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Oxygen isotope fractionation in phosphates: the role of dissolved complex anions in isotope exchange



a

Yong-Fei Zheng a

CAS Kay 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 Published online: 14 Jan 2015.

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Isotopes in Environmental and Health Studies, 2015 http://dx.doi.org/10.1080/10256016.2014.999678

Oxygen isotope fractionation in phosphates: the role of dissolved complex anions in isotope exchange†

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Yong-Fei Zheng ∗ CAS Kay 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 (Received 18 March 2014; accepted 6 November 2014) † Dedicated

to Professor Dr Jochen Hoefs on the occasion of his 75th birthday.

Oxygen isotope fractionation factors for phosphates were calculated by means of the increment method. The results suggest that Ag3 PO4 and BiPO4 are enriched in 18 O relative to AgPO4 , and the three phosphates are consistently depleted in 18 O relative to Ba3 [PO4 ]2 ; fluorapatite and chlorapatite exhibit a similar behaviour of oxygen isotope fractionation with consistent enrichment of 18 O relative to hydroxyapatite. The valence, radii and coordination of metal cations play a quantitative role in dictating the 18 O/16 O partitioning in these phosphates of different compositions. The calculated fractionation factors for the Ag3 PO4 –H2 O system are in agreement with experimental determinations derived from enzyme-catalysed isotope exchange between dissolved inorganic phosphate and water at the longest reaction durations at low temperatures. This demonstrates that the precipitated Ag3 PO4 has completely captured the oxygen isotope fractionation in the dissolved inorganic phosphate. The calculated fractionation factors for the F/Cl-apatite–water systems are in agreement with the enzyme-catalysed experimental fractionations for the dissolved phosphate–water system at the longest reaction durations but larger than fractionations derived from bacteria-facilitated exchange and inorganic precipitation experiments as well as natural observations. For the experimental calibrations of oxygen isotope fractionation involving the precipitation of dissolved phosphate species from aqueous solutions, the fractionation between precipitate and water is primarily dictated by the isotope equilibration between the dissolved complex anions and water prior to the precipitation. Therefore, the present results provide a quantitative means to interpret the temperature dependence of oxygen isotope fractionation in inorganic and biogenic phosphates. Keywords: biogenic apatite; dissolved phosphate; exchange kinetics; fractionation factor; isotope fractionation; oxygen-18; precipitated phosphate; structural carbonate

1.

Introduction

The oxygen isotope composition of biogenic apatites has been widely used in the reconstruction of Earth’s surface environments, with emphasis on surface water temperatures and mixing ratios between fresh and marine waters from which the phosphate precipitated [1–3]. For this purpose, a number of oxygen isotope fractionation equations have been calibrated between various bioapatites and water [4–6]. However, there are considerable discrepancies between different

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Y.-F. Zheng

calibrations. Depending on the equation selected from the literature, water temperatures calculated from bioapatite δ 18 O values can vary as large as 8 K [7]. This uncertainty is significant because paleoclimatic shifts during the Phanerozoic are often characterized by changes in global seawater temperatures within this range. In order to resolve these discrepancies, much attention has been paid to the geochemical procedures of these calibrations. Systematic calculations of oxygen isotope fractionation in various minerals of geochemical interest have been accomplished by the increment method [8–12]. However, discrepancies were encountered when comparing the data calculated for phosphate minerals [11] with those obtained from the laboratory experiments [13,14]. Although there is incomplete information on the thermodynamic equilibrium between phosphates and water in the experimental and empirical calibrations, an additional bias may result from the assumptions that were used in the previous calculation [11]. Nevertheless, the calculations of oxygen isotope fractionation in carbonate minerals have converged to consistent results from different methods [15]. Thus, this paper presents a revised calculation of oxygen isotope fractionation in phosphates, with an extension to silver, bismuth and barium phosphates that were chemically prepared from apatites for oxygen isotope analysis [16–18]. Also calculated is the oxygen isotope fractionation in the structural carbonates of apatite. The results are compared with the updated data from natural observations and laboratory experiments, providing new insights into the nature of oxygen isotope partitioning in dissolved and precipitated phosphates.

2.

