Equilibrium Isotope Fractionation Factors Research Articles

Ab Initio Calculation of Equilibrium Isotopic Fractionations of Potassium and Rubidium in Minerals and Water

We used first-principle approaches to calculate the equilibrium isotopic fractionation factors of potassium (K) and rubidium (Rb) in a variety of minerals of geological relevance (orthoclase, albit...

The experimental determination of equilibrium Si isotope fractionation factors among H4SiO4o, H3SiO4− and amorphous silica (SiO2·0.32 H2O) at 25 and 75 °C using the three-isotope method

Abstract The accurate interpretation of Si isotope signatures in natural systems requires knowledge of the equilibrium isotope fractionation between Si-bearing solids and the dominant Si-bearing aqueous species. Aqueous silicon speciation is dominated by silicic acid (H4SiO4o) in most natural aqueous fluids at pH 9), equilibrium Si isotope fractionation factors between solid and aqueous solution are higher, at 1.63 ± 0.23‰ at 25 °C, and 1.06 ± 0.13‰ at 75 °C. Taking account of the distribution of the aqueous Si species, equilibrium Si isotope fractionation factors between H3SiO4− and H4SiO4o of −2.34 ± 0.13‰ and −2.21 ± 0.05‰ at 25 and 75 °C, respectively, were determined. The distinct equilibrium isotope fractionation factors of H3SiO4− and H4SiO4o, and its variation with temperature can be used to establish paleo-pH and temperature proxies. The application of the three-isotope method also provides insight into the rates of isotopic exchange. For the solid grain size used (∼20 nm), these rates match closely the measured bulk dissolution rates for amorphous silica for most of the isotope exchange process, suggesting the dominant and rate controlling isotope exchange mechanism in the experiments is detachment and reattachment of material at the amorphous silica surface.

Triple oxygen isotope fractionation in the DIC-H2O-CO2 system: A numerical framework and its implications

Triple oxygen isotope composition of carbonate minerals reflects the isotope composition of the water from which carbonates precipitate, and is emerging as a promising proxy for constraining past changes in Earth hydroclimate and surface environment. However, quantitative interpretation of this proxy is not straightforward when carbonate minerals do not form under isotope equilibrium with water. For these carbonates, isotope composition of dissolved inorganic carbon (DIC) in the precipitating solution usually exerts the dominant control on their isotope composition. Here we examine the systematics of triple oxygen isotope fractionation in the DIC-H2O-CO2 system by deriving the fundamental equilibrium and kinetic triple oxygen isotope fractionation factors in this system and simulating the evolution of triple oxygen isotope composition of DIC during three common isotope fractionation processes, i.e., DIC-H2O isotope exchange, CO2 degassing and CO2 absorption.We show that under thermodynamic equilibrium dissolved HCO3– and CO32– both exhibit similar Δ′17O as calcite and aragonite (within 10 per meg at 25 °C), with temperature dependences around 0.61 per meg/°C. However, kinetic isotope fractionations associated with CO2 hydration and hydroxylation and their reverse reactions can produce a range of disequilibrium triple oxygen isotope effects in DIC during all three processes we simulated. The magnitudes of these disequilibrium effects vary with both time and the physicochemical conditions of the solution, e.g., temperature, pH and initial composition. Particularly, we predict correlated enrichments in Δ′17O and δ18O of DIC during CO2 degassing but depletions during CO2 absorption. The slopes of these correlations vary mainly as a function of solution pH but not temperature, DIC concentration or air pCO2, yielding values of 8.8 and 12.0 per meg/‰ at pH = 8 and 9, respectively, at 25 °C. Such disequilibrium isotope effects in DIC are expected to be inherited by carbonate minerals that form from these solutions (e.g., speleothem, coral skeleton, and high pH travertine) and, if not accounted for, could lead to inaccurate estimates of the triple oxygen isotope compositions of the parent water and carbonate formation temperatures. Our numerical model provides a quantitative framework for interpreting triple oxygen isotope composition of DIC and for correcting disequilibrium triple oxygen isotope effects in natural carbonates.

