Theoretical calculation of equilibrium Mg isotope fractionation between silicate melt and its vapor

Isotope fractionation during the evaporation of silicate melt and condensation of vapor has been widely used to explain various isotope signals observed in lunar soils, cosmic spherules, calcium–aluminum-rich inclusions, and bulk compositions of planetary materials. During evaporation and condensation, the equilibrium isotope fractionation factor (α) between high-temperature silicate melt and vapor is a fundamental parameter that can constrain the melt’s isotopic compositions. However, equilibrium α is difficult to calibrate experimentally. Here we used Mg as an example and calculated equilibrium Mg isotope fractionation in MgSiO₃ and Mg₂SiO₄ melt–vapor systems based on first-principles molecular dynamics and the high-temperature approximation of the Bigeleisen–Mayer equation. We found that, at 2500 K, δ²⁵Mg values in the MgSiO₃ and Mg₂SiO₄ melts were 0.141?±?0.004 and 0.143?±?0.003‰ more positive than in their respective vapors. The corresponding δ²⁶Mg values were 0.270?±?0.008 and 0.274?±?0.006‰ more positive than in vapors, respectively. The general \(\alpha - T\) equations describing the equilibrium Mg α in MgSiO₃ and Mg₂SiO₄ melt–vapor systems were: \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.264 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\) and \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.340 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\), respectively, where m is the mass of light isotope ²⁴Mg and m′ is the mass of the heavier isotope, ²⁵Mg or ²⁶Mg. These results offer a necessary parameter for mechanistic understanding of Mg isotope fractionation during evaporation and condensation that commonly occurs during the early stages of planetary formation and evolution.     

含Cu硫化物中S、Fe同位素分馏系数的第一性原理计算

Cu在自然界主要以硫化物的形式存在,目前只确定了几种含Cu硫化物的S同位素分馏系数以及黄铜矿的Fe同位素分馏系数,而且不同研究者确定的系数有很大的差别,使得S、Fe同位素在研究铜矿床的形成、演化等方面不能很好地发挥示踪作用。因此,本文基于第一性原理计算确定了0~1 000℃温度范围内主要含Cu硫化物的S同位素简约配分函数比（10³lnβ_34-32）,以及Cu-Fe硫化物的Fe同位素简约配分函数比（10³lnβ_57-54）。重S同位素在这些含Cu硫化物中的富集顺序为铜蓝>方黄铜矿>黄铜矿≈黑硫铜镍矿>斑铜矿>辉铜矿,重Fe同位素在Cu-Fe硫化物中的富集顺序为方黄铜矿≈黄铜矿>低温斑铜矿>高温斑铜矿>中温斑铜矿>Cu₈Fe₄S₈（中温斑铜矿的可能变体）。含Cu硫化物的10³lnβ_34-32与S原子的配位数、金属-S平均键长、S原子形成的所有化学键的平均键长没有明显的相关性,而Cu-Fe硫化物的10³lnβ_57-54与Fe—S平均键长基本成线性负相关关系。辉铜矿相变引起的S同位素分馏特别大,而斑铜矿相变时产生的S同位素分馏却可以忽略不计。本文的计算结果将会为探讨斑岩铜矿及其它类型的硫化物矿床的成因提供支持。     

Magnesium isotope fractionation in silicate melts by chemical and thermal diffusion

Two types of laboratory experiments were used to quantify magnesium isotopic fractionations associated with chemical and thermal (Soret) diffusion in silicate liquids. Chemical diffusion couples juxtaposing a molten natural basalt (SUNY MORB) and a molten natural rhyolite (Lake County Obsidian) were run in a piston cylinder apparatus and used to determine the isotopic fractionation of magnesium as it diffused from molten basalt to molten rhyolite. The thermal diffusion experiments were also run in a piston cylinder apparatus but with a sample made entirely of molten SUNY MORB displaced from the hotspot of the assembly furnace so that the sample would have a temperature difference of about 100-200 °C from one end to the other. The chemical diffusion experiments showed fractionations of ²⁶Mg/²⁴Mg by as much as 7‰, which resulted in an estimate for the mass dependence of the self-diffusion coefficients of the magnesium isotopes corresponding to D_26Mg/D_24Mg=(24/26)^β with β = 0.05. The thermal diffusion experiments showed that a temperature difference of about 100 °C resulted in the MgO, CaO, and FeO components of the basalt becoming slightly enriched by about 1 wt% in the colder end while SiO₂ was enriched by several wt% in the hotter end. The temperature gradient also fractionated the magnesium isotopes. A temperature difference of about 150 °C produced an 8‰ enrichment of ²⁶Mg/²⁴Mg at the colder end relative to the hotter end. The magnesium isotopic fractionation as a function of temperature in molten basalt corresponds to 3.6 × 10⁻²‰/°C/amu.     