Methods

The present calculations deal with phosphates of different compositions. These include not only crystalline minerals such as apatite groups but also dissolved phosphates in the precipitate forms of Ag3 PO4 , AgPO4 , BiPO4 and Ba3 [PO4 ]2 . The apatite group includes OH, F and Cl apatites. Their crystal structures are following those presented by Smyth and Bish [19] and Hughes and Rakovan [20]. The calculation of 18 O-increments for cation–oxygen bonds (ict–o ) in the phosphates is essentially the same as that presented by Zheng [11]. The only difference lies in the choice of ionic radii, with the present calculations referring to Muller and Roy [21]. Minor amounts of carbonate (3–6 wt %) often occur in the crystal structure of natural apatites. Such structural carbonates may substitute either monovalent anions such as F (A-type) or tetrahedral PO4 groups (B-type) [22,23]. Both types of substitution involve not only the perturbation of crystal lattice but also charge compensation in apatites, leading to a decrease in apatite crystallinity with increasing amounts of structural carbonate [2]. For this reason, this study also calculates oxygen isotope fractionation in the structural carbonates of apatite. According to the chemical formula of Ca5 [PO4 ]3 (OH, F, Cl) for apatites, A-type structural carbonate (ASC) may occur in the form of Ca10 [PO4 ]6 (CO3 ) in fluorapatite, and B–type structural carbonate (BSC) may occur in the form of Ca5 [CO3 ]4 (OH)2 or Ca5 [CO3 (OH)]3 (OH) in hydroxyapatite but Ca5 [CO3 F]3 F in fluorapatite [22,23]. The calculation of 18 O-increments for cation–oxygen bonds (ict–o ) in these structural carbonates is a combination of the approaches for carbonates [14] and hydroxyl-bearing silicates [10]. For Ca10 [PO4 ]6 (CO3 ), its chemical formula may be reorganized as CaCO3 ·Ca9 [PO4 ]6 , in which the CaCO3 unit has the same crystal structure as vaterite. The ionic radii for it are also after [21]. The normalized 18 O-increments for cation–oxygen bonds (ict−o ) are calculated by taking C−O and Ca−O bonds in calcite as reference bonds, respectively, for cation–oxygen bonds inside a chemically complexed unit and those outside the unit (Table 1). The enrichment coefficient of 18 O in a given phosphate compound is quantified by the oxygen isotope index (I–18 O) relative to the reference calcite; so are the structural carbonates of apatite. The I–18 O index of calcite

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Table 1.

The 18 O-increment of cation–oxygen bonds in phosphates and carbonates.

Bond

V ct

CNct

mct

rct

ro

rct + ro

Wct−o

C ct−o

ict−o

ict−o

C−O Ca−O P−O Ag–O Ag–O Bi–O Ba–O C−O Ca–O

4 2 5 1 3 3 2 4 2

3 6 4 4 8 8 8 3 8

12.01 40.08 30.98 200.59 200.59 208.98 137.34 12.01 40.08

0.06 1.14 0.31 1.18 0.97 1.25 1.56 0.06 1.26

1.22 1.22 1.22 1.22 1.22 1.22 1.28 1.24 1.24

1.28 2.36 1.53 2.40 2.19 2.47 2.84 1.30 2.50

1.02471 1.04224 1.03878 1.05580 1.05580 1.05598 1.05381 1.02471 1.04224

1.04167 0.14124 0.81699 0.10417 0.17123 0.15182 0.08803 1.02564 0.10000

0.02542 0.00584 0.03108 0.00566 0.00930 0.00827 0.00461 0.02503 0.00414

1.0000 1.0000 0.9606 1.0331 0.8566 0.8907 1.1254 0.9961 0.8414

is defined as unity (1.0000) for the calculation of phosphate I–18 O indices [11]. As such, the reduced partition function ratios of calcite calculated originally by Kieffer [24] and then corrected by Clayton et al. [25] are used as the reference values to calculate the thermodynamic oxygen isotope factors (equivalent to 103 ln β, which are regressed in the form of A × 106 /T 2 + B × 103 /T + C, where T is the Kelvin temperature) for the phosphates. For oxygen isotope fractionations involving water, 103 ln β data presented by Hattori and Halas [26] are used, which were based on the theoretical calculations of Richet et al. [27]. These reference 103 ln β values were also regressed in the function of 103 ln β = A × 106 /T2 + B × 103 /T + C, consistent with those calculated for minerals. Calculated fractionations in phosphates and structural carbonates are thus described in the function of 103 ln α = A × 106 /T2 + B × 103 /T + C (Tables 2 and 3), which are sufficiently precise at both high and low temperatures [15]. Although the correction to the mineral/water interaction is still retained for the present calculation of oxygen isotope fractionation factors between structural carbonates and water, such a correction is removed in dealing with the phosphate–water systems. This is because there is negligible oxygen isotope fractionation between dissolved and precipitated phosphates in the presence of water [14].

3.

