Reduced Partition Function Ratios Research Articles

Quantifying mass-dependent isotope fractionation and nuclear field shift effects for the light rare Earth elements in hydrous systems

The improving sensitivity of mass-spectrometers has opened the potential of using stable isotope signatures of the rare Earth elements (REE) as geochemical tracers. However, thus far only limited studies have utilised REE stable isotopes, despite resolvable variations having been observed in a range of systems. An interesting but poorly explored area remains variations in aqueous environments across a range of temperatures including seawater, marine sediments, ion adsorption deposits or hydrothermal systems. Furthermore, the magnitudes and competing effects of mass-dependent isotope fractionation and mass-independent nuclear field shift effects, which can be significant factor for heavy elements especially at high temperatures, remain poorly understood.To contribute to a holistic understanding of REE isotope signatures, we calculated reduced partition function ratios (as 103lnβ) for mass-dependent and nuclear field shift effects for aqueous La, Ce, and Nd complexes from first principles. Theoretical calculations were compared with experimental data, and this demonstrates that calculations involving a combination of two explicit hydration shells and additional implicit solvation effects are required to accurately describe the coordination and molecular vibrations of aqueous complexes. This data was then combined with speciation modelling of seawater and hydrothermal fluids to assess isotope fractionation in hydrous systems. The predicted magnitude of isotope fractionation is significant in low (T = 25 °C) temperature systems (Δ139/138LaMax-Min = 0.20 ‰, Δ142/140CeMax-Min = 0.33 ‰, Δ146/144NdMax-Min = 0.34 ‰) and remains above currently achievable analytical uncertainties even at high (T = 500 °C) temperatures (±0.015 ‰ for δ146/144Nd; ±0.040 ‰ for δ142/140Ce). Unless oxidation occurs, which is only relevant for Ce in terrestrial environments, nuclear field shift effects are negligible even at temperatures up to 500 °C. The large difference in nuclear charge radius between 140Ce and 142Ce strongly enriches the lighter Ce isotope in the higher oxidation state (103lnβCe(IV)-Ce(III) = −0.45 at 25 °C) which almost completely cancels out the opposing mass-dependent effect (103lnβCe(IV)-Ce(III) = +0.46 at 25 °C). This means that variations in δ142/140Ce isotope signatures cannot easily be related to oxidation in ancient or recent environments.

Reduced partition function ratios of iron, magnesium, oxygen, and silicon isotopes in olivine: A GGA and GGA + U study

Olivine, typically occurring as a forsterite-fayalite solid solution, is a major rock-forming mineral in mafic and ultramafic igneous rocks, and it is important for understanding the genesis, evolution, and alteration of its host rocks. In this study, both GGA and GGA + U methods were employed to calculate the reduced partition function ratios of Fe, Mg, O, and Si isotopes for the forsterite-fayalite solid solution, aiming to elucidate the impacts of Fe content and Hubbard U correction on the isotope fractionation signatures of Fe, Mg, O, and Si in olivine. On the whole, the βFe-factor, βMg-factor, βO-factor, and βSi-factor decrease with increasing Fe content. The linear correlations between β-factors and bond lengths obtained from GGA + U are better compared to those from GGA. The Hubbard U correction can increase the βFe-factor. When Fe/(Fe + Mg) ≤ 1/8, ≤ 1/2, and ≤ 1/2, the effect of Hubbard U correction on βMg-factor, βO-factor, and βSi-factor can be considered negligible, respectively, suggesting that the βMg-factor, βO-factor, and βSi-factor of Fe-bearing olivine calculated using GGA + U and those of Fe-free minerals calculated using GGA can be combined to derive 103lnα and trace geological processes. Furthermore, equilibrium fractionation of Fe, Mg, O, and Si isotopes between olivine and other minerals, including troilite, clinopyroxene, and garnet, were also calculated. Our results are helpful in interpreting the observed data regarding Fe, Mg, O, and Si isotopic compositions of olivine, leading to a comprehensive understanding of relevant geological processes.

