Oxygen isotope salt effects at high pressure and high temperature and the calibration of oxygen isotope geothermometers

The influence of NaCl, CaCl₂, and dissolved minerals on the oxygen isotope fractionation in mineral-water systems at high pressure and high temperature was studied experimentally. The salt effects of NaCl (up to 37 molal) and 5-molal CaCl₂ on the oxygen isotope fractionation between quartz and water and between calcite and water were measured at 5 and 15 kbar at temperatures from 300 to 750°C. CaCl₂ has a larger influence than NaCl on the isotopic fractionation between quartz and water. Although NaCl systematically changes the isotopic fractionation between quartz and water, it has no influence on the isotopic fractionation between calcite and water. This difference in the apparent oxygen isotope salt effects of NaCl must relate to the use of different minerals as reference phases. The term oxygen isotope salt effect is expanded here to encompass the effects of dissolved minerals on the fractionations between minerals and aqueous fluids. The oxygen isotope salt effects of dissolved quartz, calcite, and phlogopite at 15 kbar and 750°C were measured in the three-phase systems quartz-calcite-water and phlogopite-calcite-water. Under these conditions, the oxygen isotope salt effects of the three dissolved minerals range from ∼0.7 to 2.1‰. In both three-phase hydrothermal systems, the equilibrium fractionation factors between the pairs of minerals are the same as those obtained by anhydrous direct exchange between each pair of minerals, proving that the use of carbonate as exchange medium provides correct isotopic fractionations for a mineral pair.When the oxygen isotope salt effects of two minerals are different, the use of water as an indirect exchange medium will give erroneous fractionations between the two minerals. The isotope salt effect of a dissolved mineral is also the main reason for the observation that the experimentally calibrated oxygen isotope fractionations between a mineral and water are systematically 1.5 to 2‰ more positive than the results of theoretical calculations. Dissolved minerals greatly affect the isotopic fractionation in mineral-water systems at high pressure and high temperature. If the presence of a solute changes the solubility of a mineral, the real oxygen isotope salt effect of the solute at high pressure and high temperature cannot be correctly derived by using the mineral as reference phase.     

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.     

Temperatures of serpentinization of ultramafic rocks based on O18/O16 fractionation between coexisting serpentine and magnetite

Five lizardite-chrysotile type serpentinites from California, Guatemala and the Dominican Republic show oxygen isotope fractionations of 15.1 to 12.9 per mil between coexisting serpentine and magnetite (O¹⁸ magnetite=–7.6 to –4.6 per mil relative to SMOW). Nine antigorites (mainly from Vermont and S. E. Pennsylvania) show distinctly smaller fractionations of 8.7 to 4.8 per mil (O¹⁸ magnetite=–2.6 to +1.7 per mil). Two lizardite and chrysotile serpentinites dredged from the Mid-Atlantic Ridge exhibit fractionations of 10.0 and 12.4 per mil (O¹⁸ magnetite=–6.8 and –7.9 per mil, respectively), whereas an oceanic antigorite shows a value of 8.2 per mil (O¹⁸ magnetite=–6.2). These data all clearly indicate that the antigorites formed at higher temperatures than the chrysotilelizardites. Electron microprobe analyses of magnetites from the above samples show that they are chemically homogeneous and essentially pure Fe₃O₂. However, some magnetites from certain other samples that show a wide variation of Cr content also give very erratic oxygen isotopic results, suggesting non-equilibrium. An approximate serpentine-magnetite geothermometer curve was constructed by (1) extrapolation of observed O¹⁸ fractionations between coexisting chlorites and Fe-Ti oxides in low-grade pelitic schists whose isotopic temperatures are known from the quartz-muscovite O¹⁸ geothermometer, and (2) estimates of the O¹⁸ fractionation factor between chlorite and serpentine (assumed to be equal to unity). This serpentine-magnetite geothermometer suggests approximate equilibrium temperatures as follows: continental lizardite-chrysotile, 85° to 115° C; oceanic lizardite and chrysotile, 130° C and 185° C, respectively; oceanic antigorite, 235° C; and continental antigorites, 220° to 460° C.Contribution No. 2029 of the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91109.     

