Hydration in solution is critical for stable oxygen isotope fractionation between carbonate ion and water

Various isotope studies require accurate fractionation factors (α’s) between different chemical compounds in thermodynamic equilibrium. Although numerous isotope systems involve aqueous solutions, the conventional theory is formulated for the gas-phase and predicts incorrect α’s for many compounds dissolved in water. Here I show that quantum-chemistry calculations, which take into account solute–water interactions, accurately predict, for instance, oxygen isotope fractionation between dissolved and H₂O (hereafter ). Simple force field and quantum-chemistry calculations for the ‘gas-phase’ ion predict (15‰) at 25 °C. However, based on -clusters with up to 22 H₂O molecules, I calculate a value of 25‰, which agrees with the experimental value of 24.5 ± 0.5‰. Effects of geometry and anharmonicity on the calculated α were also examined. The calculations reveal the critical role of hydration in solution, which is ignored in the gas-phase theory. The approach presented provides an adequate framework for calculating fractionation factors involving dissolved compounds; it may also be used to predict α’s that cannot (or have not yet been) determined experimentally.     

A model for oxygen and sulfur isotope fractionation in sulfate during bacterial sulfate reduction processes

We present a model of bacterial sulfate reduction that includes equations describing the fractionation relationship between the sulfur and the oxygen isotope composition of residual sulfate (δ³⁴S_{SO4_residual}, δ¹⁸O_{SO4_residual}) and the amount of residual sulfate. The model is based exclusively on oxygen isotope exchange between cell-internal sulfur compounds and ambient water as the dominating mechanism controlling oxygen isotope fractionation processes. We show that our model explains δ³⁴S_{SO4_residual} vs. δ¹⁸O_{SO4_residual} patterns observed from natural environments and from laboratory experiments, whereas other models, favoring kinetic isotope fractionation processes as dominant process, fail to explain many (but not all) observed δ³⁴S_{SO4_residual} vs. δ¹⁸O_{SO4_residual} patterns. Moreover, we show that a “typical” δ³⁴S_{SO4_residual} vs. δ¹⁸O_{SO4_residual} slope does not exist. We postulate that measurements of δ³⁴S_{SO4_residual} and δ¹⁸O_{SO4_residual} can be used as a tool to determine cell-specific sulfate reduction rates, oxygen isotope exchange rates, and equilibrium oxygen isotope exchange factors. Data from culture experiments are used to determine the range of sulfur isotope fractionation factors in which a simplified set of equations can be used. Numerical examples demonstrate the application of the equations. We postulate that, during denitrification, the oxygen isotope effects in residual nitrate are also the result of oxygen isotope exchange with ambient water. Consequently, the equations for the relationship between δ³⁴S_{SO4_residual}, δ¹⁸O_{SO4_residual}, and the amount of residual sulfate could be modified and used to calculate the fractionation-relationship between δ¹⁵N_{NO3_residual}, δ¹⁸O_{NO3_residual}, and the amount of residual nitrate during denitrification.     

Oxygen isotope exchange rate between dissolved sulfate and water at hydrothermal temperatures

Oxygen isotope exchange rate between dissolved sulfate and water was experimentally determined at 100, 200 and 300°C. The isotope exchange rate is strongly dependent on temperature and pH of the solution. Combining the temperature and pH dependence of the reaction rate, the exchange reaction was estimated to be first-order with respect to sulfate. The logarithm of apparent rate constant of exchange reaction at a given temperature is a function of the pH calculated at the experimental temperatures. From the pH dependence of the apparent rate constant, it was deduced that the isotope exchange reaction between dissolved sulfate and water proceeds through collision between H₂SO⁰₄ and H₂O at low pH, and between HSO^?₄ and H₂O at intermediate pH. The isotope exchange rate obtained indicates that oxygen isotope geothermometry utilizing the studied isotope exchange is suitable for temperature estimation of geothermal reservoirs. The extrapolated half-life of this reaction to oceanic temperature is about 10⁹ years, implying that exchange between oceanic sulfate and water cannot control the oxygen isotope ratio of oceanic sulfates.     

Carbon isotope fractionation between dissolved and gaseous carbon dioxide

Fractionation of the stable carbon isotopes between dissolved and gaseous carbon dioxide has been measured at temperature 25°C by two methods. In the first method the open system conditions and different methods of CO₂ sampling were arranged. In the second method—the closed system conditions and CO₂ gas extraction were used. The results obtained by these methods are very consistent. Gaseous CO₂ is enriched in heavy isotope by 1.03±0.02 permil in comparison to dissolved carbon dioxide.     

