carbonate at 100 °C through the reaction of SrCO3 with nesquehonite in NaHCO3 solution was not successfull and yielded unreacted SrCO3 rather than the double carbonate under the given boundary conditions. At the end of each run, the vessels were cooled down to room temperature with water within a few minutes and the pH was measured immediately with an ion-selective pH mini-electrode (Ingold). The solids were separated from the aqueous solution using a plastic syringe (60 cm3 ) with membrane filters (0.45 µm; Sartorius). The solids were washed with deionized water and methanol, and dried at 100 °C. The solids were identified by powder X-ray diffraction (Philips XRD goniometer using Cukα radiation) and infrared spectroscopy (Perkin Elmer 683 infrared spectrometer using the KBr dispersion method), yielding the same results in the positions of peaks and their relative intensities as those previously reported by Böttcher et al. [21]. Table 3 lists the measured d values and relative intensities for the synthetic PbMg[CO3 ]2 . In situ pH and speciation of dissolved carbonate species in the experimental solutions were calculated from measured pH values of solutions quenched to room temperature with the computer program Solmineq.88 [50]. Precipitated carbonate was prepared for stable isotope analyses according to the ‘ sealed vessel method’ [51,52] by reaction with 103 % phosphoric acid to which a small surplus of P2 O5 had

6

Y.-F. Zheng and M.E. Böttcher Table 3. Powder XRD data for synthetic PbMg(CO3 )2 .

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d Value

Relative intensity (%)

5.541 4.137 3.795 2.975 2.760 2.618 2.466 2.251 2.116 2.069 1.897 1.865 1.841 1.795 1.605 1.584

18 26 37 100 21 38 26 37 27 38 12 34 54 5 8 23

Notes: (1) the d value was calibrated against a synthetic CaF2 as an internal standard; (2) the relative intensity was normalized against the dominant peak at d = 2.975.

Table 4. Oxygen and carbon isotope compositions of reactants used in the experiments. Reactant

δ 13 C (‰)

δ 18 O (‰)

NaHCO3 MgCO3 ·3H2 O PbCO3 SrCO3

− 7.77 3.02 − 21.58 − 28.39

18.02 36.13 15.82 1.52

been added [53]. The reaction for the double carbonate went to completion within 24 h. Isotope ratio measurements were performed on a Finnigan MAT-251 mass spectrometer at the Geochemical Institute in University of Göttingen, Germany, with the necessary corrections following Craig [54]. The kinetic fractionation factors for the liberation of CO2 from NaHCO3 and nesquehonite by the reaction with phosphoric acid at 25 °C were assumed to be equal to that for calcite [34]. Although this assumption is clearly a simplification, it does not significantly influence the final results because the oxygen isotope compositions of these reactants would be equilibrated with the aqueous solutions prior to the precipitation of PbMg[CO3 ]2 . The acid fractionation factor for PbCO3 has been taken from Friedman and O’Neil [55], and that for the PbMg double carbonate was estimated from the pure Pb and Mg carbonate end-members [55,56] following the approach of Böttcher [12,52] and Böttcher and Dietzel [57] by averaging the values of pure end-members, yielding a value of 1.01122 at 25 °C. The oxygen isotope composition of deionized water was determined by the CO2 –H2 O equilibration method at 25 °C using an equilibrium fractionation factor of 1.0412 [58]. The carbon and oxygen isotope ratios are presented in the conventional δ-notation with respect to the Vienna PeeDee Belemnite (VPDB) and Vienna Standard Mean Ocean Water (VSMOW) standards, respectivley. Replicate analyses agreed within ± 0.1 ‰ for δ 13 C and ± 0.15 ‰ for δ 18 O. The stable isotope compositions of reactants and products are listed in Tables 4 and 5. The partial exchange technique of Northrop and Clayton [59] was applied to data from the experiments forming BaMg[CO3 ]2 , yielding oxygen isotope fractionation factors under given experimental conditions [12]. Although PbCO3 is less soluble than BaCO3 , this technique is also applied to the

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Table 5.

Experimental conditions for synthesis of PbMg(CO3 )2 and its carbon and oxygen isotope compositions.

Run no.

