Isotopic fractionation and reaction kinetics between Cr(III) and Cr(VI) in aqueous media

The redox-sensitive stable isotope geochemistry of chromium bears the potential to monitor the attenuation of chromate pollution and to investigate changes in environmental conditions in the present and the past. The use of stable Cr isotope data as a geo-environmental tracer, however, necessitates an understanding of the reaction kinetics and Cr fractionation behaviour during redox transition and isotope exchange. Here, we report stable chromium isotope fractionation data for Cr(VI) reduction, Cr(III) oxidation and isotopic exchange between soluble Cr(III) and Cr(VI) in aqueous media. The reduction of Cr(VI) to Cr(III) with H₂O₂ under strongly acidic conditions shows a near-equilibrium isotope fractionation of Δ^53/52Cr_{(Cr(III)-Cr(VI))} of −3.54 ± 0.35‰. At pH neutrality, however, the reduction experiments show a kinetic isotope fractionation Δ^53/52Cr_{(Cr(III)-Cr(VI))} of −5‰ for the extent of reduction of up to 85% of the chromium. The oxidation of Cr(III) to Cr(VI) in alkaline media, using H₂O₂ as the oxidant, cannot be explained by a single, unidirectional reaction. Our experiments indicate that the involvement of the unstable intermediates Cr(IV) and Cr(V) and their disproportionation during redox reactions between Cr(III) and Cr(VI) influence the overall fractionation factor, depending on the prevailing pH conditions and the reaction rates. No detectable isotope exchange between soluble Cr(VI) and Cr(III) species at pH values of 5.5 and 7 was revealed over a timescale of days to weeks. This means that, at least within such a time frame, the isotopic composition of Cr(VI) in a natural system will not be influenced by equilibration with any Cr(III) and thus reveal the true extent of reduction, given that the Cr isotope composition of the source Cr(VI) and the fractionation factor for the prevailing conditions are known.     

Free energy of formation for green rust sodium sulphate (NaFe6Fe3(OH)18(SO4)2(s))

In a recent study, sulphate-bearing green rust (GR_SO4) was shown to incorporate Na⁺ in its structure (NaFe^II₆Fe^III₃(OH)₁₈(SO₄)_2(s); GR_Na,SO4). The compound was synthesised by aerial oxidation of Fe(OH)_2(s) in the presence of NaOH. This paper reports on its free energy of formation .Freshly synthesised GR_Na,SO4 was titrated with 0.5 M H₂SO₄ in an inert atmosphere at 25 °C, producing dissolved Fe²⁺ and magnetite or goethite. Solution concentrations, PHREEQC and the MINTEQ database were used to calculate reaction constants for the reactions:

     

Iron isotope fractionation during microbially stimulated Fe(II) oxidation and Fe(III) precipitation

Interpretation of the origins of iron-bearing minerals preserved in modern and ancient rocks based on measured iron isotope ratios depends on our ability to distinguish between biological and non-biological iron isotope fractionation processes. In this study, we compared ⁵⁶Fe/⁵⁴Fe ratios of coexisting aqueous iron (Fe(II)_aq, Fe(III)_aq) and iron oxyhydroxide precipitates (Fe(III)_ppt) resulting from the oxidation of ferrous iron under experimental conditions at low pH (<3). Experiments were carried out using both pure cultures of Acidothiobacillus ferrooxidans and sterile controls to assess possible biological overprinting of non-biological fractionation, and both SO₄²⁻ and Cl⁻ salts as Fe(II) sources to determine possible ionic/speciation effects that may be associated with oxidation/precipitation reactions. In addition, a series of ferric iron precipitation experiments were performed at pH ranging from 1.9 to 3.5 to determine if different precipitation rates cause differences in the isotopic composition of the iron oxyhydroxides. During microbially stimulated Fe(II) oxidation in both the sulfate and chloride systems, ⁵⁶Fe/⁵⁴Fe ratios of residual Fe(II)_aq sampled in a time series evolved along an apparent Rayleigh trend characterized by a fractionation factor α_{Fe(III)aq-Fe(II)aq} ∼ 1.0022. This fractionation factor was significantly less than that measured in our sterile control experiments (∼1.0034) and that predicted for isotopic equilibrium between Fe(II)_aq and Fe(III)_aq (∼1.0029), and thus might be interpreted to reflect a biological isotope effect. However, in our biological experiments the measured difference in ⁵⁶Fe/⁵⁴Fe ratios between Fe(III)_aq, isolated as a solid by the addition of NaOH to the final solution at each time point under N₂-atmosphere, and Fe(II)_aq was in most cases and on average close to 2.9‰ (α_{Fe(III)aq-Fe(II)aq} ∼ 1.0029), consistent with isotopic equilibrium between Fe(II)_aq and Fe(III)_aq. The ferric iron precipitation experiments revealed that ⁵⁶Fe/⁵⁴Fe ratios of Fe(III)_aq were generally equal to or greater than those of Fe(III)_ppt, and isotopic fractionation between these phases decreased with increasing precipitation rate and decreasing grain size. Considered together, the data confirm that the iron isotope variations observed in our microbial experiments are primarily controlled by non-biological equilibrium and kinetic factors, a result that aids our ability to interpret present-day iron cycling processes but further complicates our ability to use iron isotopes alone to identify biological processing in the rock record.     