Oxygen isotope fractionation of dissolved oxygen during reduction by ferrous iron

The oxygen isotope fractionation factor of dissolved oxygen gas has been measured during inorganic reduction by aqueous FeSO₄ at 10−54 °C under neutral (pH 7) and acidic (pH 2) conditions, with Fe(II) concentrations ranging up to 0.67 mol L⁻¹, in order to better understand the geochemical behavior of oxygen in ferrous iron-rich groundwater and acidic mine pit lakes. The rate of oxygen reduction increased with increasing temperature and increasing Fe(II) concentration, with the pseudo-first-order rate constant k ranging from 2.3 to 82.9 × 10⁻⁶ s⁻¹ under neutral conditions and 2.1 to 37.4 × 10⁻⁷ s⁻¹ under acidic conditions. The activation energy of oxygen reduction was 30.9 ± 6.6 kJ mol⁻¹ and 49.7 ± 13.0 kJ mol⁻¹ under neutral and acidic conditions, respectively. Oxygen isotope enrichment factors (ε) become smaller with increasing temperature, increasing ferrous iron concentration, and increasing reaction rate under acidic conditions, with ε values ranging from −4.5‰ to −11.6‰. Under neutral conditions, ε does not show any systematic trends vs. temperature or ferrous iron concentration, with ε values ranging from −7.3 to −10.3‰. Characterization of the oxygen isotope fractionation factor associated with O₂ reduction by Fe(II) will have application to elucidating the process or processes responsible for oxygen consumption in environments such as groundwater and acidic mine pit lakes, where a number of possible processes (e.g. biological respiration, reduction by reduced species) may have taken place.     

文石—水体系氧同位素分馏机理的实验研究

采用“附晶生长法”分别在５０和７０℃下合成文石下矿物,获得了两种不同的文石与水之间的氧同位素分馏关系。结果证明,文石与水之间氧同位素分馏的化学动力学机 为两步：（１）碳酸根与水之间进行氧同位素交换和平衡,即：「Ｃ＾１６Ｏ３」＾＾３－＋２Ｈ２＾１８Ｏ＝「Ｃ＾１８Ｏ３＾１６Ｏ」＾２－＋２Ｈ２Ｏ１６Ｏ;（２）与水平衡以后的「ＣＯ２」＾２－离子与Ｃａ＾２＋结合生成文石,即：Ｃａ＾２＋＋＿「Ｃ＾１８Ｏ２＾１     

Oxygen isotope fractionation between zoisite and water

Oxygen isotope fractionations between zoisite and water have been studied at 400–700°C, PH₂O = 13.4 kbar, using the three-isotope method described by Matsuhisaet al. (1978) and Matthewset al. (1983a). The zoisite-waier exchange reaction takes place extremely slowly and consequently direct-exchange calibration of equilibrium ${}^{18}\text{O}{}^{16}\text{O}$ fractionation factors was possible only at 600 and 700°C. Fractionation factors at 400–600°C were determined from samples hydrothermally crystallized from a glass of the anhydrous zoisite composition. At 600°C, both exchange procedures gave identical fractionations within experimental error. Scanning electron microscope studies showed that the zoisite-water exchange reaction occurs largely by solution-precipitation mass-transfer mechanisms. The slow kinetics of zoisite-water exchange may be typical of hydrous silicates, since additional experiments on tremolite-water and chlorite-water exchange also showed very low rates. When the zoisite-water fractionation factors determined in this study are combined with the quartz and albite-water data of Matsuhisaet al. (1979) and the calcite-water data of O'Nellet al. (1969), mineral-pair fractionations are obtained for which the coefficients “A” in the equation 1000 In α = A × 10⁶T^?2 are:

     

8.

电气石和水之间的氢同位素分馏   总被引：1，自引：0，他引：1  

钱雅倩  郭吉保 《地球学报》1994,15(Z1):189-196

作者对电气-水体系氢同位素平衡分馏和动力学分馏和动力学分馏开展了实验研究，丰富了羟基矿物氢同位素分馏资料。本文对该研究的实验技术、分析方法作了介绍，并对实验结果进行讨论与国外已有的该方面的资料作了对比。在800-650℃时电气石和水之间氢同位素平衡分馏系数与温度间线性关系为103lna电气石-水=-28.24（106/T2）+2.60；交换速率常数与温度间关系为lnk2=-0.19-6.70（103/T）     

9.

Oxygen isotope fractionation between rutile and water   总被引：1，自引：0，他引：1  

Sunit K. Addy  G. D. Garlick 《Contributions to Mineralogy and Petrology》1974,45(2):119-121

Synthetic rutile-water fractionations (1000 ln α) at 775, 675, and 575° C were found to be ?2.8, ?3.5, and ?4.8, respectively. Partial exchange experiments with natural rutile at 575° C and with synthetic rutile at 475° C failed to yield reliable fractionations. Isotopic fractionation within the range 575–775° C may be expressed as follows: 1 $$1000\ln \alpha ({\rm T}i{\rm O}_{2 } - H_2 O) = - 4.1 \frac{{10^6 }}{{T_{k^2 } }} + 0.96$$ . Combined with previously determined quartz-water fractionations, the above data permit calibration of the quartz-rutile geothermometer: 1 $$1000\ln \alpha ({\text{S}}i{\rm O}_{2 } - Ti{\rm O}_{2 } ) = 6.6 \frac{{10^6 }}{{T_{k^2 } }} - 2.9$$ . When applied to B-type eclogites from Europe, as an example, the latter equation yields a mean equilibration temperature of 565° C.     

