Methods of local analysis for study of carbon in silicates: Nuclear microprobe analysis and secondary ion mass spectrometry

New approaches are proposed to analyze the content, distribution, and diffusion of carbon in silicates using nuclear microprobe analysis and secondary-ion mass spectrometry (SIMS). Techniques based on the nuclear reaction ¹²C(d,p)¹³C were developed to determine the coefficients of radiation-enhanced carbon diffusion in olivine at 300–370 K and deuteron doses that are comparable in terms of defect formation with those of α-particles generated by the decay of uranium and thorium isotopes for ~400 Ma (olivine age). The coefficients of thermal (D _th) and radiation-enhanced (D _rad) carbon diffusion in synthetic forsterite were compared to those of natural olivines from alkaline basalt nodule (Shevaryn Tsaram volcano, Mongolia). It is demonstrated that the diffusion coefficients strongly depends on the migration mechanisms of carbon atoms in crystals. The developed techniques and software package for SIMS determination of carbon distribution in silicates allowed us to study simultaneously the carbon and hydrogen distribution in a glass vein of the Chelyabinsk meteorite. The possible presence of hydrocarbons in the studied silicate glass of meteorite is suggested.     

Alpha-recoil in U–Pb geochronology: effective sample size matters

Displacement of the daughter isotope by a-recoil results in an open system on the nanoscale. For a heterogeneous distribution of U and Th, this redistribution of intermediate and stable daughter isotopes results in subvolumes with a deficit of Pb and others with an excess of Pb. Whether such heterogeneities affect the analyzed U–Pb system depends on: (1) the volume of the analyzed sample, (2) the degree and scale of heterogeneity in the U and Th distribution, and (3) the analytical procedure. Spatial separation of parent and daughter through a-recoil affects the U–Pb systematics of leached samples, where leaching gives access to domains less than 1 µm wide. Anomalous data patterns originating from recoil induced parent-to-daughter fractionation are more important if there are strong heterogeneities in the U and Th distribution, whereby Pb excess appears more pronounced than Pb deficit. Fractionation of parent and daughter elements through selective dissolution of U-REE-rich growth zones in zircon and U-inclusions in columbite, as well as the presence of U–Th-rich micro-inclusions in silicates dated using a step-leaching scheme, may result in anomalous ²⁰⁷Pb _rad/ ²⁰⁶Pb _rad, scattered ²⁰⁶Pb _rad/ ²³⁸U and ²⁰⁷Pb _rad/ ²³⁵U, and reverse discordance. The accumulated structural damage controls the leaching and dissolution behavior, but may also influence the non-stoichiometric element mobilization during sputtering or ablation in the analysis of U-rich samples by SHRIMP and LA-MC-ICP-MS.     

The importance of organic phase diffusion in the solvent extraction of copper by LIX 64N — Experiments with a static interface cell

Previous studies have suggested that the extraction of copper by hydroxyoxime extractants involves mass transfer with chemical reaction. This paper reports the results of experiments where an aqueous copper solution (4.94 g dm^?3 copper, 5.26 g dm^?3 H₂SO₄) is contacted with a 5% v/v LIX 64N solution in Escaid 100, in a diffusion cell with a stagnant interface. The concentration-distance distribution of the diffusional band of copper complex which appeared in the organic phase was measured at various times, and the results can be modelled by equations based on diffusion about an interface with and without interfacial resistance.If the previously measured diffusion constants for copper in the aqueous and organic phases were used in the model, then an unrealistically high resistance (200,000–300,000 s cm^?1) would have to be chosen to obtain a correlation. If a low resistance (1,000 s cm^?1) is assumed and the previously measured diffusion constants for copper in the aqueous phase (5.2·10^?6 cm² s^?1) and copper in the organic phase (5.0·10^?6 cm² s^?1) are taken, then it is necessary to reduce the organic phase diffusion constant to 2·10^?6 cm² s^?1 to obtain correlation of the model with the data. It is proposed that as the organic product film develops, the diffusivity of the copper complex is reduced.     

