Equilibrium Fractionation Factors Research Articles

Experimental and theoretical constraints on lithium isotope fractionation during brine evaporation and halite precipitation

Marine evaporitic halite, precipitating from the advanced stage of extremely evaporated seawater, is the most common and abundant evaporitic mineral. The extent to which lithium (Li) is incorporated into evaporite halite during geological periods of massive halite deposition, and the mechanisms of incorporation, are both unknown. These are each important, however, for the quantification of the isotope effect of the evaporitic sink on δ7Liseawater, and for the potential use of halite as a recorder of seawater δ7Li. Here, new experimental data are presented for the Li fractionation factor for halite from an isothermal evaporation experiment (25∘C for 100 days) using marine-derived brine. The resultant solids were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM) to confirm the mineralogy and crystallinity of the product. Our results show that Li isotopes are not constant during the evaporation process implying that there must be a process that fractionates Li isotopes during halite precipitation. We suggest that this results from Li ionic substitution for sodium (Na) in crystalline halite, a scenario supported by ab-initio calculations, but we also show that Li within halite is predominantly present within fluid inclusions. Thus, the Li isotopic composition of halite is controlled by a mixture of Li within the fluid inclusions and Li that is incorporated into the halite crystalline structure. Overall, the brine becomes enriched in Li7 during evaporation due to the preferential incorporation of Li6 into chloride precipitates, and the evolution of δ7Librine is controlled by the precipitated mineral assemblage. The theoretical equilibrium fractionation factor 1000lnαmineral−fluid is -7.8▪ for Li-halite (LiNa26Cl27) at 25 C∘ at equilibrium, which is at the lower limit of Li isotope fractionation factors. Rayleigh fractionation models were fitted to the experimental data yielding a fractionation factor of -25▪3▪. The difference in Li isotope fractionation factor between brine and structurally bound Li may result from kinetic fractionation effects. This study presents a scenario highlighting that extensive halite deposits, formed over geological time in environments with relatively high Li concentration, could potentially impact the δ7Li values of seawater during that period, and place constraints on their utility as an archive for δ7Liseawater.

First-principles calculations of equilibrium barium isotope fractionation among silicate minerals

Barium isotopes have been increasingly applied to trace igneous processes, but the applications are hindered by the lack of equilibrium Ba isotope fractionation factors between silicate minerals. In this study, the reduced partition function ratios (RPFRs) of the major Ba-hosting silicate minerals, including muscovite, phlogopite, tremolite, richterite, microcline, albite, and epidote, as well as witherite and barite, are obtained using first-principles calculations. The effect of Ba concentration on the RPFR of those silicate minerals was examined, and no significant effect was observed in the natural range of Ba concentrations. Our results show a heavy Ba isotope enrichment order of tremolite > epidote > albite > witherite ∼ richterite ∼ microcline ∼ barite ∼ muscovite ∼ phlogopite. The RPFRs are controlled by the force constant of Ba and affected by the BaO bond length. The lattice environment of substituted ions controls the equilibrium Ba isotope fractionation factors of trace elements. For instance, the replacement of Ba2+ with Mg2+ or K+ in phlogopite introduces an approximately 0.16‰ offset of Ba isotope ratios (138Ba/134Ba) at 1000 K. In general, light Ba isotopes are preferentially enriched in crystalline positions with larger ion radii. Equilibrium Ba isotope fractionation among silicate minerals is up to 0.08‰ at 1000 K, which can be well resolved by the current analytical precision (∼0.05‰ for δ138/134Ba). This study provides the calculated equilibrium fractionation factors, which are the key to understanding Ba isotope fractionation in natural rocks.

No biological effect on magnesium isotope fractionation during stromatolite growth

The growth and morphology of stromatolites have been previously linked to diverse microbial activities. However, the role of microbial metabolisms on carbonate formation during stromatolite growth remains controversial. Magnesium isotopes have been proposed to serve as a tracer of microbial carbonate formation, implying a potential biological isotope fractionation. To further elucidate whether Mg isotope fractionation is modified during microbial carbonate formation, this study reports Mg isotope compositions of Holocene stromatolites and pore waters from Lagoa Salgada, a coastal ephemeral lake in Brazil. The stromatolitic carbonates are composed of high-Mg calcites characterized by extremely positive inorganic δ13C values, up to +20‰, and variable δ26Mg values, ranging from −2.98‰ to −0.68‰. Multiple pieces of evidence consistently demonstrate changes in microbial metabolism resulting from ecosystem fluid chemistry evolution. However, the direction of Mg isotope fractionation associated with carbonate precipitation remained invariable despite the changes in microbial activity. Mineralogical features indicate that the stromatolitic carbonates formed via 2-D nucleation. An isotopic mass balance calculation based on the observed variations in δ26Mg values and Mg concentrations of associated pore waters argues for an Mg isotopic equilibrium fractionation factor of −2.60‰ associating with the carbonate formation at Lagoa Salgada, well-matching experimental values for abiotic calcite precipitation. Thus, the observed δ26Mg variability of stromatolitic carbonates is primarily controlled by the changes of physicochemical conditions in the ambient fluid. We infer that during the formation of stromatolites, a consortium of different microbial communities produces extracellular polymeric substances, which serve as a substrate for carbonate nucleation from ambient fluid without significantly affecting the fractionation of Mg-isotopes. Our findings shed light on the effects of microbial processes on carbonate formation during stromatolite growth and improve the current understanding of the Mg isotope record in microbial carbonates.