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.     

First-principles calculations of equilibrium fractionation of O and Si isotopes in quartz,albite, anorthite,and zircon

In this study, we used first-principles calculations based on density functional theory to investigate silicon and oxygen isotope fractionation factors among the most abundant major silicate minerals in granites, i.e., quartz and plagioclase (including albite and anorthite), and an important accessory mineral zircon. Combined with previous results of minerals commonly occurring in the crust and upper mantle (orthoenstatite, clinoenstatite, garnet, and olivine), our study reveals that the Si isotope fractionations in minerals are strongly correlated with SiO₄ tetrahedron volume (or average Si–O bond length). The ³⁰Si enrichment order follows the sequence of quartz > albite > anorthite > olivine ≈ zircon > enstatite > diopside, and the ¹⁸O enrichment follows the order of quartz > albite > anorthite > enstatite > zircon > olivine. Our calculation predicts that measurable fractionation of Si isotopes can occur among crustal silicate minerals during high-temperature geochemical processes. This work also allows us to evaluate Si isotope fractionation between minerals and silicate melts with variable compositions. Trajectory for δ³⁰Si variation during fractional crystallization of silicate minerals was simulated with our calculated Si isotope fractionation factors between minerals and melts, suggesting the important roles of fractional crystallization to cause Si isotopic variations during magmatic differentiation. Our study also predicts that δ³⁰Si data of ferroan anorthosites of the Moon can be explained by crystallization and aggregation of anorthite during lunar magma ocean processes. Finally, O and Si isotope fractionation factors between zircon and melts were estimated based on our calculation, which can be used to quantitatively account for O and Si isotope composition of zircons crystallized during magma differentiation.     

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 studies of equilibrium iron isotope fractionation in ferric aquo-chloro complexes

Here we compare new experimental studies with theoretical predictions of equilibrium iron isotopic fractionation among aqueous ferric chloride complexes (Fe(H₂O)₆³⁺, FeCl(H₂O)₅²⁺, FeCl₂(H₂O)₄⁺, FeCl₃ (H₂O)₃, and FeCl₄^-), using the Fe-Cl-H₂O system as a simple, easily-modeled example of the larger variety of iron-ligand compounds, such as chlorides, sulfides, simple organic acids, and siderophores. Isotopic fractionation (⁵⁶Fe/⁵⁴Fe) among naturally occuring iron-bearing species at Earth surface temperatures (up to ∼3‰) is usually attributed to redox effects in the environment. However, theoretical modeling of reduced isotopic partition functions among iron-bearing species in solution also predicts fractionations of similar magnitude due to non-redox changes in speciation (i.e., ligand bond strength and coordination number). In the present study, fractionations are measured in a series of low pH ([H⁺] = 5 M) solutions of ferric chloride (total Fe = 0.0749 mol/L) at chlorinities ranging from 0.5 to 5.0 mol/L. Advantage is taken of the unique solubility of FeCl₄^- in immiscible diethyl ether to create a separate spectator phase, used to monitor changing fractionation in the aqueous solution. Δ⁵⁶Fe_aq-eth = δ⁵⁶Fe (total Fe remaining in aqueous phase)−δ⁵⁶Fe (FeCl₄^- in ether phase) is determined for each solution via MC-ICPMS analysis.Both experiments and theoretical calculations of Δ⁵⁶Fe_aq-eth show a downward trend with increasing chlorinity: Δ⁵⁶Fe_aq-eth is greatest at low chlorinity, where FeCl₂(H₂O)₄⁺ is the dominant species, and smallest at high chlorinity where FeCl₃(H₂O)₃ is dominant. The experimental Δ⁵⁶Fe_aq-eth ranges from 0.8‰ at [Cl^-] = 0.5 M to 0.0‰ at [Cl^-] = 5.0 M, a decrease in aqueous-ether fractionation of 0.8‰. This is very close to the theoretically predicted decreases in Δ⁵⁶Fe_aq-eth, which range from 1.0 to 0.7‰, depending on the ab initio model.The rate of isotopic exchange and attainment of equilibrium are shown using spiked reversal experiments in conjunction with the two-phase aqueous-ether system. Equilibrium under the experimental conditions is established within 30 min.The general agreement between theoretical predictions and experimental results points to substantial equilibrium isotopic fractionation among aqueous ferric chloride complexes and a decrease in ⁵⁶Fe/⁵⁴Fe as the Cl^-/Fe³⁺ ion ratio increases. The effects on isotopic fractionation shown by the modeling of this simple iron-ligand system imply that ligands present in an aqueous environment are potentially important drivers of fractionation, are indicative of possible fractionation effects due to other speciation effects (such as iron-sulfide systems or iron bonding with organic ligands), and must be considered when interpreting iron isotope fractionation in the geological record.     