Kinetics of silica sorption and clay dissolution reactions at 1 and 670 atm

Rates of reactions between clay minerals and silica-spiked seawater and the effect of pressure on the direction, extent and rate of such reactions have been studied. Kinetic behavior of short-term, clay-silica reaction indicates that diffusion is the rate controlling process in both clay dissolution and clay reconstitution reactions. Rate constants of these reactions are of the order of 10^?13 moles/ sec^{$\text{1}\text{2}$}cm². No significant pressure effect on the rate of clay dissolution was observed. Estimates of diffusion coefficient of silicic acid for clay dissolution and silica sorption reactions indicate that the true value lies within the range, 10^?13–10^?17cm²/sec, thus reflecting the semicrystalline or amorphous nature of the reaction product through which diffusion is occurring.     

A study on exposure ages of chondrites based on spallogenic 53Mn

Longlived spallogenic ⁵³Mn was determined in 36 individual chondrites. Combining our data with those available so far in literature (in total 91 ⁵³Mn-values of 61 individual stones) a ⁵³Mnproduction rate of 478 ± 84dpm/kg Fe was derived. Based on this figure it was possible to calculate ⁵³Mn-radiation ages for more than 30 stones with T_rad ≤ 10 × 10⁶ yr. A comparison of our results with the respective rare gas- and ²⁶Al-exposure ages (so far available) shows that in general a good agreement exists between ages calculated by these three different methods. Only in the case of ‘finds’, e.g. in Bondoc and some other stones of probably high terrestrial ages. partial losses of ⁵³Mn seem to have occurred. For well preserved objects the ⁵³Mn method is ideal for the estimation of terrestrial residence times.     

Time-dependent sorption of Cd on CaX zeolite: Experimental observations and model predictions

Sorption, fixation and desorption kinetics of Cd²⁺ on calcium-exchanged zeolite-X were studied using an isotopic dilution technique utilizing ¹⁰⁹Cd. The technique provided reliable measurements of time-dependent fixation of Cd and was validated using chabazite, which demonstrated wholly reversible Cd²⁺ ion exchange. A first-order kinetic model was developed to describe the progressive transfer of Cd²⁺ to a less reactive form in X-zeolite, following initial sorption, and subsequent desorption of Cd subject to different initial contact times. The kinetic model differentiates between two ‘pools’ of sorbed Cd²⁺ on zeolite-X, designated labile and non-labile sorbed Cd in which the labile sorbed Cd is in immediate equilibrium with the free Cd²⁺ ion activity in solution. Additionally, an intra-particle diffusion model was developed and compared with the kinetic model to determine whether time-dependent Cd sorption is controlled by reaction kinetics or diffusion within zeolite particles. The kinetic model provided a much better fit to the experimental data (R² = 0.987) than the diffusion model. The rate constants describing Cd dynamics in CaX zeolite gave a half-time for Cd desorption of ∼77 d, for release to a ‘zero-sink’.     

Making diagenesis obey thermodynamics and kinetics: the case of quartz cementation in sandstones from offshore mid-Norway

Calculation of the quantity and distribution of quartz cement as a function of time and temperature/depth in quartzose sandstones is performed using a coupled dissolution/diffusional–transport/precipitation model. This model is based on the assumptions that the source of the silica cement is quartz surfaces adjoining mica and/or clay grains at stylolite interfaces within the sandstones, and the quantity of silica transport into and out of the sandstone by advecting fluids is negligible. Integration of the coupled mass transfer/transport equations over geologically relevant time frames is performed using the quasi-stationary state approximation. Results of calculations performed using quartz dissolution rate constants and aqueous diffusion coefficients generated from laboratory data, are in close agreement with both the overall porosity and the distribution of quartz cement in the Middle Jurassic Garn Formation only after optimizing the product of the effective surface area and quartz precipitation rate constants with the field data. When quartz precipitation rate constants are fixed to equal corresponding dissolution rate constants, the effective surface area required to match field data depends on the choice of laboratory generated quartz rate constant algorithm and ranges from 0.008 cm⁻¹ to 0.34 cm⁻¹. In either case, these reactive surface areas are ∼2 to 4 orders of magnitude lower than that computed using geometric models.     