Liquid-vapor fractionation of boron and boron isotopes: Experimental calibration at 400°C/23 MPa to 450°C/42 MPa

We experimentally determined the boron partitioning and boron isotope fractionation between coexisting liquid and vapor in the system H₂O−NaCl−B₂O₃. Experiments were performed along the 400 and 450°C isotherms. Pressure conditions ranged from 23 to 28 MPa at 400°C and from 38 to 42 MPa at 450°C. Boron partitions preferentially into the liquid. Its overall liquid-vapor fractionation is, however, weak: Calculated boron distribution coefficients D_B^liquid-vapor are < 2.5 at all run conditions. With decreasing pressure (i.e. increasing opening of the solvus) D_B^liquid-vapor increases along the individual isotherms. Extrapolation to salt saturated conditions yields maximum boron liquid-vapor fractionations of D_B^liquid-vapor = 1.8 at 450°C and D_B^liquid-vapor = 2.7 at 400°C. ¹¹B preferentially fractionates into the vapor. Calculated Δ¹¹B_vapor-liquid = {[(¹¹B/¹⁰B)_vapor - (¹¹B/¹⁰B)_liquid]/(¹¹B/¹⁰B)_{NBS 951}}*1000 are small and range from 0.2 (± 0.7) to 0.9 (± 0.5) ‰ at 450°C and from 0.1 (± 0.6) to 0.7 (± 0.6) ‰ at 400°C. The data indicate increasing isotopic fractionation with decreasing pressure (i.e. increasing opening of the solvus). Extrapolation to salt saturated conditions yields maximum boron isotope liquid-vapor fractionations of Δ¹¹B_vapor-liquid = 1.5 (± 0.7) ‰ at 450°C and Δ¹¹B_vapor-liquid = 1.3 (± 0.6) ‰ at 400°C. The weak boron isotope fractionation suggests similar trigonal speciation in liquid and vapor. Although the boron and boron isotope fractionation between liquid and vapor is only weak, mass balance calculations indicate that for high degrees of fractionation liquid-vapor phase separation in an open system can significantly alter the boron and boron isotope signature of low-salinity hydrous fluids in hydrothermal systems. Comparing the model calculations with natural oceanic hydrothermal fluids, however, indicate that other processes than fluid phase separation dominate the boron geochemistry in oceanic hydrothermal fluids.     

Determination of the mass-dependence of cadmium isotope fractionation during evaporation

Mass fractionation laws relate the fractionation factor α_A for one isotope ratio to the fractionation factor α_B for a second isotope ratio of the same element, with a fractionation exponent β such that α_A = α_B^β. The exponent β defines the mass-dependence of the mass fractionation law and thus determines the slope of a mass fractionation line in linearized three isotope space. The generalized power law (GPL) defines β as a function of a variable exponent n. The laws that aim to describe equilibrium and kinetic isotope fractionations are special cases of the GPL with n = −1 and n → 0, respectively.Large isotope fractionations (up to 10% for ¹⁰⁶Cd/¹¹⁴Cd) were found to accompany the evaporation of molten Cd into vacuum at about 180°C. The slopes of the fractionation lines (β-values) were obtained by analyzing the Cd isotope compositions of the evaporation residues relative to the starting material with two different multiple collector-ICPMS instruments. For the most fractionated sample, the difference between the theoretical β-values, that describe kinetic and equilibrium isotope fractionation, is 10 to 20 times larger than the measurement uncertainty. A mass-dependence with n = −0.35 was determined for this sample. This result differs significantly from the value that would be expected for simple kinetic evaporation (n → 0), which is governed by the diffusion of monatomic Cd from the melt into vacuum. The observed “non-kinetic” mass-dependence probably results from partial recondensation (back reaction) of Cd vapor into the melt phase. This interpretation requires that equilibrium evaporation of Cd at about 180°C is associated with significant isotope fractionation.The present study demonstrates that the mechanism of isotope fractionation can be investigated by studying the associated mass-dependence, which can be determined by measuring the isotope ratios of a fractionated product relative to the starting material. The quantification of mass fractionation line slopes with the GPL should aid the interpretation of mass-dependent and small mass-independent isotope effects.     

