Equilibrium Isotope Fractionation Factors Research Articles

Equilibrium partitioning and isotopic fractionation of nitrogen between biotite, plagioclase, and K-feldspar during magmatic differentiation

A significant portion of the continental crust is composed of plutonic igneous rocks. However, little is known about the geochemical behaviour of N between the different minerals during magmatic differentiation. To provide new constraints for the behaviour of N during crust formation, we have characterised the geochemistry of nitrogen (N) in the compositionally zoned calc-alkaline pluton at Loch Doon, SW Scotland. We present N concentration and N isotope values for whole-rock data alongside biotite, plagioclase and K-feldspar mineral separates and assess the degree to which these data preserve equilibrium partitioning during magmatic differentiation. We show that whole rock likely inherited its N contents and δ15N signatures from the initial source composition and that this signature is homogenous at a pluton scale. Whilst the whole-rock data are best explained as crust-derived N in the source, the degree of homogenisation across a pluton scale is inconsistent with empirical N diffusivities, ruling out syn-emplacement crustal assimilation as the source of N. Instead, our data suggest a crustal signature inherited from depth associated with the Iapetus subduction zone. At a mineral scale, we find that N preferentially partitions into the feldspars over mica in this system in the order K-feldspar > plagioclase ≈ biotite > quartz, with average mineral–mineral distribution coefficients of DN plagioclase-biotite = 1.3 ± 0.6 and DN Kspar-biotite = 2.8 ± 0.6. Partitioning is accompanied by a large and near constant equilibrium isotope fractionation factor between biotite and both feldspars (averages are Δ15NPlag-Biotite = +7.8 ± 1.2‰ and Δ15NKspar-Biotite = +7.9 ± 1.0‰). In contrast, Δ15NKspar-Plagioclase closely approximates 0‰, where both minerals show δ15N values overlapping with the bulk rock δ15N values. These results show that mica crystallisation generates a 15N-depleted reservoir within plutonic rocks. Moreover, our dataset suggests that feldspars might be a more significant host of N in the igneous portion of Earth’s continental and oceanic crust than previously thought.

First-principles calculations of equilibrium Ga isotope fractionations between several important Ga-bearing minerals and aqueous solutions

This study predicts the equilibrium isotope fractionation factors for some important Ga-bearing species, including major minerals, aqueous solutions and gas phase systems. Equilibrium isotope fractionations of Ga were investigated by using the first-principles quantum chemistry method at the B3LYP/6-311+G(d) level. The 103ln(RPFR) values of orthoclase, albite, quartz, kaolinite, forsterite, montmorillonite, gibbsite, cassiterite, aragonite, sphalerite and calcite were calculated with the volume variable cluster model. The 103ln(RPFR)s of these minerals decrease in the following order: orthoclase > albite > quartz > kaolinite > forsterite > montmorillonite > gibbsite > cassiterite > aragonite > sphalerite > calcite. The solvation effect of Ga3+-bearing aqueous species is modeled by the water-droplet method, and the 103ln(RPFR)s of Ga3+-bearing aqueous species decrease in the following order: [Ga(OH)4]− > [Ga(OH)3] > [Ga(OH)]2+ > [Ga(OH)2]+ > [Ga(H2O)6]3+. The calculation results show that equilibrium isotope fractionations of Ga between different minerals, solutions and gas phases are appreciable. Among minerals, Ga isotope fractionation exhibits the largest value between orthoclase and calcite. Ga isotopic fractionation factor between these two minerals can reach 3.18 per mil at 100 °C. Ga isotope fractionations between Ga-bearing aqueous species and minerals are important for obtaining information about the different geochemical processes, such as surficial geochemistry. This study has provided important Ga isotope fractionation factors.

Equilibrium isotope fractionation factors of H exchange between steam and soil clay fractions.