Controls on δ34S and δ18O of dissolved sulfate in aquifers of the Murray Basin,Australia and their use as indicators of flow processes

The usefulness of stable isotopes of dissolved SO₄ (δ³⁴S and δ¹⁸O) to study recharge processes and to identify areas of significant inter-aquifer mixing was evaluated in a large, semi-arid groundwater basin in south-eastern Australia (the Murray Basin). The distinct isotopic signatures in the oxidizing unconfined Murray Group Aquifer and the deeper reducing Renmark Group confined aquifer may be more sensitive than conventional chemical tracers in establishing aquifer connections. δ³⁴S values in the unconfined Murray Group Aquifer in the south and central part of the study area decrease along the hydraulic gradient from 20.8 to 0.3‰. The concomitant increasing SO₄/Cl ratios, as well as relatively low δ¹⁸O_SO4 values, suggest that vertical input of biogenically derived SO₄ via diffuse recharge is the predominant source of dissolved SO₄ to the aquifer. Further along the hydraulic gradient towards the discharge area near the River Murray, δ³⁴S values in the unconfined Murray Group Aquifer increase, and SO₄/Cl ratios decrease, due to upward leakage of waters from the confined Renmark Group Aquifer which has a distinctly low SO₄/Cl and high δ³⁴S (14.9–56.4‰). Relatively positive δ³⁴S and δ¹⁸O_SO4 values, and low SO₄/Cl in the Renmark Group Aquifer is typical of SO₄ removal by bacterial reduction. The S isotope fractionation between SO₄ and HS⁻ of ∼24‰ estimated for the confined aquifer is similar to the experimentally determined chemical fractionation factor for the reduction process but much lower than the equilibrium fractionation (∼70‰) even though the confined groundwater residence time is >300 Ka years. Mapping the spatial distribution of δ³⁴S and SO₄/Cl of the unconfined Murray Group Aquifer provides an indicative tool for identifying the approximate extent of mixing, however the poorly defined end-member isotopic signatures precludes quantitative estimates of mixing fractions.     

S- and O-isotopic character of dissolved sulphate in the cover rock aquifers of a Zechstein salt dome

