Veniamin B. Polyakov

The use of Mössbauer spectroscopy in stable isotope geochemistry

Abstract The use of Mossbauer spectroscopic data on the second-order Doppler (SOD) shift to determine the reduced isotopic partition function ratio (β-factor) has been considered by the example of iron. Using the relation between the β-factor and the SOD shift in Mossbauer spectra, the temperature dependence of the iron β-factors for a wide range of minerals has been evaluated from experimental data on the SOD shift. It is shown that the β-factors of Fe 3+ ions are considerably higher than those of Fe 2+ . The curve describing the temperature dependence of the β-factor for native iron is the boundary separating fields that are typical for ferric and ferrous ions. The value of the iron β-factor increases with increasing covalence of chemical bonds. In the case of covalent chemical bonds, the iron β-factor achieves high values even for ferrous compounds. Possible iron isotope geothermometers magnetite–siderite and pyrite–siderite have been calibrated 10 3 ln β magnetite–siderite =0.881 776 x −0.544 105×10 −2 x 2 +0.425 639 10 −4 x 3 −0.352 191×10 −5 x 4 , 10 3 ln β pyrite–siderite =0.913 717 x −0.557 721×10 −2 x 2 +0.424 146×10 −4 x 3 −0.334 281×10 −5 x 4 , where x = 10 6 / T 2 , T is absolute temperature, ln β relates to 57 Fe/ 54 Fe fractionation. At equilibrium, a small iron isotopic shift between magnetite and pyrite along with high iron isotopic shifts between magnetite and siderite and between pyrite and siderite should be observed. A significant effect (about 7‰ at 300 K) of the aluminum substitution on the iron β-factor in hematite has been evaluated from the appropriate data on the SOD shift in Mossbauer spectra. The analogous effect of the Co-substitution in magnetite is lower (≈3.0‰ at 300 K). A new method of evaluation of the β-factor for isotopes traditionally used in geochemical studies like sulfur, oxygen, etc., is suggested. The method uses experimental Mossbauer data on the SOD shift and calorimetric data on the heat capacity. The method can be applied to compounds consisting of two chemical elements (like oxides, sulfides) if one of them has a Mossbauer-sensitive isotope. Using the new method, the β 34 S-factor of pyrite and the β 18 O-factor of hematite have been determined: 10 3 ln β pyrite =(1.5997±0.0419) x −(6.7744±0.4279)×10 −3 x 2 +(3.8254±0.5682)×10 −5 x 3 , 10 3 ln β hematite =(5.7215±0.3891) x −(0.029 41±0.004 49) x 2 .

Effect of pressure on equilibrium isotopic fractionation

The effect of pressure on the equilibrium isotope fractionation is examined theoretically. The calculation technique is developed, using the quasi-harmonic approximation for solids. The formula connecting the pressure derivative of the β-factor (reduced isotopic partition function ratio) and its temperature derivative is obtained. The application of the technique to some silicates (quartz, albite, enstatite, pyrope, grossular, forsterite), rutile and calcite (16O-18O fractionation), graphite-calcite-diamond (12C-13C fractionation) and brucite-water (H-D fractionation) shows that pressures of tens of kbars may produce a measurable effect on the equilibrium isotope fractionation and even change the sign of the isotopic shift. Estimation of the pressure effect is important for correct interpretation of high pressure experimental isotopic data and for correct calculation of equilibrium isotopic constants.

Equilibrium Iron Isotope Fractionation at Core-Mantle Boundary Conditions

The equilibrium iron isotope fractionation between lower mantle minerals and metallic iron at core-mantle boundary conditions can be evaluated from the high-pressure 57Fe partial vibrational density of states determined by synchrotron inelastic nuclear resonant x-ray scattering spectroscopy using a diamond anvil. Ferropericlase [(Mg,Fe)O] and (Fe,Mg)SiO3–post-perovskite are enriched in heavy iron isotopes relative to metallic iron at ultrahigh pressures, as opposed to the equilibrium iron isotope fractionation between these compounds at low pressure. The enrichment of Earth and Moon basalts in heavy iron isotopes relative to those from Mars and asteroid Vesta can be explained by the equilibrium iron isotope fractionation during the segregation of Earths core and the assumption that Earth was already differentiated before the Moon-forming “giant impact.”