Results and discussion

Silver phosphate can be present in the forms of Ag3 PO4 and AgPO4 , respectively, under reduced and oxidized conditions. There is a significant difference in their crystal structures due to a series of differences in their crystallographic parameters such as the valence (Vct ), radius (rct ), and coordination (CNct ) of Ag cations (Table 1). Silver in Ag3 PO4 is monovalent in the four-fold coordinated sites, whereas silver in AgPO4 is trivalent in the eight-fold coordinated sites. As a consequence, Ag3 PO4 has a greater I–18 O index of 0.9208 than 0.8790 for AgPO4 (Table 2). According to the principle of the increment method, the greater the I–18 O index of a mineral, the more 18 O-enriched it is relative to the other minerals. Thus, Ag3 PO4 is more enriched in 18 O than AgPO4 at thermodynamic equilibrium. At 25 °C, the calculated oxygen isotope fractionation between Ag3 PO4 and AgPO4 is 4.18 ‰. There is a difference in the I–18 O index between Ag3 PO4 and BiPO4 (0.9208 vs. 0.8903), suggesting different behaviours of oxygen isotope fractionation between the two phosphate precipitates. Ba3 [PO4 ]2 has the highest I–18 O index of 0.9745 and thus it is enriched in 18 O relative to the silver and bismuth phosphates (Figure 1). As illustrated in Figure 2, the fractionation factors calculated for the Ag3 PO4 –H2 O system are slightly larger than those obtained from the bacteria-facilitated experiments of Blake et al. [28] at 15 to 35 °C. It is known that geochemical cycling of phosphorus in aquatic environments

Calculated oxygen isotope fractionation in phosphates and carbonates (103 ln α = A × 106 /T 2 + B × 103 /T + C) 103 ln α Quartz−Compound

103 ln α Calcite−Compound

103 ln α Compound−Water

Crystalline compound

M Compound

I–18 O

A

B

C

A

B

C

A

B

C

Dissolved phosphates IV Ag IV PO4 3 VIII AgIV PO4 VIII BiIV PO4 VIII Ba [IV PO ] 3 4 2

0.98302 0.96073 0.96178 0.96142

0.9208 0.8790 0.8903 0.9745

0.958 1.217 1.147 0.624

0.731 1.169 1.051 0.167

− 0.38 − 0.58 − 0.52 − 0.12

0.492 0.751 0.681 0.158

0.832 1.270 1.152 0.268

− 0.38 − 0.58 − 0.52 − 0.12

3.521 3.262 3.332 3.855

− 5.496 − 5.934 − 5.816 − 4.932

0.32 0.52 0.46 0.06

VIII Ca [IV PO ] (OH) 5 4 3 VIII Ca [IV PO ] F 5 4 3 VIII Ca [IV PO ] Cl 5 4 3

0.92710 0.93264 0.93465

0.8906 0.9227 0.9212

1.145 0.946 0.955

1.048 0.711 0.726

− 0.52 − 0.37 − 0.38

0.679 0.480 0.489

1.149 0.812 0.827

− 0.52 − 0.37 − 0.38

3.334 3.533 3.524

− 5.813 − 5.476 − 5.491

0.46 0.31 0.32

Structural carbonate in apatite VIII Ca [III CO ] (OH) 5 3 4 2 VIII Ca [III CO (OH)] (OH) 5 3 3 VIII Ca [III CO F] F 5 3 3 VIII CaIII CO 3

0.92042 0.91893 0.91893 0.91638

0.9698 1.0155 1.0988 0.9445

0.653 0.370 − 0.147 0.810

0.216 − 0.264 − 1.138 0.482

− 0.14 0.07 0.47 − 0.27

0.187 − 0.096 − 0.613 0.344

0.317 − 0.163 − 1.037 0.583

− 0.14 0.07 0.47 − 0.27

3.826 4.109 4.626 3.669

− 4.981 − 4.501 − 3.627 − 5.247

1.74 1.69 1.58 1.78

Apatite group

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

Y.-F. Zheng

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Table 2.

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Table 3. Calculated oxygen isotope fractionation factors between structural carbonate and phosphates of apatite (103 ln α = A × 106 /T 2 + B × 103 /T + C). 103 ln α System A-type substitution CaCO3 – Fluoraptite

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B-type substitution Ca5 [CO3 ]4 (OH)2 – Hydroxyapatite Ca5 [CO3 (OH)]3 (OH) – Hydroxyapatite Ca5 [CO3 F]3 F – Fluorapatite

Figure 1.

Abbreviation

A

B

C

ASC−Fap

0.136

0.229

− 0.10

BSC1–Hap

0.492

0.832

− 0.38

BSC2–Hap

0.775

1.312

− 0.59

BSC3–Hap

1.093

1.849

− 0.84

Plot of calculated oxygen isotope fractionation factors between phosphates and water.