The effects of metamorphism on O and Fe isotope compositions in the Biwabik Iron Formation, northern Minnesota

The Biwabik Iron Formation of Minnesota (1.9 Ga) underwent contact metamorphism by intrusion of the Duluth Complex (1.1 Ga). Apparent quartz–magnetite oxygen isotope temperatures decrease from ∼700°C at the contact to ∼375°C at 2.6 km distance (normal to the contact in 3D). Metamorphic pigeonite at the contact, however, indicates that peak temperatures were greater than 825°C. The apparent O isotope temperatures, therefore, reflect cooling, and not peak metamorphic conditions. Magnetite was reset in δ¹⁸O as a function of grain size, indicating that isotopic exchange was controlled by diffusion of oxygen in magnetite for samples from above the grunerite isograd. Apparent quartz–magnetite O isotope temperatures are similar to calculated closure temperatures for oxygen diffusion in magnetite at a cooling rate of ∼5.6°C/kyr, which suggests that the Biwabik Iron Formation cooled from ∼825 to 400°C in ∼75 kyr at the contact with the Duluth Complex. Isotopic exchange during metamorphism also occurred for Fe, where magnetite–Fe silicate fractionations decrease with increasing metamorphic grade. Correlations between quartz–magnetite O isotope fractionations and magnetite–iron silicate Fe isotope fractionations suggest that both reflect cooling, where the closure temperature for Fe was higher than for O. The net effect of metamorphism on δ¹⁸O–δ⁵⁶Fe variations in magnetite is a strong increase in δ¹⁸O_Mt and a mild decrease in δ⁵⁶Fe with increasing metamorphic grade, relative to the isotopic compositions that are expected at the low temperatures of initial magnetite formation. If metamorphism of Iron Formations occurs in a closed system, bulk O and Fe isotope compositions may be preserved, although re-equilibration among the minerals may occur for both O and Fe isotopes. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Effect of hydrogen limitation and temperature on the fractionation of sulfur isotopes by a deep-sea hydrothermal vent sulfate-reducing bacterium

The fractionation of sulfur isotopes by the thermophilic chemolithoautotrophic Thermodesulfatator indicus was explored during sulfate reduction under excess and reduced hydrogen supply, and the full temperature range of growth (40-80 °C). Fractionation of sulfur isotopes measured under reduced H₂ conditions in a fed-batch culture revealed high fractionations (24-37‰) compared to fractionations produced under excess H₂ supply (1-6‰). Higher fractionations correlated with lower sulfate reduction rates. Such high fractionations have never been reported for growth on H₂. For temperature-dependant fractionation experiments cell-specific rates of sulfate reduction increased with increasing temperatures to 70 °C after which sulfate-reduction rates rapidly decreased. Fractionations were relatively high at 40 °C and decreased with increasing temperature from 40-60 °C. Above 60 °C, fractionation trends switched and increased again with increasing temperatures. These temperature-dependant fractionation trends have not previously been reported for growth on H₂ and are not predicted by a generally accepted fractionation model for sulfate reduction, where fractionations are controlled as a function of temperature, by the balance of the exchange of sulfate across the cell membrane, and enzymatic reduction rates of sulfate. Our results are reproduced with a model where fractionation is controlled by differences in the temperature response of enzyme reaction rates and the exchange of sulfate in and out of the cell.     

Experimental studies of oxygen and hydrogen isotope fractionations between precipitated brucite and water at low temperatures

Oxygen and hydrogen isotope fractionation factors between brucite and water were experimentally determined by chemical synthesis techniques at low temperatures of 15° to 120°C. MgCl₂, Mg3N₂, and MgO were used as reactants, respectively, to produce brucite in aqueous solutions. All of the synthesis products were identified by x-ray diffraction (XRD) for crystal structure and by scanning electron microscope (SEM) for morphology. It is observed that oxygen isotope fractionations between brucite and water are temperature dependent regardless of variations in aging time, the chemical composition, and pH value of solutions. Brucites derived from three different starting materials yielded consistent fractionations with water at the same temperatures. These suggest that oxygen isotope equilibrium has been achieved between the synthesized brucite and water, resulting in the fractionation equation of 10³lnα=1.56×10⁶/T²−14.1. When the present results for the brucite–water system are compared with those for systems of gibbsite–water and goethite–water, it suggests the following sequence of ¹⁸O-enrichment in the M−OH bonds of hydroxides: Al³⁺ − OH > Fe³⁺ − OH > Mg²⁺ − OH.Hydrogen isotope fractionations between brucite and water obtained by the different synthesis methods have also achieved equilibrium, resulting in the fractionation equation of 10³lnα=−4.88×10⁶/T²−22.5. Because of the pressure effect on hydrogen isotope fractionations between minerals and water, the present calibrations at atmospheric pressure are systematically lower than fractionations extrapolated from hydrothermal exchange experiments at high temperatures of 510° to 100°C and high pressures of 1060 to 1000 bar. Comparison of the present results with existing calibrations involving other low-temperature minerals suggests the following sequence of D-enrichment in hydroxyl-bearing minerals: Al³⁺ − OH > Mg²⁺ − OH > Fe³⁺ − OH.     

