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Effect of temperature and mass transport on transition metal isotope fractionation during electroplating
Abstract
Transition metal stable isotope signatures can be useful for tracing both natural and anthropogenic signals in the environment, but only if the mechanisms responsible for fractionation are understood. To investigate isotope fractionations due to electrochemistry (or redox processes), we examine the stable isotope behavior of iron and zinc during the reduction reaction M^(2+)_(aqueous) + 2e^− = M_(metal) as a function of electrochemical driving force, temperature, and time. In all cases light isotopes are preferentially electroplated, following a mass-dependent law. Generally, the extent of fractionation is larger for higher temperatures and lower driving forces, and is roughly insensitive to amount of charge delivered. The maximum fractionations are δ^(56/54)Fe = −4.0‰ and δ^(66/64)Zn = −5.5‰, larger than observed fractionations in the natural environment and larger than those predicted due to changes in speciation. All the observed fractionation trends are interpreted in terms of three distinct processes that occur during an electrochemical reaction: mass transport to the electrode, chemical speciation changes adjacent to the electrode, and electron transfer at the electrode. We show that a large isotope effect adjacent the electrode surface arises from the charge-transfer kinetics, but this effect is attenuated in cases where diffusion of ions to the electrode surface becomes the rate-limiting step. Thus while a general increase in fractionation is observed with increasing temperature, this appears to be a result of thermally enhanced mass transport to the reacting interface rather than an isotope effect associated with the charge-transfer kinetics. This study demonstrates that laboratory experiments can successfully distinguish isotopic signatures arising from mass transport, chemical speciation, and electron transfer. Understanding how these processes fractionate metal isotopes under laboratory conditions is the first step towards discovering what role these processes play in fractionating metal isotopes in natural systems.
... Kavner and co-workers used the electroplating technique to study reduction-induced isotope fractionation of Fe, Zn and Cu isotope systems (Kavner et al. 2005(Kavner et al. , 2008Black et al. 2010aBlack et al. , b, 2011Black et al. , 2014. They applied the constant potential technique which has the advantage to enable measurements of overpotential at the electrodes during operation. ...
... 5) is at least ~ 1‰ smaller than the observed fractionations in our study at elevated temperatures. This is in line with results for Fe-and Zn-bearing systems: experimentally observed fractionation factors at 25 °C for reduction of divalent ions to metals have been up to 4‰ smaller than the values predicted for equilibrium partitioning (Black et al. 2010a(Black et al. , b, 2014. Possible explanations are contributions of kinetics which are discussed in following. ...
... The experimental value of the exponent γ decreases from 0.02 for dissolved Na to 0.002 for dissolved Fe and Zn, respectively, (Pikal 1972;Rodushkin et al. 2004 In all cases, the diffusion-induced ∆ 65 Cu values are about − 0.2‰. Thus, this calculation confirms that diffusion in the solution causes only minor Cu isotopic fractionation, consistent with findings of Black et al. (2010aBlack et al. ( , b, 2011 for electrochemical reduction of Cu, Fe and Zn isotopes. If the solution is well stirred (e.g., ≥ 300 rpm), currents are kept low (e.g., ≤ 0.3 A, and ≤ 0.11 A cm −2 ) and the concentration of Cu 2+ is higher than 0.5 mol kg −1 , the effect of mass transport on copper isotope fractionation is negligible for short electroplating times. ...
Redox processes are ubiquitous in Earth science, and redox transitions often lead to large fractionations of the stable isotopes of many transition metals such as copper. To get insights into the mechanisms of isotope fractionations induced by electrochemical processes, we examine the behavior of copper isotopes during the reduction reaction Cu2+ + 2e− = Cu0. All experiments have been conducted by applying a controlled current between the working electrode and the auxiliary electrode, i.e., the galvanostatic electrodeposition technique, in aqueous CuSO4 solutions. Controlling parameters were tested by varying electrolyte concentration (0.01–1 mol kg−1), stirring speed (0–500 rpm), current (0.1–0.5 A), time (35–600 s), and temperature (5–80 °C). In all cases, the plated Cu metal is enriched in the light isotope (63Cu) with respect to the solution. At room temperature, the Cu isotopic fractionation between the electroplated Cu and electrolyte is found to increase with electrolyte concentration and stirring speed, and to decrease with current and run duration. These trends can be interpreted by three competing processes: copper transport in the solution, kinetics of electrochemical reduction of copper ions and surface diffusion at the electrode, i.e., transport becomes important at low copper concentration, low stirring speed, high currents and large amount of copper precipitation. Copper isotope fractionation has a maximum near 35 °C, decreasing both towards higher and lower temperatures. In the temperature range of 35–80 °C, the dependence of temperature on isotope fractionation can be described by
∆65CuCu(0)s-Cu(II)aq = -(0.27±0.04) × 106T-2 - (0.16±0.34); R2 = 0.93, where ∆65CuCu(0)–Cu(II)aq (‰) represents the copper isotopic composition differences between the product (electroplated copper) and the reactant (electrolyte solution, CuSO4(aq)), and T is the temperature in K. At low temperature (down to 5 °C), a noticeable deviation from this trend suggests a change in the controlling mechanism, i.e., transport in the solution becomes important. Our findings are best explained by a two-step reduction process including reduction from Cu(II) to Cu(I) and a subsequent reduction of Cu(I) to Cu(0). The good agreement of our high-temperature data with the results from Ehrlich et al. (2004), who used a different experimental approach to precipitate Cu(I) mineral from CuSO4 solution, implies that transformation of Cu(II) to Cu(I) dominates the isotope fractionation observed during electrochemical reduction of Cu(II) to Cu(0). These findings support that copper isotopes can be used as effective tracers of redox processes. They may have implications to processes in hydrothermal systems and the formation of ore deposits, e.g., volcanic-hosted massive sulfides, as well as to processes in near surface aquatic environment and related supergene processes.
... Over the past decade, electrochemistry experiments have been used to investigate kinetic isotope effects for Fe, Zn, and Li during redox reactions ( Fig. 15; Kavner et al. 2005Kavner et al. , 2008Black et al. 2009Black et al. , 2010aBlack et al. ,b, 2014. The observations that have been made, and the extremely well-controlled nature of the experiments, present an opportunity to develop and test models for combined reaction and diffusion (i.e., Regimes 3 and 4) in a "simple" system. ...
... For Fe in FeSO 4 (gray symbols in Fig. 15), the data are more scattered, especially in Regime 3 where surface reaction kinetics dominate. Black et al. (2010a) noted that the electrodeposition efficiency is low in these experiments, meaning that the redox reaction of interest accounts for only a small fraction of the current registered by the electrode (Kavner, pers. comm.). ...
... Over the past decade, electrochemistry experiments have been used to investigate kinetic isotope effects for Fe, Zn, and Li during redox reactions ( Fig. 15; Kavner et al. 2005Kavner et al. , 2008Black et al. 2009Black et al. , 2010aBlack et al. ,b, 2014. The observations that have been made, and the extremely well-controlled nature of the experiments, present an opportunity to develop and test models for combined reaction and diffusion (i.e., Regimes 3 and 4) in a "simple" system. ...
... For Fe in FeSO 4 (gray symbols in Fig. 15), the data are more scattered, especially in Regime 3 where surface reaction kinetics dominate. Black et al. (2010a) noted that the electrodeposition efficiency is low in these experiments, meaning that the redox reaction of interest accounts for only a small fraction of the current registered by the electrode (Kavner, pers. comm.). ...