Dual QM and MM Approach for Computing Equilibrium Isotope Fractionation Factor of Organic Species in Solution.

A dual QM and MM approach for computing equilibrium isotope effects has been described. In the first partition, the potential energy surface is represented by a combined quantum mechanical and molecular mechanical (QM/MM) method, in which a solute molecule is treated quantum mechanically, and the remaining solvent molecules are approximated classically by molecular mechanics. In the second QM/MM partition, differential nuclear quantum effects responsible for the isotope effect are determined by a statistical mechanical double-averaging formalism, in which the nuclear centroid distribution is sampled classically by Newtonian molecular dynamics and the quantum mechanical spread of quantized particles about the centroid positions is treated using the path integral (PI) method. These partitions allow the potential energy surface to be properly represented such that the solute part is free of nuclear quantum effects for nuclear quantum mechanical simulations, and the double-averaging approach has the advantage of sampling efficiency for solvent configuration and for path integral convergence. Importantly, computational precision is achieved through free energy perturbation (FEP) theory to alchemically mutate one isotope into another. The PI-FEP approach is applied to model systems for the 18O enrichment found in cellulose of trees to determine the isotope enrichment factor of carbonyl compounds in water. The present method may be useful as a general tool for studying isotope fractionation in biological and geochemical systems.

Nitrogen isotope fractionation factors (α) measured and estimated from the volatilisation of ammonia from water at pH 9.2 and pH 8.5

ABSTRACTThis paper examines the nitrogen isotope fractionation factors (α) associated with the volatilisation of ammonia from water under controlled conditions at two pH values (8.5 and 9.2). This experiment assumed the continuous removal of ammonia at a single purge rate of 10 mL air min−1. The fractionation resulting from the removal of total ammonia from the water into an acid trap was named the observed isotope fractionation factor (αobs), and it was measured as 1.019 (±0.0025) at pH 8.5 and 1.030 (±0.0025) at pH 9.2. The observed isotope fractionation factor includes the equilibrium isotope fractionation factor (αeq) and the kinetic isotope fractionation factor (αkin), each one mathematically derived from the experimental data. The equilibrium and kinetic isotope fractionation factors were estimated as αeq = 1.036 (±0.0014) and αkin = 1.050 (±0.003), respectively. Our results are compared to other previously measured and estimated fractionation factors.

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.

The theory of equilibrium isotope fractionations for gaseous molecules under super-cold conditions

It is necessary to build a proper theoretical method that can precisely describe isotope fractionation processes under super-cold (<200 K) conditions, because there have been many isotopic data obtained in our solar system that are related to such processes. However, current methods of isotope fractionation calculation, i.e., the Bigeleisen-Mayer equation and its higher-order energy corrections, may not be applicable to super-cold conditions. Here, we have checked important assumptions and higher-order corrections that can affect isotope fractionations of gas-phase molecules under super-cold conditions and developed a new theoretical method for calculating equilibrium isotope fractionation factors. Compared with previous works, we have added three new corrections into our calculation, i.e., nuclear-spin weights for quantum mechanical rotation, correction for Born-Oppenheimer approximation (BOA), and inversion splitting effect for non-planar molecules such as NH3. We further examined gaseous molecules of geochemistry and cosmochemistry relevance, e.g., H2, HF, HCl, H2O, H2S, HCHO, NH3, CH4 and their deuterated isotopologues. We found that the correction for BOA, which was rarely considered in previous studies, is important for those gaseous molecules under super-cold conditions. In case of D/H, 13C/12C and 18O/16O exchanges among organic molecules, BOA correction cannot be ignored even at ambient or higher temperature conditions. Most isotope fractionation trends at super-cold conditions reported here are quite different from their counterparts at ambient or higher temperature conditions. The method proposed here will extend our capability in interpreting equilibrium isotope fractionations to super-cold conditions in the solar system.