First experimental determination of iron isotope fractionation between hematite and aqueous solution at hydrothermal conditions

Although iron isotopes provide a new powerful tool for tracing a variety of geochemical processes, the unambiguous interpretation of iron isotope ratios in natural systems and the development of predictive theoretical models require accurate data on equilibrium isotope fractionation between fluids and minerals. We investigated Fe isotope fractionation between hematite (Fe₂O₃) and aqueous acidic NaCl fluids via hematite dissolution and precipitation experiments at temperatures from 200 to 450 °C and pressures from saturated vapor pressure (P_sat) to 600 bar. Precipitation experiments at 200 °C and P_sat from aqueous solution, in which Fe aqueous speciation is dominated by ferric iron (Fe^III) chloride complexes, show no detectable Fe isotope fractionation between hematite and fluid, Δ⁵⁷Fe_{fluid-hematite} = δ⁵⁷Fe_fluid − δ⁵⁷Fe_hematite = 0.01 ± 0.08‰ (2 × standard error, 2SE). In contrast, experiments at 300 °C and P_sat, where ferrous iron chloride species (FeCl₂ and FeCl⁺) dominate in the fluid, yield significant fluid enrichment in the light isotope, with identical values of Δ⁵⁷Fe_{fluid-hematite} = −0.54 ± 0.15‰ (2SE) both for dissolution and precipitation runs. Hematite dissolution experiments at 450 °C and 600 bar, in which Fe speciation is also dominated by ferrous chloride species, yield Δ⁵⁷Fe_{fluid-hematite} values close to zero within errors, 0.15 ± 0.17‰ (2SE). In most experiments, chemical, redox, and isotopic equilibrium was attained, as shown by constancy over time of total dissolved Fe concentrations, aqueous Fe^II and Fe^III fractions, and Fe isotope ratios in solution, and identical Δ⁵⁷Fe values from dissolution and precipitation runs. Our measured equilibrium Δ⁵⁷Fe_{fluid-hematite} values at different temperatures, fluid compositions and iron redox state are within the range of fractionations in the system fluid-hematite estimated using reported theoretical β-factors for hematite and aqueous Fe species and the distribution of Fe aqueous complexes in solution. These theoretical predictions are however affected by large discrepancies among different studies, typically ±1‰ for the Δ⁵⁷Fe _{Fe(aq)-hematite} value at 200 °C. Our data may thus help to refine theoretical models for β-factors of aqueous iron species. This study provides the first experimental calibration of Fe isotope fractionation in the system hematite-saline aqueous fluid at elevated temperatures; it demonstrates the importance of redox control on Fe isotope fractionation at hydrothermal conditions.     

Oxygen isotopic compositions of IVA iron meteorites: implications for the thermal evolution derived from in situ ultraviolet laser microprobe analyses