is generally realized by biota and involves reactions that are catalysed by enzymes. In order to elucidate processes underlying biogeochemical cycling of phosphorus and to identify possible reaction pathways for P-compounds in nature, Blake et al. [29] carried out a series of enzyme-catalysed dissolved inorganic phosphate–water exchange experiments of variable reaction durations to determine oxygen isotope effects accompanying phosphoenzymatic reactions. From their experimental results at the longest reaction durations, we have extracted fractionation values of 25.8 ‰ at 5.7 °C, 23.7 ‰ at 15 °C and 22.0 ‰ at 22 °C. A linear fitting to these data yields a fractionation equation of 103 ln α = 19.12 × 103 /T – 42.73. As shown in Figure 2, the fractionation factors calculated for the Ag3 PO4 –H2 O system are in agreement with those calibrated by the enzyme-catalysed experiments [29] at 5.7 to 22 °C with the longest reaction durations. The present calculations yields very similar I–18 O indices for fluorapatite (0.9227) and chlorapatite (0.9212), indicating a very similar behaviour of oxygen isotope fractionation between the two apatites. In contrast, hydroxyapatite exhibits a low I–18 O index of 0.8906 (Table 2) and thus is depleted in 18 O relative to both fluorapatite and chlorapatite. At 25 °C, the calculated oxygen isotope fractionation between F-apatite and OH-apatite is 3.22 ‰. The calculated fractionation between F-apatite and Ag3 PO4 is 0.20 ‰ at 20 °C and 0.17 ‰ at 45 °C, somewhat smaller than previous findings for sedimentary francolite (carbonate F-apatite) dissolved inorganic phosphate for which a fractionation of ca. 1.0 ‰ was obtained at 20 to 45 °C [30]. As depicted in Figure 3,

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Figure 2. Comparison of oxygen isotope fractionation factors between phosphates and water derived from experimental determinations by Lecuyer et al.[13] and Blake et al. [28,29] with the present calculations. The fractionations from the enzyme-catalysed experiments of Blake et al. [29] are taken from their results with the longest exchange periods.

Figure 3. Comparison of oxygen isotope fractionation factors between apatites and water derived from experimental determinations by Blake et al. [28,29] and empirical estimates by Puceat et al. [6], Lecuyer et al. [7] and Longinelli and Nutti [4] with the present calculations. The fractionations from the enzyme-catalysed experiments of Blake et al. [29] are taken from their results with the longest exchange periods.

the fractionation factors calculated for the F/Cl-apatite–water systems are in agreement with those obtained from the enzyme-catalysed experiments [29] with the longest durations. However, they are smaller than the empirical calibration of Puceat et al. [6] at low temperatures. On the other hand, the present calculations for the F/Cl-apatite–water systems are larger than the empirical calibrations of Lecuyer et al. [7] and Longinelli and Nuti [4] as well as the bacteriafacilitated experimental values of Blake et al. [28]. These differences may be caused by kinetic effects during phosphate precipitation either in the laboratory or in nature due to oxygen isotope inheritance from organic/biogenic phosphates [29]. In addition, the difference in phosphate composition may also play a role in dictating the difference in oxygen isotope fractionation between the different calibrations (Figure 1). As presented in Table 2, there are significant differences in I–18 O indices between the structural carbonates of apatite. The ASC has an I–18 O value of 0.9445 for the vaterite-structured

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CaCO3 in the Ca10 [PO4 ]6 (F2 , CO3 ). On the other hand, the BSC has I–18 O values of 0.9698 for Ca5 [CO3 ]4 (OH)2 (BSC1), 1.0155 for Ca5 [CO3 (OH)]3 (OH) (BSC2) and 1.0988 for Ca5 [CO3 F]3 F (BSC3). It appears that the B-type substitution for PO4 by either CO3 (OH) or CO3 F can lead to the significant enrichment of 18 O in the structural carbonate relative to the substitution by the pure carbonate anion. Thus, the configuration and site of carbonate, hydroxyl and fluorine anions in the crystal lattice of apatite play a substantial role in partitioning the light and heavy oxygen isotopes between carbonate and phosphate. As illustrated in Figure 4, calcite is enriched in 18 O relative to both ASC and BSC1 but depleted in 18 O relative to both BSC2 and BSC3. Lecuyer et al. [31] did precipitation experiments of carbonate-bearing hydroxyapatite and obtained that carbonate–water fractionation factors decrease from 32.46–32.80 ‰ at 10 °C to 24.50–25.24 ‰ at 37 °C. These experimental values are in good agreement with the calculated fractionation factors between BSC1 and water, but they differ from those between the BSC2 and water (Figure 4). Such agreement and difference suggest that the synthetic products in the experiments of Lecuyer et al. [31] may occur in the form of Ca5 [CO3 ]4 (OH)2 rather than Ca5 [CO3 (OH)]3 (OH). In the carbonate-bearing apatite of living vertebrates, δ 18 O values of carbonate and phosphate are linearly correlated with a nearly constant difference of 8.56 ‰ [32] or 8.86 ‰ [33]. This property was used as a test for identifying diagenetic alteration in fossil teeth and bones [33–35]. However, measured δ 18 O differences between coexisting carbonate and phosphate in the samples of terrestrial mammals do not show a constant value. Instead they exhibit a range from about 8 to 11 ‰ despite nearly constant body temperatures at 37 ± 2 °C. The present calculation does yield the temperature dependence for the oxygen isotope fractionations between structural carbonate and its host apatite (Table 3). With decreasing temperature, fractionations between BSC1 and phosphate in carbonate-bearing hydroxyapatite increase from 7.3 ‰ at 40 °C to 8.7 ‰ at 10 °C. A similar increase from 7.5 to 9.1 ‰ at 37 to 10 °C was obtained by Lecuyer et al. [31] by combining their experimental apatite-hosted carbonate–water calibration with the biogenic phosphate–water equation of Kolodny et al. [5]. On the other hand, the presently calculated fractionation factors between BSC2 and phosphate in carbonate-bearing hydroxyapatite increase from 11.5 ‰ at 40 °C to 13.7 ‰ at 10 °C. In this regard, the large δ 18 O differences between coexisting carbonate and phosphate in the mammal samples may be caused by the structural substitution of more [CO3 (OH)]3− for [CO3 ]2– in the crystal lattice of natural hydroxyapatite rather