Steam equilibration overcomes the problem of the traditional measurements of H isotope compositions, which leave an arbitrary amount of adsorbed water in the sample, by controlling for the entire exchangeable H pool, including adsorbed water and hydroxyl-H. However, the use of steam equilibration to determine nonexchangeable stable H isotope compositions in environmental media (expressed as δ2 Hn values) by mathematically eliminating the influence of exchangeable H after sample equilibration with waters of known H-isotopic composition requires the knowledge of the equilibrium isotope fractionation factor between steam-H and exchangeable H of the sample (αex-w ), which is frequently unknown. We developed a new method to determine the αex-w values for clay minerals, topsoil clay fractions, and mica by manipulating the contributions of exchangeable H to the total H pool via different degrees of post-equilibration sample drying. We measured the δ2 H values of steam-equilibrated mineral and soil samples using elemental analyzer-pyrolysis-isotope ratio mass spectrometry. The αex-w values of seven clay minerals ranged from 1.071 to 1.140, and those of 19 topsoil clay fractions ranged from 0.885 to 1.216. The αex-w value of USGS57 biotite, USGS58 muscovite, and of cellulose was 0.965, 0.871, and 1.175, respectively. The method did not work for kaolinite, because its small exchangeable H pool did not respond to the selected drying conditions. Structurally different mineral groups such as two- and three-layer clay minerals or mica showed systematically different αex-w values. The αex-w value of the topsoil clay fractions correlated with the soil clay content (r=0.63, P= 0.004), the local mean annual temperature (r = 0.68, P= 0.001), and the δ2 H values of local precipitation (r = 0.72, P< 0.001), likely to reflect the different clay mineralogy under different weathering regimes. Our new αex-w determination method yielded realistic results in line with the few previously published values for cellulose. The determined αex-w values were similar to the widely assumed values of 1.00-1.08 in the literature, suggesting that the adoption of one of these values in steam equilibration approaches is appropriate.

Equilibrium fractionation of REE isotopes in nature: Insights from NRIXS and DFT+U studies of Eu and Dy phonon density of states

Rare Earth Elements (REEs) are commonly utilized in Earth and environmental sciences to study a variety of geological processes due to their distinct patterns and radioactive-radiogenic decay systems (147Sm-143Nd, 146Sm-142Nd, 138La-138Ce). Advances in analytical techniques now enable the use of REE stable isotopic fractionations to clarify lingering ambiguities in REE systematics. In this study, we employed Nuclear Resonant Inelastic X-ray Scattering (NRIXS) to study the phonon density of states of 151Eu and 161Dy in several pure compounds, as well as in synthetic basalt and andesite glasses, and rhyolite glasses produced under various redox conditions, to determine equilibrium isotopic fractionation factors for the REEs. We additionally utilized Density Functional Theory with a Hubbard U correction (DFT+U) to calculate these factors. Our findings indicate that the directionally averaged mean force constant of Dy3+ is ∼270 N/m across various compounds, while those of Eu2+ and Eu3+ are ∼83 and 214 N/m, respectively, in geologically relevant glasses and other pure compounds. These force constants were then used to estimate those of all REEs using scaling arguments. The results suggest that equilibrium isotopic fractionation should be limited for REEs in igneous rocks, allowing for the interpretation of REE isotopic fractionation in these rocks and minerals as a result of kinetic effects. This could facilitate understanding the role of diffusion in igneous rocks and ore formation. Additionally, our results imply that significant Eu isotopic fractionation could exist in hydrothermal fluids, which could aid in understanding the formation of ore deposits and REE cycling in the oceans.

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.

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.

Density functional theory calculations of nitrogen and oxygen equilibrium isotope fractionations in NO3−–NO2−–H2O aqueous system reveal inverse kinetic isotope effects during nitrite oxidation