Oxygen isotopic compositions of silicate inclusions in IVA iron meteorites have been measured with an in situ UV laser microprobe technique. The homogeneity of oxygen isotopic compositions within and among individual mineral grains has also been examined. Oxygen isotope fractionations between coexisting mineral pairs were utilized in oxygen isotope thermometry. Our measured Δ¹⁷O values, ranging from 0.97 to 1.25‰, are characteristic of a single reservoir and fully confirm the oxygen isotopic similarity between IVA irons and L/LL chondrites. Steinbach and São João Nepomuceno, containing inclusions of two silicate minerals in mutual contact, exhibit a mass-dependent fractionation of ¹⁸O/¹⁶O between tridymite and bronzite with apparent oxygen isotopic heterogeneity. The SiO₂-bearing member, Gibeon, gives homogeneous oxygen isotopic compositions without detectable fractionation of ¹⁸O/¹⁶O between tridymite and quartz. Oxygen isotope equilibrium temperatures are estimated for coexisting tridymite and bronzite in the same sample slabs or clusters in Steinbach and São João Nepomuceno. The fractionations of ¹⁸O/¹⁶O between bronzite and tridymite range from 1.6 to 2.3‰ in different sample slabs or clusters. On the basis of the closure temperature concept, cooling rates are estimated at approximately 20 to 1000°C/Myr between 800 and 1000°C, a range of temperatures not accessible to other cooling rate methods. Using the Fast Grain Boundary diffusion model, we have demonstrated that significant oxygen heterogeneity both in tridymite and bronzite is probably due to isotope exchange during cooling between minerals with various grain sizes and mineral abundances in different regions of the samples. The new estimates of cooling rate by oxygen isotope thermometry refine previous cooling curves of IVA irons and support the breakup-reassembly model for the IVA parent body.     

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:

     

Oxygen isotopic fractionation in the system quartz-albite-anorthite-water

Oxygen isotopic fractionations have been determined between quartz and water, albite and water, and anorthite and water at temperatures from 300 to 825°C, and pressures from 1.5. to 25 kbar. The equilibrium quartz-feldspar fractionation curves can be approximated by the following equations: 1000ln α_Q?PI = (0.46 + 0.55β)10⁶T^?2 + (0.02 + 0.85β) between 500 and 800°C 1000ln α_Q?PI = (0.79 + 0.90β)10⁶T^?2 — (0.43 ? 0.30β) between 400 and 500°C where β is the mole-fraction of anorthite in plagioclase.Application of these isotopic thermometer calibrations to literature data on quartz and feldspar gives temperatures for some metamorphic rocks which are concordant with quartz-magnetite temperatures. Plutonic igneous rocks typically have quartz-feldspar fractionations which are substantially larger than the equilibrium values at solidus temperatures, indicating substantial retrograde exchange effects.     

Kinetic mechanism of oxygen isotope disequilibrium in precipitated witherite and aragonite at low temperatures: an experimental study

To study what dictates oxygen isotope equilibrium fractionation between inorganic carbonate and water during carbonate precipitation from aqueous solutions, a direct precipitation approach was used to synthesize witherite, and an overgrowth technique was used to synthesize aragonite. The experiments were conducted at 50 and 70°C by one- and two-step approaches, respectively, with a difference in the time of oxygen isotope exchange between dissolved carbonate and water before carbonate precipitation. The two-step approach involved sufficient time to achieve oxygen isotope equilibrium between dissolved carbonate and water, whereas the one-step approach did not. The measured witherite-water fractionations are systematically lower than the aragonite-water fractionations regardless of exchange time between dissolved carbonate and water, pointing to cation effect on oxygen isotope partitioning between the barium and calcium carbonates when precipitating them from the solutions. The two-step approach experiments provide the equilibrium fractionations between the precipitated carbonates and water, whereas the one-step experiments do not. The present experiments show that approaching equilibrium oxygen isotope fractionation between precipitated carbonate and water proceeds via the following two processes:

1.

Oxygen isotope exchange between [CO₃]²⁻ and H₂O:

(1)     

Experimental determination of oxygen isotope fractionations between CO2 vapor and soda-melilite melt

We report results of experiments constraining oxygen isotope fractionations between CO₂ vapor and Na-rich melilitic melt at 1 bar and 1250 and 1400°C. The fractionation factor constrained by bracketed experiments, 1000^.lnα_{CO2-Na melilitic melt}, is 2.65±0.25 ‰ (±2σ; n=92) at 1250°C and 2.16±0.16 ‰ (2σ; n=16) at 1400°C. These values are independent of Na content over the range investigated (7.5 to 13.0 wt. % Na₂O). We combine these data with the known reduced partition function ratio of CO₂ to obtain an equation describing the reduced partition function ratio of Na-rich melilite melt as a function of temperature. We also fit previously measured CO₂-melt or -glass fractionations to obtain temperature-dependent reduced partition function ratios for all experimentally studied melts and glasses (including silica, rhyolite, albite, anorthite, Na-rich melilite, and basalt). The systematics of these data suggest that reduced partition function ratios of silicate melts can be approximated either by using the Garlick index (a measure of the polymerization of the melt) or by describing melts as mixtures of normative minerals or equivalent melt compositions. These systematics suggest oxygen isotope fractionation between basalt and olivine at 1300°C of approximately 0.4 to 0.5‰, consistent with most (but not all) basalt glass-olivine fractionations measured in terrestrial and lunar basalts.     