A critical review of three methods used for the measurement of mercury (Hg)-dissolved organic matter stability constants

Three experimental techniques – ion exchange, liquid–liquid extraction with competitive ligand exchange, and solid-phase extraction with competitive ligand exchange (CLE–SPE) – were evaluated as methods for determining conditional stability constants (K) for the binding of mercury (Hg²⁺) to dissolved organic matter (DOM). To determine the utility of a given method to measure stability constants at environmentally relevant experimental conditions, experimental results should meet three criteria: (1) the data must be experimentally valid, in that they were acquired under conditions that meet all the requirements of the experimental method, (2) the Hg:DOM ratio should be determined and it should fall within levels that are consistent with environmental conditions, and (3) the stability constants must fall within the detection window of the method. The ion exchange method was found to be limited by its detection window, which constrains the method to stability constants with log K values less than about 14. The liquid–liquid extraction method was found to be complicated by the ability of Hg–DOM complexes to partition into the organic phase. The CLE–SPE method was found to be the most suitable of these methods for the measurement of Hg–DOM stability constants. Stability constants for DOM isolates measured using the CLE–SPE method at environmentally relevant Hg:DOM ratios were log K = 25–30 (M⁻¹). These values are consistent with the strong Hg²⁺ binding expected for reduced S-containing binding sites.     

Helium and carbon isotope systematics of natural gases from Taranaki Basin,New Zealand

The chemical and isotopic compositions of gases from hydrocarbon systems of the Taranaki Basin of New Zealand (both offshore and onshore) show wide variation. The most striking difference between the western and south-eastern groups of gases is the helium content and its isotopic ratio. In the west, the Maui gas is over an order of magnitude higher in helium concentration (up to 190 μmol mol⁻¹) and its ³He/⁴He ratio of 3.8 R_A (where R_A=the air ³He/⁴He ratio of 1.4×10⁻⁶) is approximately half that of upper mantle helium issuing from volcanic vents of the Taupo Volcanic Zone. In the SE, the Kupe South and most Kapuni natural gases have only a minor mantle helium input of 0.03–0.32 R_A and low total helium concentrations of 10–19 μmol mol⁻¹. The ³He/C ratio (where C represents the total carbon in the gas phase) of the samples measured including those from a recent study of on-shore Taranaki natural gases are generally high at locations where the surface heat flow is high. The ³He/CO₂ ratio of the Maui gases of 5 to 18×10⁻⁹ is higher than the MORB value of 0.2 to 0.5×10⁻⁹, a feature found in other continental basins such as the Pannonian and Vienna basins and in many high helium wells in the USA. Extrapolation to zero CO₂/³He and CO₂/C indicates δ¹³C(CO₂) values between −7 and −5‰ close to that of MORB CO₂. The remaining CO₂ would appear to be mostly organically-influenced with δ¹³C(CO₂) c.−15‰. There is some evidence of marine carbonate CO₂ in the gases from the New Plymouth field. The radiogenic ⁴He content (He_rad) varies across the Taranaki Basin with the highest He_rad/C ratios occurring in the Maui field. δ¹³C(CH₄) becomes more enriched in ¹³C with increasing He_rad and hydrocarbon maturity. Because ³He/⁴He is related to the ratio of mantle to radiogenic crustal helium and ³He/C is virtually constant in the Maui field, there is a correlation between R_C/R_A (where R_C=air-corrected ³He/⁴He) and δ¹³C(CH₄) in the Maui and New Plymouth fields, with the more negative δ¹³C(CH₄) values corresponding to high ³He/⁴He ratios. A correlation between ³He/⁴He and δ¹³C(CO₂) was also observed in the Maui field. In the fields adjacent to Mt Taranaki (2518 m andesitic volcano), correlations of some parameters, particularly CO₂/CH₄, C₂H₆/CH₄ and δ¹³C(CH₄), are present with increasing depth of the gas reservoir and with distance from the volcanic cone.     