Adsorption isotope effects of water on mesoporous silica and alumina with implications for the land-vegetation-atmosphere system

Soil water dynamics within a vadose (unsaturated) zone is a key component in the hydrologic cycle, especially in arid regions. In applying the Craig-Gordon evaporation model to obtain isotopic compositions of soil water and the evaporated vapor in land-surface models (LSMs), it has been assumed that the equilibrium isotope fractionation factors between soil water and water vapor, α(2H) and α(18O), are identical to those between liquid and vapor of bulk water. Isotope effects in water condensation arise from intermolecular hydrogen bonding in the condensed phase and the appearance of hindered rotation/translation. Hydrogen bonding between water molecules and pore surface hydroxyl groups influences adsorption isotope effects. To test whether equilibrium fractionation factors between soil water and water vapor are identical to those between liquid and vapor of bulk water and to evaluate the influence of pore size and chemical composition upon adsorption isotope effects, we extended our previous experiments of a mesoporous silica (15 nm) to two other mesoporous materials, a silica (6 nm) and an alumina (5.8 nm). Our results demonstrated that α(2H) and α(18O) between adsorbed water and water vapor are 1.057 and 1.0086 for silica (6 nm) and 1.041 and 1.0063 for alumina (5.8 nm), respectively, at saturation pressure (po), which are smaller than 1.075 and 1.0089, respectively, between liquid and vapor phases of free water at 30 °C and that the differences exaggerate at low water contents. However, the profiles of α values with relative pressures (p/po) for these three materials differ due to the differences in chemical compositions and pore sizes. Empirical formula relating α(2H) and α(18O) values to the proportions of filled pores (f) are developed for potential applications to natural soils. Our results from triple oxygen isotope analyses demonstrated that the isotope fractionation does not follow a canonical law. For the silica (15 nm), fractionation exponents (17θ) are 0.5361 ± 0.0018 and 0.5389 ± 0.0016 at p/po = 0.72 and 0.77, respectively. For the silica (6 nm), 17θ values are 0.5330 ± 0.0011 at p/po = 0.65 and 0.5278 ± 0.0010 at p/po = 0.81. For the alumina (5.8 nm), 17θ value is 0.5316 ± 0.0015 at p/po = 0.78. These values are greater than or equal to that of liquid-vapor equilibrium of bulk water (0.529 ± 0.001).

Effects of surface structural disorder and surface coverage on isotopic fractionation during Zn(II) adsorption onto quartz and amorphous silica surfaces