Site-specific isotope effect: Insights from equilibrium magnesium isotope fractionation in mantle minerals

The equilibrium Mg isotope fractionation factors (lnα) derived from both theoretical calculation and experimental studies are not consistent with the values from natural sample observation. Different cation sites, which have identical coordinate numbers but different bond strengths, contribute equally to lnα in theoretical calculations. These non-equivalent sites might complicate the inter-mineral equilibrium isotope fractionations. Here, we investigate reduced partition function ratios (103lnβ) of non-equivalent Mg cation sites (e.g., M1, M2, and M3) in forsterite, orthoenstatite, clinoenstatite, tremolite, omphacite, pyrope and spinel to explore the site-specific effect on the intra- and inter-mineral equilibrium isotope fractionation. Based on all-electron first-principles calculations, 103lnβ in different cation sites decreases in the following sequence of spinelM1 > tremoliteM3 > orthoenstatiteM1 > forsteriteM1 > omphaciteM1 > tremoliteM1 > tremoliteM2 > clinoenstatiteM1 > forsteriteM2 > orthoenstatiteM2 > clinoenstatiteM2 > pyropeM1. These findings suggest that cation sites with larger polyhedron volumes prefer light Mg isotopes to those with smaller polyhedron volumes inside minerals, and the different contribution of intra-mineral cation sites could result in significant variations of equilibrium Mg isotope fractionation between minerals. The range of lnα between minerals induced by specific sites is defined as the equilibrium isotope fractionation domain. The site-corrected lnα can provide better evaluation of equilibrium fractionation factor of Mg isotopes between spinel and olivine and clarify the equilibrium state between mantle minerals. In addition, we establish spinel-olivine and omphacite-pyrope Mg isotope geothermometers based on the site-specific effect. This study suggests that the site-specific effect could be prevalent in solid materials and thus important for other isotope systems.

Temperature and co-crystallization effects on Zr isotopes

We undertook Zr isotope measurements on zircon, titanite, biotite, amphibole, and whole rocks from the La Posta pluton (Peninsular Ranges, southern California) together with trace element analyses and U-Pb age measurements to understand the controls on Zr isotope fractionation in igneous rocks, including temperature, crystallization sequence, and kinetic effects. We find large (>0.6‰) Zr isotope fractionations (expressed as δ94/90Zr) between titanite and zircon forming at approximately the same temperature. Using equilibrium fractionation factors calculated from ionic and ab initio models, we infer the controls on Zr isotope evolution to include the relative order in which phases appear on the liquidus, with titanite fractionation resulting in isotopically lighter melt and zircon fractionation resulting in isotopically heavier melt. While these models of Zr fractionation can explain δ94/90Zr variations in zircon of up to ∼1.5‰, crystallization order, temperature and presence of co-crystallizing phases do not explain all aspects of the intracrystalline Zr isotopic distribution in zircons in the La Posta pluton or the large range of Zr isotopic values among zircons (>2‰). Without additional constraints, such as knowledge of co-crystallizing phases and a better understand of the true causes of Zr isotope fractionation, Zr isotopes in zircon remains an ambiguous proxy of magmatic evolution.

Equilibrium hydrogen isotope fractionation between portlandite/brucite and water: Implication from the vibrational spectra at elevated temperature and pressure

Minerals in brucite-type structure, including brucite (Mg(OH)2) and portlandite (Ca(OH)2), have been studied as important analogs of hydrous silicate minerals for their thermodynamic properties, including equilibrium hydrogen and oxygen isotope fractionations between minerals and water at elevated temperatures and pressures. In this study, Raman and Fourier transform infrared (FTIR) spectra were collected at high-temperature (T) and high-pressure (P) conditions on synthetic hydrogenated and deuterated portlandite samples (i.e., Ca(OH)2 and Ca(OD)2), and their isobaric and isothermal mode Grüneisen parameters, as well as anharmonic parameters, were then evaluated. These high-precision vibrational spectra enable the evaluation of thermodynamic properties of portlandite (ΔU, CV, CP and ΔS) up to 427 °C, to which anharmonicity has positive contributions. More importantly, they help to determine the isobaric (at P = 1 bar) β factors of brucite and portlandite for equilibrium D/H fractionation considering anharmonic effects, and the D/H fractionation factor (103∙lnα) between brucite/portlandite and water at high-P,T conditions. The calculated equilibrium fractionation factor (lnαbrucite-water) agrees with experimental results in the temperature range from 300 to 647 K (∼27 to ∼374 °C, the critical point of water) within analytical uncertainties estimated using Monte Carlo method. The Ab initio calculation using DFT theory and VASP program was also carried out to obtain phonon spectra for brucite and portlandite with three-split hydrogen sites and to evaluate the dispersion effect, which is found to be smaller than the statistical uncertainty at high temperatures. Our results show that the internal OH-stretching modes in brucite/portlandite play a dominant role in determining the β values, and the anharmonic OH-stretching potential (xi parameter) contributes significantly to the D/H fractionation factor. Because previous studies show that OH-stretching frequencies generally decrease with increasing mass of cation in the metallic hydroxide having similar crystal structure, our results imply that the deuterium isotope may be preferentially enriched in the hydroxide phase with the light cation bonded to the hydroxyl group, which is also consistent with the observed D/H fractionations among hydrous silicates.