Antimony stable isotope fractionation during adsorption onto birnessite: A molecular perspective from X-ray absorption spectroscopy and density functional theory

Sorption of antimony (Sb) onto birnessite significantly influences the fate of Sb in oceanic and terrestrial environments and fractionates Sb isotopes. Nevertheless, little is known about Sb isotopic fractionation during its adsorption on birnessite. Here, we show the value of Δ123Sbadsorbed-aqueous increases from −0.398 to −0.332 ‰ in 1 h and then decreases and stabilizes at −0.384 ‰ in 72 h. The enrichment of the light Sb isotope is predominantly due to the distortion of the octahedral symmetry. X-ray absorption spectroscopy results indicate Sb first forms a double-corner-sharing complex on birnessite and then transforms to a double-edge-sharing complex during adsorption. The optimized bond distances for double-corner-sharing (3.37 Å) and double-edge-sharing (2.90 Å) complexes calculated using density functional theory (DFT) fits well with the structure (3.41 and 3.00 Å) revealed by X-ray absorption spectroscopy, respectively. The fractionation derived from reduced partition function ratios calculated using DFT aligns well with the experimental results. Therefore, the variation in Sb isotopic fractionation during adsorption is attributed to the evolving structure of Sb complexes on birnessite. Our results demonstrate the isotopic fractionation of Sb during adsorption on birnessite and provide a molecular-scale understanding of Sb behavior, contributing to the correct reconstruction of the Sb isotope composition of ancient seawater using ferromanganese crusts and nodules, and efforts to trace Sb migration in epigenetic mining environments.

Oxygen Isotope Fractionation between Carbonate Minerals and Carbonic Acid Systems and Constraints for Environmental Science and Geological Processes

The equilibrium oxygen isotope fractionation factor is widely used in geological thermometry. However, under most natural conditions, the oxygen isotope exchange is rare to reach equilibrium. Especially for the complex water–rock interaction process, the contribution of the H2CO3 solution, CO32− solution, Ca(HCO3)2 solution, and CaCO3 solution to the equilibrium oxygen isotope fractionation factor of this process is poorly understood. In view of this predicament, these key parameters are obtained by ab initio calculations. The results showed that the contributions of different carbonate minerals and different aqueous solutions to the equilibrium oxygen isotope fractionation factor were different. Among all nine carbonate minerals (dolomite, calcite, aragonite, magnesite, siderite, otavite, smithsonite, ankerite, and strontianite), the minerals with the highest and lowest reduced partition function ratios (RPFR) were siderite and strontianite, respectively. At the same time, the RPFR of nitratine, which has the same structure as carbonate, was studied. The RPFRs of the three most widely distributed carbonates in nature (dolomite, calcite, and aragonite) were dolomite > calcite > aragonite. Among the H2CO3 solution, CO32− solution, Ca(HCO3)2 solution, and CaCO3 solution, the H2CO3 solution had the strongest ability to enrich 18O. In addition, the equilibrium oxygen isotope fractionation factors between aqueous solutions and gas phase species (CO2(g), H2O(g), and O2(g), etc.) were calculated systematically. The results showed that the oxygen isotope fractionation factors between solutions and gas phases were often inconsistent with the temperature change direction and that the kinetic effects played a key role. These theoretical parameters obtained in this study will provide key equilibrium oxygen isotope constraints for water-rock interaction processes.

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.

Barium isotope fractionation during granitic magmatism and potential of δ138/134Ba for distinguishing magmatic-hydrothermal transition in granitic magma systems