Effects of velocity and concentration on diffusive transport in low permeability geological systems

A new micro-fluidic method, which is known as the Micro-Reactor Simulated-Channel (MRSC) method, has been employed to rapidly determine the effective diffusion coefficients of lithium in three important representative low permeability lithologies including: Melechov granite (Czech Republic), Borrowdale tuff, and Land's End Cornish granite (both UK). The concept of MRSC is similar to the micro chemical reactor which enables fast measurements to be done on a small intact sample. The effective diffusion coefficients were measured and comparisons between the MRSC results and conventional column methods showed excellent agreement. Our measured effective diffusion coefficient for Melechov granite is 1.7 × 10⁻¹² m²/s, directly comparable to previous conventional measurements. However the measurement time of the MRSC method is at least one order of magnitude faster than the conventional method and only requires small reaction volumes (as small as 10 ml). In addition, by exploiting the advantages of the MRSC method, the effects of velocity and concentration on diffusive transport for the two different UK rock types have also been investigated. Depending on flow rate and inlet tracer concentration, the effective diffusion coefficient for lithium in the Cornish granite ranges between 0.9 and 1.5 × 10⁻¹¹ m²/s while that measured for the Borrowdale tuff varies between 1.2 and 1.6 × 10⁻¹¹ m²/s.     

Effect of the formation of EDTA complexes on the diffusion of metal ions in water

The diffusion coefficients of aquo metal ions (M^z+) and their EDTA complexes (M-EDTA^(z−4)+) were compared to understand the effect of EDTA complexation on the diffusion of metal ions by the diffusion cell method for Co²⁺, Ga³⁺, Rb⁺, Sr²⁺, Ag⁺, Cd²⁺, Cs⁺, Th⁴⁺, , and trivalent lanthanides. Most studies about ionic diffusion in water have dealt with free ion (hydrated ion). In many cases, however, polyvalent ions are dissolved as complexed species in natural waters. Hence, we need to study the diffusion behavior of complexes in order to understand the diffusion phenomenon in natural aquifer and to measure speciation by diffusive gradient in thin films (DGT), which requires the diffusion coefficients of the species examined. For many ions, the diffusion coefficients of M-EDTA^(z−4)+ are smaller than those of hydrated ions, but the diffusion coefficients of M-EDTA^(z−4)+ are larger than those of hydrated ions for ions with high ionic potentials (Ga³⁺ and Th⁴⁺). As a result, the diffusion coefficients of EDTA complexes are similar among various metal ions. In other words, the diffusion of each ion loses its characteristics by the complexation with EDTA. Although the difference is subtle, it was also found that the diffusion coefficients of EDTA complexes increase as the ionic potential increases, which can be explained by the size of the EDTA complex of each metal ion.     

Diffusion-controlled growth of wollastonite rims between quartz and calcite: comparison between nature and experiment

Growth rates of wollastonite reaction rims between quartz and calcite were experimentally determined at 0.1 and 1 GPa and temperatures from 850 to 1200 °C. Rim growth follows a parabolic rate law indicating that this reaction is diffusion‐controlled. From the rate constants, the D′δ‐values of the rate‐limiting species were derived, i.e. the product of grain boundary diffusion coefficient D′ and the effective grain boundary width, δ. In dry runs at 0.1 GPa, wollastonite grew exclusively on quartz surfaces. From volume considerations it is inferred that (D′_CaOδ)/(D′_SiO2δ)≥1.33, and that SiO₂ diffusion controls rim growth. D′_SiO2δ increases from about 10^?25 to 10^?23 m³ s^?1 as temperature increases from 850 to 1000 °C, yielding an apparent activation energy of 330±36 kJ mol^?1. In runs at 1 GPa, performed in a piston‐cylinder apparatus, there were always small amounts of water present. Here, wollastonite rims always overgrew calcite. Rims around calcite grains in quartz matrix are porous and their growth rates are controlled by a complex diffusion‐advection mechanism. Rim growth on matrix calcite around quartz grains is controlled by grain boundary diffusion, but it is not clear whether CaO or SiO₂ diffusion is rate‐limiting. D′δ increases from about 10^?21 to 10^?20 m³ s^?1 as temperature increases from 1100 to 1200 °C. D′_SiO2δ or D′_CaOδ in rims on calcite is c. 10 times larger than D′_SiO2δ in dry rims at the same temperature. Growth structures of the experimentally produced rims are very similar to contact‐metamorphic wollastonite rims between metachert bands and limestone in the Bufa del Diente aureole, Mexico, whereby noninfiltrated metacherts correspond to dry and brine‐infiltrated metacherts to water‐bearing experiments. However, the observed diffusivities were 4 to 5 orders of magnitude larger during contact‐metamorphism as compared to our experimental results.     