T Duration (°C) (h)

PbMg-1 60 PbMg-2 60 PbMg-3a 100 PbMg-4 100 a

890 891 670 890

δ 18 O (‰) (H2 O)

NaHCO3 (mol/kg)

PbCO3 (mg)

MgCO3 ·3H2 O (mol/kg)

pH (final, 20°C)

δ 13 C (‰) (product)

δ 18 O (‰) (product)

− 7.1 − 7.1 − 8.8 − 7.1

0.2 0.2 0.2 0.2

50 50 50 50

37.2 37.2 37.2 37.2

8.49 8.50 8.49 8.50

− 7.79 − 7.80 − 8.31 − 8.04

12.43 12.47 6.54 7.51

The powder XRD analysis indicates the presence of trace PbCO3 .

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present study in order to acquire the oxygen isotope fractionation factors between PbMg[CO3 ]2 and water and the carbon isotope fractionation toward dissolved inorganic carbonate (DIC).

3. 3.1.

Results Oxygen isotope fractionation

The double carbonates may occur in the structures of calcite, aragonite and mixture types. Although they have the same reduced mass (Wct–o ) and similar C–O bond strengths (CC–O ), divalent cation–oxygen bond strengths (CM–O ) are different from each other due to the differences in the coordination number and radius of divalent cations (Table 1). The double carbonates of calcite structure have I–18 O indices of 0.9759 to 1.0110 (Table 2), which are systematically greater than those of 0.9460 to 0.9663 for the double carbonates of mixed structure. Thus, the double carbonates of calcite structure are enriched in 18 O relative to the double carbonates of mixture structure (Figure 1). For the trimorphs of BaCa[CO3 ]2 , alstonite of the aragonite structure IX BaIX Ca[CO3 ]2 has the lowest I–18 O value of 0.9127, whereas barytocalcite XI BaVI Ca[CO3 ]2 and paralstonite VI BaIX Ca[CO3 ]2 of the mixture structure have I–18 O indices of 0.9605 and 0.9460, respectively (Table 2). Therefore, alstonite is depleted in 18 O relative to both barytocalcite and paralstonite (Figure 1(a)). Natural ankerite may contain considerable amounts of Mg and Mn in the solid solutions of Ca(Fe,Mg,Mn)[CO3 ]2 . In this case, the Mn-rich variety is enriched in 18 O relative to the Mg-rich variety, but depleted in 18 O relative to the Fe-rich variety (Table 2). Oxygen isotope fractionation in the ankerite of a given composition can be calculated from proportions of the three divalent metal cations. In the present experiments on PbMg[CO3 ]2 , anhydrous PbCO3 was used as the reactant. The reaction forming the double carbonate went to completion according to the overall reaction: PbCO3 + Mg2+ + CO2− 3 → PbMg[CO3 ]2 .

(1)

The formation rate of PbMg[CO3 ]2 is lower than that of norsethite [3,12], and the conditions for the establishment of oxygen isotope exchange equilibrium in the experiments are also presented in Table 4. The temperature dependence of oxygen isotope fractionation factors between the PbMg double carbonate (PbMg) and water (W) is described by the following equation (r = 0.993, n = 4): 103 ln αPbMg−W = 2.47 × 106 /T 2 − 2.75.

(2)

The result is presented in Figure 2 and compared with the calculated fractionations for cerussite (PbCO3 ), magnesite (MgCO3 ) and the dimorphs of PbMg[CO3 ]2 . The experimental data fall between curves calculated by Zheng [41] for the two Pb and Mg end-members, respectively, with the aragonite- and calcite-type structures. They are better described by the present calculation for the PbMg[CO3 ]2 with the mixture structure than that with the calcite structure.

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Y.-F. Zheng and M.E. Böttcher

Figure 1. Calculated oxygen isotope fractionation factors between double carbonates and water. The calcite structure denotes the alternative occupation of two divalent cations in the sixfold coordinated sites, whereas the mixture structure denotes the alternative occupation of two divalent cations in different coordinated sites (see the text for details).

Figure 2. Comparison of oxygen isotope fractionation factors between PbMg[CO3 ]2 and H2 O derived from synthesis experiment with the present calculation for the dimorphs of PbMg[CO3 ]2 in the calcite and mixture structures, respectively. Also compared are fractionations calculated by Zheng [41] for two Pb and Mg carbonate end-members, cerussite and magnesite, respectively.