The geochemistry of Ba is commonly used to study igneous processes and fluid-melt interaction in subduction zone and granitic environments. Recent advances in analytical techniques have also indicated that Ba isotope geochemistry has the potential to significantly augment these studies. Understanding the Ba isotope fractionation mechanisms is thus critical if this potential is to be fully realized. Hence, we have used the first-principles calculations based on the density functional theory (DFT) and long-time ab initio molecular dynamics (AIMD) simulation to calculate Ba isotope fractionation during felsic magma evolution. In fluids, the reduced partition function ratio (β factor) of aqueous Ba2+ is highly variable, depending on the coordination number (n) of H2O in the first hydration shell. At ambient surface conditions on the Earth, n = 8 best represents the aqueous Ba2+ species in natural fluid, and the temperature-dependent equilibrium Ba isotope fractionation between barite/witherite and fluids can be described by the relationships: 103lnαwitherite-fluid = −0.00009×(106/T2)2 + 0.0603×(106/T2) + 0.0003 and 103lnαbarite-fluid = −0.0001×(106/T2)2 + 0.0648×(106/T2) + 0.0004, which is consistent with previous theoretical and experimental studies. In hydrothermal fluids, the hydration number of Ba2+ varies from 4 to 6 at high P-T, and the cumulative average of 103lnβ is derived to be 0.0798 ± 0.005‰ in 923.15 K and 0.2 GPa. In silicate minerals, the enrichment of heavy Ba isotopes decreases in the sequence of muscovite > microcline ≈ celsian ≈ sanbornite > barylite > phlogopite. Variations in Ba concentrations and the degree of Al-Si disordering only induce limited Ba isotope fractionation, which would be hard to distinguish analytically. At high temperatures (> 600 °C), the melt phase is enriched in heavy Ba isotopes relative to any coexisting aqueous fluid and crystallizing minerals. During the early stages of felsic magma differentiation involving plagioclase crystallization as the main mineral, the δ138/134Ba and concentration in the residual melt remain close to their initial values, but any fluid exsolved from the melt will have light δ138/134Ba values. The high Ba distribution coefficient of K-feldspar means that the resultant K-feldspar granite inherits > 90% of the Ba contained in the initial magma reservoir. Hence, the δ138/134Ba of K-feldspar is close to that of the initial melt. During the final stage of felsic magma evolution, mixing of exsolved fluids from deeper reservoirs may significantly reduce the δ138/134Ba of the now Ba-depleted melt, and can account for the low δ138/134Ba values measured in highly differentiated leucogranites and pegmatites.

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.

Path-integral molecular dynamics predictions of equilibrium H and O isotope fractionations between brucite and water

Precise prediction of hydrogen (H) isotope fractionations among different substances is a long-standing challenge in isotope geochemistry, as it needs treatments beyond the harmonic approximation. Path-integral molecular dynamics (PIMD) simulations have recently been proved to be valid in predicting equilibrium isotope fractionations for light elements. However, the lack of reliable force fields hinders the application of PIMD to the condensed phases. In this work, the deep potential models trained on the first-principles molecular dynamics (FPMD) data are applied to PIMD simulations to determine the D/H and 18O/16O isotope fractionation factors between brucite and water. To quantitatively assess the influence of quantum effects, the D/H and 18O/16O isotope fractionations between brucite and water are also determined under the framework of harmonic approximation.By comparing the results of the PIMD and those of harmonic calculations, we find that H and O atoms in brucite and water are strongly affected by the anharmonic effects. The accuracy of the harmonic isotope fractionations mainly depends on the cancellation percentage of the anharmonic effects on the reduced partition function ratios (RPFRs) of the two substances. The isotope fractionations predicted by PIMD simulations are close to the experimental results at high temperatures. However, at low temperatures, the predicted isotope fractionations are different from those of experiments. The discrepancies are attributed to the approximations in the density functional theory (DFT) functionals used in this work, i.e., the inaccuracy in predicting the proton positions in brucite and water. Moreover, we find that the H isotope fractionations are extremely sensitive to the change of pressure. The direction of H isotope fractionation between brucite and water (at 300 K) will be even inversed as the pressure increases to more than 3 GPa. This strong pressure sensitivity may be a common characteristic of hydrous minerals and water systems. Therefore, the extrapolated H isotope fractionations used in the studies of dehydration of subducting slabs or deep Earth H distribution based on the isotope fractionations under low pressures may need to be rechecked.