Carbon isotopic fractionation between CO2 vapour,silicate and carbonate melts: an experimental study to 30 kbar

The carbon isotopic fractionation between CO₂ vapour and sodamelilite (NaCaAlSi₂O₇) melt over a range of pressures and temperatures has been investigated using solid-media piston-cylinder high pressure apparatus. Ag₂C₂O₄ was the source of CO₂ and experimental oxygen fugacity was buffered at hematite-magnetite by the double capsule technique. The abundance and isotopic composition of carbon dissolved in sodamelilite (SM) glass were determined by stepped heating and the ¹³C of coexisting vapour was determined directly by capsule piercing. CO₂ solubility in SM displays a complex behavior with temperature. At pressures up to 10 kbars CO₂ dissolves in SM to form carbonate ion complexes and the solubility data suggest slight negative temperature dependence. Above 20 kbars CO₂ reacts with SM to form immiscible Na-rich silicate and Ca-rich carbonate melts and CO₂ solubility in Na-enriched silicate melt rises with increasing temperature above the liquidus. Measured values for carbon isotopic fractionation between CO₂ vapour and carbonate ions dissoived in sodamelilite melt at 1200°–1400° C and 5–30 kbars average 2.4±0.2, favouring¹³C enrichment in CO₂ vapour. The results are maxima and are independent of pressure and temperature. Similar values of 2 are obtained for the carbon isotopic fractionation between CO₂ vapour and carbonate melts at 1300°–1400° C and 20–30 kbars.     

First-principles investigation of the concentration effect on equilibrium fractionation of Ca isotopes in forsterite

Previous theoretical studies have found that the concentration variations within a certain range have a prominent effect on inter-mineral equilibrium isotope fractionation (10³lnα). Based on the density functional theory, we investigated how the average Ca–O bond length and the reduced partition function ratios (10³lnβ) and 10³lnα of ⁴⁴Ca/⁴⁰Ca in forsterite (Fo) are affected by its Ca concentration. Our results show that Ca–O bond length in forsterite ranges from 2.327 to 2.267 Å with the Ca/(Ca + Mg) varying between a narrow range limited by an upper limit of 1/8 and a lower limit of 1/64. However, outside this narrow range, i.e., Ca/(Ca + Mg) is lower than 1/64 or higher than 1/8, Ca–O bond length becomes insensitive to Ca concentration and maintains to be a constant. Because the 10³lnβ is negatively correlated with Ca–O bond length, the 10³lnβ significantly increases with decreasing Ca/(Ca + Mg) when 1/64 < Ca/(Ca + Mg) < 2/16. As a consequence, the 10³lnα between forsterite and other minerals also strongly depend on the Ca content in forsterite. Combining previous studies with our results, the heavier Ca isotopes enrichment sequence in minerals is: forsterite > orthopyroxene > clinopyroxene > calcite ≈ diopside > dolomite > aragonite. Olivine and pyroxenes are enriched in heavier Ca isotope compared to carbonates. The 10³lnα between forsterite with a Ca/(Ca + Mg) of 1/64 and clinopyroxene (Ca/Mg = 1/1, i.e., diopside) is up to ~ 0.64‰ at 1200 K. The large 10³lnα_Fo-diopside relative to the current analytical precision for Ca isotope measurements suggests that the dependence of 10³lnα_Fo-diopside on temperature can be used as a thermometer, similar to the one based on the 10³lnα of ⁴⁴Ca/⁴⁰Ca between orthopyroxene and diopside. These two Ca isotope thermometers both have a precision approximate to that of elemental thermometers and provide independent constraints on temperature.