Figure 4. Comparison of oxygen isotope fractionation factors for apatite-hosted carbonate and water derived from the precipitation experiments of Lecuyer et al. [31] at 10–37 °C with the present calculations. As compared are the calculated fractionations involving calcite and aragonite by Zheng [12]. Abbreviations ASC and BSC denote the A-type and B-type structural carbonates, respectively, in apatites; ASC denote the vaterite-structured CaCO3 ; BSC1, BSC2 and BSC3 denote the Ca5 [CO3 ]4 (OH)2 , Ca5 [CO3 (OH)]3 (OH) and Ca5 [CO3 F]3 F, respectively.

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Y.-F. Zheng

than by the diagenetic alteration as usually thought. In addition, there may be molecular water in carbonated hydroxyapatite, complicating the behavior of oxygen isotope partitioning between structural carbonate and apatite. Thus, it is important to identify the occupation of structural hydroxyl and molecular water in carbonate-bearing apatites by spectrometric approaches.

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4.

Implications for oxygen isotope fractionation in dissolved and precipitated phosphates

It has been known for a long time that due to the strong covalent P−O bonds in [PO4 ]3– , the rate of oxygen isotope exchange between dissolved inorganic phosphate and water is very sluggish at low temperatures in the absence of biological catalysis [14,28,29]. This can be attributed to the incomplete exchange of oxygen isotopes in all the four oxygen anions in dissolved inorganic phosphate with oxygen in ambient water, whereas the complete exchange of oxygen isotopes towards equilibrium requires the breaking and reforming of covalent P−O bonds. In contrast, biogenic apatite is generally assumed to be produced in or near the oxygen isotope equilibrium with body (cellular) water as a result of multiple enzyme-catalysed hydrolytic cleavage, condensation and phosphoryl-group transfer reactions inside cells that lead to oxygen isotope equilibrium between dissolved inorganic phosphate and water [1,4,7]. This is demonstrated by Blake et al. [28,29] from their biologically catalysed experiments in both complex organic and inorganic phosphate media, where microbial metabolism and enzyme-mediated reactions of phosphate compounds were accompanied by a significant oxygen isotope exchange between environmental water and inorganic orthophosphate (or organically bound PO4 in some case). Lecuyer et al. [13] reported experimental data for oxygen isotope fractionations between dissolved orthophosphate and water at 50 to 135 °C. Their precipitation experiments showed no isotope exchange at 50 °C between the dissolved phosphate and water at run times from 768 to 3504 h, but showed significant exchange at 75 to 135 °C. It is from the latter experiments at the higher temperatures that the authors conclude that the inorganically dissolved phosphate is systematically enriched in 18 O (about 8 ‰ at 20 °C by extrapolation) relative to the biogenic apatites that were empirically calibrated by Longinelli and Nuti [4] and then confirmed by Kolodny et al. [5]. Lecuyer et al. [13], thus, presented a hypothetical view that the empirical oxygen isotope fractionation factors between biogenic apatite and water (environmental water such as seawater, river water and lake water) do not represent the isotope fractionations at thermodynamic equilibrium. However, O’Neil et al. [14] ascribed this 18 O enrichment of about 8 ‰ to the effect of pH values on the speciation of inorganically dissolved phosphates, which has bearing on the oxygen isotope fractionation between dissolved phosphates and water. On the other hand, it is possible that an oxygen isotope disequilibrium between inorganically dissolved phosphate and water occurred in the experiments of Lecuyer et al. [13]. It is known that the resistance of apatites to oxygen isotope exchange with water and diagenetic alteration at low temperatures makes their oxygen isotope record a very attractive paleoenvironmental indicator. Currently used apatite–water oxygen isotope paleothermometer equations were developed solely on the basis of the empirical measurements of biogenic apatites such as shells, bones and teeth [4,5]. Similar equations were obtained by measuring the oxygen isotope fractionations between coexisting chert and phosphate [36] and between carbonate and phosphate in phosphorite francolite [37]. However, all of these relations were not verified by laboratory-controlled experiments of equilibrium oxygen isotope exchange due to very sluggish reaction rates at low temperatures [28,29]. As outlined by Lecuyer et al. [7], potential bias from thermodynamic equilibrium fractionations could be caused by the following processes: (1) the application of different wet chemistry protocols to concentration and purification of the phosphate compound as Ag3 PO4 or BiPO4 ;