Density Functional Theory Calculations of Equilibrium Mo Isotope Fractionation Factors among MoOxS4–x2– Species in the Aqueous Phase by the ONIOM Method

Molybdenum (Mo) is a redox-sensitive metal element. Its isotope composition (δ98Mo) has the potential to reconstruct oceanic oxygenation extent in deep time. To accurately reconstruct the bulk δ98Mo value of ancient seawater from sediment records, it is necessary to clarify the Mo isotope fractionation mechanism during the transformation among thiomolybdates (MoOxS4–x2–, x = 0∼4) in marine environments. For aqueous systems, predicting the equilibrium isotope fractionation factors theoretically needs careful treatment of solvent effects. The commonly used water-droplet or periodical boundary condition methods are not only troublesome but also time-consuming. We test the efficiency of the two-layer own N-layer integrated molecular orbital molecular mechanics (ONIOM) method in predicting the reduced partition function ratios (β factors) of the MoOxS42– species in aqueous phases. Compared to other methods, the ONIOM method can produce β factors with the same accuracy and considerably fewer computational resources. The predicted β factors are in the order MoO4(aq)2– > MoO3S(aq)2– > MoO2S2(aq)2– > MoOS3(aq)2– > MoS4(aq)2–, which are in line with previous laboratory experiments and field observations. The new results provide the basic data for reconstructing δ98Mo values in suboxic, ferruginous, and weakly euxinic sediments.

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.

Theoretical study of carbon isotope effects in the nonclassical carbonyl cation CO/[M(CO)n]+ (M = Cu, Ag, Au; n = 1–4)

In order to find an ideal exchange system for carbon isotope separation, carbon isotope effects in the CO/[M(CO)n]+ (M = Cu, Ag, Au; n = 1–4) complex system were analyzed using density functional theory calculations, and the isotopic equilibrium constants were calculated as the ratio of the reduced partition function ratios of the 13C/12C isotopic pairs. It is shown that the isotope equilibrium constant changes with the coordination number of CO to the complex as the temperature changes. In CO/[Au(CO)n]+, the contribution of bending vibration to the isotope effect increases, so that a higher isotope effect is expected than CO/[Ag(CO)n]+.

The factors controlling equilibrium inter-mineral Ca isotope fractionation: Insights from first-principles calculations

Equilibrium isotope fractionation factors are crucial to quantitatively interpreting Ca isotope data of natural samples. Recent studies have revealed significant equilibrium Ca isotope fractionation between minerals, but the controlling factors remain poorly understood. Using density functional theory, this study calculates the reduced partition function ratios (RPFRs) among amphiboles (richterite and tremolite), sorosilicates (akermanite and gehlenite), K-bearing carbonates (butschliite), Na-bearing diopside (jadeite), and other Ca-bearing minerals (fluorapatite, anhydrite, CaTiO3 perovskite, and fluorite) at 0 GPa. The RPFRs of diopside and anorthite over a pressure range from 0 to 5 GPa are calculated to investigate the pressure effect. The effect of force constant, bond length, coordination number, anion type, solid solution composition, and pressure on RPFRs are discussed by compiling the literature data. The RPFRs show good correlations with the force constant and bond length but have no clear correlation with the coordination number. This suggests that the bond length is more reliable than the coordination number for roughly predicting the signs and magnitudes of inter-mineral isotope fractionation. Na-bearing clinopyroxene (e.g., jadeite) has similar RPFR with Na-free clinopyroxene, suggesting that the jadeite effect should be insignificant in natural samples. The RPFR of anorthite is lower than that of diopside at low pressure, and the two minerals both show a positive correlation between RPFR and pressure. Notably, the heavy Ca isotope enrichment between these two minerals can be reversed at high pressure (>3 GPa at 1000 K) because anorthite’s RPFR changes more sharply with increasing pressure than that of diopside. However, such a reverse may not occur in Earth's modern crust due to the stability of anorthite at lower pressures. Combining the theoretical predictions of amphibole and plagioclase and natural sample observation on granitoids, we infer that the RPFR of granitic magma may be lower than that of basaltic magma.