3.2.

Carbon isotope fractionation

Carbon isotope data are also available from the present experiments (Tables 4 and 5). The carbon isotope discrimination between the double carbonate and the DIC species is expressed by αPbMg−DIC =

δ 13 CPbMg + 1000 . δ 13 CDIC + 1000

(3)

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Since the speciation of DIC depends on the pH, Equation (3) is also a function of the proton activity. In a closed system, the δ 13 CDIC can be calculated from the initial amounts and isotope compositions (Tables 4 and 5) considering reaction (1) for completion by applying a mass balance: [C · δ 13 CC − N · δ 13 CPbMg ] , (4) δ 13 CDIC = C − N where C is the total amount of carbon in the system and N represents the amount of the double carbonate formed. By analogy to the transformation reaction of BaCO3 to norsethite [2,9], this reaction runs to completion. Conventionally, the isotope fractionation in the carbon system is given with respect to a CO2 gas phase. The relationship for the PbMg double carbonate is, therefore, described by summing the fractionation factors for dissolved carbonate species H2 CO3 (C1), [HCO3 ]− (C2 ) and [CO3 ]2− (C3) with respect to CO2 : · αC3 ), αPbMg−CO2 = αPbMg−DIC · (XC1 · αC1 + XC2 · αC2 + XCO2− 3

(5)

where X represents the mole fractions of individual carbonate species and α denotes their fractionation factors with respect to the CO2 gas phase [60]. Equation (5) describes the carbon isotope fractionation between PbMg double carbonate and carbon dioxide under the assumption that all carbon-bearing species have contributed to the carbonate precipitation and thus their individual fractionation factors have contributed to the bulk fractionation factors. At the equilibrium of dissolution and precipitation, the precipitated carbonate is at isotopic equilibrium with dissolved carbonate ions. The mole fractions under the experimental conditions were calculated based on the quenched pH values (Table 5) by taking into account all relevant ion pairs and complexes. This practice could lead to a difference in the calculated mole fractions because the quenched pH values may differ from the experimental pH values at running temperatures. In terms of the fractionation factors between dissolved carbonate species and CO2 following Lesniak and Sakai [61], we have derived the following temperature-dependent relationship (r = 0.999; n = 4): (6) 103 ln αPbMg−CO2 = 1.96 × 106 /T 2 − 13.28. If the fractionation factors of Halas et al. [62] are used for the isotope discrimination in the dissolved carbonate system, it only yields minor differences (less than about 0.2 ‰) to Equation (6) in the investigated temperature range. As illustrated in Figure 3, the experimental data for the carbon isotope fractionation between PbMg[CO3 ]2 and CO2 are close to fractionations calculated by Golyshev et al. [64] for cerussite, but they do not fall between curves calculated for the two Pb and Mg end-members.

4.

Discussion

For the crystal structure of single carbonates, divalent metal cations of the calcite group occupy the sixfold coordinated sites, whereas those of the aragonite groups are in the ninefold coordinated sites [45,46]. Because of the difference in the coordination number of divalent cations, the calcite-group single carbonates are consistently enriched in 18 O relative to the aragonite-group single carbonates [41]. This is the structural effect on the oxygen isotope partitioning in carbonate minerals, an intrinsic property of the minerals in terms of their physical chemistry. When double carbonates are precipitated from aqueous solutions, they may take one of the three structures: (1) the calcite structure with the alternative distribution of divalent cations X and Y in the sixfold coordinated sites, (2) the aragonite structure with the alternative distribution of divalent