Nitrate and nitrite play key roles in the nitrogen cycle on Earth's surface. The isotope fractionation during nitrate reduction on enzymatic level involves multiple steps, including transfer of free NO3− to the activate site on nitrate reductase and NO2− equilibration with ambient water. However, the isotope fractionation factors of 15N and 18O among NO3−, NO2−, and H2O molecules in aqueous phases are poorly constrained. It strongly impedes the understanding of the involved processes and using stable isotopes to quantitatively examine the biogeochemical nitrogen cycle. In this contribution, we employ the density functional theory method with the Urey-Bigeleisen-Goeppert-Mayer model to predict the nitrogen and oxygen equilibrium isotope fractionation factors of NO3−, NO2−, and H2O molecules in gaseous and aqueous phases. Our calculation results show that the solvent effect has a large influence on equilibrium isotope fractionation for oxygen in water (+10.1‰ between liquid and vapor water at 25 °C), which is different to the little solvent effects on both oxygen and nitrogen in nitrate and nitrite. The calculated temperature-dependent equilibrium isotope fractionations between nitrogen of NO3− and NO2−, and oxygen of H2O and NO2− are consistent with previous laboratory experiments. Our results confirm that the oxygen equilibrium isotope fractionations between NO3− and NO2− should be +9.4‰ at 25 °C. Integrating the new results and previously reported kinetic isotope effects of nitrate reduction, we demonstrate inverse kinetic isotope effects for both nitrogen (+15.4‰) and oxygen (+5.2‰) during nitrite oxidation, which falls in the range of previous experiments. The new results enable us to use both nitrogen and oxygen isotopes as a bonded isotope tool to quantitatively assess the nitrogen cycle in low-temperature environments.

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.

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.

Clues from Ab Initio Calculations on Titanium Isotopic Fractionation in Tholeiitic and Calc-Alkaline Magma Series

Magmatic differentiation produces positive correlations between δ49Ti and SiO2. The equilibrium Ti isotope fractionation factors of Ti-bearing minerals are essential for understanding the mechanisms driving this isotopic fractionation. We present ab initio-derived mean force constants of Ti-bearing minerals (barium orthotitanate, potassium titanium oxide, fresnoite, diopside, geikielite, karrooite, titanite, pseudobrookite, anatase, and titanium oxide) based on density functional theory (DFT) to calculate equilibrium isotopic fractionation factors. We find that the main driver for Ti isotopic fractionation is its coordination, with four-, five-, and sixfold-coordinated Ti characterized by mean force constants of 547, 462, and 310 N/m, respectively. The coordination number of Ti in silicate melts is thought to be lower than in minerals, driving magmas toward higher δ49Ti values by fractional crystallization. The mineral-melt fractionation factors allow modeling of the observed Ti isotope trends in tholeiitic and calc-alkaline rocks. Our model results indicate that to first order, the steeper δ49Ti trend observed in tholeiitic versus calc-alkaline magmas is most likely due to enhanced removal of Ti into sequestered minerals at low SiO2 concentration in tholeiitic series compared to calc-alkaline series. The δ49Ti–SiO2 differentiation trends, however, depend on Ti coordination in the melt and the strengths of Ti bonds in diverse Fe- and Ti-oxides, which are still uncertain. Our results show that Ti isotopes can be used to reconstruct the crystallization history and identify the magmatic series parentage of magmas that otherwise lack context, but further work is needed to identify the drivers behind Ti isotopic fractionation in igneous rocks.

First-principles investigation of equilibrium iron isotope fractionation in Fe1−xSx alloys at Earth's core formation conditions

Iron is one of the most abundant non-volatile elements in the solar system. As a major component of planetary metallic alloys, its immiscibility with silicates plays a major role in planetary formation and differentiation. Information about these processes can be gained by studying the equilibrium Fe isotope fractionation between metal alloys and molten silicates at conditions of core formation. In particular, recent attention has been paid to 56Fe/54Fe equilibrium isotope fractionation at conditions relevant to Earth's core formation and the influence that light elements (O, H, C, Ni, Si and S) have had in this process. Most of these experimental studies relied on the measurement of Fe isotope fractionation from quenched phases of silicate melts and molten iron alloys. The experimental works are extremely challenging, and may suffer different drawbacks. To overcome this, we use ab-initio computational methods to perform a systematic study of the 56Fe/54Fe equilibrium isotope fractionation in molten and solid Fe1−xSx alloys at conditions of the core formation (60 GPa, 3000 K). We show for the first time, that equilibrium isotope fractionation factors from solid systems can be used as proxies for molten systems with differences between these two methods less than 0.01‰ at the relevant P-T conditions. Additionally, we discuss the effect of sulphur concentration on the equilibrium Fe isotope fractionation and show that although there are some structural changes due to atom substitutions, the wide range of studied concentrations produces β-factors that are constant within ∼0.02‰. Finally, we discuss the implications of our results for the interpretation of recent experiments and the understanding of core crystallisation processes.