Pressure and concentration effects on intermineral calcium isotope fractionation involving garnet

To better understand the behaviors of calcium (Ca) isotopes during igneous and metamorphic processes that differentiate the Earth and other rocky planets, we investigated the effects of pressure and Ca/Fe concentration on the average CaO bond length and the reduced partition function ratio of 44Ca/40Ca (103ln44/40Caβ) in garnet using first-principles calculations. Our calculations show that (1) the average CaO bond length increases and 103ln44/40Caβ decreasing (approximately 0.41‰ at 1000 K from a Ca/(Fe + Ca + Mg) of 1/24 to 12/12) with increasing Ca concentrations. In contrast to orthopyroxene and forsterite, whose CaO bond lengths and 103ln44/40Caβ are sensitive to Ca concentrations only in narrow range, the garnet CaO bond length and 103ln44/40Caβ vary with Ca concentrations in wide ranges. (2) The average CaO bond length increases and 103ln44/40Caβ decreases with increasing Fe concentrations (by 0.12‰ at 1000 K, FeO content of 12.4 wt%). (3) The average CaO bond length decreases by ~0.014 Å, and 103ln44/40Caβ increases by 0.1‰–0.2‰ at 1000 K when the pressure increases from 0 to 3 GPa. (4) However, the pressure effect on 103ln44/40Caαgarnet–clinopyroxene is insignificant.Using our new results of the effects of pressure and Ca/Fe concentration on 103ln44/40Caαgarnet–clinopyroxene, we evaluated the observed difference in Ca isotope compositions between garnet and clinopyroxene in natural samples. Most have reached equilibrium, whereas some samples exceed our prediction, which might reflect the majorite effect or kinetic fractionation.

A density functional theory (DFT) study on reduced partition function ratios of oxygen species adsorbed on a Pt19 cluster and oxygen isotope effects

ABSTRACT A density functional theory (DFT) computation on oxygen species adsorbed on platinum (Pt) catalyst surfaces has been carried out to elucidate oxygen isotope fractionation observed at the cathode of a polymer electrolyte membrane fuel cell (PEMFC). The Pt(111) catalyst surface was modelled by a Pt19 cluster, and O, OH, OHH, OO, OOH, OHOH and HOHOH were assumed to be the oxygen species adsorbed on the Pt(111) surface. The oxygen isotope reduced partition function ratios (RPFRs) of the adsorbed species were calculated using the vibrational frequencies obtained by normal mode analyses performed on the optimized structures. Various oxygen isotope exchange equilibria among the adsorbed oxygen species and oxygen and water molecules in the gas phase were examined using their RPFRs. Experimental observation that the lighter 16O is enriched in water molecules exhausted from the cathode is explainable in a satisfactory manner by assuming oxygen isotope exchange equilibria of O2 molecule with O, OH, OO and OOH adsorbed on the Pt(111) surface that appear in the first half of the conversion reaction from O2 to H2O and those of H2O molecule with the adsorbed oxygen species, OHH, OHOH and HOHOH, formed in the latter half of the conversion reaction.

Experimental calibration of the reduced partition function ratios of tetrahedrally coordinated silicon from the Debye–Waller factors

Experimental calibration of the reduced partition function ratios of tetrahedrally coordinated silicon from the Debye–Waller factors

X-ray diffraction and spectroscopic study of SrxCa1−xCO3: Implications for equilibrium Sr2+ incorporation and carbon/oxygen isotope fractionation in aragonite

Eight SrxCa1−xCO3 (0.2 < x < 0.9) solid solutions with orthorhombic aragonite structure were synthesized at P = 1.5 GPa and T = 1300 °C over 48 hours. Powder X-ray diffraction (XRD) analyses show that their unit-cell parameters and volumes increase systematically with increasing Sr2+ concentration, and the excess volume (ΔV) has been found to be insignificant at temperatures up to 700 K, or pressures up to 3 GPa. The Raman and Fourier-transform infrared (FTIR) spectra of these solid solutions show that all lattice and internal vibrational modes shift systematically to lower frequencies with increasing Sr2+ content, exhibiting a negative dependence of vibrational frequencies on the average mass of divalent cation for the aragonite-group carbonates in the order of aragonite > strontianite > witherite > cerussite. The vibrational contribution to the excess Gibbs free energy is constrained for the SrxCa1−xCO3 solid solution, whose miscibility gap shrinks at elevated temperatures and disappears above ~400 K. The calculated equilibrium Sr-Ca exchange coefficient (KDSr/Ca) between aragonite and seawater is systematically lower than the measured ones below ~80 °C, suggesting kinetic control on Sr partitioning at low temperatures. We also evaluate the metal cation effect on the carbon and oxygen isotope fractionations between aragonite-group carbonates and CO2 or H2O. Our results show that the 1000∙lnβ (where β is the reduced partition function ratio) for both carbon and oxygen isotope fractionations decrease linearly with increasing average atomic mass of the divalent cation in these aragonite-group carbonates, and the compositional effect on isotope fractionations can be treated as a linear function of Sr2+ concentration in the SrxCa1−xCO3 solid solution.