Natural variations in the isotopic composition of some 50 chemical elements are now being used in geochemistry for studying transport processes, estimating temperature, reconstructing ocean chemistry, identifying biological signatures, and classifying planets and meteorites. Within the past decade, there has been growing interest in measuring isotopic variations in a wider variety of elements, and improved techniques make it possible to measure very small effects. Many of the observations have raised questions concerning when and where the attainment of equilibrium is a valid assumption. In situations where the distribution of isotopes within and among phases is not representative of the equilibrium distribution, the isotopic compositions can be used to access information on mechanisms of chemical reactions and rates of geological processes. In a general sense, the fractionation of stable isotopes between any two phases, or between any two compounds within a phase, can be ascribed to some combination of the mass dependence of thermodynamic (equilibrium) partition coefficients, the mass dependence of diffusion coefficients, and the mass dependence of reaction rate constants.
Many documentations of kinetic isotope effects (KIEs), and their practical applications, are described in this volume and are therefore not reviewed here. Instead, the focus of this chapter is on the measurement and interpretation of mass dependent diffusivities and reactivities, and how these parameters are implemented in models of crystal growth within a fluid phase. There are, of course, processes aside from crystal growth that give rise to KIEs among non-traditional isotopes, such as evaporation (Young et al. 2002; Knight et al. 2009; Richter et al. 2009a), vapor exsolution (Aubaud et al. 2004), thermal diffusion (Richter et al. 2009a, 2014b; Huang et al. 2010; Dominguez et al. 2011), mineral dissolution (e.g., Brantley et al. 2004; Wall et al. 2011; Pearce et al. 2012 …
... Kinetic isotope effects (KIEs) for redox reactions have been relatively less studied. Kinetic isotope effects are considered dominant in many unidirectional reactions of Fe including electrochemical reduction (Black et al., 2010;Kavner et al., 2005), chemical oxidation of Fe(II) bipyridine complexes (Matthews et al., 2001), biological oxidation of Fe (Balci et al., 2006;Croal et al., 2004), and mineral dissolution (Brantley et al., 2004;Chapman et al., 2009;Kiczka et al., 2010;Revels et al., 2015;Wiederhold et al., 2007aWiederhold et al., , 2007b. However, developing theoretical predictions of KIEs, and testing such theory with experiments has proved more challenging than for equilibrium isotope effects, especially for redox reactions. ...
Iron stable isotopes (δ⁵⁶Fe) are a useful tool for studying Earth processes, many of which involve redox transformations between Fe(III) and Fe(II). Here, we present two related experimental efforts, a study of the kinetic isotope effects (KIEs) associated with the reduction of Fe(III)‐ethylenediaminetetraacetic acid (EDTA) to Fe(II), and measurements of the biological fractionation of Fe isotopes by phytoplankton in culture. Reductants tested were ascorbate, hydroxylamine, Mn(II), dithionite, and photoreduction at pH between 5 and 9 and temperatures from 0 to 100°C. Isotope fractionations were very large, and included both normal and inverse KIEs, ranging from −4‰ to +5‰. Experiments were reproducible, yielding similar results for triplicate experiments run concurrently and for experiments run weeks apart. However, fractionations were not predictable, without a clear relationship to reaction rate, temperature, pH, or the reductant used. Acquisition of Fe by eukaryotic phytoplankton also often involves the reduction of Fe(III) to Fe(II). Several species of diatoms and a coccolithophore were tested for Fe isotope fractionation in culture using EDTA, NTA, and DFB as Fe(III) chelating ligands, yielding fractionations from −1.3‰ to +0.6‰. Biological isotope effects were also unpredictable, showing no clear relationship to species, growth rate, or Fe concentration. Variability in Fe isotope fractionation observed in culture may be explained in part by the sensitivity of KIEs. This work has implications for the industrial purification of isotopes, interpretation of natural δ⁵⁶Fe, and the use of Fe isotopes as a tracer Fe source and biological processes in the ocean and other natural systems.
... A growing number of studies have described Mg isotope analytical procedures for organic samples, silicate or carbonate rocks, and meteorites Chang et al., 2003;Black et al., 2006;Buhl et al., 2007;Teng et al., 2007Teng et al., , 2010aTipper et al., 2008b;Bolou-Bi et al., 2009;Handler et al., 2009;Hippler et al., 2009;Huang et al., 2009b;Young et al., 2009;Higgins and Schrag, 2010;Wang et al., 2011). After the pioneering work of Lee and Papanastassiou (1974) using cation exchange resin (AG50W-X8, 200-400 mesh) to extract Mg from meteorites with 1N HNO 3 (Lee and Papanastassiou, 1974), many studies used different resins, acids or column lengths to quantitatively purify Mg from matrix elements (K, Fe, Al, Na, Ca, etc.) (Wilde et al., 2001;Galy et al., 2002;Chang et al., 2003;Bizzarro et al., 2004;Baker et al., 2005;Tipper et al., 2006;Teng et al., 2007Teng et al., , 2010aPogge von Strandmann, 2008;Bolou-Bi et al., 2009;Handler et al., 2009;Huang et al., 2009b;Shen et al., 2009;Black et al., 2010;Bourdon et al., 2010;Foster et al., 2010;Schiller et al., 2010;Wang et al., 2011;Choi et al., 2012;Bouvier et al., 2013). For example, Chang et al. (2003) presented two separate steps of ion-exchange chromatography to purify Mg in low-Mg biogenic carbonate materials (~0.1-1 wt.% MgCO 3 ) with a high (N 99.9%) Mg yield. ...
... A recurring theme in studies of the biogeochemistry of metals in aquatic environments is the importance of ligand-exchange reactionsparticularly, binding to organic ligands (Zhu et al., 2002;Corry and Chung, 2006;Gussone et al., 2006;Lacan et al., 2006) or to mineral surfaces (Stumm and Morgan, 1996;Sposito, 2004;Ohlin et al., 2009;Black et al., 2010;Stack et al., 2012)as the rate-controlling steps in metal cycling. The important kinetic role of these reactions suggests that they may contribute significantly to metal kinetic isotope effects in natural settings. ...
Aqueous electrochemical atom transfer radical polymerisation (eATRP) can be challenging due to deleterious side reactions leading to the loss of the ω-chain end, increased rates of activation (k¬act) leading to...
Chemicals enriched in lithium isotopes are of paramount importance in the current nuclear fission technology, in future nuclear fusion technology, and in neutron detectors. Currently, lithium isotopes are obtained by using mercury amalgams, a non-environmentally friendly procedure. An interesting alternative is to take advantage of the electrochemical isotope effect. Here we take as the departure point experimental data already reported for a prospective first stage of an electrochemical process, and we numerically simulate different scale-up possibilities. We calculate the minimum number of repetitive stages needed to reach a certain degree of isotopic enrichment. Secondly, we improve our simulations considering that different operating conditions are used while keeping the same fundamental electrochemical process: a minimum of 145 stages are necessary to produce a sample with 90% enrichment in ⁶Li. We finish by a comparison on the different electrochemical technologies in view of complementary steps necessary for scaling up.
A number of shallow aquifers in industrial regions have been polluted by toxic Cr(VI). At some sites, spontaneous reduction of dissolved Cr(VI) to insoluble Cr(III) has been observed. Precipitation of non-toxic Cr(III) is accompanied by a Cr isotope fractionation, with the residual Cr(VI) becoming enriched in the heavier isotope ⁵³Cr, and depleted in the lighter isotope ⁵²Cr. Thus far, δ⁵³Cr values of the contamination source have been poorly constrained. These values are needed to quantify the extent of Cr(VI) reduction in the aquifers. We present δ⁵³Cr values of solutions generated during Cr-electroplating, chromating and anodizing at nine industrial sites. The source chemical, CrO3, had a mean δ⁵³Cr of 0.0‰. A small-to-negligible Cr isotope fractionation was observed between the solutions of the plating baths and the source chemical. Across all sample types, the mean δ⁵³Cr(VI) value was 0.2‰. The mean δ⁵³Cr(VI) value of contaminated groundwater in the same region, studied previously, was significantly higher (2.9‰), indicating Cr(VI) reduction. Based on low δ⁵³Cr(VI) values of plating baths and rinsewaters as potential contamination sources, and their low variability, we suggest that most aquifer δ⁵³Cr(VI) values higher than 1.0‰ are a result of in-situ Cr(VI) reduction.