Metal ion-mineral surface interactions and the attendant isotopic fractionation depend on the properties of the mineral surface and the local atomic-level chemical environment. However, these factors have not been systematically examined for phases of the same composition with different levels of surface disorder. We present pH-dependent adsorption edges, X-ray absorption spectra, and isotopic measurements to illustrate the effects of surface structural disorder and surface coverage on zinc(II) (Zn(II)) surface complexation and isotope fractionation. Our results demonstrate that Zn(II) surface complexes on quartz and amorphous silica (SiO2(am)) transition from octahedral to tetrahedral coordination by oxygen as surface coverage increases. In low ionic strength solutions (I=0.004M) and at low surface loadings (Γ<0.6μmolm−2), Zn(II) adsorbs to the quartz surface predominantly as outer-sphere octahedral complexes (RZn-O=2.05Å) with no significant isotopic fractionation (Δ66/64Znaqueous-sorbed=−0.01±0.06‰) from aqueous Zn(II). In contrast, under similar chemical conditions and surface loading, outer-sphere Zn(II) adsorption complexes are not observed on SiO2(am) surfaces. At high ionic strength (I=0.1M) and low surface loading (Γ<0.2μmolm−2), inner-sphere, monodentate octahedral Zn(II) complexes (RZn-O=2.05–2.07Å) are observed on both quartz and SiO2(am) surfaces. At the same ionic strength (I=0.1M) and higher surface loading (Γ=0.6–1.4μmolm−2), Zn(II) forms inner-sphere, monodentate tetrahedral complexes (RZn-O=1.98Å) at the quartz surface. On the SiO2(am) surface under similar chemical conditions and surface loading, Zn(II) forms dominantly inner-sphere, monodentate tetrahedral complexes with shorter ZnO bond distances (RZn-O=1.94Å). Despite different coordination numbers, the measured equilibrium isotope fractionation factors for inner-sphere octahedral and tetrahedral complexes versus dissolved Zn, under the same conditions and on the same silica substrate, are not distinguishable beyond uncertainties. However, there is a larger measured equilibrium isotope fractionation with preferential sorption of heavy Zn as inner-sphere complexes on SiO2(am) (Δ66/64Znaqueous-sorbed=−0.94±0.11‰) than on quartz (Δ66/64Znaqueous-sorbed=−0.60±0.11‰).The propensity for Zn(II) to occur in tetrahedral and octahedral coordination with oxygen may help explain these observations. We posit that the low energetic difference between octahedral and tetrahedral Zn(II) may be why changes in inner-sphere Zn(II) coordination numbers with increasing coverage do not manifest as distinguishable isotope fractionations or asan observable alteration to the macroscopic sorption edges. Thus, we attribute the larger magnitude of Zn isotope fractionation on SiO2(am) compared to quartz to differences in the bonding environments on the two types of silica surfaces rather than to a change in the coordination number of Zn(II).

Redefining the utility of the three-isotope method

The equilibrium isotope fractionation factor αeq is a fundamental parameter in the study of stable isotope effects. Experimentally, it has been difficult to establish that a system has attained equilibrium. The three-isotope method, using the initial trajectory of changing isotope ratios (e.g. 16O, 17O, and 18O) to deduce the final equilibrium point of isotope exchange, has long been hailed as the most rigorous experimental approach. However, over the years some researchers have cautioned on the limitations of this method, but the foundation of three-isotope method has not been properly examined and the method is still widely used in calibrating αeq for both traditional and increasingly non-traditional isotope systems today. Here, using water-water and dissolved CO2-water oxygen exchange as model systems, we conduct an isotopologues-specific kinetic analysis of the exchange processes and explore the underlying assumptions and validity of the three-isotope method. We demonstrate that without knowing the detailed exchange kinetics a priori the three-isotope method cannot lead to a reliable αeq. For a two-reservoir exchanging system, α determined by this method may be αeq, kinetic isotope effect, or apparent kinetic isotope effect, which can all bear different values. When multiple reservoirs exist during exchange, the evolving trajectory can be complex and hard to predict. Instead of being a tool for αeq determination, three-isotope method should be used as a tool for studying kinetic isotope effect, apparent kinetic isotope effect, and detailed exchange kinetics in diverse systems.

Concentration effect on equilibrium fractionation of Mg-Ca isotopes in carbonate minerals: Insights from first-principles calculations

Naturally occurring carbonates have a wide variation in Mg and Ca contents. Using the density-functional-theory calculations, this study examines the effect of Mg and Ca concentrations on bond lengths and equilibrium fractionation factors of Mg-Ca isotopes among calcite-type carbonate minerals (MgxCa1−xCO3). Mg content x and Ca content (1−x) of the investigated carbonate minerals range from 1/12 to 1 and from 1/36 to 1, respectively. Concentration of Ca and Mg in carbonates have significant effects on Ca–O and Mg–O bond lengths when x is close to 0, 0.5 or 1. Because equilibrium isotope fractionation factors (103lnα) are mainly controlled by their relevant bond strengths, which can be measured using their average bond lengths, 103lnα of 26Mg/24Mg and 44Ca/40Ca between calcite-type carbonate minerals and dolomite also vary dramatically with Mg content, especially when x is close to 0 and 1. For instance, at 300K, 103lnα of 26Mg/24Mg between Mg1/12Ca11/12CO3 and dolomite (x=0.5) is ∼−4.3‰, while 103lnα of 44Ca/40Ca between Mg23/24Ca1/24CO3 and dolomite is ∼6‰. Dolomite is enriched in 26Mg but depleted in 44Ca relative to all other carbonate minerals, which is consistent with it having the shortest Mg–O bond length and the longest Ca–O bond lengths among all carbonates. At 300K, a small change of x from 0.5 to 0.6 in dolomite could result in 1‰ variation in 103lnβ of 26Mg/24Mg. Therefore, the concentration effect in carbonate minerals should be taken into account when applying the isotope fractionation factors of carbonate minerals to understand geochemical processes.