Iron, magnesium, and titanium isotopic fractionations between garnet, ilmenite, fayalite, biotite, and tourmaline: Results from NRIXS, ab initio, and study of mineral separates from the Moosilauke metapelite

Interpreting isotopic signatures documented in natural rocks requires knowledge of equilibrium isotopic fractionation factors. Here, we determine equilibrium Fe isotope fractionation factors between several common rock-forming minerals using a comparative approach involving three independent methods: (i) isotopic analyses of natural minerals from a metapelite from Mt. Moosilauke, New Hampshire, for which equilibration temperature and pressure are well constrained to be near the aluminosilicate triple point (T ≃ 500 °C, P ≃ 4 kbar), (ii) Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements of Fe force constants of minerals, and (iii) Density Functional Theory (DFT) ab initio calculations of Fe force constants of minerals.The minerals studied for Fe isotopes include, in increasing order of their β-factors: garnet < ilmenite ≈ fayalite < biotite < tourmaline < muscovite ≈ plagioclase. Some of this ordering is affected by the presence of Fe3+ in the minerals, which tends to form stiffer bonds and be associated with heavy Fe isotope enrichments relative to Fe2+. We are, however, able to assess the magnitude of the effect of the ratio Fe3+/ΣFe on equilibrium fractionation factors, notably on the ilmenite-hematite solid solution. Equilibrium Fe isotopic fractionation factors between garnet, ilmenite, biotite, tourmaline and fayalite are determined. We also report Mg and Ti isotopic compositions of selected Moosilauke minerals that allow us to better constrain the equilibrium fractionation factors for garnet-biotite-tourmaline (Mg isotopes) and biotite-ilmenite (Ti isotopes).We show how the newly determined equilibrium fractionation factors can be used to address diverse problems in Earth and planetary sciences, notably (i) Fe and Mg isotopic fractionation during anatexis, (ii) Fe isotopic fractionation in lunar ilmenite, and (iii) Ti isotopic fractionation during fluvial transport of minerals.

First-principles calculations of equilibrium nitrogen isotope fractionations among aqueous ammonium, silicate minerals and salts

Nitrogen isotopes are a robust tool to study geological nitrogen cycle between Earth’s reservoirs. However, the application of nitrogen isotope system to understanding geological processes has been limited by the lack of constraints on equilibrium isotope fractionation factors between mineral and fluid and between mineral pairs. Here, we use first-principles methods to calculate the nitrogen isotope fractionations among aqueous ammonium, ammonium- and/or nitrate-bearing salts, and ammonium-bearing silicate minerals that commonly occur in Earth’s lithosphere. Our results show a first-order, large nitrogen isotope fractionations between the nitrate group and the ammonium group, with 15N being more enriched in the nitrate group. In detail, the nitrogen isotope fractionations among nitrate group minerals (NaNO3, KNO3, Ba(NO3)2, NH4NO3) are very small. The nitrogen isotope fractionations are also small among the ammonium group (e.g., aqueous ammonium, ammonium salts, phyllosilicate, and tectosilicate minerals) except inosilicate minerals (e.g., diopside and jadeite), which are however significantly more enriched in 15N than the other ammonium-bearing minerals. These results suggest that nitrogen isotopes may serve as a robust geothermometer only when the rock contains coexisting ammonium and nitrate minerals, or contain diopside and/or jadeite together with other ammonium-bearing silicate minerals. Given that common silicate minerals in crustal rocks (clays, micas, feldspars) do not significantly discriminate nitrogen isotopes, nitrogen isotopes can thus be used as a sensitive tool to trace material source and infer geochemical processes that may cause isotope disequilibrium, such as metamorphic devolatilization, hydrothermal alteration, crust-mantle interaction. Our results also demonstrate that authigenic clay minerals can inherit the nitrogen isotopic signature of organic matter and aqueous ammonium and thus can serve as an environmental proxy. However, it is crucial to distinguish detrital minerals from authigenic minerals in sediments when reconstruct marine and lacustrine environments in the deep time (Archean and Proterozoic).