Electrochemical reduction/oxidation (redox) reactions have been observed to drive stable isotope fractionation in many metal systems, where the lighter isotopes of a metal are typically partitioned into the reduced chemical species. While physical processes such as diffusive mass transport lead to small isotope fractionations, charge transfer processes can lead to isotope fractionations up to ten times larger and twice that predicted by equilibrium stable isotope theory. Control over physical and chemical variables during electrochemical experiments, such as overpotential and temperature, allow for the isotopic composition of deposited metals to be fine tuned to a specific value.
The isotopic composition of zinc metal electrodeposited on a rotating disc electrode from a Zn-citrate aqueous solution was investigated as a function of overpotential (electrochemical driving force), temperature, and rotation rate. Zn metal was measured to be isotopically light with respect to Zn+2 in solution, with observed fractionations varying from Δ66/64Znmetal-aqueous = −1.0‰ to −3.9‰. Fractionation varies continuously as a function of a dimensionless parameter described by the ratio of observed deposition rate to calculated mass-transport limiting rate, where larger fractionations are observed at lower deposition rates, lower temperature, and at faster electrode rotation rates. Thus, the large fractionation and its rate dependence is interpreted as a competition between the two kinetic processes with different effective activation energies: mass-transport-limited (diffusion limited) kinetics with a large activation energy, which creates small fractionations close to the predicted diffusive fractionation; and electrochemical deposition kinetics, with a smaller effective activation energy, which creates large fractionations at low deposition rates and high hydrodynamic fluxes of solute to the electrode. The results provide a framework for predicting isotope fractionation in processes controlled by two competing reactions with different kinetic isotope effects.
Ancient Judaean bronze coins are important for reconstructing the timing of events, for their cultural information, and for understanding alliances in the Eastern Mediterranean as Roman influence replaced the Hellenic Empires. Isotopic analyses of metals important in archaeology have become increasingly routine using multiple collector–inductively coupled plasma–mass spectrometry. A relatively nondestructive acid swab method for the isotopic analysis of lead (Pb) and copper (Cu) in bronze is described and tested for various isotopic sampling biases. The method is used to examine changes over time in fiduciary metal sources in the Levant during the first centuries bce and ce. The metal sources, timing, and attribution of Judaean “widow's mites” (ca. 80–40 bce) and the bronze coins of Roman governors Valerius Gratus and Pontius Pilate under Tiberius (14–37 ce) are used to illustrate how changes in the isotopes of Pb (widow's mites) and Cu (Roman governors) can be used to elucidate the compositional chronology of archaeological bronzes from this region and period.
The goal of this study is to determine reduced partition function ratios for a variety of species of zinc, both as a metal and in aqueous solutions in order to calculate equilibrium stable isotope partitioning. We present calculations of the magnitude of Zn stable-isotope fractionation (66,67,68Zn/64Zn) between aqueous species and metallic zinc using measured vibrational spectra (fit from neutron scattering studies of metallic zinc) and a variety of electronic structure models. The results show that the reduced metal, Zn(0), will be light in equilibrium with oxidized Zn(II) aqueous species, with the best estimates for the Zn(II)–Zn(0) fractionation between hexaquo species and metallic zinc being Δ66/64Znaq-metal ∼ 1.6‰ at 25 °C, and Δ66/64Znaq-metal ∼ 0.8‰ between the tetrachloro zinc complex and metallic zinc at 25 °C using B3LYP/aug-cc-pVDZ level of theory and basis set. To examine the behavior of zinc in various aqueous solution chemistries, models for Zn(II) complex speciation were used to determine which species are thermodynamically favorable and abundant under a variety of different conditions relevant to natural waters, experimental and industrial solutions. The optimal molecular geometries for [Zn(H2O)6]2+, [Zn(H2O)6]·SO4, [ZnCl4]2− and [Zn(H2O)3(C3H5O(COO)3)]− complexes in various states of solvation, protonation and coordination were calculated at various levels of electronic structure theory and basis set size. Isotopic reduced partition function ratios were calculated from frequency analyses of these optimized structures. Increasing the basis set size typically led to a decrease in the calculated reduced partition function ratios of ∼0.5‰ with values approaching a plateau using the aug-cc-pVDZ basis set or larger. The widest range of species were studied at the B3LYP/LAN2DZ/6-31G∗ level of theory and basis-set size for comparison. Aqueous zinc complexes where oxygen is bound to the metal center tended to have the largest reduced partition function ratios, with estimated fractionations ranging from 2.2 to 2.9‰ (66Zn/64Zn) at 25 °C relative to metallic zinc. The tetrahedrally coordinated tetrachloro zinc complex, where zinc is bound exclusively to chloride, had the lowest reduced partition function ratio for a Zn(II) species (Δ66/64Znaq-metal ∼ 1–1.3‰ at 25 °C). Increasing the number of waters in the second shell of solvation of the above complexes led to variable results, most commonly leading to a decrease of ∼0.2 to 0.3‰ in calculated Δ66/64Znaq-metal at 25 °C.These estimates are useful in the interpretation of observed fractionations during the electrochemical deposition of zinc, where aqueous-metal fractionations of up to 5.5‰ are observed. The models show these are not caused by an equilibrium fractionation process. These results suggest that the redox cycle of zinc during industrial processing may be responsible for isotopically distinct reservoirs of zinc observed in polluted environments. The leaching of metallic zinc or zinc tailings from industrial sites could lead to the observed heavy signature in river systems, the magnitude of which will be reliant on the source material and the aqueous species that form.
We report new molecular dynamics results elucidating the structure of the electrical double layer (EDL) on smectite surfaces contacting mixed NaCl-CaCl(2) electrolyte solutions in the range of concentrations relevant to pore waters in geologic repositories for CO(2) or high-level radioactive waste (0.34-1.83 mol(c) dm(-3)). Our results confirm the existence of three distinct ion adsorption planes (0-, β-, and d-planes), often assumed in EDL models, but with two important qualifications: (1) the location of the β- and d-planes are independent of ionic strength or ion type and (2) "indifferent electrolyte" ions can occupy all three planes. Charge inversion occurred in the diffuse ion swarm because of the affinity of the clay surface for CaCl(+) ion pairs. Therefore, at concentrations ≥0.34 mol(c) dm(-3), properties arising from long-range electrostatics at interfaces (electrophoresis, electro-osmosis, co-ion exclusion, colloidal aggregation) will not be correctly predicted by most EDL models. Co-ion exclusion, typically neglected by surface speciation models, balanced a large part of the clay mineral structural charge in the more concentrated solutions. Water molecules and ions diffused relatively rapidly even in the first statistical water monolayer, contradicting reports of rigid "ice-like" structures for water on clay mineral surfaces.