Equilibrium Fractionation of Non-traditional Stable Isotopes: an Experimental Perspective

In 1986, O’Neil wrote a Reviews in Mineralogy chapter on experimental aspects of isotopic fractionation. He noted that in order to fully understand and interpret the natural variations of light stable isotope ratios in nature, it was essential to know the magnitude and temperature dependence of the isotopic fractionation factor amongst minerals and fluids. At that time it was difficult to imagine that this would become true for the heavier, so called non-traditional stable isotopes, as well. Since the advent of the multiple collector inductively coupled plasma-source mass spectrometer (MC–ICP–MS), natural variations of stable isotope ratios have been found for almost any polyisotopic element measured. Although it has been known that as temperature and mass increase, isotope fractionation decreases very quickly, the MC–ICP–MS has revolutionized the ability of a geochemist to measure very small differences in isotope ratios. It was then that the field of experimental non-traditional stable isotope geochemistry was born. As O’Neil (1986) pointed out there are three ways to obtain isotopic fractionation factors: theoretical calculations, measurements of natural samples with well-known formation conditions, and laboratory calibration studies. This chapter is devoted to explaining the techniques involved with laboratory experiments designed to measure equilibrium isotope fractionation factors as well as the best practices that have been learned. Although experimental petrology has been around for a long time and basic experimental methods have been well-refined, there are additional considerations that must be taken into account when the goal is to measure isotopic compositions at the end of the experiment. It has been only about ten years since these initial studies were published, but much has been learned in that time about how best to conduct experiments aimed at determining equilibrium fractionation factors. We will not focus on the scientific results that have been determined by such experiments, as each …

Equilibrium zinc isotope fractionation in Zn-bearing minerals from first-principles calculations

Isotopic composition analysis contributes significantly to the investigation of the biogeochemical cycle of zinc with its economical, environmental and health implications. Interpretation of isotopic measurements is however hindered by the lack of a set of equilibrium isotopic fractionation factors between Zn-bearing minerals. In this study, equilibrium mass-dependent Zn isotope fractionation factors in Zn-bearing minerals are determined from first-principles calculations within the density functional theory (DFT) scheme. A wide range of minerals belonging to sulfide, carbonate, oxide, silicate, sulfate and arsenate mineral groups are modelled to account for the natural diversity of Zn crystal-chemical environment. Calculated reduced partition function ratios (β-factors) span a range smaller than 2‰ at 22°C. All studied secondary minerals (adamite, gahnite, gunningite, hemimorphite, hydrozincite, zincite) but zinc carbonate (smithsonite) are isotopically heavier than zinc sulfide minerals (sphalerite and wurtzite) from which they could form through supergene processes. Zinc–aluminium spinel and zinc silicate are the isotopically heaviest minerals. The investigation of the crystal-chemical parameters at the origin of differences in isotopic properties shows an excellent linear correlation between lnβ and Zn interatomic force constants. β-factors are also observed to increase when the Zn-first neighbour bond lengths decrease and charges on atoms involved in the bonding increase and vice versa. These findings are in line with the observation of heavy isotope enrichment in systems having the largest bond strength.