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cations X and Y in the ninefold coordinated sites and (3) the mixture structure in which X may occupy the 6-fold to 12-fold coordinated site and Y may occupy the sixfold or ninefold coordinated site [46]. In the present case of PbMg[CO3 ]2 , for instance, Pb2+ occurs in the eightfold coordinated sites and Mg2+ occurs in the sixfold coordinated sites. As a consequence, the double carbonates of calcite structure are consistently enriched in 18 O relative to those of aragonite and mixture structures (Table 2). Therefore, there is also the intrinsic relationship between the cation coordination and oxygen isotope fractionation of double carbonates. In the present calibrations of oxygen isotope fractionation factors between PbMg[CO3 ]2 and H2 O, the experimental data are close to the calculated results for PbMg[CO3 ]2 with the mixture structure (Figure 2). This suggests that the synthetic PbMg[CO3 ]2 has approached the oxygen isotope equilibrium with water. In addition, the experimental results are closer to the PbCO3 end-member than the MgCO3 end-member, suggesting a predominated control of ninefold coordinated Pb2+ in cerussite on the oxygen isotope fractionation in the synthetic PbMg[CO3 ]2 . Nevertheless, the synthetic PbMg[CO3 ]2 was precipitated via reaction (1) in which not only one half of the ninefold coordinated Pb2+ is substituted by the sixfold coordinated Mg2+ , but also another half of the ninefold coordinated Pb2+ is tranformed to the eightfold coordinated Pb2+ . Such structural transformation involves a series of physicochemical processes from dissolution of PbCO3 and MgCO3 ·3H2 O in the aqueous solutions to precipitation of PbMg[CO3 ]2 . As such, the thermodynamic equilibrium for the oxygen isotope fractionation between PbMg[CO3 ]2 and H2 O was approached through reaction (1) in association with the new occupation of Pb2+ and Mg2+ , respectively, in the eightfold and sixfold coordinated sites. On the other hand, the present experimental data for carbon isotope fractionation in PbMg[CO3 ]2 are close to fractionations calculated by Golyshev et al. [64] for cerussite, but far from those calculated for magnesite (Figure 3). While this is consistent with the common wisdom that the rate of isotope exchange between dissolved carbonate species is slower for carbon than for oxygen, it is possible that the both oxygen and carbon isotope equilibrium fractionations would be achieved by the unidirectional chemical reaction. As such, the calculation of Golyshev et al. [64] would have overestimated carbon isotope fractionation factors between cerussite and CO2 . Nevertheless, it is also likely that there is carbon isotope inheritance from PbCO3 without considerable incorporation of the carbon isotope signature from MgCO3 . The presence of PbCO3 as the reactant in reaction (1) would have played a predominant role in dictating the

Figure 3. Comparison of carbon isotope fractionation factors between PbMg[CO3 ]2 and CO2 derived from synthesis experiment with those calculated by Golyshev et al. [64] for two Pb and Mg carbonate end-members, cerussite and magnesite, respectively.

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synthetic PbMg[CO3 ]2 . Although the DIC pool during the synthesis of PbMg[CO3 ]2 is dominated by the initial dissolved NaHCO3 and nesquehonite, the carbon isotope inheritance, if did exist, suggests that PbMg[CO3 ]2 would have nucleated from tiny PbCO3 grains in this aqueous solution. Nevertheless, the oxygen isotope exchange would have been sufficient between the carbonates PbMg[CO3 ]2 , PbCO3 and MgCO3 and H2 O during the synthesis experiments, resulting in the close approaching of equilibrium fractionation between the synthetic PbMg[CO3 ]2 and H2 O (Figure 2). In this regard, the processes of dissolution and precipitation in the synthesis of PbMg[CO3 ]2 during reaction (1) have exerted different controls on carbon and oxygen isotope partitioning in the resulted PbMg[CO3 ]2 . Norsethite BaMg[CO3 ]2 was experimentally synthesized by Böttcher [12] from aqueous solutions to determine its carbon and oxygen isotope fractionation factors between 20 °C and 90 °C. The resultant norsethite exbihits the same structure as dolomite, with the regular distribution of a Ba2+ layer, a [CO3 ]2− layer, a Mg2+ layer, another [CO3 ]2− layer and so forth. A series of isotopically different reactants were used in the synthesis experiments in order to prove the achievement of isotope equilibrium fractionations. The experimental carbon isotope fractionation factors between BaMg[CO3 ]2 and CO2 are close to fractionations calculated by Golyshev et al. [64] for witherite but far from those calculated for magnesite (Figure 4). This indicates that the calculation of Golyshev et al. [64] would have overestimated carbon isotope fractionation factors between witherite and CO2 since the both oxygen and carbon isotope equilibrium fractionations would be achieved by the unidirectional chemical reaction. On the other hand, there could be the carbon isotope inheritance from witherite, as hypothesized from the present study of PbMg[CO3 ]2 (Figure 3). As such, the norsethite in the synthesis experiments of Böttcher [12] would be precipitated via the chemical reaction similar to reaction (1), in which both BaCO3 and MgCO3 ·3H2 O would have been dissolved in aqueous solutions prior to the precipitation of BaMg[CO3 ]2 . This also involves a series of physicochemical processes in which not only one half of the ninefold coordinated Ba2+ is substituted by the sixfold coordinated Mg2+ , but also the other half is tranformed to the sixfold coordination. Nevertheless, the oxygen isotope exchange between BaMg[CO3 ]2 , PbCO3 , MgCO3 and H2 O would have been sufficient during the chemical recation. As a consequence, the experimental oxygen isotope fractionation factors for the norsethite–water system not only agree with those calculated in the present study for the calcitestructured norsethite–water system (Figure 5), but also fall between two curves calculated by