First-principles calculation of iron and silicon isotope fractionation between Fe-bearing minerals at magmatic temperatures: The importance of second atomic neighbors

In order to elucidate the processes involved in iron and silicon isotopes partitioning during magmatic differentiation, it is essential to know the precise value of equilibrium fractionation factors between the main minerals present in the evolving silicic melts. In this study, we performed first-principles calculations based on the density functional theory to determine the equilibrium iron and silicon isotopes fractionation factors between eleven relevant silicate or oxide minerals in the context of magmatic differentiation, namely: aegirine, hedenbergite, augite, diopside, enstatite, fayalite, hortonolite, Fe-rich and Fe-free forsterites, magnetite and ulvospinel. Results show that Fe2+-bearing silicate minerals display significant differences in iron isotope fractionation factors that cannot be neglected, even at high temperature (1000 °C). Various physical and chemical parameters control the iron isotopic fractionation of silicate minerals. However, the main parameter, after temperature and the iron oxidation state, is the nature and number of iron second neighbors (i.e. the local chemical composition around Fe atoms). This conclusion is also valid for silicon isotopes. In the investigated nesosilicates and inosilicates, silicon isotope reduced partition function ratios (also called β-factors) show no correlation with the average Si-O bond length, which remains almost constant, but Si β-factors are correlated with the local chemical composition of the minerals. Fractional crystallization is one of the mechanisms, which could explain the evolution of iron isotopic compositions during magmatic differentiation. Using the present theoretical set of equilibrium fractionation factors allows us to assess the impact of inter-mineral isotopic fractionations, and shows that pyroxene appears to be the main mineral phase driving the isotopic evolution to a heavier signature in the most evolved lavas.

Theoretical isotope fractionation of cadmium during complexation with organic ligands

Cadmium (Cd) isotopes are an important tool to better understand the inorganic and organic geochemistry of Cd. Organic ligands play a key role to control the toxicity and mobility of Cd in living organisms and also in terrestrial and aquatic environments. Therefore, knowledge of the equilibrium isotope fractionation of Cd with organic ligands is crucial to further advance Cd isotope source and process tracing in the field of biogeochemistry. In this study, we calculated reduced partition function ratios (103lnβ) of Cd isotopes in various organic Cd complexes by density functional theory. The calculations revealed that the 103lnβ of 114Cd/110Cd for these complexes decreased in the order of Cd(Hcit)(H2cit)− > Cd(cit)(H2O)3− > CdH(cit)(H2O)4 > CdEDTA > Cd(his)2H2O > Cd(cit)24− ≈ Cd(H2O)62+ > Cd(H2O)42+ > Cd(cys)(H2O)32+ > Cd(GS)2(H2O)22− > Cd(DMPS)(H2O)2− > Cd(DMPS)24− at 0–100 °C. In general, heavier Cd isotopes preferably bind to oxygen and nitrogen donor atoms while lighter Cd isotopes bind to sulfur donor atoms of organic ligands. Thus, the previously observed immobilization of light Cd isotopes in living organisms could be related to Cd detoxification processes with sulfur. The predicted equilibrium isotope fractionation will strengthen Cd isotopes as a process tracing tool in living organisms and will improve the understanding of Cd isotope cycling in aquatic and terrestrial systems.