Theoretical calculation of oxygen equilibrium isotope fractionation factors involving various NOy molecules, [rad]OH, and H2O and its implications for isotope variations in atmospheric nitrate

The oxygen stable isotope composition (δ18O) of nitrogen oxides [NOx=nitric oxide (NO)+nitrogen dioxide (NO2)] and their oxidation products (NOy=NOx+nitric acid (HNO3)+particulate nitrate (p-NO3−)+nitrate radical (NO3)+dinitrogen pentoxide (N2O5)+nitrous acid (HONO)+…) have been shown to be a useful tool for inferring the proportion of NOx that is oxidized by ozone (O3). However, isotopic fractionation processes may have an influence on δ18O of various NOy molecules and other atmospheric O-bearing molecules pertinent to NOx oxidation chemistry. Here we have evaluated the impacts of O isotopic exchange involving NOy molecules, the hydroxyl radical (OH), and water (H2O) using reduced partition function ratios (xβ) calculated by hybrid density functional theory. Assuming atmospheric isotopic equilibrium is achieved between NO and NO2 during the daytime, and NO2, NO3, and N2O5 during the nighttime, δ18O–δ15N compositions were predicted for the major atmospheric nitrate formation pathways using our calculated exchange fractionation factors and isotopic mass-balance. Our equilibrium model predicts that various atmospheric nitrate formation pathways, including NO2+OH→HNO3, N2O5+H2O+surface→2HNO3, and NO3+R→HNO3+R will yield distinctive δ18O–δ15N compositions. Our calculated δ18O–δ15N compositions match well with previous atmospheric nitrate measurements, and will potentially help better understand the role oxidation chemistry plays on the N and O isotopic composition of atmospheric nitrate.

Unbiased isotope equilibrium factors from partial isotope exchange experiments in 3-exchange site systems

Two methods are available in order to evaluate the equilibrium isotope fractionation factors between exchange sites or phases from partial isotope exchange experiments. The first one developed by Northrop and Clayton (1966) is designed for isotope exchanges between two exchange sites (hereafter, the N&C method), the second one from Zheng et al. (1994) is a refinement of the first one to account for a third isotope exchanging site (hereafter, the Z method).In this paper, we use a simple model of isotope kinetic exchange for a 3-exchange site system (such as hydroxysilicates where oxygen occurs as OH and non-OH groups like in muscovite, chlorite, serpentine, or water or calcite) to explore the behavior of the N&C and Z methods. We show that these two methods lead to significant biases that cannot be detected with the usual graphical tests proposed by the authors.Our model shows that biases originate because isotopes are fractionated between all these exchanging sites. Actually, we point out that the variable mobility (or exchangeability) of isotopes in and between the exchange sites only controls the amplitude of the bias, but is not essential to the production of this bias as previously suggested. Setting a priori two of the three exchange sites at isotopic equilibrium remove the bias and thus is required for future partial exchange experiments to produce accurate and unbiased extrapolated equilibrium fractionation factors.Our modeling applied to published partial oxygen isotope exchange experiments for 3-exchange site systems (the muscovite-calcite (Chacko et al., 1996), the chlorite-water (Cole and Ripley, 1998) and the serpentine–water (Saccocia et al., 2009)) shows that the extrapolated equilibrium fractionation factors (reported as 1000ln(α)) using either the N&C or the Z methods lead to bias that may reach several δ per mil in a few cases. These problematic cases, may be because experiments were conducted at low temperature and did not reach high exchange percentages (<50%) such as the chlorite–water and the serpentine–water experiments.