Isotopic fractionation of the major elements of molten basalt by chemical and thermal diffusion

Samples produced in piston cylinder experiments were used to document the thermal isotopic fractionation of all the major elements of basalt except for aluminum and the fractionation of iron isotopes by chemical diffusion between a natural basalt and rhyolite. The thermal isotopic fractionations are summarized in terms of a parameter Ω_i defined as the fractionation in per mil per 100 °C per atomic mass units difference between the isotopes. For molten basalt we report Ω_Ca = 1.6, Ω_Fe = 1.1, Ω_Si = 0.6, Ω_O = 1.5. In an earlier paper we reported Ω_Mg = 3.6. These fractionations represent a steady state balance between thermal diffusion and chemical diffusion with the mass dependence of the thermal diffusion coefficient being significantly larger than the mass dependence of the chemical diffusion coefficients for isotopes of the same element. The iron isotopic measurements of the basalt-rhyolite diffusion couple showed significant fractionation that are parameterized in terms of a parameter β_Fe = 0.03 when the ratio of the diffusion coefficients D₅₄ and D₅₆ of ⁵⁴Fe and ⁵⁶Fe is expressed in terms of the atomic mass as D₅₄/D₅₆ = (56/54)^β_Fe. This value of β_Fe is smaller than what we had measured earlier for lithium, magnesium and calcium (i.e., β_Li = 0.215, β_Ca = 0.05, β_Mg = 0.05) but still significant when one takes into account the high precision with which iron isotopic compositions can be measured (i.e., ±0.03‰) and that iron isotope fractionations at magmatic temperatures from other causes are extremely small. In a closing section we discuss technological and geological applications of isotopic fractionations driven by either or both chemical and thermal gradients.     

Oxygen isotope composition of carbonates,silicates, and oxides in selected carbonatites: constraints on crystallization temperatures of carbonatite magmas

Oxygen isotope compositions and fractionations between calcite (Cc) and magnetite (Mt), diopside-rich clinopyroxene (Di), monticellite (Mnt), kimzeyite-rich garnet (Gt), and biotite (Bt) were measured for carbonatites from Oka (Canada), Magnet Cove (USA), Jacupiranga (Brazil), and Essonville (Canada), to obtain crystallization temperatures and explore the crystallization history of carbonatites. The highest isotopic temperatures are obtained from Cc–Mt fractionations from Oka (745–770 °C) and Cc–Mnt fractionations from Magnet Cove (700 and 760 °C). Cc–Mt temperatures for very coarse-grained, euhedral magnetite phenocrysts and calcite from Jacupiranga are 700 °C. In samples that contain diopside and magnetite, the Cc–Mt temperatures are always higher than Cc–Di temperatures. This difference is consistent with crystallization of magnetite before diopside, minor retrograde resetting of magnetite isotopic compositions, and the order of crystallization inferred from inclusions of Mt in Di. Cc–Mt, Cc–Di, and Cc–Mnt fractionations are thus interpreted to represent those established during crystallization at rapid cooling rates (10³–10⁴ °C/my). Diffusion model calculations indicate that at slower post-crystallization cooling rates (10–10² °C/my), magnetite compositions should experience significant isotopic resetting by diffusional exchange with Cc, Bt, and apatite, and yield lower temperatures than Cc–Di. Cc–Bt fractionations correspond to the lowest temperatures (440–560 °C). Although some of these are relatively high isotopic temperatures for biotite, they most likely represent those established during subsolidus retrograde exchange between biotite and calcite during rapid subsolidus cooling.     