Figure 4. Comparison of carbon isotope fractionation factors between norsethite and carbon dioxide derived from experimental determination of Böttcher [12] with those calculated by Golyshev et al. [64] for two Ba and Mg carbonate end-members, witherite and magnesite, respectively.

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Figure 5. Comparison of oxygen isotope fractionation factors between norsethite and water derived from experimental determination of Böttcher [12] with the present calculation for the dimorphs of BaMg[CO3 ]2 in the calcite and mixture structures, respectively. Also compared are fractionations calculated by Zheng [41] for two Ba and Mg carbonate end-members, witherite and magnesite, respectively.

Zheng [41] for witherite and magnesite. This provides indirect evidence for the achievement of thermodynamic equilibrium for the oxygen isotope fractionation between norsethite and water during the synthesis experiments. The experimentally determined oxygen isotope fractionation factors by Böttcher [12] for the norsethite–water system are closer to the MgCO3 end-member than the BaCO3 end-member (Figure 5). This suggests a predominated control of sixfold coordinated Mg2+ on the oxygen isotope partitioning in the synthetic BaMg[CO3 ]2 . Although BaCO3 was also present as the reactant during the synthesis experiments of Böttcher [12], the addition of MgCO3 ·3H2 O to the aqueous solution had played a crucial role in dictating the crystal structure of the synthetic BaMg[CO3 ]2 . In a series of kinetic experiments, it was shown that MgCO3 ·3H2 O was completely dissolved in the solution at first before the solution slowly reacted with the BaCO3 to form norsethite [12]. The structural transformation during the norsethitization of BaCO3 always takes place via a dissolution–precipitation pathway. Since the slow process was dominant for the precipitation of norsethite from the aqueous solution, there would be sufficient time for oxygen isotope equilibration between the dissolved carbonate species and water [63,65]. As a consequence, the oxygen isotope partitioning in dissolved MgCO3 species would have controlled the overall isotope composition of norsethite. Although the formation of BaMg[CO3 ]2 in the synthesis experiments involves the substitution of ninefold coordinated Ba2+ by the sixfold coordinated Mg2+ , the precipitated norsethite has taken the calcite structure rather than the aragonite structure. On the other hand, the rate of oxygen isotope exchange between dissolved norsethite species and water could be faster than the rate of carbon isotope exchange between dissolved norsethite species and carbon dioxide prior to the precipitation of norsethite. As a consequence, it is likely for the carbon isotope fractionation in witherite to be almost fully conveyed to that in the norsethite, but the oxygen isotope fractionation in witherite has been changed to that in norsethite. The differences in the carbon and oxygen isotope fractionations involving the synthetic PbMg[CO3 ]2 and BaMg[CO3 ]2 are evident with respect to the calculated values. This may be attributed either to the incorrect calculations of Golyshev et al. [64] for the carbon isotope fractionation factors, or to the difference in the extent of isotope exchange toward thermodynamic equilibia despite the unidirectional chemical reactions. The latter case involves a kind of kinetic effect in stable isotope fractionation with respect to chemical reaction-driven isotope equilibria.