An experimental study on isotope fractionation in a mesoporous silica-water system with implications for vadose-zone hydrology

Soil water dynamics within a thick vadose (unsaturated) zone is a key component in the hydrologic cycle in arid regions. In isotopic studies of soil water, the isotopic composition of adsorbed/pore-condensed water within soils has been assumed to be identical to that of bulk liquid water. To test this critical assumption, we have conducted laboratory experiments on equilibrium isotope fractionation between adsorbed/condensed water in mesoporous silica (average pore diameter 15nm) and the vapor at relative pressures p/po=0.3–1.0 along the adsorption–desorption isotherm at 30°C. The isotope fractionation factors between condensed water in the silica pores and the vapor, α(2H) and α(18O), are smaller than those between liquid and vapor of bulk water (1.074 and 1.0088, respectively, at 30°C). The α(2H) and α(18O) values progressively decrease from 1.064 and 1.0083 at p/po=1 to 1.024 and 1.0044 at p/po=0.27 for hydrogen and oxygen isotopes, respectively, establishing trends very similar to the isotherm curves. Empirical formulas relating α(2H) and α(18O) to the proportions of filled pores (f) are developed. Our experimental results challenge the long-held assumption that the equilibrium isotope fractionation factors for the soil water–vapor are identical to those of liquid water–vapor system with potential implications for arid-zone and global water cycles, including paleoclimate proxies in arid regions.

Equilibrium and kinetic Si isotope fractionation factors and their implications for Si isotope distributions in the Earth’s surface environments

Abstract Several important equilibrium Si isotope fractionation factors among minerals, organic molecules and the H4SiO4 solution are complemented to facilitate the explanation of the distributions of Si isotopes in Earth’s surface environments. The results reveal that, in comparison to aqueous H4SiO4, heavy Si isotopes will be significantly enriched in secondary silicate minerals. On the contrary, quadra-coordinated organosilicon complexes are enriched in light silicon isotope relative to the solution. The extent of 28Si-enrichment in hyper-coordinated organosilicon complexes was found to be the largest. In addition, the large kinetic isotope effect associated with the polymerization of monosilicic acid and dimer was calculated, and the results support the previous statement that highly 28Si-enrichment in the formation of amorphous quartz precursor contributes to the discrepancy between theoretical calculations and field observations. With the equilibrium Si isotope fractionation factors provided here, Si isotope distributions in many of Earth’s surface systems can be explained. For example, the change of bulk soil δ30Si can be predicted as a concave pattern with respect to the weathering degree, with the minimum value where allophane completely dissolves and the total amount of sesqui-oxides and poorly crystalline minerals reaches their maximum. When, under equilibrium conditions, the well-crystallized clays start to precipitate from the pore solutions, the bulk soil δ30Si will increase again and reach a constant value. Similarly, the precipitation of crystalline smectite and the dissolution of poorly crystalline kaolinite may explain the δ30Si variations in the ground water profile. The equilibrium Si isotope fractionations among the quadra-coordinated organosilicon complexes and the H4SiO4 solution may also shed light on the Si isotope distributions in the Si-accumulating plants.

Silicon isotope fractionation during the precipitation of quartz and the adsorption of H4SiO4(aq) on Fe(III)-oxyhydroxide surfaces

Equilibrium Si isotope fractionation factors among orthosilicic acid (i.e.,H4SiO4(aq)), quartz and the adsorption complexes of H4SiO4(aq) on Fe(III)-oxyhydroxide surface were calculated using the full-electron wave-function quantum chemistry methods [i.e., B3LYP/6-311G(2df,p)] with a new cluster-model-based treatment. Solvation effects were carefully included in our calculations via water-droplet method combined with implicit solvent models (e.g., PCM). The results revealed that, if it is under equilibrium conditions, heavy Si isotopes would be significantly enriched in quartz in comparison to H4SiO4(aq). However, most of the field observations suggested that quartz would have identical or even depleted δ30Si values compared to that of H4SiO4(aq). To explain this discrepancy between the equilibrium calculation results and the field observations, the kinetic isotope effect (KIE) associated with the formation of amorphous silica, which usually is the precursor of crystalline quartz, was investigated using quantum chemistry methods. The KIE results showed that amorphous silica would be significantly enriched in light Si isotopes during its formation. Our equilibrium fractionation results, however, matched a special type of quartz (i.e., Herkimer “diamond”) very well, due to its nearly equilibrated precipitation condition. Opposite to the case of precipitated quartz, a large equilibrium Si isotope fractionation (i.e., −3.0 ‰) was found between the absorbed bidentate Si surface complexes (i.e., 2C > Fe2O2Si(OH)2) and H4SiO4(aq). This calculated equilibrium Si isotope fractionation factor largely differed from a previous experimental result (ca. −1.08 ‰). We found that the formation of transient or temporary surface complexes [e.g., 1V > Fe2OSi(OH)3] may have accounted for the smaller net fractionation observed. With the equilibrium and kinetic Si isotope fractionation factors provided here, the distributions and changes of Si isotope compositions in the Earth’s surface systems can be better understood.