10.

The hydrogen isotope fractionation between kaolinite and water   总被引：1，自引：0，他引：1  

Kon-Kee Liu  Samuel Epstein 《Chemical Geology》1984,46(4):335-350

Hydrogen isotope fractionation factors between kaolinite and water were determined at temperatures between 200° and 352°C. Five-gram samples of kaolinite were heated in contact with 8-mg samples of water in sealed glass reaction tubes. Under these conditions the approach to equilibrium with time will be reflected primarily in the change of the δ D in the water. Also the δ D of the hydrogen in the kaolinite will be relatively constant, subject to minor corrections. About seventy sealed vessels were heated for various times at various temperatures. During four months of heating, ～ 25% of kaolinite hydrogen exchanged with the water at 200°C, whereas 100% exchanged at 352°C. The α-values were estimated assuming equilibrium between exchanged kaolinite and water. The 10³lnα-values are estimated to be ?20, ?15, ?6 and +7 for 352°, 300°, 250° and 200°C, respectively, which are in approximate agreement with reported values previously determined at 400°C using conventional methods as well as those estimated from kaolinite in hydrothermally active systems. The curve representing the relationship between the hydrogen isotope fractionation factor for the kaolinite-water system and temperatures between 400° and 25°C is not monotonic but rather has a maximum at 200°C.     

11.

Hydrogen isotope fractionation between kaolinite and water revisited     

《Geochimica et cosmochimica acta》1996,60(3):529-533

The equilibrium hydrogen isotope fractionation factor (α) between kaolinite and water in the temperature range 330 to 0°C is 1000 In α_kaol-water = −2.2 × 10⁶T⁻² − 7.7. This monotonic expression is based on a combination of experimental data with >75% of exchange and empirical calibrations. The previously proposed and widely accepted complex fractionation expression is considered to reflect the role of surface and intersite fractionation effects in the low percent of exchange experiments(Liu and Epstein, 1984), and incorrect δD water values for the empirical values (Lambert and Epstein, 1980). There is no measurable fractionation between dickite and kaolinite. The temperature dependence of the kaolinite-water hydrogen isotope fractionation factor can probably be used as a model for other phyllosilicate-water systems below 350°C.     

12.

Oxygen isotope fractionation between hydroxide minerals and water     

Yong-Fei Zheng 《Physics and Chemistry of Minerals》1998,25(3):213-221

The modified increment method has been applied to the calculation of oxygen isotope fractionation factors for hydroxide minerals. The results suggest the following sequence of ¹⁸O-enrichment in the common hydroxides: limonite > gibbsite > goethite > brucite > diaspore. The hydroxides are significantly enriched in ¹⁸O relative to the corresponding oxides. The sequence of ¹⁸O-enrichment in the hydroxides and oxides of trivalent cations is as follows: M(OH)₃ > MO(OH) > M₂O₃. There are also considerable fractionations within the polymorphos of Al(OH)₃. The internally consistent fractionation factors for hydroxide–water systems are obtained for the temperature range of 0 to 1200 °C, which are comparable with the data derived from synthesis experiments and natural samples at surficial temperatures. Temperature dependence of oxygen isotope fractionations between goethite, gibbsite, boehmite and diaspore and water are significant enough for the purpose of geothermometry. Thus the hydroxide–water pairs hold great promise of serving as reliable paleothermometers in surficial geological environments. Received: 22 January 1997 / Revised, accepted: 2 June 1997     

13.

Hydrogen isotope fractionation between OH-bearing minerals and water     

Tetsuro Suzuoki  Samuel Epstein 《Geochimica et cosmochimica acta》1976,40(10):1229-1240

Hydrogen isotope fractionation factors between hydroxyl-bearing minerals and water were determined at temperatures ranging between 400 and 850°C. The hydrogen isotope exchange rates for the mineral-water pairs examined were very slow. In most cases it was necessary to use an interpolation method for the determination of the hydrogen isotope equilibrium fractionation factor, α_e.For the temperature range of 450–850°C the hydrogen isotope fractionation factors for the mica-water and amphibole-water systems are simply expressed as a function of temperature and the molar fractions of the six-fold coordinated cations in the crystal, regardless of mineral species, as follows: 10³ In α_{e(mineral-water)} = ? 22.4 (10⁶T^?2) + 28.2 + (2X_Al ? 4X_Mg ? 68X_Fe), where X is the molar fraction of the cations. As the equation indicates, for any specific composition of the OH-bearing minerals, the change of α_e with temperature, over the temperature range investigated, is the same for all minerals studied. Thus for any specified values of X_Al, X_Mg, and X_Fe for these minerals, the relationship between α_e and T is 10³ In α_e = αT^?2 + k. Consequently, hydrogen isotope fractionation among coexisting minerals is temperature independent and cannot be used as a hydrogen isotope geothermometer.Some exceptions to the above general observations exist for minerals such as boehmite and kaolinite. In these minerals hydrogen bonding modifies the equilibrium hydrogen isotopic fractionation between mineral and water.     