Global distribution of nonexchangeable stable hydrogen isotope ratios of topsoil clay fractions

Stable isotope ratios of hydrogen (δ2H values) in local meteoric water correlate with those of nonexchangeable H (δ2Hn) in bulk soil and organic matter, allowing for probabilistic spatial assignments to soil samples. We hypothesized that there is a similar correlation between the δ2H values of local meteoric water and the δ2Hn value of soil clay fractions. The H pool of topsoil clay fractions is usually dominated by pedogenic clay minerals, which contain structural hydroxyl-H, preserving the δ2H values of ambient water at the time mineral formation. We applied a steam equilibration method with water vapors of known δ2H values to determine δ2Hn values in soil clay fractions by eliminating the influence of easily exchangeable H. We collected topsoil samples from 24 locations on five continents with a wide variation in δ2H values of meteoric water. To calculate δ2Hn values via steam equilibration, the equilibrium fractionation factor between exchangeable H in the clay fractions and equilibration waters (αex–w) is needed, which is, however, unknown. We therefore assessed the effect of αex-w values from 1 (no fractionation) to αex-w = 1.08, which has been used in steam equilibration approaches of organic matter and bulk soil, on the δ2Hn values of soil clay fractions. The δ2Hn values of the clay fractions ranged from –167 ± SD1‰ for a northern Siberian sample to –44 ± 4‰ in western Kenya for αex-w = 1 and from −191 ± 5 to –81 ± 5‰ for αex-w = 1.08. The δ2H values of local meteoric water correlated significantly with the δ2Hn values of the clay fractions (r = 0.85 for αex-w = 1 and 0.65 for αex-w = 1.08, p < 0.001). A multiple regression model including hillslope as a possible measure of the accumulation of clay minerals with a slightly different δ2Hn value from nearby locations by eolian or aqueous transport in addition to the mean seasonal δ2H values of local meteoric water explained up to 89% of the observed variation in δ2H values of the clay fractions. Our results demonstrate that the δ2Hn values of soil clay fractions are driven by the δ2H values of local precipitation on a global scale, irrespective of the used αex–w value and influenced by the mineral type. Overcoming previous methodological limitations opens up opportunities for probabilistic spatial assignments of unknown organic matter-poor topsoil samples, applications to paleosoil problems or to experimentally track clay mineral neoformation in soils by tracer experiments.

Iron and silicon isotope fractionation in silicate melts using first-principles molecular dynamics

The direct determination of silicate melts iron and silicon isotopes signature remains a major challenge of high-temperature isotope geochemistry. For this reason, melts are often approximated by silicate glasses. Calculation of precise equilibrium Si and Fe isotopes fractionation factors between minerals and melt would indeed allow us to distinguish equilibrium fractionation from diffusion-driven kinetic fractionation involved in the iron and silicon isotopes signatures of Earth and other planets. In this study, we use for the first time, first-principles molecular dynamics based on density functional theory to determine iron and silicon isotope compositions of different silicate melts, namely: iron-rich basalt, iron-depleted basalt, basanite, trachyte and phonolite. The 57Fe/54Fe reduced partition function ratios (β-factors) of the different melts span over a 1.1 ‰ range at 1000 Kelvin (K) while 30Si/28Si β-factors are much less influenced by the melt composition with a 0.5 ‰ fractionation range at the same temperature. The main parameter controlling iron isotope fractionation in silicate melts having similar iron oxidation state is, after temperature, the average Fe-O bond length. The chemical environment around iron (e.g. Fe-Fe distances) is suggested to contribute to Fe isotope fractionation as well. Silicon isotopes fractionation seems also affected, but to a lesser extent, by its local chemical composition with decreasing Si-Fe distances leading to slightly higher Si β-factor in the melt. From these melts Fe and Si β-factors, a new set of equilibrium fractionation factors between a variety of minerals and melts has been calculated. These new Δ57Femin-melt and Δ30Simin-melt sets allow us to discuss whether processes such as fractional crystallization, partial melting and diffusion could be responsible for the documented Fe and Si isotopes variations in igneous rocks. Our results suggest that: 1) fractional crystallization may explain at least part of the Fe and Si isotopic evolution during magmatic differentiation, for values up to δ57Fe = 0.65 ‰ and δ30Si = -0.1 ‰, respectively, 2) partial melting of the upper mantle can produce the Mid-Ocean Ridge Basalts (MORB) iron isotopes signature. Finally, we calculated that olivine at equilibrium with a basaltic melt could display an iron isotope composition down to −0.1 ‰ for δ57Fe. Hence, the lower isotopic compositions (δ57Fe < -0.1 ‰) observed in natural olivines are most likely due to diffusion-driven kinetic fractionation.