Raman and infrared spectra for aqueous ZnSO4 and (NH4)(2)SO4 solutions have been recorded over broad concentration and temperature ranges. Whereas the v(1)(a(1))-SO42- band profile is symmetrical in (NH4)(2)SO4 solutions, in ZnSO4 solutions a shoulder appears on the high frequency side which increases in intensity with increasing concentration and temperature. The molar scattering coefficient of the v(1)(a(1))-SO42- band is the same for all forms of sulfate in (NH4)(2)SO4 and ZnSO4 solutions and is independent of temperature up to 165 degrees C. The high frequency shoulder is attributed to the formation of a 1.1 contact ion pair [Zn2+OSO32-]. Also the v(3)(f(2))-SO42- antisymmetric stretching mode shows a splitting in the ZnSO4 solution. Additionally, the bending modes, v(2)(e)-SO42- and v(4)(f(2))-SO42- normally forbidden in the isotropic spectrum show with increasing ion pair formation a gain in intensity. A polarized band at 275 cm(-1) has been assigned to the Zn2+-OSO32- Ligand vibration. Further spectroscopic evidence for contact ion pair formation at 25 degrees C is provided by i.r. spectroscopy. No higher associates or anionic complexes are required to interpret the spectroscopic data. In concentrated ZnSO4 the majority of the sulfate is occurring in the outer-sphere. With temperature increase, the amount of inner-sphere complex is increasing (entropically driven reaction). The degree of association has been measured as a function of concentration and temperature. At concentrations above 0.8 mol kg(-1) the concentration quotient, Q(A), has a relatively high and constant value of 0.06+/-0.02. The thermodynamic association constant and the enthalpy of formation for the contact ion pair are estimated to be K-A = 30+/-8, Delta H-O = (12+/-2) kJ . mol(-1) and Delta S-O = (70+/-10) J . K-1 . mol(-1).
PHREEQC version 2 is a computer program written in the C programming language that is designed to perform a wide variety of low-temperature aqueous geochemical calculations.
The high precision with which Mg isotope ratios can be measured using MC-ICPMS opens new opportunities for using Mg as a tracer in both terrestrial and extraterrestrial materials. A key advance is the ability to resolve kinetic from equilibrium mass-dependent fractionation processes. From these new data it appears that Mg in waters is related to mantle and crustal reservoirs of Mg by kinetic fractionation while Mg in carbonates is related in turn to the waters by equilibrium processes. Resolution of different fractionation laws is only possible for measurements of Mg in solution at present; laser ablation combined with MC-ICPMS (LAMC-ICPMS) is not yet sufficiently precise to measure different fractionation laws. Variability in Mg isotope ratios among ch ondritic meteorites and their constituents is dominated by mixing between a radiogenic CAI-like reservoir and a reservoir resembling ordinary chondrites. The mixing is evident in δ25Mg and δ26Mg, Al/Mg, and Δ17O values but will require substantiation by collection of more MC-IPMS Mg isotope data together with oxygen isotope and elemental compositions of bulk objects. Laser ablation combined with LA-MC-ICPMS provides a new dimension to the analysis of Mg isotopes in calcium aluminum-rich inclusions from primitive meteorites. Dispersion in 26Mg*-27 Al/24Mg evolution lines can be correlated with mass-dependent variations in δ 25Mg that distinguish open-system from closed-system processes. The ultimate product of such studies will be a better understanding of the chronological significance of variations in 26Mg* in these objects.
An objective of the research performed on this grant is the understanding of the detailed behavior of a variety of electron transfer processes. Theories were developed for (a) the rate of electron transfer between a reagent in one liquid phase and another in a second (immiscible) liquid or polymer, (b) the rate of long distance electron transfer in proteins, (c) charge transfers spectra in frozen media, (d) scanning tunneling microscopy (stm) of molecular adsorbates, and (e) analysis of models of solvents used in computer simulations of electron transfer, particularly examining the error incurred by their common neglect of the electronic and vibrational contributions of the solvent's dielectric response.
A unified theory of homogeneous and electrochemical electron‐transfer rates is developed using statistical mechanics. The treatment is a generalization of earlier papers of this series and is concerned with seeking a fairly broad basis for the quantitative correlations among chemical and electrochemical rate constants predicted in these earlier papers. The atomic motions inside the inner coordination shell of each reactant are treated as vibrations. The motions outside are treated by the ``particle description,'' which emphasizes the functional dependence of potential energy and free energy on molecular properties and which avoids, thereby, some unnecessary assumptions about the molecular interactions.
In its usual form activated complex theory assumes a quasiequilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced. The new equation for the transmission coefficient contains internal centrifugal terms. The fourth assumption can also be weakened and a rotational interaction included in the formalism. In applications of the rate equation use can be made of the recent finding that in the immediate vicinity of a saddle point or a minimum, a potential energy surface can be imitated in some major topographical respects by a surface permitting separation of variables. The separated wave equation for the reaction coordinate is then curvilinear because of the usual curvature of the path of steepest ascent to the saddle point. Calculations of transmission coefficients and rates can be made and compared with those obtainable from the usual one‐dimensional Cartesian‐like calculations on the one hand and with some based on the numerical integration of the n‐dimensional Schrödinger equation on the other. An application to a common three‐center problem is discussed.
Isopiestic vapor pressure measurements were made for {xZnCl2+(1−x)ZnSO4}(aq) solutions with ZnCl2 molality fractions of x=(0,0.3062,0.5730,0.7969, and1) at the temperature 298.15K, using KCl(aq) as the reference standard. These measurements
cover the water activity range 0.901–0.919≤a
w≤0.978. The experimental osmotic coefficients were used to evaluate the parameters of an extended ion-interaction (Pitzer)
model for these mixed electrolyte solutions. Asimilar analysis was made of the available activity data for ZnCl2(aq) at 298.15K, while assuming the presence of equilibrium amounts of ZnCl+(aq) ion-pairs, to derive the ion-interaction parameters for the hypothetical pure binary electrolytes (Zn2+,2Cl−) and (ZnCl+,Cl−). These parameters are required for the analysis of the mixture results. Although significant concentrations of higher-order
zinc chloride complexes may also be present in these solutions, it was possible to represent the osmotic coefficients accurately
by explicitly including only the predominant complex ZnCl+(aq) and the completely dissociated ions. The ionic activity coefficients and osmotic coefficients were calculated over the
investigated molality range using the evaluated extended Pitzer model parameters.
Isotope fractionation of electroplated Fe was measured as a function of applied electrochemical potential. As plating voltage was varied from −0.9 V to 2.0 V, the isotopic signature of the electroplated iron became depleted in heavy Fe, with δ56Fe values (relative to IRMM-14) ranging from −0.18(±0.02) to −2.290(±0.006) ‰, and corresponding δ57Fe values of −0.247(±0.014) and −3.354(±0.019) ‰. This study demonstrates that there is a voltage-dependent isotope fractionation associated with the reduction of iron. We show that Marcus’s theory for the kinetics of electron transfer can be extended to include the isotope effects of electron transfer, and that the extended theory accounts for the voltage dependence of Fe isotope fractionation. The magnitude of the electrochemically-induced fractionation is similar to that of Fe reduction by certain bacteria, suggesting that similar electrochemical processes may be responsible for biogeochemical Fe isotope effects. Charge transfer is a fundamental physicochemical process involving Fe as well as other transition metals with multiple isotopes. Partitioning of isotopes among elements with varying redox states holds promise as a tool in a wide range of the Earth and environmental sciences, biology, and industry.
Iron nucleation mechanisms from aqueous solutions onto vitreous carbon electrode were comparatively investigated in iron sulfate and iron chloride systems by utilizing the electrochemical techniques of cyclic voltammetry (cv) and chronoamperometry (ca), coupled with atomic force microscopy (AFM) studies. The investigated parameters were pH, scanning rate, iron concentration, deposition potential and temperature. It was found that iron nuclei population density decreased with increase of pH. On the other hand, the population density increased with increase of iron concentration and cathodic deposition potential. Increase of solution temperature resulted in the increase of nuclei population density in the sulfate system, while the dependence of nuclei population density on temperature in the chloride system was more complex. The experimental electrochemical data fitted the theoretical model describing progressive nucleation mechanisms, which was also confirmed by the AFM morphological studies. In addition, the atomic force microscopy was successful in determining the possible crystallographic orientations of electrodeposited iron nuclei.