14.

A revised isotope fractionation model for dissimilatory sulfate reduction in sulfate reducing bacteria   总被引：1，自引：0，他引：1  

Benjamin Brunner 《Geochimica et cosmochimica acta》2005,69(20):4759-4771

Sulfur isotope fractionation during dissimilatory sulfate reduction has been conceptually described by the widely accepted Rees model as related to the stepwise reduction of sulfate to sulfide within the cells of bacteria. The magnitude of isotope fractionation is determined by the interplay between different reduction steps in a chain of reactions. Here we present a revision of Rees’ model for bacterial sulfate reduction that includes revised fractionation factors for the sulfite-sulfide step and incorporates new forward and reverse steps in the reduction of sulfite to sulfide, as well as exchange of sulfide between the cell and ambient water. With this model we show that in contrast to the Rees model, isotope fractionations well in excess of −46‰ are possible. Therefore, some of the large sulfur isotope fractionations observed in nature can be explained without the need of alternate pathways involving the oxidative sulfur cycle. We use this model to predict that large fractionations should occur under hypersulfidic conditions and where electron acceptor concentrations are limiting.     

15.

Influence of the enzyme dissimilatory sulfite reductase on stable isotope fractionation during sulfate reduction     

Muna Mangalo  Rainer U. Meckenstock  Willibald Stichler 《Geochimica et cosmochimica acta》2008,72(6):1513-1520

The stable isotopes of sulfate are often used as a tool to assess bacterial sulfate reduction on the macro scale. However, the mechanisms of stable isotope fractionation of sulfur and oxygen at the enzymatic level are not yet fully understood. In batch experiments with water enriched in ¹⁸O we investigated the effect of different nitrite concentrations on sulfur isotope fractionation by Desulfovibrio desulfuricans.With increasing nitrite concentrations, we found sulfur isotope enrichment factors ranging from −11.2 ± 1.8‰ to −22.5 ± 3.2‰. Furthermore, the δ¹⁸O values in the remaining sulfate increased from approximately 50-120‰ when ¹⁸O-enriched water was supplied. Since ¹⁸O-exchange with ambient water does not take place in sulfate, but rather in intermediates of the sulfate reduction pathway (e.g. ), we suggest that nitrite affects the steady-state concentration and the extent of reoxidation of the metabolic intermediate sulfite to sulfate during sulfate reduction. Given that nitrite is known to inhibit the production of the enzyme dissimilatory sulfite reductase, our results suggest that the activity of the dissimilatory sulfite reductase regulates the kinetic isotope fractionation of sulfur and oxygen during bacterial sulfate reduction. Our novel results also imply that isotope fractionation during bacterial sulfate reduction strongly depends on the cell internal enzymatic regulation rather than on the physico-chemical features of the individual enzymes.     

16.

Experimental calibration of oxygen isotope fractionation between quartz and zircon   总被引：3，自引：0，他引：3  

Dustin Trail  Ilya N. Bindeman  E. Bruce Watson  Axel K. Schmitt 《Geochimica et cosmochimica acta》2009,73(23):7110-7126

We report the results of an experimental calibration of oxygen isotope fractionation between quartz and zircon. Data were collected from 700 to 1000 °C, 10–20 kbar, and in some experiments the oxygen fugacity was buffered at the fayalite–magnetite–quartz equilibrium. Oxygen isotope fractionation shows no clear dependence on oxygen fugacity or pressure. Unexpectedly, some high-temperature data (900–1000 °C) show evidence for disequilibrium oxygen isotope partitioning. This is based in part on ion microprobe data from these samples that indicate some high-temperature quartz grains may be isotopically zoned. Excluding data that probably represent non-equilibrium conditions, our preferred calibration for oxygen isotope fractionation between quartz and zircon can be described by:

This relationship can be used to calculate fractionation factors between zircon and other minerals. In addition, results have been used to calculate WR/melt–zircon fractionations during magma differentiation. Modeling demonstrates that silicic magmas show relatively small changes in δ¹⁸O values during differentiation, though late-stage mafic residuals capable of zircon saturation contain elevated δ¹⁸O values. However, residuals also have larger predicted melt–zircon fractionations meaning zircons will not record enriched δ¹⁸O values generally attributed to a granitic protolith. These results agree with data from natural samples if the zircon fractionation factor presented here or from natural studies is applied.     

17.

Oxygen isotope fractionation between biogenic silica and ocean water     

Kenneth Mopper 《Geochimica et cosmochimica acta》1971

     

18.