Laboratory determination of thermal diffusion constants for N2/N2 in air at temperatures from −60 to 0°C for reconstruction of magnitudes of abrupt climate changes using the ice core fossil-air paleothermometer

Rapid temperature change causes fractionation of isotopic gaseous species in air in firn (snow) by thermal diffusion, producing a signal that is preserved in trapped air bubbles as the snow forms ice. Using a model of heat penetration and gas diffusion in the firn, as well as the values of appropriate thermal diffusion constants, it is possible to reconstruct the magnitude of a particular paleoclimate change. Isotopic nitrogen in air serves as a convenient tracer for such paleoreconstruction, because the ratio ²⁹N₂/²⁸N₂ has stayed extremely constant in the atmosphere for ≥10⁶ years. However, prior to this work no data were available for thermal diffusion of ²⁹N₂/²⁸N₂ in air, but only in pure N₂. We devised a laboratory experiment allowing fractionation of gases by thermal diffusion in a small, tightly controlled temperature difference. A mass spectrometer was employed in measuring the resulting fractionations yielding measurement precision greater than was attainable by earlier thermal diffusion investigators.Our laboratory experiments indicate that the value of the thermal diffusion sensitivity (Ω) for ²⁹N₂/²⁸N₂ in air is +(14.7 ± 0.5) × 10⁻³ per mil/°C when the average temperature is -30.0°C. The corresponding value for ²⁹N₂/²⁸N₂ in pure N₂ that we find is +(15.3 ± 0.4) × 10⁻³ per mil/°C at -30.6°C, in agreement with the previously available literature data within their large range of uncertainty. We find that an empirical equation, Ω = (8.656/T_K − 1232/T K2) ± 3% per mil/°C, describes the slight variation of the sensitivity values for ²⁹N₂/²⁸N₂ in air with temperature in the range of -60 to 0°C. A separate set of experiments also described in this paper rules out adsorption as a candidate for producing additional temperature change-driven fractionation of ²⁹N₂/²⁸N₂ in the firn air. The combined newly obtained data constitute a calibration of the fossil-air paleothermometer with respect to isotopic nitrogen and will serve to improve the estimates of the magnitudes of past abrupt climate changes recorded in ice cores.     

Modelling of the thermal dependence of structural and elastic properties of calcite, CaCO3

A computational method, based on the quasiharmonic approximation, has been computer-coded to calculate the temperature dependence of elastic constants and structural features of crystals. The model is applied to calcite, CaCO₃; an interatomic potential based on a C-O Morse function and Ca-O and O-O Borntype interactions, including a shell model for O, has been used. Equilibrations in the range 300–800 K reproduce the experimental unit-cell edges and bond lengths within 1%. The simulated thermal expansion coefficients are 22.3 (//c) and 2.6 (⊥ c), against 25.5 and-3.7×10^?6K^?1 experimental values, respectively. The thermal coefficients of elastic constants tend to be underestimated; for the bulk modulus, -2.3 against-3.7×10^?4K^?1 is obtained.     