Sulfur and O isotope analyses of dissolved SO₄ were used to constrain a hydrogeological model for the area overlying the Gorleben–Rambow Salt Structure, Northern Germany. Samples were collected from 80 wells screened at different depth-intervals. The study area consists of a set of two vertically stacked aquifer systems. Generally, the isotope data show a good spatial correlation, outlining well-defined groundwater zones containing SO₄ of characteristic isotopic composition. Highly saline waters from deeper parts of the lower aquifer system are characterized by rather constant SO₄ isotopic compositions, which are typical of Permian Zechstein evaporites (δ³⁴S=9.6–11.9‰; δ¹⁸O=9.5–12.1‰). Above this is a transition zone containing ground waters of intermediate salinity and slightly higher isotopic values (average δ³⁴S=16.6‰; δ¹⁸O=15.3‰). The confined groundwater horizon on the top of the lower aquifer system below the low permeable Hamburg Clays is low in total dissolved solids and is characterized by an extreme ³⁴S enrichment (average δ³⁴S=39.1‰; δ¹⁸O=18.4‰), suggesting that bacterially mediated SO₄ reduction is a dominant geochemical process in this zone. Two areas of distinct isotopic composition can be identified in the shallow ground water horizons of the upper hydrogeological system. Sulfate in groundwaters adjacent to the river Elbe and Löcknitz has a typical meteoric isotopic signature (δ³⁴S=5.2‰; δ¹⁸O=8.2‰), whereas the central part of the area is characterized by more elevated isotopic ratios (δ³⁴S=12.7‰; δ¹⁸O=15.6‰). The two major SO₄ pools in the area are represented by Permian seawater SO₄ and a SO₄ of meteoric origin that has been mixed with SO₄ resulting from the oxidation of pyrite. It is suggested that the S-isotope compositions observed reflect the nature of the SO₄ source that have been modified to various extent by bacterial SO₄ reduction. Groundwaters with transitional salinity have resulted from mixing between brines and low-mineralized waters affected by bacterial SO₄ reduction.     

Sulphur isotopic fractionation between sulphate and sulphide in hydrothermal ore deposits: disequilibrium vs equilibrium processes

Correlative fractionation relationships of sulphur isotope data for coexisting sulphate and sulphide pairs from hydrothermal ore deposits on δ³⁸S versus Δ³⁴S diagrams are deciphered theoretically. Taking into account dissolved H₂S and SO₄^2- in hydrothermal fluids during precipitation of both sulphate and sulphide minerals, a 4-species closed system is suggested for describing the conservation of mass among all sulphur-bearing species on the δ-Δ diagrams. The covariation in the δ³⁴S values of both sulphate and sulphide is ascribed to isotopic exchange between oxidized and reduced sulphur species during mineral precipitation. The isotopic exchange could be a thermodynamic process due to simple cooling of high temperature fluids, which results in an equilibrium fractionation, or a kinetic process due to mixing of two sulphur reservoirs, which leads to a disequilibrium fractionation. The δ³⁴S value of total sulphur in a hydrothermal system could change due to the precipitation of minerals, or due to the escape of H₂S and/or SO₄^2-. Sulphur isotope data for anhydrite and pyrite pairs from the Luohe porphyrite iron deposit in the Yangtze River Valley is used to illustrate the mixing responsible for the disequilibrium fractionation.     

A theoretical model of the stable sulfur isotope distribution in marine sediments

A diffusion-diagenesis model of the sulfur cycle is developed to calculate theoretical distributions of stable sulfur isotopes in marine sediments. The model describes the depth variation in δ³⁴S of dissolved sulfate and H₂S. and of pyrite. The effects of sulfate reduction, sulfate and H₂S diffusion. and of sedimentation are considered as well as the bacterial isotope fractionation and the degree of pyrite formation. Under open system conditions of sulfur diagenesis the isotopic difference, ΔSO^2?₄ — H₂S, tends to increase with depth being smaller than the bacterial fractionation factor near the sediment surface and larger in deeper layers. The two isotopes in SO^2?₄ or in H₂S do not diffuse in the same proportion as they occur in the porewater. This explains why sulfur, which is incorporated from seawater sulfate by diffusion and precipitation as pyrite, can be enriched in ³²S relative to the seawater sulfate. The model calculations demonstrate the importance of taking the whole dynamic sulfur cycle into account before drawing conclusions about sulfur diagenesis from the stable isotope distribution.     

Geochemical evidence for Se mobilization by the weathering of pyritic shale, San Joaquin Valley, California, U.S.A.