An experimental study of oxygen isotope fractionation between inorganically precipitated aragonite and water at low temperatures   总被引：1，自引：0，他引：1  

Gen-Tao Zhou 《Geochimica et cosmochimica acta》2003,67(3):387-399

To determine oxygen isotope fractionation between aragonite and water, aragonite was slowly precipitated from Ca(HCO₃)₂ solution at 0 to 50°C in the presence of Mg²⁺ or SO₄²⁻. The phase compositions and morphologies of synthetic minerals were detected by X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. The effects of aragonite precipitation rate and excess dissolved CO₂ gas in the initial Ca(HCO₃)₂ solution on oxygen isotope fractionation between aragonite and water were investigated. For the CaCO₃ minerals slowly precipitated by the CaCO₃ or NaHCO₃ dissolution method at 0 to 50°C, the XRD and SEM analyses show that the rate of aragonite precipitation increased with temperature. Correspondingly, oxygen isotope fractionations between aragonite and water deviated progressively farther from equilibrium. Additionally, an excess of dissolved CO₂ gas in the initial Ca(HCO₃)₂ solution results in an increase in apparent oxygen isotope fractionations. As a consequence, the experimentally determined oxygen isotope fractionations at 50°C indicate disequilibrium, whereas the relatively lower fractionation values obtained at 0 and 25°C from the solution with less dissolved CO₂ gas and low precipitation rates indicate a closer approach to equilibrium. Combining the lower values at 0 and 25°C with previous data derived from a two-step overgrowth technique at 50 and 70°C, a fractionation equation for the aragonite-water system at 0 to 70°C is obtained as follows:

     

19.

Prediction of high-temperature oxygen isotope fractionation factors between mantle minerals     

Yong-Fei Zheng 《Physics and Chemistry of Minerals》1997,24(5):356-364

The increment method is adopted to calculate oxygen isotope fractionation factors for mantle minerals, particularly for the polymorphic phases of MgSiO₃ and Mg₂SiO₄. The results predict the following sequence of ¹⁸O-enrichment: pyroxene (Mg,Fe,Ca)₂Si₂O₆>olivine (Mg,Fe)₂SiO₄>spinel (Mg,Fe)₂SiO₄>ilmenite (Mg,Fe, Ca)SiO₃>perovskite (Mg,Fe,Ca)SiO₃. The calculated fractionations for the calcite-perovskite (CaTiO₃) system are in excellent agreement with experimental calibrations. If there would be complete isotopic equilibration in the mantle, the spinel-structured silicates in the transition zone are predicted to be enriched in ¹⁸O relative to the perovskite-structured silicates in the lower mantle but depleted in ¹⁸O relative to olivines and pyroxenes in the upper mantle. The oxygen isotope layering of the mantle would essentially result from differences in the chemical composition and crystal structure of mineral phases at different mantle depths. Assuming isotopic equilibrium on a whole earth scale, the chemical structure of the Earth's interior can be described by the following sequence of ¹⁸O-enrichment: uppr crust>lower crust>upper mantle>transition zone>lower mantle >core.     

20.

A global model of mass independent mercury stable isotope fractionation     

Jeroen E. Sonke 《Geochimica et cosmochimica acta》2011,75(16):4577-9916

Mass independent fractionation (MIF) of stable isotopes associated with terrestrial geochemical processes was first observed in the 1980s for oxygen and in the 1990s for sulfur isotopes. Recently mercury (Hg) was added to this shortlist when positive odd Hg isotope anomalies were observed in biological tissues. Experimental work identified photoreduction of aquatic inorganic divalent Hg^II and photodegradation of monomethylmercury species as plausible MIF inducing reactions. Observations of continental receptors of atmospheric Hg deposition such as peat, lichens, soils and, indirectly, coal have shown predominantly negative MIF. This has led to the suggestion that atmospheric Hg has negative MIF signatures and that these are the compliment of positive Hg MIF in the aquatic environment. Recent observations on atmospheric vapor phase Hg⁰ and Hg^II in wet precipitation reveal zero and positive Hg MIF respectively and are in contradiction with a simple aquatic Hg^II photoreduction scenario as the origin for global Hg MIF observations.This study presents a synthesis of all terrestrial Hg MIF observations, and these are integrated in a one-dimensional coupled continent-ocean-atmosphere model of the global Hg cycle. The model illustrates how Hg MIF signatures propagate through the various Earth surface reservoirs. The scenario in which marine photoreduction is the main MIF inducing process results in negative atmospheric Δ¹⁹⁹Hg and positive ocean Δ¹⁹⁹Hg of −0.5‰ and +0.25‰, yet does not explain atmospheric Hg⁰ and Hg^II wet precipitation observations. Alternative model scenarios that presume in-cloud aerosol Hg^II photoreduction and continental Hg^II photoreduction at soil, snow and vegetation surfaces to display MIF are necessary to explain the ensemble of natural observations. The model based approach is a first step in understanding Hg MIF at a global scale and the eventual incorporation of Hg stable isotope information in detailed global mercury chemistry and transport models.     