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(2) the measurement of oxygen isotope ratios for phosphates, which can be obtained from the CO2 or CO gases either by quantitative fluorination of the precipitated phosphate, or by partial reduction with graphite at moderate temperatures (1100 °C –1250 °C) or high temperatures (up to 1500 °C); (3) oxygen isotope heterogeneity in the standard materials (e.g. a large range of δ 18 O values from 21.3 to 22.7 ‰ has been found for the phosphate standard reference material SRM 120c in the past two decades). As argued below, on the other hand, the extent of oxygen isotope equilibrium between dissolved inorganic phosphate and water has played a critical role in dictating the resultant fractionations between precipitated phosphate and water. It is generally accepted that the oxygen isotopes in the phosphate are readily exchanged and equilibrated with body water of living organisms via multiple enzyme-catalysed metabolic reactions. By using the enzyme inorganic pyrophosphatase to catalyse the isotope exchange reaction at the low temperatures of 5.7 to 22 °C, Blake et al. [29] obtained the first laboratory-controlled calibration of oxygen isotope fractionation factors between dissolved inorganic phosphate and water. As illustrated in Figure 2, their calibrations with the longest exchange periods are in agreement with the presently calculated fractionations for the Ag3 PO4 –H2 O system. This provides theoretical evidence for the possible achievement of equilibrium oxygen isotope fractionations in their experiments with the longest periods. In particular, the chosen experimental values are in agreement with the theoretical values for the F/Cl-apatite–water systems (Figure 3), suggesting the applicability of the experimental calibration to natural apatite. The precipitation experiments of Lecuyer et al. [13] were conducted by dissolving a synthetic potassium dihydrogen phosphate (KH2 PO4 ) in deionized water. They heated the solutions from room temperature to higher temperatures (50–135 °C) and maintained them at the higher temperatures for the given durations (6–4392 h). After oxygen isotope exchange between the dissolved phosphate species and water had proceeded for the required time, the solutions were quenched to room temperature, and AgCl was added to them, in which each sample of the inorganically dissolved phosphate species was precipitated as Ag3 PO4 following the procedures described by Crowson et al. [18]. These procedures are similar to the hydrothermal experiments of Mizutani and Rafter [38] for determining the oxygen isotope fractionation between bisulphate ion and water, where the dissolved sulphate species were precipitated as barium sulphate. The oxygen of the precipitated Ag3 PO4 was then converted to CO2 by reaction with graphite at 1100 °C for isotope ratio measurements following an approach adapted after O’Neil et al. [39]. Although these laboratory procedures are routine in synthesis experiments for the determination of oxygen isotope fractionation factors, oxygen isotope fractionation in precipitated phosphates is not necessarily responsible for that in dissolved phosphates. Physicochemically, the precipitation of crystalline phosphates from aqueous solutions is a complex process that involves numerous phosphate intermediates or precursors depending on pH, saturation state and chemical compositions of solutions [14,30]. In particular, oxygen isotope fractionations between phosphate precipitates and ambient water are quantitatively controlled by the combined isotopic effects of two intermediate processes: (1) oxygen isotope exchange and equilibrium between dissolved phosphate species and water (path I in Figure 5), and (2) oxygen isotope exchange and equilibrium between the dissolved phosphate species and the precipitated phosphate (path II in Figure 5). Because of the differences in oxygen isotope fractionation between dissolved phosphate species [14,30], a resolution to the oxygen isotope fractionations between Ag3 PO4 , apatite, dissolved inorganic phosphate and water requires consideration of the oxygen isotope effects in the two intermediate steps. It is known that the Ca, Ba, Pb and Sr carbonate minerals have different behaviours of oxygen isotope fractionation [12,15,40,41], and so do the Ca and Ba sulphate minerals [12,42,43].