Sn(II) chloride speciation and equilibrium Sn isotope fractionation under hydrothermal conditions: A first principles study

Knowledge of Sn(II) speciation in aqueous and gaseous phases and the corresponding isotope effects are critical for understanding the transport and deposition of Sn in various geological and cosmochemical processes. In this study, we use first principles method to investigate the speciation of stannous (Sn(II)) chloride in fluids under hydrothermal and supercritical conditions. The results show that SnCl3−, SnCl2(H2O) and SnCl(H2O)2+ are stable in hydrothermal solutions at temperatures of up to 300 °C, with SnCl3− being the dominant species, whereas SnCl2 and SnCl2(H2O) are the stable species in vapor phases. Notably, SnCl2 is found to be stable under supercritical conditions. The reduced partition function ratios (β factors) for the stable Sn(II) species and three major Sn minerals (cassiterite, megawite, and romarchite) are also calculated by first principles methods. The calculation results show that under equilibrium, heavy Sn isotopes are preferentially partitioned into stannic (Sn(IV)) species, and gaseous species enrich heavy Sn isotopes relative to aqueous species. Based on the equilibrium Sn isotope fractionation factors derived in this study, we use a transport-precipitation model to evaluate the Sn isotope response to cassiterite precipitation in hydrothermal fluids. The modeling results show that significant Sn isotope variability could be produced during cassiterite precipitation, with temperature and Sn speciation being the primary controlling factors. Furthermore, by comparing the Sn isotope variability in natural cassiterite and those derived from the model, we argue that Sn should occur predominantly as Sn(IV) species in hydrothermal fluids during cassiterite precipitation in tin mineralizing systems.

First-principles calculations of equilibrium bromine isotope fractionations

Significant bromine (Br) isotope composition variations are found in natural salts and brines, which are often even larger than those of co-existing chlorine isotope compositions. The cause of such large Br isotope variations remains elusive. In this study, equilibrium Br isotope fractionations among Br-bearing gaseous molecules, aqueous species and crystalline minerals are provided via the density functional theory (DFT) based first-principles calculations. These fractionation factors form the base for future Br isotope geochemistry studies. Specifically, the first-principles molecular dynamics (FPMD) method is used to evaluate the tricky solvation effects, i.e., dozens of snapshots of FPMD trajectories are selected and re-optimized to their lowest energy atomic coordinates, then the reduced partition function ratios (i.e., β factors) of aqueous Br-bearing species are obtained by computing the average values of those snapshots. In this way, the configurational effects of aqueous Br-bearing species are included. For crystalline compounds, the static first-principles periodic DFT methods are used. We find that the β factors generally increase as the oxidation states of Br increase, indicating that heavy Br isotopes tend to be enriched in substances with higher Br oxidation states. The aqueous Br-bearing species in brines have detectable but small Br isotope fractionations with each other. However, the fractionations between gaseous molecules and NaBr(aq) are significantly larger, e.g., Δ81BrCH3Br(gas)-NaBr(aq) is 0.95 ± 0.041‰ at 20 °C. As for minerals, the fractionation between Br-halite(p) (pure NaBr crystal) and NaBr(aq) is close to zero, but for Br-halite(1/124) (Na125Cl124Br1) and NaBr(aq), the fractionation is 0.206 ± 0.041‰. Similar results are found for the fractionations between Br-sylvite, Br-bischofite and Br-bearing solutions, indicating that Br isotope compositions are closely related to Br/Cl ratios in minerals.By using the calculated isotope fractionation factors, we have modeled the Br isotope composition variations during salt precipitation processes. At 20 °C, the total variations of Br isotopes of salts and brines are found to be −0.45‰ to +0.21‰ and −0.39‰ to 0‰, respectively. They are much smaller than the observed Br isotope variations in natural samples. There must be other ways to fractionate Br isotopes to the extent that observed in nature. Based on the predicted equilibrium Br isotope fractionations among substances with different Br oxidation states, the large Br isotope variations in nature can be explained by the change of Br oxidation state. The sudden change of Br isotope compositions hence can be used as a new indicator for the change of redox conditions.