The (56)Fe/(54)Fe of Fe-bearing phases precipitated in sedimentary environments varies by 2.5 per mil (delta(56)Fe values of +0.9 to -1. 6 per mil). In contrast, the (56)Fe/(54)Fe of Fe-bearing phases in igneous rocks from Earth and the moon does not vary measurably (delta(56)Fe = 0.0 +/- 0.3 per mil). Experiments with dissimilatory Fe-reducing bacteria of the genus Shewanella algae grown on a ferrihydrite substrate indicate that the delta(56)Fe of ferrous Fe in solution is isotopically lighter than the ferrihydrite substrate by 1.3 per mil. Therefore, the range in delta(56)Fe values of sedimentary rocks may reflect biogenic fractionation, and the isotopic composition of Fe may be used to trace the distribution of microorganisms in modern and ancient Earth.
Measurements of chromium (Cr) stable-isotope fractionation in laboratory experiments and natural waters show that lighter
isotopes reacted preferentially during Cr(VI) reduction by magnetite and sediments. The 53Cr/52Cr ratio of the product was 3.4 ± 0.1 per mil less than that of the reactant.53Cr/52Cr shifts in water samples indicate the extent of reduction, a critical process that renders toxic Cr(VI) in the environment
immobile and less toxic.
Isotope ratios and elemental concentrations were measured in aqueous solutions sampled at varying distances from sources of Fe or Zn ions. The measurements reveal fractionation of isotopes resulting from pure diffusion in solution. Our data demonstrate that diffusion alone can cause changes in (56)Fe/(54)Fe and (66)Zn/(64)Zn isotope ratios in excess of -0.3 per thousand. These findings thus confirm previous suspicions that transport processes contribute to observed variations in isotopic compositions. Diffusion must therefore be considered when attempting to make inferences from isotope measurements on samples originating from aqueous systems where concentration gradients may develop.
The oxygen fugacity of the mantle exerts a fundamental influence on mantle melting, volatile speciation, and the development of the atmosphere. However, its evolution through time is poorly understood. Changes in mantle oxidation state should be reflected in the Fe3+/Fe2+ of mantle minerals, and hence in stable iron isotope fractionation. Here it is shown that there are substantial (1.7 per mil) systematic variations in the iron isotope compositions (delta57/54Fe) of mantle spinels. Spinel delta57/54Fe values correlate with relative oxygen fugacity, Fe3+/sigmaFe, and chromium number, and provide a proxy of changes in mantle oxidation state, melting, and volatile recycling.
The response of the ocean redox state to the rise of atmospheric oxygen about 2.3 billion years ago (Ga) is a matter of controversy. Here we provide iron isotope evidence that the change in the ocean iron cycle occurred at the same time as the change in the atmospheric redox state. Variable and negative iron isotope values in pyrites older than about 2.3 Ga suggest that an iron-rich global ocean was strongly affected by the deposition of iron oxides. Between 2.3 and 1.8 Ga, positive iron isotope values of pyrite likely reflect an increase in the precipitation of iron sulfides relative to iron oxides in a redox stratified ocean.
Magmatic differentiation helps produce the chemical and petrographic diversity of terrestrial rocks. The extent to which magmatic differentiation fractionates nonradiogenic isotopes is uncertain for some elements. We report analyses of iron isotopes in basalts from Kilauea Iki lava lake, Hawaii. The iron isotopic compositions (56Fe/54Fe) of late-stagemeltveins are 0.2 permil (per thousand) greater than values for olivine cumulates. Olivine phenocrysts are up to 1.2 per thousand lighter than those of whole rocks. These results demonstrate that iron isotopes fractionate during magmatic differentiation at both whole-rock and crystal scales. This characteristic of iron relative to the characteristics of magnesium and lithium, for which no fractionation has been found, may be related to its complex redox chemistry in magmatic systems and makes iron a potential tool for studying planetary differentiation.
The development of numerical modeling of reactive transport relies on the availability of thermodynamic properties for the solid, surface, aqueous, and vapor species stable at the conditions of interest. The lack of experimental studies and comprehensive activity-composition models severely limits the predictive capabilities of these models in systems involving highly saline fluids or low-density volatile-rich fluids. X-ray absorption near-edge structure spectroscopy (XANES) is a powerful technique to study the speciation of transition metals in aqueous fluids: it is element specific; sensitive to the oxidation state of the metal, the ligand field and the coordination geometry of the complex; and it is suitable for measuring trace amounts of metals (< 1 wt%) in solutions over a wide pressure and temperature range. Formation constants for the aqueous complexes of transition metals can be determined from a series of XANES spectra obtained on solutions containing a constant amount of the metal of interest and variable concentrations of a ligand. The method relies on a non-linear, least-squares-fitting approach, with full distribution of species calculations based on a complete thermodynamic model for the experimental system under consideration. The technique is particularly suitable for following octahedral to tetrahedral transitions among weak chloride complexes of transition metals. The log K for the reaction Zn-(octahedral)(2+) + 4Cl(-) = ZnCl4(tetrahedral)2- at 25 degrees C is retrieved to be 0.1(6), within error of the accepted literature value. The same method applied to Fe2+-chloride complexes shows that the log K for the reaction Fe-(octahedral)(2+) + 4Cl(-) = Fe-4(2-)((tetrahedral)) increases from -6.2(6) at 25 degrees C to -2.9(3) at 150 degrees C . This study confirms that tetrahedral chloride complexes play an important role in Fe transport in hypersaline brines especially at elevated temperatures, and shows that XANES is well suited to study systems that may be difficult to study with other techniques.
The magnitude of equilibrium iron isotope fractionation between Fe(H2O)63+ and Fe(H2O)62+ is calculated using density functional theory (DFT) and compared to prior theoretical and experimental results. DFT is a quantum chemical approach that permits a priori estimation of all vibrational modes and frequencies of these complexes and the effects of isotopic substitution. This information is used to calculate reduced partition function ratios of the complexes (103 · ln(β)), and hence, the equilibrium isotope fractionation factor (103 · ln(α)). Solvent effects are considered using the polarization continuum model (PCM). DFT calculations predict fractionations of several per mil in 56Fe/54Fe favoring partitioning of heavy isotopes in the ferric complex. Quantitatively, 103 · ln(α) predicted at 22°C, ∼ 3 ‰, agrees with experimental determinations but is roughly half the size predicted by prior theoretical results using the Modified Urey-Bradley Force Field (MUBFF) model. Similar comparisons are seen at other temperatures. MUBFF makes a number of simplifying assumptions about molecular geometry and requires as input IR spectroscopic data. The difference between DFT and MUBFF results is primarily due to the difference between the DFT-predicted frequency for the ν4 mode (O-Fe-O deformation) of Fe(H2O)63+ and spectroscopic determinations of this frequency used as input for MUBFF models (185–190 cm−1 vs. 304 cm−1, respectively). Hence, DFT-PCM estimates of 103 · ln(β) for this complex are ∼ 20% smaller than MUBFF estimates. The DFT derived values can be used to refine predictions of equilibrium fractionation between ferric minerals and dissolved ferric iron, important for the interpretation of Fe isotope variations in ancient sediments. Our findings increase confidence in experimental determinations of the Fe(H2O)63+ − Fe(H2O)62+ fractionation factor and demonstrate the utility of DFT for applications in “heavy” stable isotope geochemistry.
The response of the ocean redox state to the rise of atmospheric oxygen about 2.3 billion years ago (Ga) is a matter of controversy.
Here we provide iron isotope evidence that the change in the ocean iron cycle occurred at the same time as the change in the
atmospheric redox state. Variable and negative iron isotope values in pyrites older than about 2.3 Ga suggest that an iron-rich
global ocean was strongly affected by the deposition of iron oxides. Between 2.3 and 1.8 Ga, positive iron isotope values
of pyrite likely reflect an increase in the precipitation of iron sulfides relative to iron oxides in a redox stratified ocean.