Quantifying Li isotope fractionation during smectite formation and implications for the Li cycle

Tri-octahedral Li-Mg smectites (hectorites) were synthesized at temperatures ranging from 25 to 250 °C, in the presence of solutions highly enriched in lithium. After removing all the exchangeable lithium from the synthesized clays, Li isotope fractionation (Δ⁷Li_{clay-solution}) was determined. This fractionation was linked to Li incorporation into the structural octahedral site, substituting for Mg²⁺. As predicted, experimental Δ⁷Li_{clay-solution} inversely correlates with temperature, and ranges from −1.6‰ ± 1.3‰ at 250 °C to −10.0‰ ± 1.3‰ at 90 °C, and then stays relatively constant down to 25 °C. The relatively constant isotope fractionation factor below 90 °C may be due to high concentrations of edge octahedra in low crystallinity smectites. The isotopic fractionation factor (α), for a given temperature, does not depend on the solution matrix, nor on the amount of structural Li incorporated into the clay. Empirical linear laws for α as a function of 1/T (K) were inferred. Smectite Li contents and smectite-solution distribution coefficients (D_Li/Mg) increase with temperature, as expected for a substitution process. The fractions of dissolved Li incorporated into the smectite octahedral sites are small and do not depend on the duration of the experiment. In a seawater-like matrix solution, less Li is incorporated into the smectites, probably as a result of competition with dissolved Mg²⁺ ions for incorporation into the octahedral sites. The high Li contents observed in marine smectites are therefore best explained either by a significant contribution from basalts, by adsorption processes, or by the influence of seawater chemical composition on distribution coefficients. We also calculate, using present-day estimates of hydrothermal water and river fluxes, that a steady-state ocean would require a relatively large global clay-water Li isotope fractionation (−12‰ to −21‰). This study demonstrates the ability of laboratory experiments to quantify the impact of secondary phases on the Li geochemical cycle and associated isotope fractionations.     

Experimental constraints on Fe isotope fractionation during magnetite and Fe carbonate formation coupled to dissimilatory hydrous ferric oxide reduction

Iron isotope fractionation between aqueous Fe(II) and biogenic magnetite and Fe carbonates produced during reduction of hydrous ferric oxide (HFO) by Shewanella putrefaciens, Shewanella algae, and Geobacter sulfurreducens in laboratory experiments is a function of Fe(III) reduction rates and pathways by which biogenic minerals are formed. High Fe(III) reduction rates produced ⁵⁶Fe/⁵⁴Fe ratios for Fe(II)_aq that are 2-3‰ lower than the HFO substrate, reflecting a kinetic isotope fractionation that was associated with rapid sorption of Fe(II) to HFO. In long-term experiments at low Fe(III) reduction rates, the Fe(II)_aq-magnetite fractionation is −1.3‰, and this is interpreted to be the equilibrium fractionation factor at 22°C in the biologic reduction systems studied here. In experiments where Fe carbonate was the major ferrous product of HFO reduction, the estimated equilibrium Fe(II)_aq-Fe carbonate fractionations were ca. 0.0‰ for siderite (FeCO₃) and ca. +0.9‰ for Ca-substituted siderite (Ca_0.15Fe_0.85CO₃) at 22°C. Formation of precursor phases such as amorphous nonmagnetic, noncarbonate Fe(II) solids are important in the pathways to formation of biogenic magnetite or siderite, particularly at high Fe(III) reduction rates, and these solids may have ⁵⁶Fe/⁵⁴Fe ratios that are up to 1‰ lower than Fe(II)_aq. Under low Fe(III) reduction rates, where equilibrium is likely to be attained, it appears that both sorbed Fe(II) and amorphous Fe(II)(s) components have isotopic compositions that are similar to those of Fe(II)_aq.The relative order of δ⁵⁶Fe values for these biogenic minerals and aqueous Fe(II) is: magnetite > siderite ≈ Fe(II)_aq > Ca-bearing Fe carbonate, and this is similar to that observed for minerals from natural samples such as Banded Iron Formations (BIFs). Where magnetite from BIFs has δ⁵⁶Fe >0‰, the calculated δ⁵⁶Fe value for aqueous Fe(II) suggests a source from midocean ridge (MOR) hydrothermal fluids. In contrast, magnetite from BIFs that has δ⁵⁶Fe ≤0‰ apparently requires formation from aqueous Fe(II) that had very low δ⁵⁶Fe values. Based on this experimental study, formation of low-δ⁵⁶Fe Fe(II)_aq in nonsulfidic systems seems most likely to have been produced by dissimilatory reduction of ferric oxides by Fe(III)-reducing bacteria.     