Hydrogen isotope behavior during rhyolite glass hydration under hydrothermal conditions

The diffusion of molecular water (H2Om) from the environment into volcanic glass can hydrate the glass up to several wt% at low temperature over long timescales. During this process, the water imprints its hydrogen isotope composition (δDH2O) to the glass (δDgl) offset by a glass-H2O fractionation factor (ΔDgl-H2O = δDgl – δDH2O) which is approximately −33‰ at Earth surface temperatures. Glasses hydrate much more rapidly at higher, sub-magmatic temperatures as they interact with H2O during eruption, transport, and emplacement. To aid in the interpretation of δDgl in natural samples, we present hydrogen isotope results from vapor hydration experiments conducted at 175–375 °C for durations of hours to months using natural volcanic glasses. The results can be divided into two thermal regimes: above 250 °C and below 250 °C. Lower temperature experiments yield raw ΔDgl-H2O values in the range of −33 ± 11‰. Experiments at 225 °C using both positive and negative initial ΔDgl-H2O values converge on this range of values, suggesting this range represents the approximate equilibrium fractionation for H isotopes between glass and H2O vapor (103lnαgl-H2O) below 250 °C. Variation in ΔDgl-H2O (−33 ± 11‰) between different experiments and glasses may arise from incomplete hydration, analytical uncertainty, differences in glass chemistry, and/or subordinate kinetic isotope effects. Experiments above 250 °C yield unexpectedly low δDgl values with ΔDgl-H2O values of ≤–85‰. While alteration alone is incapable of explaining the data, these run products have more extensive surface alteration and are not interpreted to reflect equilibrium fractionation between glass and H2O vapor. Fourier transform infrared spectroscopy (FTIR) shows that glass can hydrate with as much as 5.9 wt% H2Om and 1.0 wt% hydroxl (OH−) in the highest P-T experiment at 375 °C and 21.1 MPa. Therefore, we employ a 1D isotope diffusion–reaction model of glass hydration to evaluate the roles of equilibrium fractionation, isotope diffusion, water speciation reactions internal to the glass, and changing boundary conditions (e.g. alteration and dissolution). At lower temperatures, the best fitting model results to experimental data for low silica rhyolite (LSR) glasses require only an equilibrium fractionation factor and yield 103lnαgl-H2O values of −33‰ ± 5‰ and −25‰ ± 5‰ at 175 °C and 225 °C, respectively. At higher temperatures, ΔDgl-H2O is dominated by boundary layer effects during glass hydration and glass surface alteration. The modeled bulk δDgl value is highly responsive to changes in the δDgl boundary condition regardless of the magnitude of other kinetic effects. Observed glass dissolution and surficial secondary mineral formation are likely to impose a disequilibrium boundary layer that drives extreme δDgl fractionation with progressive glass hydration. These results indicate that the observed ΔDgl-H2O of ∼−33 ± 11‰ can be cautiously applied as an equilibrium 103lnαgl-H2O value to natural silicic glasses hydrated below 250 °C to identify hydration sources. This approximate ΔDgl-H2O may be applicable to even higher temperature glasses hydrated on short timescales (of seconds to minutes) in phreatomagmatic or submarine eruptions before H2O in the glass is primarily affected by boundary layer effects associated with alteration on the glass surface.

Equilibrium fractionation of S, Fe, and Ni isotopes in Fe-Ni sulfides: A first-principles investigation

Fe, Ni, and S isotopes are important chemical tracers, and they complement each other to improve our understanding of the Earth's evolution. As common accessory minerals in the Earth's interior and the most important group of ore minerals, sulfide minerals display a wide range of Fe and Ni contents. Using first-principles methods, we investigated the equilibrium fractionation factors of Fe, Ni, and S isotopes of the β-(Ni, Fe)S, FeS2-NiS2, and Fe3S4-Ni3S4 solid solutions, to constrain the effect of cation contents on Fe, Ni, and S isotopic signatures. For the β-(Ni, Fe)S solid solution, the iron β-factors, nickel β-factors, and sulfur β-factors all decrease approximately linearly with the increasing Fe content. For the FeS2-NiS2 solid solution, the iron β-factors, nickel β-factors, and sulfur β-factors show a positive linear relationship with the Fe content. For the Fe3S4-Ni3S4 solid solution, the iron β-factors and nickel β-factors have a strong negative correlation with the Fe content, while the sulfur β-factors have a weak negative correlation with the Fe content. In general, the trend of variation of the β-factors with Fe content is the opposite to that of the average bond lengths with the Fe content. Our results provide an improved understanding of Fe, Ni, and S isotopic fractionation in natural systems that may be used to better constrain physical, chemical, and geo-biological evolution on Earth.

Determination of the equilibrium magnesium isotope fractionation factors between brucite and aqueous inorganic and organic species