Theoretical estimates of equilibrium carbon and hydrogen isotope effects in microbial methane production and anaerobic oxidation of methane

Microbial production and consumption of methane are widespread in natural and artificial environments, with important economic and climatic implications. Attempts to use the isotopic composition of methane to identify its sources are complicated by incomplete understanding of the mechanisms of variation in methane’s isotopic composition. Knowledge of the equilibrium isotope fractionations among the large organic intracellular intermediates in the microbial pathways of methane production and consumption must form the basis of any exploration of the mechanisms of isotopic variation, but estimates of these equilibrium isotope fractionations are currently unavailable. To address this gap, we calculated the equilibrium isotopic fractionation of carbon (13C/12C) and hydrogen (D/H) isotopes among compounds in the anaerobic methane metabolisms, as well as the abundance of double isotope substitutions (“clumping,” i.e., a single 13C–D bond or two 12C–D bonds) in these compounds. The isotope fractionation factors were calculated using density functional theory at the M06-L/def2-TZVP level of theory with the SMD implicit solvation model, which we recently tested against measured equilibrium isotope fractionations. The computed 13β and 2β values decrease with decreasing oxidation state of the carbon atom in the molecules, resulting in a preference for enrichment in 13C and D in the molecules with more oxidized carbon. Using the computed β values, we calculated the equilibrium isotope fractionation factors in the prominent methanogenesis pathways (hydrogenotrophic, methylotrophic and acetoclastic) and in the pathway for anaerobic oxidation of methane (AOM) over a temperature range of 0–700 °C. Our calculated equilibrium fractionation factors compare favorably with experimental constraints, where available, and were then used to investigate the relation between the apparent isotope fractionation during methanogenesis or AOM and the thermodynamic drive for these reactions. We show that a detailed map of the equilibrium fractionation factors along these metabolic pathways allows for an evaluation of the contribution of equilibrium and kinetic isotope effects to apparent isotope fractionations observed in laboratory, natural and artificial settings. The comprehensive set of equilibrium isotope fractionation factors calculated in this study provides a firm basis for future explorations of isotope effects in methane metabolism.

Ideas and perspectives: The same carbon behaves like different elements – an insight into position-specific isotope distributions

Abstract. It is expected that information on the source, reaction pathway, and reaction kinetics of an organic compound can be obtained from its position-specific isotope compositions or intramolecular isotope distribution (Intra-ID). To retrieve the information, we could use its predicted equilibrium Intra-ID as a reference for understanding the observed Intra-IDs. Historically, observed, apparently close-to-equilibrium carbon Intra-ID has prompted an open debate on the nature of biosystems and specifically the pervasiveness of reversible biochemical reactions. Much of the debate remains unresolved, and the discussion has not clearly distinguished between two states of equilibrium: (1) the equilibrium among the corresponding bond-breaking and bond-forming positions in reactant and product and (2) the equilibrium among all carbon positions within a compound. For an organic molecule with multiple carbon positions, equilibrium carbon Intra-ID can be attained only when a specific reaction is in equilibrium and the sources of each position are also in equilibrium with each other. An observed Intra-ID provides limited information on if the sources and pathways are both unconstrained. Here, we elaborate on this insight using examples of the observed Intra-IDs of hydroxyl-bearing minerals, N2O, and acetic acid. Research effort aiming to calibrate position-specific equilibrium and kinetic isotope fractionation factors for defined processes will help to interpret observed Intra-IDs of a compound accurately and fully.

Evidence from Ab Initio and Transport Modeling for Diffusion-Driven Zirconium Isotopic Fractionation in Igneous Rocks

We use density functional theory to calculate the equilibrium isotopic fractionation factors of zirconium (Zr) in a variety of minerals including zircon, baddeleyite, Ca-catapleiite, ilmenite, geik...