Summary The value of energy and entropy of activation, obtained by applying the theory of absolute reaction rates for the diffusion
of ·002 M ferric ion in 1-N sulphuric acid at varying temperatures, is found to be 9·8 K-cals. and −23·8 cal./degree respectively.
The negative value of entropy of activation can be explained due to stronger polarization of the solvent by the enhanced electrostatic
field, which is caused as a result of approaching of the two reactants of like sign towards each other.
Electron-transfer related isotope fractionation may produce large stable isotope geochemical signatures as a result of a variety of Earth processes, including biology, chemical weathering, fluid–rock interactions, and deep Earth redox reactions. In the laboratory, isotope fractionation at a charged electrode has been observed for electroplating of Fe and Zn; however these can arise from a variety of effects besides the electron transfer process. Here, we examine the effect of mass transport on observed isotope fractionation during potentiostatic electroplating of iron. We examine the observed isotope fractionation as a function of the ratio of the observed plating current to the mass-transport limited current (the Cottrell current). When the electroplating experiments are run at currents greater than the Cottrell current, the observed fractionation is ~−1.15(±0.40) ‰, and the extent of fractionation shows a tendency to decrease with increasing plating rate. When electroplating experiments are run at currents below the Cottrell current, observed fractionations are strongly dependent on the plating rate, with a maximum value of δ56Fe=−4.8. The data set demonstrates that mass transport to the electrode tends to attenuate a large fractionation factor associated with other, non-mass transport, processes at the electrode.
Theoretical activation energy of self-diffusion of zinc, chloride and chromate ions has been computed on the basis of the Onsager and Arrhenius equations. These values are compared with the experimentally determined ones for the self-diffusion of Zn2+ ions in the present work as well as previously reported values for self-diffusion of Cl– and CrO
4
2–
ions. A reasonably good agreement is observed between the two values.
Variations in the stable isotope abundances of transition metals have been observed in the geologic record and trying to understand and reconstruct the physical/environmental conditions that produced these signatures is an area of active research. It is clear that changes in oxidation state lead to large fractionations of the stable isotopes of many transition metals such as iron, suggesting that transition metal stable isotope signatures could be used as a paleo-redox proxy. However, the factors contributing to these observed stable isotope variations are poorly understood. Here we investigate how the kinetics of iron redox electrochemistry generates isotope fractionation. Through a combination of electrodeposition experiments and modeling of electrochemical processes including mass-transport, we show that electron transfer reactions are the cause of a large isotope separation, while mass transport-limited supply of reactant to the electrode attenuates the observed isotopic fractionation. Furthermore, the stable isotope composition of electroplated transition metals can be tuned in the laboratory by controlling parameters such as solution chemistry, reaction overpotential, and solution convection. These methods are potentially useful for generating isotopically-marked metal surfaces for tracking and forensic purposes. In addition, our studies will help interpret stable isotope data in terms of identifying underlying electron transfer processes in laboratory and natural samples.
The kinetics of iron electrodeposition from acid sulphate solutions onto a platinum electrode was investigated by means of stationary polarisation curves and electrochemical impedance spectroscopy. Together with interfacial pH data previously obtained, the effect of pH was analysed. The formation of at least three adsorbed intermediates at the cathode surface was evidenced in all pH values. The relative rate of their formation and its surface concentration depend on the solution pH as well as on the electrode potential. It is suggested that two of these species catalyses the H+ reduction whereas the other one may have a blocking effect on this reaction.
The largest Fe isotope fractionations occur during redox changes, as well as differences in bonding, but these are expressed only in natural environments in which significant quantities of Fe may be mobilized and separated. At the circumneutral pH of most low-temperature aqueous systems, Fe2+aq is the most common species for mobilizing Fe, and Fe2+aq has low 56Fe/54Fe ratios relative to Fe3+-bearing minerals. Of the variety of abiologic and biologic processes that involve redox or bonding changes, microbial Fe3+ reduction produces the largest quantities of isotopically distinct Fe by several orders of magnitude relative to abiologic processes and hence plays a major role in producing Fe isotope variations on Earth. In modern Earth, the mass of Fe cycled through redox boundaries is small, but in the Archean it was much larger, reflecting juxtaposition of large inventories of Fe2+ and Fe3+. Development of photosynthesis produced large quantities of Fe3+ and organic carbon that fueled a major expansion in mi...
It is pointed out that the possibility of chemical separation of isotopes is a quantum effect. This permits a direct calculation of the difference in the free energies of two isotopic molecules. Tables and approximation methods are given which permit a rapid calculation of equilibrium constants if the frequency shifts on isotopic substitution are known. Several applications are discussed.
Here we compare new experimental studies with theoretical predictions of equilibrium iron isotopic fractionation among aqueous ferric chloride complexes (Fe(H2O)63+, FeCl(H2O)52+, FeCl2(H2O)4+, FeCl3 (H2O)3, and FeCl4–), using the Fe–Cl–H2O system as a simple, easily-modeled example of the larger variety of iron–ligand compounds, such as chlorides, sulfides, simple organic acids, and siderophores. Isotopic fractionation (56Fe/54Fe) among naturally occuring iron-bearing species at Earth surface temperatures (up to ∼3‰) is usually attributed to redox effects in the environment. However, theoretical modeling of reduced isotopic partition functions among iron-bearing species in solution also predicts fractionations of similar magnitude due to non-redox changes in speciation (i.e., ligand bond strength and coordination number). In the present study, fractionations are measured in a series of low pH ([H+] = 5 M) solutions of ferric chloride (total Fe = 0.0749 mol/L) at chlorinities ranging from 0.5 to 5.0 mol/L. Advantage is taken of the unique solubility of FeCl4– in immiscible diethyl ether to create a separate spectator phase, used to monitor changing fractionation in the aqueous solution. Δ56Feaq-eth = δ56Fe (total Fe remaining in aqueous phase)−δ56Fe (FeCl4– in ether phase) is determined for each solution via MC-ICPMS analysis.
Anthropogenic sources account for much of the zinc (Zn) in the environment. Constraining the isotopic composition of anthropogenic Zn is therefore essential to understanding the environmental biogeochemical cycling of Zn isotopes. This study examines the isotopic variability in several different categories of anthropogenic Zn. Pure Zn metal and Zn dust are the raw materials used in many Zn-containing products. We have measured δ 66 Zn for Zn dust purified by thermal distillation, electrochemically purified Zn metal, and US pennies which are made from the most common grade of Zn metal (Special High Grade). Zn in galvanized steel and electroplated hardware was studied because this is a common use of Zn, and Zn in these products may be easily released into the environment through corrosion. Vitamins were studied because they are more highly purified than typical Zn metals and are made from processed chemical compounds such as Zn oxide or Zn gluconate. The isotopic composition of samples measured in this study are as follows (reported as δ 66 Zn compared to Lyon-JMC Zn): laboratory standards (seven samples): −9.15‰ to +0.17‰; Zn metal dust purified by thermal distillation (three samples): +0.09‰ to +0.19‰; Zn metal shot purified by electrochemically (one sample): +0.22‰; Special High Grade Zn, as represented in US pennies (six samples): +0.14‰ to +0.31‰; galvanized steel (three samples): +0.12‰ to +0.58‰; electroplated hardware (three samples): −0.56‰ to −0.20‰; and health products (five samples): +0.09‰ to +0.24‰. Based on these results, we suggest that the isotopic composition of "common" anthropogenic Zn products ranges from +0.1‰ to +0.3‰. All samples studied here had δ 66 Zn values within this range except four laboratory standards, all electroplated hardware samples, and a single galvanized steel sample. The isotopic range for common anthropogenic Zn is much smaller than the total δ 66 Zn range found in Zn ore-field hydrothermal samples, demonstrating the effects of Zn isotope homogenization during ore processing and purification. Laboratory standards may have anomalously light δ 66 Zn values because they undergo extra purification steps and Zn recovery during these steps is not quantitative. Electroplated hardware was also isotopically light, consistent with previous studies showing that lighter isotopes are electroplated more quickly than heavy isotopes. Our results suggest that isotopically heavy Zn may be incorporated into the waste stream during the electroplating process. By defining the range of δ 66 Zn values that is typical for some common Zn products, and discovering some kinds of products that fall outside this range, we will be better able to use Zn isotopes to trace different anthropogenic Zn sources.