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Figure 5. Oxygen isotope exchange and equilibrium between dissolved phosphate species, precipitated phosphates and water systems (revised after Liang and Blake [30]). (I) Oxygen isotope exchange between dissolved phosphates and water, which is usually slow; (II) oxygen isotope exchange between the precipitated and dissolved phosphates, which is generally fast. For the experimental calibrations of oxygen isotope fractionation involving the precipitation of dissolved complex anions from aqueous solutions, the fractionation between precipitate and water is primarily controlled by the isotope equilibration between the dissolved phosphate species and water prior to the precipitation.

Furthermore, there are significant oxygen isotope fractionations between the dissolved complex anions such as [H2 PO4 ]− vs. [PO4 ]3– [16], [HCO3 ]– vs. [CO3 ]2– [44,45] and [HSO4 ]– vs. [SO4 ]2– [46]. The protonated complex anions are generally enriched in 18 O relative to the non-protonated complex anion. This may be ascribed to the effects of hydration and structure on oxygen isotope partitioning in these dissolved complex anions. In addition, the results from isotope exchange experiments for dissolved sulphate species show that [HSO4 ]– is enriched in 18 O relative to barite (BaSO4 ) but consistent with partitioning in anhydrite (CaSO4 ) at the same temperatures [37,43,46,47]. On the other hand, the hydrothermal experiments of Poulson and Schoonen [48] indicate that oxygen isotope fractionations between dissolved Na-carbonate and water are smaller than those between divalent carbonate minerals and water. Therefore, oxygen isotope fractionations in dissolved protonated complex anions such as [H2 PO4 ]– , [HCO3 ]– and [HSO4 ]– do not simply correspond either to those in dissolved unprotonated forms such as [PO4 ]3– , [CO3 ]2– and [SO4 ]2– or to those in the corresponding crystalline minerals. However, negligible fractionations may occur between dissolved and precipitated compounds if the isotope exchange approaches the steady-state equilibration between dissolved complex anions and water [46,49]. Although the rate of oxygen isotope exchange between carbonate and water is much faster than that between phosphate and water, known results for the mechanism of oxygen isotope exchange between dissolved carbonate species and water can be used to provide insights into the kinetics of oxygen isotope exchange between dissolved phosphate species and water. For the low-temperature calibration of oxygen isotope fractionation between CaCO3 and H2 O, a variety of dissolved [HCO3 ]– solutions were used for the precipitation of calcium carbonates [40,41,49–52]. Because oxygen isotope fractionation between precipitated and dissolved carbonate species is insignificant, the precipitated CaCO3 can completely capture the isotope fractionation in the dissolved carbonate species [49]. However, this does not mean the automatic establishment of an isotope equilibrium between the precipitated CaCO3 and H2 O, because the isotope exchange between the dissolved carbonate species and water is the ratelimiting step for the isotope equilibrium [53]. Importantly, the precipitated carbonate is able to achieve the isotope equilibrium with water provided that the dissolved carbonate species have achieved the isotope equilibrium with the water. Prior to the precipitation of crystalline carbonates, dissolved [CO3 ]2– would form from the dissociation of dissolved [HCO3 ]– and sustain in solution for a long time [54]. It takes time to exchange oxygen isotopes with H2 O to achieve the thermodynamic equilibrium [53,55]. If the carbonate precipitation takes place prior to the achievement of the isotope equilibrium between the dissolved carbonate species