     

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.     

Determination of carbon fractionation factor between aqueous carbonate and CO2(g) in two-direction isotope equilibration

The experiments were conducted in the open CO₂ system to find out the equilibrium fractionation between the carbonate ion and CO₂(g). The existence of isotopic equilibrium was checked using the two-direction approach by passing the CO₂−N₂ gases with different δ¹³C compositions (− 1.5‰ and − 23‰) through the carbonate solution with δ¹³C = − 4.2‰. The Δ_{CO3T²⁻−CO2(g)} equilibrium fractionation is given as 6.03 ± 0.17‰ at 25 °C. Discussion is provided about the significance of carbonate complexing in determination of Δ_{CO3T²⁻−CO2(g)} and Δ_{HCO3T⁻−CO2(g)} fractionations. Finally, an isotope numerical model of flow and kinetics of hydration and dehydroxylation is built to predict the isotopic behaviour of the system with time.     

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.     

Equilibrium mercury and lead isotope fractionation caused by nuclear volume effects in crystals

Acta Geochimica - To investigate equilibrium mercury (Hg) and lead (Pb) isotope fractionation caused by the nuclear volume effect (NVE) in crystals, the electron densities at nuclei (i.e.,...     

Ab-initio structure, energy and stable Fe isotope equilibrium fractionation of some geochemically relevant H-O-Fe complexes

The hexa-aqua complexes [Fe(H₂O)_6−m−n(OH)_n]⁽²⁻ⁿ⁾⁺n = 0 → 3, m = 0 → 6 − n; [Fe(H₂O)_6−m−n(OH)_n]⁽³⁻ⁿ⁾⁺n = 0 → 4, m = 0 → 6 − n were investigated by ab-initio methods with the aim of determining their ground-state geometries, total energies and vibrational properties by treating their inner solvation shell as part of their gaseous precursor¹ (or “hybrid approach”). After a gas-phase energy optimization within the Density Functional Theory (DFT), the molecules were surrounded by a dielectric representing the Reaction Field through an implicit Polarized Continuum Model (PCM). The exploration of several structural ligand arrangements allowed us to quantify the relative stabilities of the various ionic species and the role of the various forms of energy (solute-solvent electronic interaction, cavitation, dispersion, repulsion, liberation free energy) that contribute to stabilize the aqueous complexes. A comparison with experimental thermochemistries showed that ab-initio gas-phase + solvation energies are quite consistent with experimental evidence and allow the depiction of the most stable form in solution and the eventual configurational disorder of water/hydroxyl species around central cations. A vibrational analysis performed on the ⁵⁴Fe, ⁵⁶Fe, ⁵⁷Fe and ⁵⁸Fe isotopomers indicated important separative effects systematically affected by the extent of deprotonation. The role of the system’s redox state (fO₂) and acidity (pH) on the isotopic imprinting of the aqueous species in solution was investigated by coupling the separative effects with speciation calculations. The observed systematics provided a tool of general utility in the interpretation of the iron isotopic signature of natural waters. Applications to the interpretation of isotopic fractionation in solution dictated by redox equilibria and to the significance of the Fe-isotopic imprinting of Banded Iron Formations are given.     

Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance

The mass-dependent fractionation laws that describe the partitioning of isotopes are different for kinetic and equilibrium reactions. These laws are characterized by the exponent relating the fractionation factors for two isotope ratios such that α_2/1 = α_3/1^β. The exponent β for equilibrium exchange is (1/m₁ − 1/m₂)/(1/m₁ − 1/m₃), where m_i are the atomic masses and m₁ < m₂ < m₃. For kinetic fractionation, the masses used to evaluate β depend upon the isotopic species in motion. Reduced masses apply for breaking bonds whereas molecular or atomic masses apply for transport processes. In each case the functional form of the kinetic β is ln(M₁/M₂)/ln(M₁/M₃), where M_i are the reduced, molecular, or atomic masses. New high-precision Mg isotope ratio data confirm that the distinct equilibrium and kinetic fractionation laws can be resolved for changes in isotope ratios of only 3‰ per amu. The variability in mass-dependent fractionation laws is sufficient to explain the negative Δ¹⁷O of tropospheric O₂ relative to rocks and differences in Δ¹⁷O between carbonate, hydroxyl, and anhydrous silicate in Martian meteorites. (For simplicity, we use integer amu values for masses when evaluating β throughout this paper.)     

硅酸盐岩中微量碳酸盐的碳氧同位素分析及其地球化学应用

硅酸盐岩中总是或多或少地含有一些微量碳酸盐，但是至今尚未对其碳氧同位素地球化学开展研究。本文建立了对硅酸盐岩中微量碳酸盐的碳氧同位素分析方法，并以大别山双河地区两种片麻岩为例，讨论了其地球化学应用。通过对比实验证明，微量法通常可将碳含量检出限降低至5μg/g。对大别山双河两种片麻岩中微量碳酸盐的碳氧同位素测量发现，黑云母副片麻与花岗质正片麻岩具有明显不同的特征。副片麻岩的碳含量较高，δ^13值为－4．5‰－0‰，批示其原岩为正常海相沉积环境，并与邻近大理岩原岩的灰岩沉积环境不同。正片麻岩的碳含量较低，δ^13值为－23．4‰－－2．1‰，反映出地表有机碳对岩浆岩原岩的混染。两种片麻岩中碳酸盐与硅酸盐全岩之间的氧同位素分馏既仍处于平衡状态，也有处于不平衡状态。不平衡分馏指示其受到过后期退变质流体的影响。不过，变质岩中微量碳酸盐的碳含量和碳机位素比值分析能够对原岩类型提供有效的区别。     

Role of nuclear volume in driving equilibrium stable isotope fractionation of mercury, thallium, and other very heavy elements

Equilibrium stable isotope fractionations of mercury and thallium are estimated for molecules, atoms and ions using first-principles vibrational frequency and electronic structure calculations. These calculations suggest that isotopic variation in nuclear volume is the dominant cause of equilibrium fractionation, driving ²⁰⁵Tl/²⁰³Tl and ²⁰²Hg/¹⁹⁸Hg fractionations of up to 3‰ at room temperature. Mass-dependent fractionations are smaller, ca. 0.5-1‰ for the same isotopes. Both fractionation mechanisms tend to enrich the neutron-rich isotopes in oxidized mercury- and thallium-bearing phases (Tl³⁺ and Hg²⁺) relative to reduced phases (Tl⁺ and Hg⁰). Among Hg²⁺-bearing species, inorganic molecules and complexes like HgCl₂, and will have higher ²⁰²Hg/¹⁹⁸Hg than coexisting methylmercury species, suggesting a possible application of Hg-isotope measurements to understanding mercury methylation and increasing methylmercury concentrations at the top of the food chain. Estimated ²⁰⁵Tl/²⁰³Tl fractionation between and is in reasonable agreement with the fractionations previously observed between seawater and Fe-Mn crusts, supporting an equilibrium-like reduction/oxidation fractionation mechanism.More generally, nuclear-volume isotope fractionation will concentrate larger (heavier) nuclei in species where the electron density at the nucleus is small—due to lack of s-electrons (e.g., Hg²⁺—[Xe]4f¹⁴5d¹⁰6s⁰ vs. Hg⁰—[Xe]4f¹⁴5d¹⁰6s²) or enhanced s-electron screening by extra p, d, or f electrons (e.g., Tl⁰—[Xe]4f¹⁴5d¹⁰6s²6p¹ vs. Tl⁺—[Xe]4f¹⁴5d¹⁰6s²6p⁰). Nuclear-volume fractionations become much smaller for lighter elements, declining from ∼1‰/amu for thallium and mercury to ∼0.2‰/amu for ruthenium and ∼0.02‰/amu for sulfur.     