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The carbon isotope fractionations in PbMg[CO3 ]2 and BaMg[CO3 ]2 would have nearly inherited from those in cerussite and witherite, respectively, without considerable change toward equilibrium values. This suggests differential contributions of the dissolved carbonate species to the carbon isotope fractionations in the precipitated double carbonates. In contrast, the oxygen isotope fractionations in the synthetic PbMg[CO3 ]2 and BaMg[CO3 ]2 have significantly changed toward equilibrium values. The difference in the crystal structure between the synthetic PbMg[CO3 ]2 and BaMg[CO3 ]2 has played a key role in dictating their oxygen isotope partitioning. Taken together, it appears that oxygen isotope fractionation in the double carbonates is quantitatively dictated by the outcome whether the two divalent cations occur either in the calcite structure or in the mixture structure. Therefore, the relationship between the crystal structure and isotope fractionation of double carbonates is dictated by their intrinsic property rather than by their extrinsic property such as the species of initial reactants. Dolomite is a very common carbonate mineral [2,66,67], but it does not form easily under Earth’s surface conditions. There are also experimental problems in the inorganic synthesis of dolomite at surface temperature [68–70]. Nevertheless, the microbially catalyzed synthesis of dolomite has been demonstrated to be successful at low temperatures [68]. Oxygen isotope fractionation in dolomite has been enigmatic [3,6,41,71–75]. As illustrated in Figure 6, the fractionation factors recalculated for the dolomite–water system are the lowest, but are in agreement with empirical calibrations by Matthews and Katz [3] and Vasconcelos et al.[6] respectively, at high and low temperatures. However, all the aforementioned calibrations are consistently lower than those obtained from isotope exchange experiments by Northrop and Clayton [59]. Dolomite is composed of CaCO3 and MgCO3 . Since magnesite is enriched in 18 O relative to calcite [41,76,77], it is expected that oxygen isotope fractionation factors for the dolomite–water system are systematically smaller than those for the magnesite–water system, but larger than those for the calcite–water system. Theoretical calculations by Chacko and Deines [32] also suggested a more significant enrichment of 18 O in magnesite than in both calcite and dolomite. As such, dolomite would behave the same as the other double carbonates in that its oxygen isotope fractionation is bracketed by fractionations between the two pure CaCO3 and MgCO3 end-members (Figure 6). The experimental values of Northrop and Clayton [59] for the dolomite–water system, however, are even higher than the theoretical values of Chacko and Deines [32] for the magnesite–water system (Figure 6). Natural observations also suggested larger dolomite–water fractionations than magnesite–water fractionations [77]. It appears that there would be disequilibrium oxygen isotope fractionations in the majority of experimental and natural samples containing dolomite. For the disequilibrium fractionation in the experiment results of Northrop and Clayton [59], it may be ascribed to dissolution–reprecipitation of the starting dolomite, which is common in fluid-present isotope exchange experiments [78–80]. In general, Ca–Mg double carbonate may occur in ordered and disordered structures [46]. The dolomite of ordered structure is composed of a Ca2+ layer, a [CO3 ]2– layer, a Mg2+ layer, another [CO3 ]2– layer and so forth. If some of the Ca2+ layers contain Mg2+ and some of the Mg2+ layers contain Ca2+ , this yields the protodolomite of disordered structure. Most dolomites of ancient dolostones are well ordered. Protodolomite is generally defined as single-phase rhombohedral Ca–Mg double carbonates that deviate from the composition of dolomite, or are imperfectly ordered, or both [81]. There is a metastable intermediate phase during the dolomitization of calcium carbonate in experimental and in many natural systems, with a high degree of cation ordering. Because there is no difference in the coordination of divalent metal cations between dolomite and protodolomite, we propose that protodolomite may exhibit a behavior of oxygen isotope fractionation similar to that of dolomite. This is confirmed by the observations that oxygen isotope fractionations involving protodolomite in the precipitation experiments of Horita [75] at 80–100 °C and Fritz and Smith [73] at 25–79 °C do not differ from those involving dolomite in the other experiments (Figure 6).