Equilibrium fractionation of the iron isotopes: Estimation from Mössbauer spectroscopy data

Abstract A close relationship between the second-order Doppler shift (SOD) of the Mossbauer resonant recoil-free frequency and the equilibrium stable isotope fractionation has been established. The reduced isotopic partition function ratios (β-factors) of the iron isotopes for a set of substances has been evaluated from appropriate experimental data on the SOD. The extent of the equilibrium stable iron isotope fractionation has been estimated. The equilibrium fractionation of the iron isotopes is notable at temperatures up to 1000 K and may be essential not only at surface conditions but in geothermal and metamorphic processes in the Earths crust as well. This opens up new possibilities for applications of iron isotope fractionation in geochemistry and cosmochemistry.

Experimental and theoretical study of pressure effects on hydrogen isotope fractionation in the system brucite-water at elevated temperatures

Abstract A detailed, systematic experimental and theoretical study was conducted to investigate the effect of pressure on equilibrium D/H fractionation between brucite (Mg(OH)2) and water at temperatures from 200 to 600°C and pressures up to 800 MPa. A fine-grained brucite was isotopically exchanged with excess amounts of water, and equilibrium D/H fractionation factors were calculated by means of the partial isotope exchange method. Our experiments unambiguously demonstrated that the D/H fractionation factor between brucite and water increased by 4.4 to 12.4‰ with increasing pressure to 300 or 800 MPa at all the temperatures investigated. The observed increases are linear with the density of water under experimental conditions. We calculated the pressure effects on the reduced partition function ratios (β-factor) of brucite (300–800 K and P ≤ 800 MPa) and water (400–600°C and P ≤ 100 MPa), employing a statistical-mechanical method similar to that developed by Kieffer (1982) and a simple thermodynamic method based on the molar volumes of normal and heavy waters, respectively. Our theoretical calculations showed that the reduced partition function ratio of brucite increases linearly with pressure at a given temperature (as much as 12.6‰ at 300 K and 800 MPa). The magnitude of the pressure effects rapidly decreases with increasing temperature. On the other hand, the β-factor of water decreases 4 to 5‰ with increasing pressure to 100 MPa at 400 to 600°C. Overall D/H isotope pressure effects combined from the separate calculations on brucite and water are in excellent agreement with the experimental results under the same temperature-pressure range. Our calculations also suggest that under the current experimental conditions, the magnitude of the isotope pressure effects is much larger on water than brucite. Thus, the observed pressure effects on D/H fractionation are common to other systems involving water. It is very likely that under some geologic conditions, pressure is an important variable in controlling D/H partitioning.

On anharmonic and pressure corrections to the equilibrium isotopic constants for minerals

Abstract Specifies of the calculations of the reduced isotopic partition function ratios (β-factor) of minerals are discussed. Comparative calculations in the framework of the fully harmonic, quasi-harmonic, and intrinsic anharmonic approximations show minor anharmonic corrections to the harmonic values of the β-factor. In the case of calcite, the difference between the fully harmonic and intrinsic anharmonic values of 10 3 lnβ varies from 0.60 at 300 K to 0.37 at 1200 K and is close to typical values of the anharmonic correction in gas molecules. A new treatment for calculating isotopic effects in molar volumes of minerals and pressure effects on their β-factors is developed on the basis of the Mie-Gruneisen equation of state. There is no significant difference between the quasi-harmonic and intrinsic harmonic values of (∂lnβ/∂ P ) T . For calcite, the pressure derivative of the β-factor is positive, decreases monotonically with temperature, and becomes small at T ∼ 1000 K (10 3 (∂lnβ/ ∂P ) T ≈ 0.1–0.15 GPa −1 ). These results contradict the large anharmonic and pressure effects to the β-factor of calcite calculated by Gillet et al. (1996) as well as their conclusion that the pressure correction to the β-factor of calcite is negative at higher temperatures and increases in its absolute value with increasing temperature.