First-principles investigation of vanadium isotope fractionation in solution and during adsorption

Equilibrium fractionation factors of vanadium (V) isotopes among tri- (V(III)), tetra- (V(IV)) and penta-valent (V(V)) inorganic V species in aqueous system and during adsorption of V(V) to goethite are estimated using first-principles calculation. Our results highlight the dependence of V isotope fractionation on valence states and the chemical binding environment. The heavy V isotope (51V) is enriched in the main V species following a sequence of V(III)<V(IV)<V(V). According to our calculations, at 25 °C, the equilibrium isotope fractionation factor between [V5+O2(OH)2]− and [V4+O(H2O)5]2+ (ln⁡αV(V)–V(IV)) is 3.9‰, and the equilibrium isotope fractionation factor between [V5+O2(OH)2]− and [V3+(OH)3(H2O)3] (ln⁡αV(V)–V(III)) is 6.4‰. In addition, isotope fractionation between +5 valence species [V5+O2(OH)2]− and [V5+O2(H2O)4]+ is 1.5‰ at 25 °C, which is caused by their different bond lengths and coordination numbers (CN). Theoretical calculations also show that light V isotope (50V) is preferentially adsorbed on the surface of goethite. Our work reveals that V isotopes can be significantly fractionated in the Earth's surface environments due to redox reaction and mineral adsorption, indicating that V isotope data can be used to monitor toxic V(V) attenuation processes through reduction or adsorption in natural water systems. In addition, a simple mass balance model suggests that V isotope composition of seawater might vary with change of ambient oxygen levels. Thus our theoretical investigations imply a promising future for V isotopes as a potential new paleo-redox tracer.

Equilibrium magnesium isotope fractionation between aqueous Mg2+ and carbonate minerals: Insights from path integral molecular dynamics

The theoretical determination of the isotopic fractionation between an aqueous solution and a mineral is of utmost importance in Earth sciences. While for crystals, it is well established that equilibrium isotopic fractionation factors can be calculated using a statistical thermodynamic approach based on the vibrational properties, several theoretical methods are currently used to model ions in aqueous solution. In this work, we present a systematic study to determine the reduced partition function ratio (β-factor) of aqueous Mg2+ using several levels of theory within the simulations. In particular, using an empirical force field, we compare and discuss the performance of the exact results obtained from path integral molecular dynamics (PIMD) simulations, with respect to the more traditional methods based on vibrational properties and the cluster approximation. The results show the importance of including configurational disorder for the estimation of the equilibrium isotope fractionation factor. We also show that using the vibrational frequencies computed from snapshots taken from equilibrated classical molecular dynamics represents a good approximation for the study of aqueous ions.Based on these conclusions, the β-factor of aqueous Mg2+ have been estimated from a Car–Parrinello molecular dynamics (CPMD) simulation with an ab initio force field, and combined with the β-factors of carbonate minerals (magnesite, dolomite, calcite and aragonite). Mg β-factor of Mg-bearing aragonite, calculated here for the first time, displays a lower value than the three other carbonate minerals. This is explained by a strong distortion of the cationic site leading to a decrease of the coordination number during Ca–Mg substitution. Overall, the equilibrium magnesium isotope fractionation factors between aqueous Mg2+ and carbonate minerals that derive from this methodological study support the previous theoretical results obtained from embedded cluster models.