Acidic (pH 4) seeps issue from the weathered Upper Cretaceous-Paleocene marine sedimentary shales of the Moreno Formation in the semi-arid Coast Ranges of California. The chemistry of the acidic solutions is believed to be evidence of current reactions ultimately yielding hydrous sodium and magnesium sulfate salts, e.g. mirabilite and bloedite, from the oxidation of primary pyrite. The selenate form of Se is concentrated in these soluble salts, which act as temporary geological sinks. Theoretically, the open lattice structures of these hydrous minerals could incorporate the selenate (SeO₄⁻²) anion in the sulfate (SO₄⁻²) space. When coupled with a semi-arid to arid climate, fractional crystallization and evaporative concentration can occur creating a sodium-sulfate fluid that exceeds the U.S. Environmental Protection Agency limit of 1000 μg l⁻¹ for a toxic Se waste. The oxidative alkaline conditions necessary to ensure the concentration of soluble selenate are provided in the accompanying marine sandstones of the Panoche and Lodo Formations and the eugeosynclinal Franciscan assemblage. Runoff and extensive mass wasting in the area reflect these processes and provide the mechanisms which transport Se to the farmlands of the west-central San Joaquin Valley. Subsurface drainage from these soils consequently transports Se to refuge areas in amounts elevated to cause a threat to wildlife.     

Kinetic oxygen isotope effects during dissimilatory sulfate reduction: A combined theoretical and experimental approach

Kinetic isotope effects related to the breaking of chemical bonds drive sulfur isotope fractionation during dissimilatory sulfate reduction (DSR), whereas oxygen isotope fractionation during DSR is dominated by exchange between intercellular sulfur intermediates and water. We use a simplified biochemical model for DSR to explore how a kinetic oxygen isotope effect may be expressed. We then explore these relationships in light of evolving sulfur and oxygen isotope compositions (δ³⁴S_SO4 and δ¹⁸O_SO4) during batch culture growth of twelve strains of sulfate-reducing bacteria. Cultured under conditions to optimize growth and with identical δ¹⁸O_H2O and initial δ¹⁸O_SO4, all strains show ³⁴S enrichment, whereas only six strains show significant ¹⁸O enrichment. The remaining six show no (or minimal) change in δ¹⁸O_SO4 over the growth of the bacteria. We use these experimental and theoretical results to address three questions: (i) which sulfur intermediates exchange oxygen isotopes with water, (ii) what is the kinetic oxygen isotope effect related to the reduction of adenosine phosphosulfate (APS) to sulfite (SO₃²⁻), (iii) does a kinetic oxygen isotope effect impact the apparent oxygen isotope equilibrium values? We conclude that oxygen isotope exchange between water and a sulfur intermediate likely occurs downstream of APS and that our data constrain the kinetic oxygen isotope fractionation for the reduction of APS to sulfite to be smaller than 4‰. This small oxygen isotope effect impacts the apparent oxygen isotope equilibrium as controlled by the extent to which APS reduction is rate-limiting.     

Evidence for equilibrium iron isotope fractionation by nitrate-reducing iron(II)-oxidizing bacteria

Iron isotope fractionations produced during chemical and biological Fe(II) oxidation are sensitive to the proportions and nature of dissolved and solid-phase Fe species present, as well as the extent of isotopic exchange between precipitates and aqueous Fe. Iron isotopes therefore potentially constrain the mechanisms and pathways of Fe redox transformations in modern and ancient environments. In the present study, we followed in batch experiments Fe isotope fractionations between Fe(II)_aq and Fe(III) oxide/hydroxide precipitates produced by the Fe(III) mineral encrusting, nitrate-reducing, Fe(II)-oxidizing Acidovorax sp. strain BoFeN1. Isotopic fractionation in ⁵⁶Fe/⁵⁴Fe approached that expected for equilibrium conditions, assuming an equilibrium Δ⁵⁶Fe_{Fe(OH)3-Fe(II)aq} fractionation factor of +3.0‰. Previous studies have shown that Fe(II) oxidation by this Acidovorax strain occurs in the periplasm, and we propose that Fe isotope equilibrium is maintained through redox cycling via coupled electron and atom exchange between Fe(II)_aq and Fe(III) precipitates in the contained environment of the periplasm. In addition to the apparent equilibrium isotopic fractionation, these experiments also record the kinetic effects of initial rapid oxidation, and possible phase transformations of the Fe(III) precipitates. Attainment of Fe isotope equilibrium between Fe(III) oxide/hydroxide precipitates and Fe(II)_aq by neutrophilic, Fe(II)-oxidizing bacteria or through abiologic Fe(II)_aq oxidation is generally not expected or observed, because the poor solubility of their metabolic product, i.e. Fe(III), usually leads to rapid precipitation of Fe(III) minerals, and hence expression of a kinetic fractionation upon precipitation; in the absence of redox cycling between Fe(II)_aq and precipitate, kinetic isotope fractionations are likely to be retained. These results highlight the distinct Fe isotope fractionations that are produced by different pathways of biological and abiological Fe(II) oxidation.     