Constraining speleothem oxygen isotope disequilibrium driven by rapid CO2 degassing and calcite precipitation: Insights from monitoring and modeling

Oxygen isotopes are the most commonly applied speleothem proxy for reconstructing Quaternary changes in precipitation and/or temperature. These interpretations are either limited to qualitative wetting and drying trends or rely on theoretical, experimental and/or empirical equilibrium isotope fractionation factors for more quantitative constraints. These various fractionation factors have similar temperature sensitivities, but their absolute values differ, and cave calcite does not appear to generally precipitate in isotopic equilibrium with its drip water. Rapid CO2 degassing paired with calcite precipitation, both occurring under disequilibrium conditions, are a set of mechanisms commonly invoked to explain offsets between observed and equilibrium isotopic fractionation between cave calcites and drip waters. However, the relevance of these disequilibrium mechanisms to speleothem records remains unresolved. Here, we compare measured δ18O values of modern speleothem calcite from a tropical cave in Guam to calcite δ18O values predicted by a modified version of the ISOLUTION proxy system model. This extends the global comparison of cave drip water and modern calcite δ18O values to higher temperatures. We initialize the model using contemporaneous measurements of drip water (δ18O values, [Ca+], and pH), and cave air (CO2, and T) from four drip sites over 3.5 years of monitoring in the cave. Through this comparison, we show that for a slow drip-rate site, ventilation-driven CO2 degassing can explain seasonal variations in calcite oxygen isotope composition. At faster-dripping sites in this cave, the seasonal effect is limited. At these sites, the DIC reservoir is replenished by new drips faster than its isotopic composition can be modified by degassing CO2 and calcite precipitation, whether occurring each is occurring as an equilibrium or kinetic process. For the slow drip rate site, however, this is the first observation of cave air CO2 variations exerting a control on cave calcite oxygen isotope values. The confirmation of ventilation-driven processes controlling oxygen isotope values at a slow-drip site advances the process-based understanding of stalagmite formation that is required to move beyond the wetter-or-drier paradigm and make quantitative interpretations of speleothem oxygen isotope records.

Inelastic neutron scattering: a novel approach towards determination of equilibrium isotopic fractionation factors. Size effects on heat capacity and beta-factor of diamond.

A new experimental method for the determination of equilibrium isotopic properties of substances based on inelastic neutron scattering (INS) is proposed. We present a mathematical formalism, which allows the calculation of the beta-factor of single-element solids based on INS-derived Phonon Density of States (PDOS). PDOS data for nanodiamonds of widely different sizes and of macroscopic diamond were determined from inelastic neutron scattering experiments. This allowed the determination of heat capacities and, for the first time, β-factors of the diamond nanoparticles. We demonstrate a considerable size-dependent increase of the heat capacities and decrease of the beta-factors for nanodiamonds relative to bulk diamond. Contributions of surface impurities/phases and phonon confinement to the size effects are evaluated. Applications in the formation of diamond nanoparticles in nature are briefly discussed.

Calibrating equilibrium Fe isotope fractionation factors between magnetite, garnet, amphibole, and biotite