	Ab	Cc	Zo
Q	0.50	0.50	1.56
Ab		0.00	1.06
Cc			1.06

电气石和水之间的氢同位素分馏

作者对电气-水体系氢同位素平衡分馏和动力学分馏和动力学分馏开展了实验研究，丰富了羟基矿物氢同位素分馏资料。本文对该研究的实验技术、分析方法作了介绍，并对实验结果进行讨论与国外已有的该方面的资料作了对比。在800-650℃时电气石和水之间氢同位素平衡分馏系数与温度间线性关系为103lna电气石-水=-28.24（106/T2）+2.60；交换速率常数与温度间关系为lnk2=-0.19-6.70（103/T）     

Oxygen isotope fractionation between rutile and water

Synthetic rutile-water fractionations (1000 ln α) at 775, 675, and 575° C were found to be ?2.8, ?3.5, and ?4.8, respectively. Partial exchange experiments with natural rutile at 575° C and with synthetic rutile at 475° C failed to yield reliable fractionations. Isotopic fractionation within the range 575–775° C may be expressed as follows: 1 $$1000\ln \alpha ({\rm T}i{\rm O}_{2 } - H_2 O) = - 4.1 \frac{{10^6 }}{{T_{k^2 } }} + 0.96$$ . Combined with previously determined quartz-water fractionations, the above data permit calibration of the quartz-rutile geothermometer: 1 $$1000\ln \alpha ({\text{S}}i{\rm O}_{2 } - Ti{\rm O}_{2 } ) = 6.6 \frac{{10^6 }}{{T_{k^2 } }} - 2.9$$ . When applied to B-type eclogites from Europe, as an example, the latter equation yields a mean equilibration temperature of 565° C.     

The hydrogen isotope fractionation between kaolinite and water

Hydrogen isotope fractionation factors between kaolinite and water were determined at temperatures between 200° and 352°C. Five-gram samples of kaolinite were heated in contact with 8-mg samples of water in sealed glass reaction tubes. Under these conditions the approach to equilibrium with time will be reflected primarily in the change of the δ D in the water. Also the δ D of the hydrogen in the kaolinite will be relatively constant, subject to minor corrections. About seventy sealed vessels were heated for various times at various temperatures. During four months of heating, ～ 25% of kaolinite hydrogen exchanged with the water at 200°C, whereas 100% exchanged at 352°C. The α-values were estimated assuming equilibrium between exchanged kaolinite and water. The 10³lnα-values are estimated to be ?20, ?15, ?6 and +7 for 352°, 300°, 250° and 200°C, respectively, which are in approximate agreement with reported values previously determined at 400°C using conventional methods as well as those estimated from kaolinite in hydrothermally active systems. The curve representing the relationship between the hydrogen isotope fractionation factor for the kaolinite-water system and temperatures between 400° and 25°C is not monotonic but rather has a maximum at 200°C.     

Hydrogen isotope fractionation between kaolinite and water revisited

The equilibrium hydrogen isotope fractionation factor (α) between kaolinite and water in the temperature range 330 to 0°C is 1000 In α_kaol-water = −2.2 × 10⁶T⁻² − 7.7. This monotonic expression is based on a combination of experimental data with >75% of exchange and empirical calibrations. The previously proposed and widely accepted complex fractionation expression is considered to reflect the role of surface and intersite fractionation effects in the low percent of exchange experiments(Liu and Epstein, 1984), and incorrect δD water values for the empirical values (Lambert and Epstein, 1980). There is no measurable fractionation between dickite and kaolinite. The temperature dependence of the kaolinite-water hydrogen isotope fractionation factor can probably be used as a model for other phyllosilicate-water systems below 350°C.     

Oxygen isotope fractionation between hydroxide minerals and water

The modified increment method has been applied to the calculation of oxygen isotope fractionation factors for hydroxide minerals. The results suggest the following sequence of ¹⁸O-enrichment in the common hydroxides: limonite > gibbsite > goethite > brucite > diaspore. The hydroxides are significantly enriched in ¹⁸O relative to the corresponding oxides. The sequence of ¹⁸O-enrichment in the hydroxides and oxides of trivalent cations is as follows: M(OH)₃ > MO(OH) > M₂O₃. There are also considerable fractionations within the polymorphos of Al(OH)₃. The internally consistent fractionation factors for hydroxide–water systems are obtained for the temperature range of 0 to 1200 °C, which are comparable with the data derived from synthesis experiments and natural samples at surficial temperatures. Temperature dependence of oxygen isotope fractionations between goethite, gibbsite, boehmite and diaspore and water are significant enough for the purpose of geothermometry. Thus the hydroxide–water pairs hold great promise of serving as reliable paleothermometers in surficial geological environments. Received: 22 January 1997 / Revised, accepted: 2 June 1997     