The effect of aqueous diffusion on the fractionation of chlorine and bromine stable isotopes

Diffusive isotopic fractionation factors are important in order to understand natural processes and have practical application in radioactive waste storage and carbon dioxide sequestration. We determined the isotope fractionation factors and the effective diffusion coefficients of chloride and bromide ions during aqueous diffusion in polyacrylamide gel. Diffusion was determined as functions of temperature, time and concentration. The effect of temperature is relatively large on the diffusion coefficient (D) but only small on isotope fractionation. For chlorine, the ratio, D_³⁵Cl/D_³⁷Cl varied from 1.00128 ± 0.00017 (1σ) at 2 °C to 1.00192 ± 0.00015 at 80 °C. For bromine, D_⁷⁹Br/D_⁸¹Br varied from 1.00098 ± 0.00009 at 2 °C to 1.0064 ± 0.00013 at 21 °C and 1.00078 ± 0.00018 (1σ) at 80 °C. There were no significant effects on the isotope fractionation due to concentration. The lack of sensitivity of the diffusive isotope fractionation to anything at the most common temperatures (0 to 30 °C) makes it particularly valuable for application to understanding processes in geological environments and an important natural tracer in order to understand fluid transport processes.     

Theoretical calculation of oxygen isotope fractionation factors in carbonate systems

Using established methods of statistical mechanical calculation and a recent compilation of vibrational frequency data, we have computed oxygen isotope reduced partition function ratios (β values) for a large number of carbonate minerals. The oxygen isotope β values of carbonates are inversely correlated to both the mass and radius of the cation bonded to the carbonate anion but neither correlation is good enough to be used as a precise and accurate predictor of β values. There is an approximately 0.6% relative increase in the β values of aragonite per 10 kbar increase in pressure. These estimates of the pressure effect on β values are broadly similar to those deduced previously for calcite using the methods of mineral physics. In comparing the β values of our study with those derived recently from first-principles lattice dynamics calculations, we find near-perfect agreement for calcite and witherite (<0.3% deviation), reasonable agreement for dolomite (<0.9% deviation) and somewhat poorer agreement for aragonite and magnesite (1.5-2% deviation). In the system for which we have the most robust constraints, CO₂-calcite, there is excellent agreement between our calculations and experimental data over a broad range of temperatures (0-900 °C). Similarly, there is good to excellent correspondence between calculation and experiment for most other low to moderate atomic mass carbonate minerals (aragonite to strontianite). The agreement is not as good for high atomic mass carbonates (witherite, cerussite, otavite). In the case of witherite and cerussite, the discrepancy may be due, in part, to our calculation methodology, which does not account for the effect of cation mass on the magnitude of vibrational frequency shifts associated with heavy isotope substitution. However, the calculations also reveal an incompatibility between the high- and low-temperature experimental datasets for witherite and cerussite. Specifically, the shapes of fractionation factor versus 1/T² curves in the calcite-witherite and calcite-cerussite systems do not conform to the robust constraints on the basic shape of these curves provided by theory. This suggests that either the high- or low-temperature datasets for both minerals is in error. Dolomite-calcite fractionation factors derived from our calculations fall within the wide range of fractionations for this system given by previous experimental and natural sample studies. However, our compilation of available low-temperature (25-80 °C) experimental data reveal an unusual temperature dependence of fractionations in this system; namely, the data indicate an increase in the magnitude of fractionations between dolomite (or proto-dolomite) and calcite with increasing temperature. Such a trend is incompatible with theory, which stipulates that fractionations between carbonate minerals must decrease monotonically with increasing temperature. We propose that the anomalous temperature dependence seen in the low-temperature experimental data reflect changes in the crystallinity and degree of cation ordering of the dolomite phase over this temperature interval and the effect these changes have on the vibrational frequencies of dolomite. Similar effects may be present in natural systems at low-temperature and must be considered in applying experimental or theoretical fractionation data to these systems. In nearly all cases, carbonate mineral-calcite fractionation factors given by the present calculations are in as good or better agreement with experimental data than are fractionations derived from semi-empirical bond strength methods.