Magnesium (Mg) is a major element in seawater, rock-forming minerals, and biological systems. Stable Mg isotopes fractionate during silicate weathering and carbonate mineralization, and hence are a promising tool to trace these processes. Magnesium can be present in natural aqueous solutions as a number of distinct inorganic and organic complexes including MgHCO3+, MgCO30, MgSO40, Mg(OH)+, Mg(citrate)− and Mg(EDTA)2−, in addition to Mg(H2O)62+ commonly referred to as Mg2+. The formation of these species can significantly alter the fractionation of Mg isotopes between minerals and natural fluids. To quantify these effects, isotope exchange experiments were performed at bulk chemical equilibrium between brucite and aqueous solutions containing different organic (citrate, EDTA) and inorganic (SO4−) ligands at 25 °C. The ‘three isotope’ method was used to determine the equilibrium Mg isotope fractionation factors Δeq26Mg between brucite and several major aqueous magnesium species. The experimentally measured equilibrium Mg isotope fractionation factor between brucite and aqueous Mg2+ was found to be Δeq26Mgbrucite-Mg2+ = -0.35 ± 0.39‰. First-principle calculations to retvieve the brucite β-factor were performed consistently with the calculations of Pinilla et al. (2015) for Mg2+(aq) β-factor. The combination of both studies yield values of Δeq26Mgbrucite-Mg2+ between +0.3 and +0.8 ± 1.0‰, which is the lowest theoretical estimate of this constant obtained to date. An average value Δeq26Mgbrucite-MgSO40 = 0.48 ± 0.16‰ was retrieved from the experiments for the isotope fractionation between brucite and aqueous MgSO40. Mg isotope equilibrium fractionation factors between brucite and aqueous Mg(citrate)− and between brucite and aqueous Mg(EDTA)2− retrieved from the experiments performed in the presence of these organic ligands are Δeq26Mgbrucite-Mg(citrate)− = 0.35 ± 0.21, and Δeq26Mgbrucite-Mg(EDTA)2− = 2.41 ± 0.20‰.The experimental values determined in this study for Δeq26Mgbrucite-Mg2+ agree with the experimental values reported by Li et al. (2014). There is also an excellent agreement between the experimental values of this study and Li et al. (2014) with the density functional theory (DFT) estimates from Schott et al. (2016) for Δeq26MgMg2+-Mg(EDTA)2−. In contrast, the Mg isotope fractionation factor measured in this study between aqueous Mg2+ and both aqueous Mg sulphate or citrate species is significantly smaller than predictions from the ab initio calculations reported by Schott et al. (2016). The results of the present study confirm that the mineral-fluid equilibrium fractionation of Mg isotopes is strongly dependent on the identity of the inorganic or organic ligands present in the aqueous fluid and the nature of the complexes, (e.g. inner-sphere versus outer-sphere complexes), formed by magnesium with these ligands. Therefore, Mg speciation in natural fluids and the structure of aqueous Mg complexes have to be known for an accurate interpretation of Mg isotopic signatures in natural environments.

A Combined Model for Kinetic Clumped Isotope Effects in the CaCO3‐DIC‐H2O System

AbstractMost Earth surface carbonates precipitate out of isotopic equilibrium with their host solution, complicating the use of stable isotopes in paleoenvironment reconstructions. Disequilibrium can arise from exchange reactions in the DIC‐H2O system as well as during crystal growth reactions in the DIC‐CaCO3 system. Existing models account for kinetic isotope effects (KIEs) in these systems separately but the models have yet to be combined in a general framework. Here, an open‐system box model is developed for describing disequilibrium carbon, oxygen, and clumped (Δ47, Δ48, and Δ49) isotope effects in the CaCO3‐DIC‐H2O system. The model is used to simulate calcite precipitation experiments in which the fluxes and isotopic compositions of CO2 and CaCO3 were constrained. Using a literature compilation of equilibrium and kinetic fractionation factors, modeled δ18O and Δ47 values of calcite are in good agreement with the experimental data covering a wide range in crystal growth rate and solution pH. This relatively straightforward example provides a foundation for adapting the model to other situations involving CO2 absorption (e.g., corals, foraminifera, and high‐pH travertines) or degassing (e.g., speleothems, low‐pH travertines, and cryogenic carbonates) and/or mixing with other dissolved inorganic carbon sources.

Improved volume variable cluster model method for crystal-lattice optimization: effect on isotope fractionation factor

The isotopic fractionation factor and element partition coefficient can be calculated only after the geometric optimization of the molecular clusters is completed. Optimization directly affects the accuracy of some parameters, such as the average bond length, molecular volume, harmonic vibrational frequency, and other thermodynamic parameters. Here, we used the improved volume variable cluster model (VVCM) method to optimize the molecular clusters of a typical oxide, quartz. We documented the average bond length and relative volume change. Finally, we extracted the harmonic vibrational frequencies and calculated the equilibrium fractionation factor of the silicon and oxygen isotopes. Given its performance in geometrical optimization and isotope fractionation factor calculation, we further applied the improved VVCM method to calculate isotope equilibrium fractionation factors of Cd and Zn between the hydroxide (Zn–Al layered double hydroxide), carbonate (cadmium-containing calcite) and their aqueous solutions under superficial conditions. We summarized a detailed procedure and used it to re-evaluate published theoretical results for cadmium-containing hydroxyapatite, emphasizing the relative volume change for all clusters and confirming the optimal point charge arrangement (PCA). The results showed that the average bond length and isotope fractionation factor are consistent with those published in previous studies, and the relative volume changes are considerably lower than the results calculated using the periodic boundary method. Specifically, the average Si–O bond length of quartz was 1.63 Å, and the relative volume change of quartz centered on silicon atoms was − 0.39%. The average Zn–O bond length in the Zn–Al-layered double hydroxide was 2.10 Å, with a relative volume change of 1.96%. Cadmium-containing calcite had an average Cd–O bond length of 2.28 Å, with a relative volume change of 0.45%. At 298 K, the equilibrium fractionation factors between quartz, Zn–Al-layered double hydroxide, cadmium-containing calcite, and their corresponding aqueous solutions were Delta ^{30/28} {text{Si}}_{{{text{Qtz-H}}_{4} {text{SiO}}_{4} }} = 2.20{permil} , Delta^{18/16} {text{O}}_{ {text{Qtz}}{-} ( {text{H}}_{2} {text{O}} )_{text{n}}} = 36.05{permil}, Delta^{66/64} {text{Zn}}_{ {text{Zn}} {-} {text{Al LDH-Zn}} ( {text{H}}_{2} {text{O}} )_{text{n}}^{2+}} = 1.12{permil} and Delta^{114/110} {text{Cd}}_{ {text{(Cd--Cal)-Cd}} ( {text{H}}_{2} {text{O}} )_ {text{n}}^{2 +} } = - 0.26{permil} respectively. These results strongly support the reliability of the improved VVCM method for geometric optimization of molecular clusters.