Carbon-bearing iron phases and the carbon isotope composition of the deep Earth

Significance Due to its bonding environments, carbon can make up numerous compounds with many other elements. However, the abundance and dynamics of carbon in the deep Earth remains uncertain due to its complex behavior during the primary accretion and differentiation of the Earth in its early history. The naturally occurring stable isotopes of carbon serve as a useful tracer to study the carbon cycle, both on the surface and in the deep Earth. Here, a new model is presented for understanding a first-order carbon cycle within the Earth, including the sources of the building blocks and core formation processes. Low carbon isotope compositions of carbonaceous materials from ancient rocks have to be used with a caution as biosignatures. The carbon budget and dynamics of the Earth’s interior, including the core, are currently very poorly understood. Diamond-bearing, mantle-derived rocks show a very well defined peak at δ13C ≈ −5 ± 3‰ with a very broad distribution to lower values (∼−40‰). The processes that have produced the wide δ13C distributions to the observed low δ13C values in the deep Earth have been extensively debated, but few viable models have been proposed. Here, we present a model for understanding carbon isotope distributions within the deep Earth, involving Fe−C phases (Fe carbides and C dissolved in Fe−Ni metal). Our theoretical calculations show that Fe and Si carbides can be significantly depleted in 13C relative to other C-bearing materials even at mantle temperatures. Thus, the redox freezing and melting cycles of lithosphere via subduction upwelling in the deep Earth that involve the Fe−C phases can readily produce diamond with the observed low δ13C values. The sharp contrast in the δ13C distributions of peridotitic and eclogitic diamonds may reflect differences in their carbon cycles, controlled by the evolution of geodynamical processes around 2.5–3 Ga. Our model also predicts that the core contains C with low δ13C values and that an average δ13C value of the bulk Earth could be much lower than ∼−5‰, consistent with those of chondrites and other planetary body. The heterogeneous and depleted δ13C values of the deep Earth have implications, not only for its accretion−differentiation history but also for carbon isotope biosignatures for early life on the Earth.

Simulation of Molecular Mass Distributions and Evaluation of O 2- Concentrations in Polymerized Silicate Melts

A new statistical model is proposed for the molecular mass distributions (MMD) of polymerized anions in silicate melts. The model is based on the known distribution of Qn species in the MeO-Me2O-SiO2 system. In this model, chain and ring complexes are regarded as a random series of Qn structons with various concentrations of bridging bonds (1 ≤ n ≤ 4, Q0 corresponds to SiO44−). This approach makes it possible to estimate the probability of formation of various ensembles of polymer species corresponding to the general formula (SiiO3i+1−j)2(i+1−j)−, where i is the size of the ion, and j is the cyclization number of intrachain bonds. The statistical model is utilized in the STRUCTON computer model, which makes use of the Monte Carlo method and is intended for the calculation of the composition and proportions of polyanions at a specified degree of polymerization of silicate melts (STRUCTON, version 1.2; 2007). Using this program, we simulated 1200 MMD for polyanions in the range of 0.52 ≤ p ≤98, where p is the fraction of nonbridging bonds in the silicon-oxygen matrix. The average number of types of anions in this range was determined to increase from three (SiO44−, Si2O76−, and Si3O108−) to 153, and their average size increases from 1 to 7.2. A special option of the STRUCTON program combines MMD reconstructions in silicate melts with the formalism of the Toop-Samis model, which enables the calculation of the mole fraction of the O2− ion relative to all anions in melts of specified composition. It is demonstrated that, with regard for the distribution and average size of anion complexes, the concentration of the O2− ion in the MeO-SiO2 system is characterized by two extrema: a minimum at 40–45 mol % SiO2, which corresponds to the initial stages of the gelenization of the polycondensated silicate matrix, and a maximum, which is predicted for the range of 60–80 mol % SiO2.