Hydrogen isotope fractionation between OH-bearing minerals and water

Hydrogen isotope fractionation factors between hydroxyl-bearing minerals and water were determined at temperatures ranging between 400 and 850°C. The hydrogen isotope exchange rates for the mineral-water pairs examined were very slow. In most cases it was necessary to use an interpolation method for the determination of the hydrogen isotope equilibrium fractionation factor, α_e.For the temperature range of 450–850°C the hydrogen isotope fractionation factors for the mica-water and amphibole-water systems are simply expressed as a function of temperature and the molar fractions of the six-fold coordinated cations in the crystal, regardless of mineral species, as follows: 10³ In α_{e(mineral-water)} = ? 22.4 (10⁶T^?2) + 28.2 + (2X_Al ? 4X_Mg ? 68X_Fe), where X is the molar fraction of the cations. As the equation indicates, for any specific composition of the OH-bearing minerals, the change of α_e with temperature, over the temperature range investigated, is the same for all minerals studied. Thus for any specified values of X_Al, X_Mg, and X_Fe for these minerals, the relationship between α_e and T is 10³ In α_e = αT^?2 + k. Consequently, hydrogen isotope fractionation among coexisting minerals is temperature independent and cannot be used as a hydrogen isotope geothermometer.Some exceptions to the above general observations exist for minerals such as boehmite and kaolinite. In these minerals hydrogen bonding modifies the equilibrium hydrogen isotopic fractionation between mineral and water.     

A revised isotope fractionation model for dissimilatory sulfate reduction in sulfate reducing bacteria

Sulfur isotope fractionation during dissimilatory sulfate reduction has been conceptually described by the widely accepted Rees model as related to the stepwise reduction of sulfate to sulfide within the cells of bacteria. The magnitude of isotope fractionation is determined by the interplay between different reduction steps in a chain of reactions. Here we present a revision of Rees’ model for bacterial sulfate reduction that includes revised fractionation factors for the sulfite-sulfide step and incorporates new forward and reverse steps in the reduction of sulfite to sulfide, as well as exchange of sulfide between the cell and ambient water. With this model we show that in contrast to the Rees model, isotope fractionations well in excess of −46‰ are possible. Therefore, some of the large sulfur isotope fractionations observed in nature can be explained without the need of alternate pathways involving the oxidative sulfur cycle. We use this model to predict that large fractionations should occur under hypersulfidic conditions and where electron acceptor concentrations are limiting.     

Influence of the enzyme dissimilatory sulfite reductase on stable isotope fractionation during sulfate reduction

The stable isotopes of sulfate are often used as a tool to assess bacterial sulfate reduction on the macro scale. However, the mechanisms of stable isotope fractionation of sulfur and oxygen at the enzymatic level are not yet fully understood. In batch experiments with water enriched in ¹⁸O we investigated the effect of different nitrite concentrations on sulfur isotope fractionation by Desulfovibrio desulfuricans.With increasing nitrite concentrations, we found sulfur isotope enrichment factors ranging from −11.2 ± 1.8‰ to −22.5 ± 3.2‰. Furthermore, the δ¹⁸O values in the remaining sulfate increased from approximately 50-120‰ when ¹⁸O-enriched water was supplied. Since ¹⁸O-exchange with ambient water does not take place in sulfate, but rather in intermediates of the sulfate reduction pathway (e.g. ), we suggest that nitrite affects the steady-state concentration and the extent of reoxidation of the metabolic intermediate sulfite to sulfate during sulfate reduction. Given that nitrite is known to inhibit the production of the enzyme dissimilatory sulfite reductase, our results suggest that the activity of the dissimilatory sulfite reductase regulates the kinetic isotope fractionation of sulfur and oxygen during bacterial sulfate reduction. Our novel results also imply that isotope fractionation during bacterial sulfate reduction strongly depends on the cell internal enzymatic regulation rather than on the physico-chemical features of the individual enzymes.     

Experimental calibration of oxygen isotope fractionation between quartz and zircon

We report the results of an experimental calibration of oxygen isotope fractionation between quartz and zircon. Data were collected from 700 to 1000 °C, 10–20 kbar, and in some experiments the oxygen fugacity was buffered at the fayalite–magnetite–quartz equilibrium. Oxygen isotope fractionation shows no clear dependence on oxygen fugacity or pressure. Unexpectedly, some high-temperature data (900–1000 °C) show evidence for disequilibrium oxygen isotope partitioning. This is based in part on ion microprobe data from these samples that indicate some high-temperature quartz grains may be isotopically zoned. Excluding data that probably represent non-equilibrium conditions, our preferred calibration for oxygen isotope fractionation between quartz and zircon can be described by:

This relationship can be used to calculate fractionation factors between zircon and other minerals. In addition, results have been used to calculate WR/melt–zircon fractionations during magma differentiation. Modeling demonstrates that silicic magmas show relatively small changes in δ¹⁸O values during differentiation, though late-stage mafic residuals capable of zircon saturation contain elevated δ¹⁸O values. However, residuals also have larger predicted melt–zircon fractionations meaning zircons will not record enriched δ¹⁸O values generally attributed to a granitic protolith. These results agree with data from natural samples if the zircon fractionation factor presented here or from natural studies is applied.     