Chromium isotope fractionation during magmatic processes: Evidence from mid-ocean ridge basalts

Chromium (Cr) isotopes represent a powerful tool for tracing the redox conditions during planetary magmatic evolution. However, so far, the systematic investigation of Cr isotope variation has been only performed on ocean island basalts (OIBs) in terrestrial magmatic rocks. Therefore, the Cr stable isotope compositions (expressed as δ53Cr relative to NIST SRM 979) of other magmatic rocks, formed under different oxygen fugacity, have remained unconstrained. In this paper, we present the first Cr stable isotopic data of mid-ocean ridge basalts (MORBs) from the Eastern Pacific Ocean ridge, the Indian ridge, and the Atlantic Ocean ridge. The oxygen fugacity of such basalts is different from that of the above-mentioned OIBs. The Rhyolite-MELTS model shows that the chemical composition variations in the studied basalts are induced by varying extents of fractional crystallization of olivine, clinopyroxene, plagioclase, and spinel. The δ53Cr values of the MORBs range from −0.27 ± 0.03‰ to −0.07 ± 0.02‰ (n = 28), and two distinct groups of basalts are identified based on the correlation between δ53Cr and MgO. On the one hand, the δ53Cr of group I basalts (−0.27 ± 0.03‰ to −0.14 ± 0.03‰; n = 24) are systematically lower than the established average value of the Bulk Silicate Earth (BSE) (δ53Cr = −0.12 ± 0.04‰; 2SD), which are positively correlated with their MgO and Cr concentrations, indicating that Cr isotopes are fractionated during magmatic differentiation. Moreover, Rayleigh fractionation modelling suggests that the crystallization of olivine, clinopyroxene, and spinel gives rise to the Cr depletion and thereby decreases δ53Cr values. On the other hand, group II basalts (−0.10 ± 0.03‰ to −0.07 ± 0.02‰; n = 4) exhibit higher δ53Cr values than group I with identical MgO and Cr concentrations. This is possibly associated with the crystallization of clinopyroxene under low pressure.The average Cr isotope composition (δ53Cr = −0.16 ± 0.02‰, n = 3) of the primitive basalts (MgO > 9%) represents that of the primary MORB melt, which is lighter than the average value of BSE. Using the non-modal melting equations, the δ53Cr of the MORB mantle source is estimated to be −0.12 ± 0.02‰ (2σ), which is consistent with that of BSE. Compared with the Cr isotopic data of OIBs from Fangataufa island, we find that the equilibrium fractionation factors (Δ53Crcrystal-melt = +0.04‰ to +0.13‰) of MORBs during fractional crystallization are larger than that of Fangataufa island lavas (Δ53Crcrystal-melt = 0.010 ± 0.005‰ for low-K suite, and 0.020 ± 0.010‰ for high-K suite; Bonnand et al., 2020a), indicating that the basalts from Fangataufa island have higher oxygen fugacity than those of MORBs analyzed in this study, which is strongly supported by their higher V/Sc ratios.

Effect of growth rate and pH on Li isotope fractionation during its incorporation in calcite

Lithium isotope compositions were determined for synthetic calcite and fluid, reported in Füger et al. (2019). Calcite was precipitated at 25 °C, and mineral growth rate and pH varied within the range of 10−8.1 ≤ rp (mol m−2 s−1) ≤ 10−7.2 and 6.3 ≤ pH ≤ 9.5, respectively. At pH = 8.25 ± 0.15, the Δ7Licalcite-fluid = δ7Licalcite - δ7Lifluid value of −2.76 ± 0.22‰ (n = 4) was yielded when calcite growth rate was lower than ∼ 10−7.7 (mol m−2 s−1). As calcite growth rate increased, Δ7Licalcite-fluid values progressively decreased to about −4.5‰. The dependence of Li isotope fractionation on calcite growth rate is described by the surface reaction kinetic model developed by DePaolo (2011). In this model the equilibrium and kinetic isotope fractionation factors obtain values of −2.7 ± 0.1‰ and −8.8 ± 0.1‰, respectively. In addition, for experiments performed under similar surface-normalized growth rate of 10−7.7±0.2 (mol m−2 s−1) a significant decrease in Δ7Licalcite-fluid from pH 9.5 to 6.3 was observed. These variations of Δ7Licalcite-fluid as a function of pH for experiments performed under low degrees of solution saturation with respect to calcite point towards the incorporation of two or more Li-bearing species in the solid phase. Thus, the Li isotope composition of the solid reflects the abundance of these species, which depends on solution pH and fluid composition.Overall the results of this study suggest that both calcite growth rate and pH are parameters that can significantly affect the measured Li isotope fractionation between calcite and fluid. The high sensitivity of Δ7Licalcite-fluid to calcite growth rate observed in this study suggests that a high variability of δ7Licalcite in natural samples, such as foraminifera, brachiopods, and speleothems can be expected in natural environments. The implications for the potential use of elemental and isotope fractionation of Li during calcite formation are discussed in the light of reconstruction of paleo-environmental conditions.