On algorithm for the calculation of the equilibrium composition of water-salt systems on the basis of the Pitzer model

Calculating the equilibrium composition of systems under given conditions (usually, temperature and pressure) is a core in the majority of the existing computer models of geochemical processes. Recently, Shvarov [1] investigated the thermodynamic consistency of the models of nonideal aqueous solutions that are used in geochemical calculations. He distinguished necessary and sufficient conditions for the thermodynamic consistency of the physicochemical models of real (nonideal) solutions and presented particular examples of errors appearing when these criteria are not met. In addition, Shvarov [1] claimed that the models that are currently used for concentrated electrolyte solutions are thermodynamically inconsistent. Such a pessimistic conclusion is related to a large extent to the fact that Shvarov’s [1] analysis was limited to the Debye‐Huckel model, which is applicable to diluted aqueous solutions, and its empirical modifications aimed at extending to concentrated aqueous solutions. Indeed, such models are thermodynamically inconsistent. However, models have been developed allowing adequate description of the behavior of concentrated aqueous solutions. One of them is the wellknown Pitzer model [2, 3] proposed for the description of the properties of dense electrolyte solutions in a wide range of temperatures, pressures, and compositions. The Pitzer model was developed on the basis of the Gibbs method and is, consequently, thermodynamically sound. If correct numerical algorithms are employed, the Pitzer model allows for the calculation of chemical equilibria in water‐ salt systems within a wide concentration range. The Pitzer model is an example of the rigorous statistical mechanical description of a multicomponent fluid system and the calculation of free energy by the Gibbs method. The derivation of an expression for free energy in the Pitzer model was described in detail in [2, 3], and only its basic principles are shortly discussed here. It is based on the approach developed by McMillan and Mayer [4], who described interactions between dissolved species within the mean field approximation and ignored the detailed description of interactions between individual particles. It should be emphasized that these approximations concern interactions between particles, i.e., a microscopic Hamiltonian. The free energy function is further derived in accordance with the statistical method of Gibbs using the methods of group expansion of Mayer [5, 6] and divergence elimination [6, 7] for the calculation of the configuration integrals of the long-range potentials of electrostatic interactions. Eventually, the excess Gibbs free energy of solution is given in the Pitzer model, after transition from volume concentrations to molalities, as [2]

Analysis of disproportionation of Q n structons in the simulation of the structure of melts in the Na 2 O-SiO 2 system

A new version of the STRUCTON-1.2 computer program (2009) has been presented. The program combines the algorithm for calculating real distributions of Qn structons in binary silicate melts (with allowance made for their disproportionation) and the statistical simulation of molecular-mass distributions of polymerized ions at different temperatures. This model has been used to perform test calculations for two melts in the Na2O-SiO2 system (Na6Si2O7, Na6Si3O9). The results of the calculations have made it possible to trace variations in the set and concentrations of chain and ring silicon-oxygen complexes with a decrease in the temperature in the order: stochastic molecular-mass → distribution molecular-mass distribution at T = 2000 K → molecular-mass distribution at the liquidus temperature. The main result of these calculations is that the dominant species of silicon-oxygen anions at the liquidus temperatures (in contrast to the stochastic distributions) exactly correspond to the stoichiometry of the initial melts: the Si2O76− chain anions and (SinO3n)3n− ring complexes are dominant in the Na6Si2O7 and Na6Si3O9 melts, respectively. It has been established that, with a decrease in the temperature, the average size of polymer complexes varies weakly in the Na6Si2O7 melt but increases by a factor of approximately 1.5 in the metasilicate system.