Grain boundary diffusion in enstatite

We have investigated grain boundary diffusion rates in enstatite by heating single crystals of quartz packed in powdered San Carlos olivine (Mg_0.90Fe_0.10)₂SiO₄ at controlled oxygen fugacities in the range 10^?5.7 to 10^?8.7?atm and temperatures from 1350° to 1450?°C for times from 5 to 100?h at 1?atm total pressure. Following the experiments, the thickness of the coherent polycrystalline reaction rim of pyroxene that had formed between the quartz and olivine was measured using backscatter scanning imaging in the electron microprobe. Quantitative microprobe analysis indicated that the composition of this reaction phase is (Mg_0.92Fe_0.08)₂Si₂O₆. The rate of growth of the pyroxene increases with increasing temperature, is independent of the oxygen fugacity, and is consistent with a parabolic rate law, indicating that the growth rate is controlled by ionic diffusion through the pyroxene rim. Microstructural observations and platinum marker experiments suggest that the reaction phase is formed at the olivine-pyroxene interface, and is therefore controlled by the diffusion of silicon and oxygen. The parabolic rate constants determined from the experiments were analyzed in terms of the oxide activity gradient across the rim to yield mean effective diffusivities for the rate-limiting ionic species, assuming bulk transport through the pyroxene layer. These effective diffusivities are faster than the lattice diffusivities for the slowest species (silicon) calculated from creep experiments, but slower than measured lattice diffusivities for oxygen in enstatite. Thus, silicon grain boundary diffusion is most likely to be the rate-limiting process in the growth of the pyroxene rims. Also, as oxygen transport through the pyroxene rims must be faster than silicon transport, diffusion of oxygen along the grain boundaries must be faster than through the lattice. The grain boundary diffusivity for silicon in orthopyroxenite is then given by D¯gbSiδ=(3.3±3.0)×10^?9f0.0O₂e^?400±65/RT?m³s^?1, where the activation energy for diffusion is in kJ/mol, and δ is the grain boundary width in m. Calculated growth rates for enstatite under these conditions are significantly slower than predicted by an extrapolation from similar experiments performed at 1000?°C under high pressure (hydrous) conditions by Yund and Tullis (1992), perhaps due to water-enhancement of diffusion in their experiments.     

Diffusion-controlled growth of albite and pyroxene reaction rims

The growth rates of albite and pyroxene (enstatite + diopside + spinel) reaction rims were measured at 1000°C and ˜700 MPa and found to be parabolic indicating diffusion-controlled growth. The parabolic rate constants for the pyroxene (+ spinel) rims in samples with 0.5 wt% H₂O added or initially vacuum dried at 25°C and 250°C are 1.68 ± 0.09, 0.54 ± 0.05 and 0.25 ± 0.06 μm²/h, respectively. The values for albite rim growth in samples initially dried at 60°C and with 0.1 wt% H₂O added are 0.25 ± 0.04 and 0.33 ± 0.03 μm²/h, respectively. The latter values were used to derive the product of the grain boundary diffusion coefficient D′_A, where A = SiO₂, NaAlO₂, or NaAlSi₋₁, and the grain boundary thickness δ in albite. The calculated D′_SIO2δ in the albite aggregate for the situations of two different water contents are about 9.9 × 10⁻²³ and 1.4 × 10⁻²² m³ s⁻¹, respectively. Both the rate constants and the calculated D′_Aδ demonstrate that the effect of water content on the grain boundary diffusion rate in monomineralic albite and polymineralic pyroxene (+ spinel) aggregates is small, consistent with recent studies of monomineralic enstatite and forsterite rims. Received: 1 July 1995 / Accepted: 1 August 1996     

4He diffusion in specular hematite

In order to test the chronometer qualities of speculante for the (U + Th)/He dating method, ⁴He release experiments by stepwise heating of two specularites from the Rimbach mineralization locality in the southern Vosgues (France) have been carried out. The diffusion coefficients define linear Arrhenius plots within a temperature interval of 250 to 830 °C, which is suggestive of volume diffusion. Extrapolation of the diffusion behavior to 20° C yields diffusion coefficients (D₂₀ values) smaller than 10^?26 [cm² s^?1] for both hematites with activation energies at 116 [kJ/mole]. The results of our study suggest that specularite is a very helium retentive hematite variety which is capable of quantitatively retaining radiogenic helium over geologic periods of time.     