Four or five sets of ab initio models, including Unrestricted Hartree Fock (UHF) and hybrid Density Functional Theory (DFT) are calculated for each species in a series of aqueous ferric aquo-chloro complexes: , , , FeCl3(H2O)3, FeCl3(H2O)2, , FeCl5H2O²⁻, , ) in order to determine the relative isotopic fractionation among the complexes, to compare the results of different models for the same complexes, to examine factors that influence the magnitude of the isotopic fractionation, and to compare bond-partner-driven fractionation with redox-driven fractionation.
The magnitude and direction of equilibrium iron-isotope (54Fe–56Fe) fractionations among simple iron-bearing complexes and α-Fe metal are calculated using a combination of force-field modeling and existing infrared, Raman, and inelastic neutron scattering measurements of vibrational frequencies. Fractionations of up to several per mil are predicted between complexes in which iron is bonded to different ligands (i.e. 4 per mil for [Fe(H2O)6]3+ vs. [FeCl4]− at 25°C). Similar fractionations are predicted between the different oxidation states of iron. The heavy iron isotopes will be concentrated in complexes with high-frequency metal-ligand stretching vibrations, which means that 56Fe/54Fe will be higher in complexes with strongly bonding ligands such as CN− and H2O relative to complexes with weakly bonding ligands like Cl− and Br−. 56Fe/54Fe will also usually be higher in Fe(III) compounds than in Fe(II)-bearing species; the Fe(II) and Fe(III) hexacyano complexes are exceptions to this rule of thumb. Heavy iron isotopes will be concentrated in sites of 4-fold coordination relative to 6-fold coordination. Model results for a ferrous hexacyanide complex, [Fe(CN)6]4−, are in agreement with predictions based on Mössbauer spectra (Polyakov, 1997), suggesting that both approaches give reasonable estimates of iron-isotope partitioning behavior.
The stable isotope geochemistry of Fe has attracted intense interest in the past five years. This interest was originally motivated by the possible use of Fe isotopes in biosignature applications, particularly in sediments from the ancient Earth or Mars. This application is still being developed, with particular attention to fractionation mechanisms. Understanding such mechanisms should also provide new insights into the environmental biogeochemistry of Fe. At the same time, the Fe isotope system holds promise for other exciting frontiers, including applications in oceanography, solid Earth geochemistry and biomedicine. Such applications will be increasingly attractive as Fe isotope analysis becomes routine.
Ultraviolet absorption spectra of solutions in the system FeC12-HCl-H2O with chloride concentrations ranging from 0.01 to 3.4 m and Fe(II) concentrations ranging from 0.005 to 0.025 m have been measured at 25, 50, 100, 150, and 200°C and the equilibrium saturation vapor pressure of the system. Non-linear least squares regression was used to estimate cumulative thermodynamic association constants and molar absorptivities. At 25, 50, and 100°C, only Fe2+ and FeCl+ are detectable, whereas at higher temperatures a minor concentration of a third species, interpreted to be FeCl02, starts to contribute substantially to total absorbance. Recommended values of the association constants, β1 and β2, for the equilibria Fe2+ Cl−1 = FeCl+ and Fe2+ + 2C1− = FeCl02, respectively, (and their estimated maximum uncertainty range) are as follows: View Within ArticleIn combination with published thermodynamic data for the Fe-S-O-H system, the equilibrium formation constants are used to calculate solubilities of selected Fe mineral assemblages in NaCl-rich hydrothermal solutions. The results are in satisfactory agreement with published analytical data from basinal brines and geothermal fluids.
Rapid crystal growth can lead to disequilibrium uptake of growth-medium components whose diffusivities limit their dispersal near an advancing crystal interface. The recent documentation of an isotope mass effect on diffusion raises the possibility that even isotope ratios in crystals may be subject to this effect. Building upon existing 1-dimensional treatments, we describe a numerical modeling approach in which a spherical grain grows at the center of an infinite spherical medium of predetermined composition. Local equilibrium at the interface between the crystal and the growth medium is assumed, but the concentration of the species of interest in the growth medium is allowed to vary near the interface as a consequence of slow diffusion combined with rejection from (or incorporation within) the growing crystal. The disequilibrium uptake of elements and isotopes depends upon the ratio of crystal growth rate (R) to diffusivity in the growth medium (D). Conditions of fast mineral growth in a viscous magma—e.g., in lava lakes or small igneous bodies—result in accumulation of elements with K << 1 (or depletion of elements with K >> 1) near the growing mineral interface, forming a compositional boundary layer in the growth medium. In a static system, the magnitude of this compositional perturbation depends critically upon the diffusivity of the element or isotope of interest in the growth medium. If the system is dynamic—i.e., experiencing free or forced convection—then the vigor of convection also affects behavior. Significant fractionation of elements and isotopes is predicted to occur within the boundary layer during progressive crystal growth because diffusion rates of individual elements vary with size and charge and those of isotopes of the same element depend on their masses. Local equilibrium at the interface between the crystal and its growth medium means that a fast-growing crystal will record this fractionation in its resulting radial concentration profile. If the boundary-layer thickness, BL, is small (say, < 100 μm) and the equilibrium partition coefficient, K, is < 0.5, then a first-order estimate of the steady-state isotopic fractionation in a growing crystal is given bywhere DA and DB are the diffusivities of the faster and slower species in the growth medium and δ is the deviation from the equilibrium isotope ratio in parts per thousand. For isotopes of a single element, DA and DB will generally differ by < 1%, but plausible R/D ratios can nevertheless lead to deviations from equilibrium between the crystal and the growth medium of up to ~ 3‰. The model may bear on disequilibrium crystal-growth phenomena in a variety of geologic settings—including element- and isotopic profiles in crystals of both igneous and metamorphic rocks. It is suggested that compositional core to rim profile of a crystal may be a proxy for the near surface composition of the growth medium during crystal growth. Isotopic effects are discussed in detail because these have not been addressed previously; igneous systems are emphasized because higher crystal growth rates are more conducive to disequilibrium (including in the compositions of melt inclusions).
Large equilibrium isotope fractionation occurs between Fe(III) and Fe(II) in very dilute (≤22 mM Cl−) aqueous solutions, reflecting significant differences in bonding environments. Separation of Fe(III) and Fe(II) is attained by rapid and complete precipitation of Fe(III) through carbonate addition, followed by separation of supernatant and ferric precipitate; experiments reported here produce an equilibrium ΔFe(III)–Fe(II)=+2.75±0.15‰ for 56Fe/54Fe at room temperature (22±2°C). The timescales required for attainment of isotopic equilibrium have been determined by parallel isotope tracer experiments using 57Fe-enriched iron, which are best fitted by a second-order rate law, with K=0.18±0.03 s−1. Based on this rate constant, ∼15–20% isotopic exchange is estimated to have occurred during Fe(III)–Fe(II) separation, which contributes <0.10‰ uncertainty to the equilibrium ΔFe(III)–Fe(II). Under the experimental conditions used in this study, >97% Fe(II) exists as [FeII(H2O)6]2+, and >82% Fe(III) exists as [FeIII(H2O)6]3+ and [FeIII(H2O)6−n(OH)n]3−n; assuming these are the dominant species, the measured Fe isotope fractionation is approximately half that predicted by Schauble et al. [Geochim. Cosmochim. Acta 65 (2001) 2487–2497] at 20–25°C. Although this discrepancy may be due in part to the experimentally unknown isotopic effects of chloride interacting with Fe-hexaquo or Fe-hydroxide complexes, or directly bonded to Fe, there still appears to be at this stage a >1‰ difference between prediction and experiment.