Multi-isotope (Ba,C, O) partitioning during experimental carbonatization of a hyper-alkaline solution

Carbonates formed from hyperalkaline aqueous solutions at the Earth?s surface are known to bear the most extreme disequilibrium isotope signatures reported so far in nature. We present here the results for stable carbon (C), oxygen (O), and barium (Ba) isotope fractionation during the precipitation of witherite (BaCO₃) induced by the chemical absorption of atmospheric carbon dioxide (CO₂) into an aqueous hyper-alkaline solution (at 4° and 21?°C; 1?atm total pressure). Independent from temperature, the barium carbonate formation was associated with a substantial enrichment of the lighter C and O isotopes in the solid compared to the atmosphere (C, O), close to previous results found in experiments and nature. A new approach is introduced to explain oxygen isotope fractionation upon hydroxylation of CO₂. With Ba isotope enrichment factors between ?0.45 and ?0.53‰ (^138/134ε) or ?0.34 and ?0.40‰ (^137/134ε), respectively, the synthesized BaCO₃ displays the highest kinetic enrichment of the light Ba isotope in the carbonate solid reported so far.     

Experimental studies of oxygen isotope fractionation between rhodochrosite (MnCO3) and water at low temperatures

Rhodochrosite crystals were precipitated from Na-Mn-Cl-HCO₃ parent solutions following passive, forced and combined passive-to-forced CO₂ degassing methods. Forced and combined passive-to-forced CO₂ degassing produced rhodochrosite crystals with a small non-equilibrium oxygen isotope effect whereas passive CO₂ degassing protocols yielded rhodochrosite in apparent isotopic equilibrium with water. On the basis of the apparent equilibrium isotopic data, a new temperature-dependent relation is proposed for the oxygen isotope fractionation between rhodochrosite and water between 10 and 40 °C:

1000lnα_{rhodochrosite-water}=17.84±0.18(10³/T)-30.24±0.62     

Calculation of individual isotope equilibrium constants for geochemical reactions

Theory is derived from the work of Urey (Urey H. C. [1947] The thermodynamic properties of isotopic substances. J. Chem. Soc. 562-581) to calculate equilibrium constants commonly used in geochemical equilibrium and reaction-transport models for reactions of individual isotopic species. Urey showed that equilibrium constants of isotope exchange reactions for molecules that contain two or more atoms of the same element in equivalent positions are related to isotope fractionation factors by α = (K^ex)^1/n, where n is the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example ¹³C¹⁶O¹⁸O and ¹H²H¹⁸O. The equilibrium constants of the isotope exchange reactions can be expressed as ratios of individual isotope equilibrium constants for geochemical reactions. Knowledge of the equilibrium constant for the dominant isotopic species can then be used to calculate the individual isotope equilibrium constants.Individual isotope equilibrium constants are calculated for the reaction CO_2g = CO_2aq for all species that can be formed from ¹²C, ¹³C, ¹⁶O, and ¹⁸O; for the reaction between ¹²C¹⁸O_2aq and ¹H₂¹⁸O_l; and among the various ¹H, ²H, ¹⁶O, and ¹⁸O species of H₂O. This is a subset of a larger number of equilibrium constants calculated elsewhere (Thorstenson D. C. and Parkhurst D. L. [2002] Calculation of individual isotope equilibrium constants for implementation in geochemical models. Water-Resources Investigation Report 02-4172. U.S. Geological Survey). Activity coefficients, activity-concentration conventions for the isotopic variants of H₂O in the solvent ¹H₂¹⁶O_l, and salt effects on isotope fractionation have been included in the derivations. The effects of nonideality are small because of the chemical similarity of different isotopic species of the same molecule or ion. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation factors.The derivations can be extended to calculation of individual isotope equilibrium constants for ion pairs and equilibrium constants for isotopic species of other chemical elements. The individual isotope approach calculates the same phase isotopic compositions as existing methods, but also provides concentrations of individual species, which are needed in calculations of mass-dependent effects in transport processes. The equilibrium constants derived in this paper are used to calculate the example of gas-water equilibrium for CO₂ in an acidic aqueous solution.     