An ion microprobe study of anhydrous oxygen diffusion in anorthite: a comparison with hydrothermal data and some geological implications

The diffusion rate of ¹⁸O tracer atoms in anorthite (An₉₇Ab₀₃) under anhydrous conditions has been measured using SIMS techniques. The tracer source was ¹⁸O₂ 98.4% gas at 1 bar, in the temperature range 1300° C–850° C. The measured diffusion constants are D ₀=1 _–0.6 ⁺¹ ×10^–9 m²s^–1 Q=236±8 kJ mol^–1 Comparison of these values with published data for ¹⁸O diffusion in anorthite under hydrothermal conditions shows that dry oxygen diffusivities are orders of magnitude lower than equivalent wet values at similar temperatures. The effect of these differences on oxygen isotope equilibration during cooling is discussed.     

Calculation of individual isotope equilibrium constants for geochemical reactions

Theory is derived from the work of Urey (Urey H. C. [1947] The thermodynamic properties of isotopic substances. J. Chem. Soc. 562-581) to calculate equilibrium constants commonly used in geochemical equilibrium and reaction-transport models for reactions of individual isotopic species. Urey showed that equilibrium constants of isotope exchange reactions for molecules that contain two or more atoms of the same element in equivalent positions are related to isotope fractionation factors by α = (K^ex)^1/n, where n is the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example ¹³C¹⁶O¹⁸O and ¹H²H¹⁸O. The equilibrium constants of the isotope exchange reactions can be expressed as ratios of individual isotope equilibrium constants for geochemical reactions. Knowledge of the equilibrium constant for the dominant isotopic species can then be used to calculate the individual isotope equilibrium constants.Individual isotope equilibrium constants are calculated for the reaction CO_2g = CO_2aq for all species that can be formed from ¹²C, ¹³C, ¹⁶O, and ¹⁸O; for the reaction between ¹²C¹⁸O_2aq and ¹H₂¹⁸O_l; and among the various ¹H, ²H, ¹⁶O, and ¹⁸O species of H₂O. This is a subset of a larger number of equilibrium constants calculated elsewhere (Thorstenson D. C. and Parkhurst D. L. [2002] Calculation of individual isotope equilibrium constants for implementation in geochemical models. Water-Resources Investigation Report 02-4172. U.S. Geological Survey). Activity coefficients, activity-concentration conventions for the isotopic variants of H₂O in the solvent ¹H₂¹⁶O_l, and salt effects on isotope fractionation have been included in the derivations. The effects of nonideality are small because of the chemical similarity of different isotopic species of the same molecule or ion. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation factors.The derivations can be extended to calculation of individual isotope equilibrium constants for ion pairs and equilibrium constants for isotopic species of other chemical elements. The individual isotope approach calculates the same phase isotopic compositions as existing methods, but also provides concentrations of individual species, which are needed in calculations of mass-dependent effects in transport processes. The equilibrium constants derived in this paper are used to calculate the example of gas-water equilibrium for CO₂ in an acidic aqueous solution.     

Experimental measurements of the diffusion parameters of light hydrocarbons in water-saturated sedimentary rocks—I. A new experimental procedure

An automatic experimental set-up has been developed for the determination of diffusion parameters of hydrocarbon gases through water-saturated rock samples. Diffusive flow of hydrocarbons through rock slices is monitored by gas chromatography. Experiments are carried out according to the time lag method yielding diffusion coefficients, solubility coefficients, and diffusion permeabilities. Diffusion coefficients down to 10⁻¹² m² s⁻¹ (10⁻⁸ cm⁻² s⁻¹) may be determined routinely on rock samples of 2–10 mm thickness. Maximum errors in diffusion coefficients are estimated around 20% and reproducibility was found to range between 10 and 20%. Specific features of this set-up are automatic sampling and data acquistion, high sampling frequency, and maintenance of water-saturation of the rock samples throughout the experiment.