Kinetic isotope effect in siderite growth: Implications for the origin of banded iron formation siderite

The widespread occurrence of siderite (FeCO3) at Earth's modern surface and in sedimentary rocks has led to its frequent use as a tool for palaeoenvironmental reconstruction. Isotopic studies of siderite associated with Archaean-Palaeoproterozoic banded iron formations show negative δ13C values, which coupled with δ56Fe values, have been considered to support an important role of dissimilatory iron reduction (DIR) in the genesis of iron formations.Facies-specific analyses show that texturally and petrographically syndepositional and/or early diagenetic, finely laminated microsparitic (≤10 µm in diameter) siderite exhibits δ13C between −3 and −7‰. This siderite δ13C range can be interpreted in three ways: (1) precipitation of siderite from dissolved inorganic carbon (DIC) produced by DIR coupled to partial oxidation of organic carbon with δ13C < −25‰, (2) precipitation from a mixed hydrothermal-seawater fluid bearing mantle-derived DIC with δ13C ≅ −6.5‰, and (3) precipitation from seawater-derived DIC and expression of a kinetic isotope effect (KIE) associated with siderite growth.We present the carbon isotopic composition of siderite formed in abiotic seeded growth experiments over a wide range of solution siderite saturation at 25 °C and 1 bar. With a complete set of chemical kinetic data, we develop and apply a model of disequilibrium siderite precipitation to constrain the carbon KIE as a function of growth rate. Sampling of model parameters from distributions that represent uncertainty in the parameter values, we find best-fit values of equilibrium and kinetic fractionation factors: 103lnαeq = −0.2 and 103lnαf = −14.9.These constraints allow us to assess the origins of δ13C values in microsparitic siderite in iron formations. For example, a moderate level of siderite supersaturation (e.g., Ωsid = 100) in the hydrothermal-seawater mixing fluids (source of dissolved iron) would have induced a carbon KIE of ∼−8‰ in fluid-buffered early diagenetic siderite growth; a range that encompasses essentially all negative δ13C values reported from microsparitic siderite in Campbellrand-Kuruman iron formations, Transvaal Supergroup, South Africa. We suggest that a straightforward, abiotic explanation for the range of δ13C values in microsparitic siderite in Archaean-Palaeoproterozoic banded iron formations is pulsed deposition of iron-rich sediments associated with intense hydrothermal activity. Specifically, the siderite-δ13C range is well explained by a partial expression of carbon KIE associated with siderite growth from supersaturated solutions, and from a bottom-water DIC reservoir with near-zero δ13C values (seawater with a possible contribution of mantle carbon).

The Extent, Nature, and Origin of K and Rb Depletions and Isotopic Fractionations in Earth, the Moon, and Other Planetary Bodies

Abstract Moderately volatile elements (MVEs) are depleted and isotopically fractionated in the Moon relative to Earth. To understand how the composition of the Moon was established, we calculate the equilibrium and kinetic isotopic fractionation factors associated with evaporation and condensation processes. We also reassess the levels of depletions of K and Rb in planetary bodies. Highly incompatible element ratios are often assumed to be minimally affected by magmatic processes, but we show that this view is not fully warranted, and we develop approaches to mitigate this issue. The K/U weight ratios of Earth and the Moon are estimated to be 9704 and 2448, respectively. The 87Rb/86Sr atomic ratios of Earth and the Moon are estimated to be 0.072 5 and 0.015 4, respectively. We show that the depletions and heavy isotopic compositions of most MVEs in the Moon are best explained by evaporation in 99%-saturated vapor. At 99% saturation in the protolunar disk, Na and K would have been depleted to levels like those encountered in the Moon on timescales of ∼40–400 days at 3500–4500 K, which agrees with model expectations. In contrast, at the same saturation but a temperature of 1600–1800 K relevant to hydrodynamic escape from the lunar magma ocean, Na and K depletions would have taken 0.1–103 Myr, which far exceeds the 1000 yr time span until plagioclase flotation hinders evaporation from the magma ocean. We conclude that the protolunar disk is a much more likely setting for the depletion of MVEs than the lunar magma ocean.

The effect of solution chemistry on elemental and isotopic fractionation of lithium during inorganic precipitation of calcite

The elemental and isotopic fractionation of lithium between inorganic calcite and aqueous solutions has been measured as a function of solution chemistry in mixed CaCl2-NaHCO3 aqueous solutions spanning a range of pH from ~6 to ~9.5 at room temperature. Vaterite added to the solution recrystallized to calcite with limited change in solution chemistry. With this experimental design solution pH and Na/Ca strongly correlate. The ratio of the concentration of Li in the calcite to that of the solution (Kd,Li = [Li]calcite/[Li]solution), increased by about an order of magnitude with increasing pH. The Li exchange coefficient (Kd,Li/Ca=([Li]calcite/[Ca]calcite)/([Li]solution/[Ca]solution) decreased by about four orders of magnitude, from ~10−2 to ~10−6 with increasing pH due to the large decrease in solution Ca content with increasing experiment pH. The Li isotope fractionation also changed systematically as the pH of the solution increased from 6.5 to 9.5 with the calcite ranging from about −6‰ to +2‰ relative to the solution it grew from. No change in either the elemental or isotopic partitioning was observed with either a change in the Li concentration of the solution or with a change in the experimental duration (5–400 days). To better understand the role of diffusive Li isotope fractionation a series of experiments were performed to determine the relative diffusivity of 6Li and 7Li in solutions with different pH. The results suggest little or no difference in relative diffusivity (D6Li ~ 0.998D7Li) across the range of solution chemistry considered (pH 4 to ~7.5). The change in Li partitioning between calcite and solution with changing solution chemistry is consistent with Li incorporation into calcite as LiHCO3 and hence a dependence on solution H+/Ca2+. If this interpretation is correct, it means that the concentration of Li in inorganic calcite precipitated from seawater at fixed Ca and Li concentrations will increase with decreasing pH. The change in the Li isotope fractionation factor with changing solution chemistry may either reflect a kinetic isotope fractionation associated with changing calcite growth rates or a change in the equilibrium fractionation factor due to changing Li speciation in the solution. These results, while not directly applicable to pristine biogenic calcite, have important implications for interpreting the Li content of calcite that has undergone any diagenetic modification (e.g., all bulk carbonate Li isotope data). Diagenesis under variable conditions provides a plausible alternative explanation for Li isotope excursions in carbonate sediment sequences that have been interpreted as indicating changing seawater δ7Li that deserves further investigation.