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As mentioned earlier, the stable isotope fractionation in double carbonates is dictated not only by their chemical composition and crystal structures, but also by the kinetic isotopes effect that may take place during the processes of dissolution–reprecipitation. For oxygen isotope fractionation involving the precipitation of dissolved complex anions such as single and double carbonates from aqueous solutions, there are basically two steps that determine the oxygen isotope equilibration between a precipitate and water (Figure 7). The first one is the isotope exchange between the dissolved carbonate species and water, and the second one is the isotope exchange between the dissolved species and the crystallizing precipitate, probably followed by further isotope exchange between the precipitate and water (always via dissolved reactive species). According to the experimental study of Zhou and Zheng [63] for oxygen isotope exchange and equilibration between carbonate and water, the oxygen isotope exchange reaction between dissolved carbonate species and water is the rate-limiting step for the oxygen

Figure 6. Comparison of oxygen isotope fractionation factors between dolomite and water derived from available experimental and empirical calibrations with the present calculation. Also compared are fractionations calculated by Chacko and Deines [32] for two Ca and Mg carbonate end-members, calcite and magnesite, respectively (extended to higher temperatures than 130 °C by Zheng [31]). It is noticed that the experimental data for protodolomite at 80–100 °C from Horita [75] and at 25–79 °C from Fritz and Smith [73] are concordant with data derived from experimental, empirical and theoretical calibrations for dolomite.

Figure 7. Oxygen isotope exchange and equilibrium between dissolved carbonate species, precipitated carbonate and water systems (abstracted after Zhou and Zheng [63]). (I) Oxygen isotope exchange between dissolved carbonate species and water which is usually slow with significant fractionation; (II) oxygen isotope exchange between the precipitated and dissolved carbonates which is generally fast with insignificant fractionation. The final isotope fractionation between the precipitated carbonate and water is primarily dictated by the oxygen isotope equilibration between dissolved carbonate species and water (Zhou and Zheng [65]).

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isotope equilibration between the precipitated carbonate and water. The combination of divalent cations with dissolved carbonate species results in the precipitation of carbonate minerals, which has bearing on the structural effect of carbonate crystallization on the oxygen isotope fractionation between the mineral and water [31,41]. Thus, the second step is generally fast and associated with less significant fractionation, but the first step is slow and associated with much more significant fractionation. As a consequence, the finally observed fractionations between the precipitated carbonate and water primarily depend on the extent of isotope exchange in the first step [65].

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5.

Conclusions

The calculations of oxygen isotope fractionation between double carbonates and water suggest that the double carbonates of calcite structure are systematically enriched in 18 O relative to those of aragonite and mixture structures. The internally consistent fractionation factors for the double carbonate minerals are generally consistent with the data available from laboratory experiments. Synthesis experiments on PbMg[CO3 ]2 and norsethite BaMg[CO3 ]2 yield oxygen isotope fractionations that fall between those for pure carbonate end-members. The coordination and radii of divalent metal cations play a substantial role in dictating the 18 O-increments in the different structures of double carbonates. Therefore, the present calibrations provide a geochemical constraint on the relationship between the crystal structure and chemical composition of double carbonates in laboratory and nature. In contrast, experimentally determined carbon isotope fractionations between PbMg[CO3 ]2 and CO2 are much closer to theoretical predictions for the cerussite–CO2 than those for the magnesite–CO2 system, similar to the previously observed fractionation behavior for BaMg[CO3 ]2 . Substantially, stable isotope fractionation between all crystalline carbonates and water is kinetically dictated not only by their crystal structure but also by the kinetics of isotope exchange between dissolved carbonate species and water prior to and during their crystallization. Therefore, the combined theoretical and experimental results provide insights into the effects of cation coordination and exchange kinetics on stable isotope partitioning in the double carbonates. Acknowledgements This contribution is dedicated to Jochen Hoefs on the occasion of his 75th birthday. He is thanked for hosting YFZ to study stable isotope geochemistry in the University of Göttingen and for providing MEB to use the mass spectrometer at the Geochemical Institute. We are grateful to Dr Gerhard Strauch and Taylor & Francis for the invaluable support in realizing this special issue. Thanks are due to Dr Zhengrong Wang and the two anonymous reviewers for their comments on this manuscript, which helped in the improvement of the presentation.

Funding This study was supported by funds from the National Natural Science Foundation of China [41621022] and by Leibniz Institute for Baltic Sea Research.

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Oxygen isotope fractionation in double carbonates.

Oxygen isotope fractionations in double carbonates of different crystal structures were calculated by the increment method. Synthesis experiments were...
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