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and water, the isotope fractionation between the precipitated carbonate and water tends to deviate from the equilibrium. Therefore, the achievement of the isotope equilibrium between the dissolved complex anions and water prior to the precipitation of phosphate, carbonate and sulphate is a key to the attainment of the isotope equilibrium for the precipitate–water systems. Because chemical bonds to heavier isotopes are stronger than bonds to lighter isotopes, the lighter isotopologues are preferentially taken up by the less hydrated species such as [CO3 ]2– [45]. In this regard, it is critical to assess which dissolved complex anions would be combined with metal cations to result in the crystalline precipitate. Importantly, the rates of isotopic exchange either in the laboratory or in nature may be significantly different in two or more systems that differ in the isotope composition of not only dissolved reactants but also precipitated products. This is common for extensively exchanged systems that are of heterogeneous compositions, where the rates of isotope exchange are controlled by a number of factors that depend on the isotope systems themselves in addition to the temperature. These factors include alkalinity and salinity when precipitating carbonates from seawater [49] and rates of recrystallization of a mineral or rates of diffusion in ambient fluids [56,57]. In the absence of fluids, on the other hand, the oxygen isotope composition of primary aragonite is completely inherited by secondary calcite after the polymorphic transformation [58]. For oxygen isotope fractionation involving the precipitation of dissolved complex anions such as phosphate, carbonate and sulphate from water, there are basically two steps that determine the oxygen isotope equilibration between precipitate and water. As illustrated in Figure 5 for the phosphate–water system, the first one is the oxygen isotope exchange between the dissolved phosphate species and water, and the second one is the oxygen isotope uptaking when the crystalline phosphate precipitates from the water. According to the experimental study of Zhou and Zheng [53] for oxygen isotope exchange and equilibrium between carbonate and water, the oxygen isotope exchange reaction between dissolved complex anions and water is slow and thus the rate-limiting step for the equilibrium oxygen isotope fractionation between precipitate and water. The combination of divalent cations with dissolved complex anions results in mineral precipitation, which has bearing on the effect of crystal structure on oxygen isotope fractionation in crystalline precipitates [12]. The two-step exchange kinetics for the carbonate–water system is also applicable to the oxygen isotope fractionation in the phosphate–water systems. As a consequence, the observed final fractionation values between precipitated phosphate and water primarily depend on the extent of isotope exchange in the first step (Figure 5). Now, we return to the precipitation experiments of Lecuyer et al. [13]. The inorganically dissolved phosphate was precipitated as Ag3 PO4 in their experiments. There would be negligible oxygen isotope fractionations between Ag3 PO4 and the dissolved phosphate at their experimental conditions. However, the 18 O enrichment of about 8 ‰ in their experimental results relative to the empirical and theoretical data indicates that the experiments did not achieve oxygen isotope exchange equilibrium between the dissolved phosphate species [PO4 ]3– and H2 O. In this regard, the dissolved [H2 PO4 ]– was rapidly dissociated into the dissolved [PO4 ]3– prior to the precipitation of Ag3 PO4 , without the achievement of oxygen isotope equilibrium between the dissolved [PO4 ]3– and H2 O. This argument is based on the experimental observations of O’Neil et al. [14] that show significant enrichment of 18 O in the dissolved [H2 PO4 ]– relative to the dissolved [PO4 ]3– , which was referred to the pH effect on the speciation of dissolved phosphates. Therefore, the oxygen isotope fractionations obtained by Lecuyer et al. [13] between their silver phosphate and water at 75 to 135 °C cannot be used as a proxy either for the apatite–water system or for the Ag3 PO4 –H2 O system. As such, the oxygen isotope disequilibrium is evident between the dissolved inorganic phosphate and water when precipitating the silver phosphate in their experiments.

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Conclusions

The calculation of oxygen isotope fractionations in phosphates suggest that Ag3 PO4 is enriched in 18 O relative to AgPO4 ; fluorapatite and chlorapatite have similar 18 O-increments with consistent enrichment of 18 O relative to hydroxyapatite. Taken together, the sequence of 18 Oenrichment in the phosphates is: AgPO4 ≤ BiPO4 ≤ OH-apatite < Ag3 PO4 ≤ Cl-apatite ≤ F-apatite < Ba3 [PO4 ]2 . The internally consistent fractionation factors for these phosphates are generally comparable with data available from laboratory experiments and natural observations. The calculated fractionations for the Ag3 PO4 –H2 O system is in agreement with experimental calibrations by enzyme-catalysed isotope exchange between dissolved inorganic phosphate and water at the longest reaction durations at low temperatures. This demonstrates that the precipitated Ag3 PO4 can completely capture the oxygen isotope fractionation in the dissolved inorganic phosphate. Thus, the present calculations provide a valuable means to interpret oxygen isotope data from inorganic and biogenic phosphates in the laboratory and in nature. For the experimental calibrations of oxygen isotope fractionation involving the precipitation of dissolved phosphate species from aqueous solutions, the fractionation between precipitate and water is primarily controlled by the isotope equilibration between the dissolved complex anions and water prior to the precipitation. This involves the two steps of isotope exchange equilibrium during the dissolution and precipitation of phosphates: (1) between dissolved phosphate species and water and (2) between precipitated and dissolved phosphate species. The first step is slow with very significant fractionation, whereas the second step is generally fast with insignificant oxygen isotope fractionation. Because chemical bonds to heavier isotopes are stronger than the bonds to lighter isotopes, the lighter isotopologues are preferentially taken up by the nonprotonated species like [PO4 ]3± . As such, further studies are required to assess which dissolved complex anions would be combined with metal cations to result in crystalline precipitates, and how much time is required for isotope exchange equilibrium to be achieved between dissolved complex anions and water. Acknowledgements This paper is dedicated to Prof. J. Hoefs for his lifelong contributions to stable isotope geochemistry. I thank him for hosting me to study at the University of Göttingen in Germany. Thanks are due to Ruth Blake and Zhengrong Wang for their comments that greatly helped to improve this manuscript.

Disclosure statement No potential conflict of interest was reported by the author.

Funding This study was supported by the Natural Science Foundation of China [grant number 41621022].

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Oxygen isotope fractionation in phosphates: the role of dissolved complex anions in isotope exchange.

Oxygen isotope fractionation factors for phosphates were calculated by means of the increment method. The results suggest that Ag3PO4 and BiPO4 are en...
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