Zinc isotopic fractionation between aqueous fluids and silicate magmas: An experimental study

Fluids in magmas play a key role in magma differentiation and transportation of economic metals for ore deposits. As a chalcophile and incompatible element, zinc and its isotopes have been increasingly applied to study the magmatic-hydrothermal processes. However, zinc isotopic fractionation between aqueous fluids and magmas has not been well constrained. Here we experimentally determined equilibrium fractionation factors of Zn isotopes between aqueous fluids and silicate magmas (Δ66Znfluid-magma = δ66Znfluid – δ66Znmagma). The results reveal that aqueous fluids are isotopically heavier than the coexisting silicate magmas. No correlation between Δ66Znfluid-magma and temperature or chlorine contents in fluids is observed under our experimental conditions. Instead, Δ66Znfluid-magma is negatively corresponded with NBO/T of the melt (the ratio of non-bridge oxygen and tetrahedron ions), and positively correlated with the molar ratio of Al/(0.5 K + Ca + Fe) in the bulk magmas, suggesting the controlling of silicate composition on Zn isotope fractionation. Our data therefore indicate that the isotopically heavier Zn in the fluids exsolved from magmas may account for the higher δ66Zn of pegmatites and high-silica granitic rocks. Moreover, involvement of magmatic fluids can explain the highly variable and remarkably heavier Zn isotopic signatures of fumaroles, thermal spring waters, and seafloor hydrothermal fluids compared to the igneous rocks. This study provides information that can be used to guide research using Zn isotopes to trace fluid activity and magmatism.

Experimental and theoretical determinations of hydrogen isotopic equilibrium in the system CH4[sbnd]H2[sbnd]H2O from 3 to 200 °C

The stable isotopic composition of methane (CH4) is commonly used to fingerprint natural gas origins. Over the past 50 years, there have been numerous proposals that both microbial and thermogenic CH4 can form in or later attain hydrogen isotopic equilibrium with water (H2O) and carbon isotopic equilibrium with carbon dioxide (CO2). Evaluation of such proposals requires knowledge of the equilibrium fractionation factors between CH4 and H2O or CO2 at the temperatures where microbial and thermogenic CH4 form in or are found in the environment, which is generally less than 200 °C. Experimental determinations of these fractionation factors are only available above 200 °C, requiring extrapolation of these results beyond the calibrated range or the use of theoretical calculations at lower temperatures. Here, we provide a calibration of the equilibrium hydrogen isotopic fractionation factor for CH4 and hydrogen gas (H2) (DαCH4(g)–H2(g)) based on experiments using γ-Al2O3 and Ni catalysts from 3 to 200 °C. Results were regressed as a 2nd order polynomial of 1000 × lnDαCH4(g)–H2(g) vs. 1/T (K−1) yielding:1000×lnDαCH4(g)-H2(g)=3.5317×107T2+2.7749×105T-179.48We combine this calibration with previous experimental determinations of hydrogen isotope equilibrium between H2, H2O(g), and H2O(l) and we provide an interpolatable experimental calibration of 1000 × lnDαCH4(g)–H2O(l) from 3 to 200 °C. Our resulting 4th order polynomial is the following equation:1000×lnDαCH4(g)-H2Ol=-7.9443×1012T4+8.7772×1010T3-3.4973×108T2+5.4398×105T-382.05At 3 °C, the value from our calibration differs by 93‰ relative to what would be calculated based on the extrapolation of the only experimental calibration currently available to temperatures below its calibrated range (lowest temperature of 200 °C; Horibe and Craig, 1995). We additionally provide new theoretical estimates of hydrogen isotopic equilibrium between CH4(g), H2(g), and H2O(g) and carbon isotopic equilibrium between CH4(g) and CO2(g) using Path Integral Monte Carlo (PIMC) calculations. Our PIMC calculations for hydrogen isotopic equilibrium between CH4 and H2 agree 1:1 with our experiments. Finally, we compile carbon and hydrogen isotopic measurements of CH4, CO2, and H2O from various environmental systems and compare observed differences between carbon and hydrogen isotopes to those expected based on isotopic equilibrium. We find that isotopic compositions of some microbial gases from marine sedimentary, coalbed, and shale environments are consistent with those expected for CH4H2O(l) hydrogen and CH4CO2 carbon isotopic equilibrium. In contrast, microbial terrestrial and pure culture gases are not consistent with both CH4H2O(l) hydrogen and CH4CO2 carbon isotopic equilibrium. These results are explained qualitatively using previously developed conceptual models that link free energy gradients available to microorganisms to the degree that their enzymes can promote isotope-exchange reactions between CH4, CO2, and H2O.