The mass-dependent fractionation laws that describe the partitioning of isotopes are different for kinetic and equilibrium reactions. These laws are characterized by the exponent relating the fractionation factors for two isotope ratios such that α2/1 = α3/1β. The exponent β for equilibrium exchange is (1/m1 − 1/m2)/(1/m1 − 1/m3), where mi are the atomic masses and m1 < m2 < m3. For kinetic fractionation, the masses used to evaluate β depend upon the isotopic species in motion. Reduced masses apply for breaking bonds whereas molecular or atomic masses apply for transport processes. In each case the functional form of the kinetic β is ln(M1/M2)/ln(M1/M3), where Mi are the reduced, molecular, or atomic masses. New high-precision Mg isotope ratio data confirm that the distinct equilibrium and kinetic fractionation laws can be resolved for changes in isotope ratios of only 3‰ per amu. The variability in mass-dependent fractionation laws is sufficient to explain the negative Δ17O of tropospheric O2 relative to rocks and differences in Δ17O between carbonate, hydroxyl, and anhydrous silicate in Martian meteorites. (For simplicity, we use integer amu values for masses when evaluating β throughout this paper.)
Equilibrium and kinetic Fe isotope fractionation between aqueous ferrous and ferric species measured over a range of chloride concentrations (0, 11, 110 mM Cl−) and at two temperatures (0 and 22°C) indicate that Fe isotope fractionation is a function of temperature, but independent of chloride contents over the range studied. Using 57Fe-enriched tracer experiments the kinetics of isotopic exchange can be fit by a second-order rate equation, or a first-order equation with respect to both ferrous and ferric iron. The exchange is rapid at 22°C, ∼60–80% complete within 5 seconds, whereas at 0°C, exchange rates are about an order of magnitude slower. Isotopic exchange rates vary with chloride contents, where ferrous-ferric isotope exchange rates were ∼25 to 40% slower in the 11 mM HCl solution compared to the 0 mM Cl− (∼10 mM HNO3) solutions; isotope exchange rates are comparable in the 0 and 110 mM Cl− solutions.
Redox processes are ubiquitous in Earth science and are often associated with large isotope fractionations. In a previous study, voltage-dependent amplification of stable isotope fractionation was observed for an Fe reduction process. Here, we describe experiments showing a similar effect for a second transition metal, zinc. After electrochemical reduction, the composition of plated Zn metal is enriched in the light isotope (64Zn) with respect to the Zn2+ leftover in solution, with a voltage-dependent fractionation factor. Results from voltage-dependent electroplating experiments are in good agreement with a second data set following equilibrium fractional isotope evolution of Zn isotopes during an electroplating process which stepwise removes most of the Zn from the aqueous reservoir. Taken together, the results indicate a voltage-dependent isotope fractionation (in permil) of 66Zn with respect to 64Zn to be equal to −3.45 to 1.71 V. The negative slope trend is in contrast with previously published results on iron isotope fractionation during electroplating which shows a positive slope. These results are interpreted using an extension of Marcus theory, which predicts isotope fractionations as a function of driving force in an electrochemical system. Taken together with observations of natural fractionation of redox-sensitive and non redox-active elements, our modified Marcus theory provides a framework for quantitatively predicting transition metal isotope geochemical signatures during environmentally relevant redox processes in terms of simple energetic parameters.
Experimental diffusion couples were used to study chemical diffusion between molten rhyolite and basalt with special emphasis on the associated fractionation of calcium and lithium isotopes. Diffusion couples were made by juxtaposing firmly packed powders of a natural basalt (SUNY MORB) and a natural rhyolite (Lake County Obsidian) and then annealing them in a piston cylinder apparatus for times ranging from 0.1 to 15.7 h, temperatures of 1350–1450°C, and pressures of 1.2–1.3 GPa. Profiles of the major elements and many trace elements were measured on the recovered quenched glasses. The diffusivities of all elements except lithium were found to be remarkably similar, while the diffusivity of lithium was two to three orders of magnitude larger than that of any of the other elements measured. Chemical diffusion of calcium from molten basalt into rhyolite was driven by a concentration ratio of ∼18 and produced a fractionation of 44Ca from 40Ca of about 6 ‰. Because of the relatively low concentration of lithium in the natural starting materials a small amount of spodumene (LiAlSi2O6) was added to the basalt in order to increase the concentration difference between basalt and rhyolite, which was expected to increase the magnitude of diffusive isotopic fractionation of lithium. The concentration ratio between Li-doped basalt and natural rhyolite was ∼15 and the resulting diffusion of lithium into the rhyolite fractionated 7Li from 6Li by about 40‰. We anticipate that several other major rock-forming elements such as magnesium, iron and potassium will also exhibit similarly larger isotopic fractionation whenever they diffuse between natural melts with sufficiently large differences in the abundance of these elements.
The redox potential of ZoBell's solution, consisting of 3.33 × 10−3 molar K4Fe(CN)6, 3.33 × 10−3 molar K3Fe(CN)6 and 0.10 molar KCl, has been measured by a polished platinum electrode vs a saturated KCl, Ag/AgCl reference electrode. Measurements in the temperature range 8–85°C fit the equation where t is in degrees Celsius. Evaluation of literature data was necessary to obtain a reliable value for the Ag/AgCl half-cell reference potential as a function of temperature. Combining the measurements from this study with the literature evaluation of the Ag/AgCl reference potential yields the temperature dependent potential for ZoBell's solution: relative to the standard hydrogen potential. From these data the enthalpy, entropy, free energy and heat capacity for the ferro-ferricyanide redox couple have been calculated. The temperature equation for the potential of ZoBell's solution may be used for checking potentiometric equipment in the determination of the redox potential of natural waters.
A large electrochemical isotopic effect is observed upon the electrodeposition of lithium from solutions of propylene carbonate producing isotopically light metal deposits. The magnitude of fractionation is controlled by the applied overpotential and is largest close to equilibrium. Calculated partition function ratios for tetrahedrally coordinated lithium complexes and metallic lithium predict an equilibrium fractionation close to that measured experimentally.
Rouxel et al. (Reports, 18 February 2005, p. 1088) argued that changes in the iron isotopic composition of sedimentary sulfides reflect
changes in the oxidation state of the atmosphere-ocean system between 2.3 and 1.8 million years ago. We show that misinterpretations
of the origins of these minerals undermine their conclusions.
Variations in stable isotope ratios of redox sensitive elements are often used to understand redox processes occurring near the Earth's surface. Presented here are measurements of mass-dependent U isotope fractionation induced by U(VI) reduction by zerovalent iron (Fe0) and bacteria under controlled pH and HCO3- conditions. In abiotic experiments, Fe0 reduced U(VI), but the reaction failed to induce an analytically significant isotopic fractionation. Bacterial reduction experiments using Geobacter sulfurreducens and Anaeromyxobacter dehalogenans reduced dissolved U(VI) and caused enrichment of 238U relative to 235U in the remaining U(VI). Enrichmentfactors (epsilon) calculated using a Rayleigh distillation model are -0.31% per hundred and -0.34% per hundred for G. sulfurreducens and A. dehalogenans, respectively, under identical experimental conditions. Further studies are required to determine the range of possible values for 238U/235U fractionation factors under a variety of experimental conditions before broad application of these results is possible. However, the measurable variations in delta(5238)U show promise as indicators of reduction for future studies of groundwater contamination, geochronology, U ore deposit formation, and U biogeochemical cycling.