Isotopic evidence of enhanced carbonate dissolution at a coal mine drainage site in Allegheny County,Pennsylvania, USA

Stable isotopes were used to determine the sources and fate of dissolved inorganic C (DIC) in the circumneutral pH drainage from an abandoned bituminous coal mine in western Pennsylvania. The C isotope signatures of DIC (δ¹³C_DIC) were intermediate between local carbonate and organic C sources, but were higher than those of contemporaneous Pennsylvanian age groundwaters in the region. This suggests a significant contribution of C enriched in ¹³C due to enhanced carbonate dissolution associated with the release of H₂SO₄ from pyrite oxidation. The Sr isotopic signature of the drainage was similar to other regional mine waters associated with the same coal seam and reflected contributions from limestone dissolution and cation exchange with clay minerals. The relatively high δ³⁴S_SO4 and δ¹⁸O_SO4 isotopic signatures of the mine drainage and the presence of presumptive SO₄-reducing bacteria suggest that SO₄ reduction activity also contributes C depleted in ¹³C isotope to the total DIC pool. With distance downstream from the mine portal, C isotope signatures in the drainage increased_, accompanied by decreased total DIC concentrations and increased pH. These data are consistent with H₂SO₄ dissolution of carbonate rocks, enhanced by cation exchange, and C release to the atmosphere via CO₂ outgassing.     

Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(II) and Fe(III)

Equilibrium and kinetic Fe isotope fractionation between aqueous ferrous and ferric species measured over a range of chloride concentrations (0, 11, 110 mM Cl⁻) and at two temperatures (0 and 22°C) indicate that Fe isotope fractionation is a function of temperature, but independent of chloride contents over the range studied. Using ⁵⁷Fe-enriched tracer experiments the kinetics of isotopic exchange can be fit by a second-order rate equation, or a first-order equation with respect to both ferrous and ferric iron. The exchange is rapid at 22°C, ∼60-80% complete within 5 seconds, whereas at 0°C, exchange rates are about an order of magnitude slower. Isotopic exchange rates vary with chloride contents, where ferrous-ferric isotope exchange rates were ∼25 to 40% slower in the 11 mM HCl solution compared to the 0 mM Cl⁻ (∼10 mM HNO₃) solutions; isotope exchange rates are comparable in the 0 and 110 mM Cl⁻ solutions.The average measured equilibrium isotope fractionations, Δ_{Fe(III)-Fe(II)}, in 0, 11, and 111 mM Cl⁻ solutions at 22°C are identical within experimental error at +2.76±0.09, +2.87±0.22, and +2.76±0.06 ‰, respectively. This is very similar to the value measured by Johnson et al. (2002a) in dilute HCl solutions. At 0°C, the average measured Δ_{Fe(III)-Fe(II)} fractionations are +3.25±0.38, +3.51±0.14 and +3.56±0.16 ‰ for 0, 11, and 111 mM Cl⁻ solutions. Assessment of the effects of partial re-equilibration on isotope fractionation during species separation suggests that the measured isotope fractionations are on average too low by ∼0.20 ‰ and ∼0.13 ‰ for the 22°C and 0°C experiments, respectively. Using corrected fractionation factors, we can define the temperature dependence of the isotope fractionation from 0°C to 22°C as: where the isotopic fractionation is independent of Cl⁻ contents over the range used in these experiments. These results confirm that the Fe(III)-Fe(II) fractionation is approximately half that predicted from spectroscopic data, and suggests that, at least in moderate Cl⁻ contents, the isotopic fractionation is relatively insensitive to Fe-Cl speciation.     

Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(III) and hematite

Application of the Fe isotope system to studies of natural rocks and fluids requires precise knowledge of equilibrium Fe isotope fractionation factors among various aqueous Fe species and minerals. These are difficult to obtain at the low temperatures at which Fe isotope fractionation is expected to be largest and requires careful distinction between kinetic and equilibrium isotope effects. A detailed investigation of Fe isotope fractionation between [Fe^III(H₂O)₆]³⁺ and hematite at 98°C allows the equilibrium ⁵⁶Fe/⁵⁴Fe fractionation to be inferred, which we estimate at 10³lnα_{Fe(III)-hematite} = −0.10 ± 0.20‰. We also infer that the slope of Fe(III)-hematite fractionation is modest relative to 10⁶/T², which would imply that this fractionation remains close to zero at lower temperatures. These results indicate that Fe isotope compositions of hematite may closely approximate those of the fluids from which they precipitated if equilibrium isotopic fractionation is assumed, allowing inference of δ⁵⁶Fe values of ancient fluids from the rock record. The equilibrium Fe(III)-hematite fractionation factor determined in this study is significantly smaller than that obtained from the reduced partition function ratios calculated for [Fe^III(H₂O)₆]³⁺ and hematite based on vibrational frequencies and Mössbauer shifts by [Polyakov 1997] and [Polyakov and Mineev 2000], and Schauble et al. (2001), highlighting the importance of experimental calibration of Fe isotope fractionation factors. In contrast to the long-term (up to 203 d) experiments, short-term experiments indicate that kinetic isotope effects dominate during rapid precipitation of ferric oxides. Precipitation of hematite over ∼12 h produces a kinetic isotope fractionation where 10³lnα_{Fe(III)-hematite} = +1.32 ± 0.12‰. Precipitation under nonequilibrium conditions, however, can be recognized through stepwise dissolution in concentrated acids. As expected, our results demonstrate that dissolution by itself does not measurably fractionate Fe isotopes.     

Experimental investigation on the carbon isotope fractionation of methane during gas migration by diffusion through sedimentary rocks at elevated temperature and pressure

Molecular transport (diffusion) of methane in water-saturated sedimentary rocks results in carbon isotope fractionation. In order to quantify the diffusive isotope fractionation effect and its dependence on total organic carbon (TOC) content, experimental measurements have been performed on three natural shale samples with TOC values ranging from 0.3 to 5.74%. The experiments were conducted at 90°C and fluid pressures of 9 MPa (90 bar). Based on the instantaneous and cumulative composition of the diffused methane, effective diffusion coefficients of the ¹²CH₄ and ¹³CH₄ species, respectively, have been calculated.Compared with the carbon isotopic composition of the source methane (δ¹³C₁ = −39.1‰), a significant depletion of the heavier carbon isotope (¹³C) in the diffused methane was observed for all three shales. The degree of depletion is highest during the initial non-steady state of the diffusion process. It then gradually decreases and reaches a constant difference (Δ δ = δ¹³C_diff −δ¹³C_source) when approaching the steady-state. The degree of the isotopic fractionation of methane due to molecular diffusion increases with the TOC content of the shales. The carbon isotope fractionation of methane during molecular migration results practically exclusively from differences in molecular mobility (effective diffusion coefficients) of the ¹²CH₄ and ¹³CH₄ entities. No measurable solubility fractionation was observed.The experimental isotope-specific diffusion data were used in two hypothetical scenarios to illustrate the extent of isotopic fractionation to be expected as a result of molecular transport in geological systems with shales of different TOC contents. The first scenario considers the progression of a diffusion front from a constant source (gas reservoir) into a homogeneous “semi-infinite” shale caprock over a period of 10 Ma.In the second example, gas diffusion across a 100 m caprock sequence is analyzed in terms of absolute quantities and isotope fractionation effects. The examples demonstrate that methane losses by molecular diffusion are small in comparison with the contents of commercial size gas accumulations. The degree of isotopic fractionation is related inversely to the quantity of diffused gas so that strong fractionation effects are only observed for relatively small portions of gas.The experimental data can be readily used in numerical basin analysis to examine the effects of diffusion-related isotopic fractionation on the composition of natural gas reservoirs.     