Equilibrium isotope fractionation factors are the basis for application of stable isotopes in geological studies. Experimental calibration and theoretical calculations have been employed to determine Fe isotope fractionation factors for a variety of minerals, however, these methods have their limitations. An alternative approach to calibrating inter-mineral Fe isotope fractionation factors is to use well-characterized geological samples; this approach has unique advantages over the other methods including attainment of equilibrium at relatively low temperatures. In this study, we investigated the Fe isotope composition of magnetite (Mt), garnet (Grt), amphibole (Amp) and biotite (Bt) from the metamorphosed Yingshan iron formation in South China. Two independent geothermometers, quartz–magnetite oxygen isotope and amphibole–garnet–biotite Fe–Mg exchange geothermometers, give a consistent metamorphic temperature of 538 ± 39 °C. The Fe isotope composition of the different Fe-bearing minerals is highly variable in different ironstone samples, with δ56Fe values (relative to IRMM-014) ranging from −0.23 to +0.37‰ in magnetite, −0.44 to +0.09‰ in amphibole, −0.78 to +0.02‰ in garnet, and −0.61 to +0.04‰ in biotite. Despite that, the offsets of δ56Fe values for mineral pairs are consistent, implying attainment of equilibrium isotope fraction between these minerals. Inter-mineral Fe isotopic fractionations (±2 standard deviation) measured from the multiple mineral pairs are Δ56FeMt–Grt = +0.55 ± 0.08‰, Δ56FeMt–Amp = +0.25 ± 0.06‰, Δ56FeMt–Bt = +0.42 ± 0.11‰, Δ56FeAmp–Grt = +0.34 ± 0.15‰, Δ56FeAmp–Bt = +0.26 ± 0.04‰, and Δ56FeBt–Grt = +0.13 ± 0.08‰. Based on the well-defined metamorphic temperature (538 ± 39 °C) and internally consistent inter-mineral fractionation factors, the temperature-dependent functions for equilibrium Fe isotope fractionation between the following mineral pairs are derived:103lnαMt–Grt = 0.36(±0.05) × 106/T2, 103lnαMt–Bt = 0.28(±0.07) × 106/T2,103lnαMt–Amp = 0.16(±0.04) × 106/T2, 103lnαAmp–Grt = 0.22(±0.10) × 106/T2,103lnαAmp–Bt = 0.17(±0.03) × 106/T2, and 103lnαBt–Grt = 0.09(±0.05) × 106/T2,where Fe3+/ΣFe ratio is 0.05 ± 0.02 in garnet, 0.29 ± 0.04 in biotite, and 0.24 ± 0.06 in amphibole for the above functions. The equilibrium Fe isotope fractionation factors derived in this study enable estimation of the metamorphic temperature of rocks that contain these mineral pairs, and identification of secondary processes that may have induced disequilibrium Fe isotope distribution in rocks, such as retrograde metamorphism and hydrothermal alteration.

Experimental and theoretical modelling of kinetic and equilibrium Ba isotope fractionation during calcite and aragonite precipitation

Barium isotope fractionation during calcite and aragonite inorganic precipitation was studied in mixed flow reactors as a function of precipitation rate at 25 °C and pH = 6.3 ± 0.1. The measured Ba isotope fractionation that occurs between calcite and the forming fluid in the investigated range of calcite growth rates (10-8.0 ≤ Rp(calcite) ≤ 10−7.3 mol/m2/s) is insignificant. Barium isotope fractionation between aragonite and the fluid decreases with increasing precipitation rate from Δ137/134Baaragonite-fluid = +0.25 ± 0.06‰ for Rp(aragonite) ≤ 10−8.7 mol/m2/s to −0.10 ± 0.08‰ for Rp(aragonite) = 10−7.6 mol/m2/s, thus reflecting preferential incorporation of either heavy or light Ba isotopes in aragonite at slow and fast growth rates, respectively. The dependence of Ba isotope fractionation on aragonite growth rate is well described by the surface reaction kinetic model developed by DePaolo (2011) when the values +0.27‰ and −2.0 ± 0.2‰ are used for the equilibrium and kinetic Ba isotope fractionation factor, respectively. The enrichment of aragonite in the heavier Ba isotopes is consistent with the equilibrium fractionation factor of +0.34‰, calculated here between Ba-substituted aragonite and Ba2+ (aq), from first-principles calculations. This positive fractionation is related to a shorter average BaO bond length in the aragonite structure while the coordination number does not change much (i.e. 9). The lack of isotope fractionation between the Ba aquo ions and the 6-coordinated Ba in calcite likely suggests that the coordination reduction required for the incorporation in the lattice of Ba adsorbed at calcite growing sites proceeds without isotope fractionation with the fluid. Otherwise the precipitated calcite should have been enriched in heavy isotopes by ∼0.17‰, as predicted by first-principles calculations. These results are the first experimental measurements of Ba isotope fractionation during inorganic calcite and aragonite mineral formation and set the basis for understanding the mechanisms controlling Ba isotope composition in CaCO3 minerals that is an essential perquisite for application of this isotopic system in natural samples.