An experimental study of oxygen isotope fractionation between inorganically precipitated aragonite and water at low temperatures

To determine oxygen isotope fractionation between aragonite and water, aragonite was slowly precipitated from Ca(HCO₃)₂ solution at 0 to 50°C in the presence of Mg²⁺ or SO₄²⁻. The phase compositions and morphologies of synthetic minerals were detected by X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. The effects of aragonite precipitation rate and excess dissolved CO₂ gas in the initial Ca(HCO₃)₂ solution on oxygen isotope fractionation between aragonite and water were investigated. For the CaCO₃ minerals slowly precipitated by the CaCO₃ or NaHCO₃ dissolution method at 0 to 50°C, the XRD and SEM analyses show that the rate of aragonite precipitation increased with temperature. Correspondingly, oxygen isotope fractionations between aragonite and water deviated progressively farther from equilibrium. Additionally, an excess of dissolved CO₂ gas in the initial Ca(HCO₃)₂ solution results in an increase in apparent oxygen isotope fractionations. As a consequence, the experimentally determined oxygen isotope fractionations at 50°C indicate disequilibrium, whereas the relatively lower fractionation values obtained at 0 and 25°C from the solution with less dissolved CO₂ gas and low precipitation rates indicate a closer approach to equilibrium. Combining the lower values at 0 and 25°C with previous data derived from a two-step overgrowth technique at 50 and 70°C, a fractionation equation for the aragonite-water system at 0 to 70°C is obtained as follows:

     

Prediction of high-temperature oxygen isotope fractionation factors between mantle minerals

The increment method is adopted to calculate oxygen isotope fractionation factors for mantle minerals, particularly for the polymorphic phases of MgSiO₃ and Mg₂SiO₄. The results predict the following sequence of ¹⁸O-enrichment: pyroxene (Mg,Fe,Ca)₂Si₂O₆>olivine (Mg,Fe)₂SiO₄>spinel (Mg,Fe)₂SiO₄>ilmenite (Mg,Fe, Ca)SiO₃>perovskite (Mg,Fe,Ca)SiO₃. The calculated fractionations for the calcite-perovskite (CaTiO₃) system are in excellent agreement with experimental calibrations. If there would be complete isotopic equilibration in the mantle, the spinel-structured silicates in the transition zone are predicted to be enriched in ¹⁸O relative to the perovskite-structured silicates in the lower mantle but depleted in ¹⁸O relative to olivines and pyroxenes in the upper mantle. The oxygen isotope layering of the mantle would essentially result from differences in the chemical composition and crystal structure of mineral phases at different mantle depths. Assuming isotopic equilibrium on a whole earth scale, the chemical structure of the Earth's interior can be described by the following sequence of ¹⁸O-enrichment: uppr crust>lower crust>upper mantle>transition zone>lower mantle >core.     

A global model of mass independent mercury stable isotope fractionation

Mass independent fractionation (MIF) of stable isotopes associated with terrestrial geochemical processes was first observed in the 1980s for oxygen and in the 1990s for sulfur isotopes. Recently mercury (Hg) was added to this shortlist when positive odd Hg isotope anomalies were observed in biological tissues. Experimental work identified photoreduction of aquatic inorganic divalent Hg^II and photodegradation of monomethylmercury species as plausible MIF inducing reactions. Observations of continental receptors of atmospheric Hg deposition such as peat, lichens, soils and, indirectly, coal have shown predominantly negative MIF. This has led to the suggestion that atmospheric Hg has negative MIF signatures and that these are the compliment of positive Hg MIF in the aquatic environment. Recent observations on atmospheric vapor phase Hg⁰ and Hg^II in wet precipitation reveal zero and positive Hg MIF respectively and are in contradiction with a simple aquatic Hg^II photoreduction scenario as the origin for global Hg MIF observations.This study presents a synthesis of all terrestrial Hg MIF observations, and these are integrated in a one-dimensional coupled continent-ocean-atmosphere model of the global Hg cycle. The model illustrates how Hg MIF signatures propagate through the various Earth surface reservoirs. The scenario in which marine photoreduction is the main MIF inducing process results in negative atmospheric Δ¹⁹⁹Hg and positive ocean Δ¹⁹⁹Hg of −0.5‰ and +0.25‰, yet does not explain atmospheric Hg⁰ and Hg^II wet precipitation observations. Alternative model scenarios that presume in-cloud aerosol Hg^II photoreduction and continental Hg^II photoreduction at soil, snow and vegetation surfaces to display MIF are necessary to explain the ensemble of natural observations. The model based approach is a first step in understanding Hg MIF at a global scale and the eventual incorporation of Hg stable isotope information in detailed global mercury chemistry and transport models.