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.     

Iron speciation and isotope fractionation during silicate weathering and soil formation in an alpine glacier forefield chronosequence

The chemical weathering of primary Fe-bearing minerals, such as biotite and chlorite, is a key step of soil formation and an important nutrient source for the establishment of plant and microbial life. The understanding of the relevant processes and the associated Fe isotope fractionation is therefore of major importance for the further development of stable Fe isotopes as a tracer of the biogeochemical Fe cycle in terrestrial environments. We investigated the Fe mineral transformations and associated Fe isotope fractionation in a soil chronosequence of the Swiss Alps covering 150 years of soil formation on granite. For this purpose, we combined for the first time stable Fe isotope analyses with synchrotron-based Fe-EXAFS spectroscopy, which allowed us to interpret changes in Fe isotopic composition of bulk soils, size fractions, and chemically separated Fe pools over time in terms of weathering processes. Bulk soils and rocks exhibited constant isotopic compositions along the chronosequence, whereas soil Fe pools in grain size fractions spanned a range of 0.4‰ in δ⁵⁶Fe. The clay fractions (<2 μm), in which newly formed Fe(III)-(hydr)oxides contributed up to 50% of the total Fe, were significantly enriched in light Fe isotopes, whereas the isotopic composition of silt and sand fractions, containing most of the soil Fe, remained in the range described by biotite/chlorite samples and bulk soils. Iron pools separated by a sequential extraction procedure covered a range of 0.8‰ in δ⁵⁶Fe. For all soils the lightest isotopic composition was observed in a 1 M NH₂OH-HCl-25% acetic acid extract, targeting poorly-crystalline Fe(III)-(hydr)oxides, compared with easily leachable Fe in primary phyllosilicates (0.5 M HCl extract) and Fe in residual silicates. The combination of the Fe isotope measurements with the speciation data obtained by Fe-EXAFS spectroscopy permitted to quantitatively relate the different isotope pools forming in the soils to the mineral weathering reactions which have taken place at the field site. A kinetic isotope effect during the Fe detachment from the phyllosilicates was identified as the dominant fractionation mechanism in young weathering environments, controlling not only the light isotope signature of secondary Fe(III)-(hydr)oxides but also significantly contributing to the isotope signature of plants. The present study further revealed that this kinetic fractionation effect can persist over considerable reaction advance during chemical weathering in field systems and is not only an initial transient phenomenon.     

硅酸盐和金属氧化物矿物氧同位素组成的CO2激光氟化分析

我室采用MIR-10型CO2激光器,在一种富BrF5的氛围中使激光对硅酸盐和氧化物矿物样品加热形成O2,经多次纯化后用5A的分子筛吸收,再直接送至气体质谱仪进行氧同位素比值测定.这个实验流程与传统方法相比的改进不仅在使用激光加热技术及样品的放置上,而且在直接采用O2而不是CO2进行质谱测定.采用O2进行直接分析的优点不仅避免了向CO2转化过程中的潜在同位素分馏,而且能够得到样品的δ17O值,因此为宇宙样品分析提供了可能.CO2激光氟化技术的优点是所需样品量小(可低达1～2 mg),因此能够分析微小岩石区域或单矿物晶体内的氧同位素分布.同时,激光可以达到非常高的温度(＞4000K),因此能够对某些难熔矿物(如锆石、蓝晶石、橄榄石等)进行氧同位素分析.