Boron isotopic fractionation between minerals and fluids: New insights from in situ high pressure-high temperature vibrational spectroscopic data

Equilibrium boron isotopic fractionations between trigonal B(OH)₃ and tetragonal B(OH)₄⁻ aqueous species have been calculated at high P-T conditions using measured vibrational spectra (Raman and IR) and force-field modeling to compute reduced partition function ratios for B-isotopic exchange following Urey’s theory. The calculated isotopic fractionation factor at 300 K, α_3/4 = 1.0176(2), is slightly lower than the formerly calculated value of α_3/4 = 1.0193 (Kakihana and Kotaka, 1977), due to differences in the determined vibrational frequencies. The effect of pressure on α_3/4 up to 10 GPa and 723 K is shown to be negligible relative to temperature or speciation (pH) effects. Implications for the interpretation of boron fractionation in experimental and natural systems are discussed. We also show that the relationship between seawater-mineral B isotope fractionation and pH can be expressed using two variables, α_3/4 on one hand, and the pK_a of the boric acid-borate equilibrium on the other hand. This latter value is given by the equilibrium of boron species in water for the carbonate-water exchange, but could be governed by mineral surface properties in the case of clays. This may allow defining intrinsic paleo-pHmeters from B isotope fractionation between carbonate and authigenic minerals. Finally, it is shown that fractionation of boron isotopes can be rationalized in terms of the changes in 1) coordination of B from trigonal to tetrahedral in both fluids and minerals; and 2) the ligand nature around B from OH⁻ in the fluid and some hydrous minerals to non-hydrogenated O in many minerals. Relationships are established that allow predicting the isotopic fractionation factor of B between minerals and fluid.     

Biogeochemical implications of inverse sulfur isotope effects during reduction of sulfur compounds by Clostridium pasteurianum

Large inverse sulfur isotope effects such as those encountered during SO₃^2? reduction by the non-symbiotic dinitrogen fixing soil anaerobe C. pasteurianum may induce ambiguity into calculations of isotopic and mass balance of sulfur compounds in the environment.     

Lithium isotopes in island arc geothermal systems: Guadeloupe, Martinique (French West Indies) and experimental approach

We report lithium (Li) isotopic measurements in seawater-derived waters that were discharged from geothermal wells, thermal springs, and sub-marine springs located in volcanic island arc areas in Guadeloupe (the Bouillante geothermal field) and Martinique (Lamentin plain and the Diamant areas). While Li isotopic signatures of the geothermal fluids collected from deep reservoirs were found to be homogeneous for a given site, the δ⁷Li signatures for each of these reservoirs were significantly different. The first low temperature (25-250 °C) experiments of Li isotope exchange during seawater/basalt interaction confirmed that Li isotopic exchange is strongly temperature dependent, as previously inferred from natural studies. Li isotopic fractionation ranged from +19.4‰ (Δ_{solution-solid}) at 25 °C to +6.7‰ at 250 °C. These experiments demonstrated the importance of Li isotopic fractionation during the formation of Li-bearing secondary minerals and allowed us to determine the following empirical relationship between isotopic fractionation and temperature: Δ_{solution-solid} = 7847/T − 8.093. Application of experimental results and literature data to the Bouillante area suggested that geothermal water was in equilibrium at 250-260 °C. It likely has a deep and large reservoir located in the upper sheeted dike complex of the oceanic crust, just below the transition zone between andesite volcanic flows and the basaltic dikes. The upper dike section, from which Li is extracted by hydrothermal fluids, was characterized by light Li isotopic values in the rocks, indicating retention of ⁶Li by the altered rocks. For the Lamentin and Diamant areas, the geothermal fluids appeared to be in equilibrium with reservoir volcano-sedimentary rocks at 90-120 °C and 180 °C, respectively. Further evidence for this argument is provided by the fact that only the Na/Li thermometric relationship determined for sedimentary basins yielded temperature values in agreement with those measured or estimated for the reservoir fluids. This suggests the importance of a sedimentary signature in these reservoir rocks. Altogether, this study highlights that the use of Li isotopic systematics is a powerful tool for characterizing the origin of geothermal waters as well as the nature of their reservoir rocks.