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.     

Effects of dry density and exchangeable cations on the diffusion process of sodium ions in compacted montmorillonite

As a part of the safety assessment of the geological disposal of high-level radioactive waste, the effects of dry density and exchangeable cations on the diffusion process of Na⁺ ions in compacted bentonite were studied from the viewpoint of the activation energy for diffusion. The apparent self-diffusion coefficients of Na⁺ ions in compacted Na-montmorillonite and in a Na- and Ca-montmorillonite mixture were determined by one-dimensional, non-steady diffusion experiments at different temperatures and dry densities. A unique change in activation energy as a function of dry density was found for the Na⁺ ions in compacted Na-montmorillonite. The activation energy suddenly decreased from 18.1 to 14.1 kJ mol^− 1 as the dry density increased from 0.9 to 1.0 Mg m^− 3, whereas it increased to 24.7 kJ mol^− 1 as the dry density increased to 1.8 Mg m^− 3. Examination of the effect of exchangeable cations on the activation energies determined that the activation energies were almost constant, approximately 25 kJ mol^− 1, for the montmorillonite specimens at a dry density of 1.8 Mg m^− 3. However, three different activation energy values were obtained at a dry density of 1.0 Mg m^− 3. These findings cannot be explained by the conventional diffusion model (the pore water diffusion model), which suggests that the predominant diffusion process alternates among pore water diffusion, interlayer diffusion, and external surface diffusion.     

Interdiffusion of Na,K,and Ca Between Granitic Melts and NaCl Liquid

This study is aimed at determining the diffusion coefficient of net-work modifiers (mainly Na, K, and Ca) in a two-phase melt-NaCl system, in which the melts are granitic and the system is NaCl-rich in composition. The diffusion coefficients of Na, K, and Ca were measured at the temperatures of 750 – 1400°C, pressures of 0.001 × 10⁸ – 2 × 10⁸ Pa, and initial H₂O contents of 0 wt% –6.9 wt% in the granitic melts. The diffusion coefficients of Fe and Mg were difficult to resolve. In all experiments a NaCl melt was present as well. In the absence of H₂O, the diffusion of net-work modifiers follows an Arrhanious equation at 1 × 10⁵ Pa: lgD_ca=−3. 88−5140/T, lgD_k =−3. 79−4040/T, and lgD_Na, =−4.99−3350/T, where D is in cm² /s andT is in K. The diffusion coefficients of Ca, Na, K, and Fe increase non-linearly with increasing H₂O content in the melt. The presence of about 2 wt% H₂O m the melt will lead to a dramatical increase in diffusivity, but higher H₂O content has only a minor effect. This change is probably the result of a change in the melt structure when H₂O is present. The diffusion coefficients measured in this study are significantly different from those in previous works. This may be understood in terms of the “transient two-liquid equilibrium” theory. Element interdiffusion depends not only on its concentration, but also on its activity co-efficient gradient, which is reflected by the distribution coefficient, of the two contacting melts.     

Transport phenomena in kaolinite clay: Molecular simulation,homogenization analysis and similitude law

Kaolinite is a common clay mineral. It is a nanomaterial with a platelet crystalline structure. In order to analyze the behavior of kaolinite, its microscopic structure and material properties must be specified correctly. A molecular dynamics (MD) simulation is used for determining the microscale properties of hydrated kaolinite, and these properties are introduced into a multiscale homogenization analysis (HA). We previously developed such an MD/HA technique to investigate seepage, diffusion, sorption and consolidation in bentonite clay (Proceedings of the Science Basis for Nuclear Waste Management, Davos, Switzerland, vol. XXI. Material Research Society: Warrendale, PA, 1997; 359–366; Eng. Geol. 1999; 54 :21–31; Eng. Geol. 2001; 60 :127–138; Coupled Thermo‐Hydro‐Mechanical‐Chemical Processes in Geo‐systems. Elsevier: Amsterdam, 2005; 457–464). We here apply the method to kaolinite clay to investigate the permeability, diffusion and related similitude law. The obtained results are supported by existing experimental data. Copyright © 2008 John Wiley & Sons, Ltd.     

Diffusive transport of water in porous feldspars from granitic saprolites: In situ experiments using FTIR spectroscopy

A novel experimental cell was developed for in situ measurements of transport phenomena in porous media using Fourier-Transform Infrared (FTIR) Spectroscopy. The technique was employed at ambient pressure in the temperatures range of 11–44 °C to study the H₂O → D₂O exchange between water-saturated weathered feldspars (bulk porosity of 5–19 vol% for feldspar) from granitic saprolites and a surrounding aqueous liquid. Such measurements are an important step for understanding internal weathering reactions of feldspars in soils and aquifers. Effective diffusion coefficients D_eff for water in water-saturated porous feldspars were determined assuming one-dimensional diffusion in a quasi-homogeneous medium. The values of D_eff vary from 7.2 × 10⁻¹⁰ to 1.9 × 10⁻¹¹ m²/s and are 1–2 orders of magnitude lower than the diffusion coefficients (D) of protons and molecular H₂O in liquid water. The activation energy for the H₂O → D₂O exchange process in porous feldspars ranges from 7.8 to 18.8 kJ/mol.The results imply that the effective diffusivity of water is mainly controlled by physical properties of the feldspars like porosity, pore connectivity, pore geometry and distribution. Perthitic feldspars with homogeneous pore distribution in the albitic lamellas have diffusional tortuosity factors X = D/D_eff between 3 and 10 while alkali feldspars with inhomogeneously distributed and disconnected pores have much higher X values up to 129. Diffusion anisotropy has been verified for a vein perthite with diffusion perpendicular to the lamellas being faster by 0.3–0.5 log units than within the lamellas. It has to be emphasized that the study is based only on few selected feldspars, including perthitic feldspar, and additional work on samples with different weathering stages is needed to test the importance of the different parameters controlling diffusive transport in the pore system.     

Diffusion of Na,K, Rb and Cs in glasses of albite and orthoclase composition

The measurement of diffusion coefficients for Na, K, Rb and Cs has been realized by the technique of active salt deposits on glasses of albite and orthoclase composition, at normal pressure and in the temperature range 300–1000°C. The values of D are between 10^?6 and 10^?12 cm² s^?1 and, for every type of run, they vary with temperature according to Arrhenius laws, with activation energies ranging from 13 to 68 kcal mole^?1. These important variations are related to the size of the diffusing element (at 700°C in albite glass D_Na/D_K/D_RbD_Cs ～- 10⁷/10⁵/10³/1) and to the size of the major alkali element (for rubidium at 800°C D_or·gl/D_ab·gl ～- 20). By comparison with available data on diffusion in feldspars, we emphasize the influence of the defect density on the diffusion process.     

Isotopic fractionation of noble gases by diffusion in liquid water: Molecular dynamics simulations and hydrologic applications

Despite their great importance in low-temperature geochemistry, diffusion coefficients of noble gas isotopes in liquid water (D) have been measured only for the major isotopes of helium, neon, krypton and xenon. Data on the diffusion coefficients of minor noble gas isotopes are essentially non-existent and so typically have been estimated by a kinetic-theory model in which D varies as the inverse square root of the isotopic mass (m): D ∝ m^−0.5. To examine the validity of the kinetic-theory model, we performed molecular dynamics (MD) simulations of the diffusion of noble gases in ambient liquid water. Our simulation results agree with available experimental data on the solvation structure and diffusion coefficients of the major noble gas isotopes and reveal for the first time that the isotopic mass-dependence of all noble gas self-diffusion coefficients has the power-law form D ∝ m^−β with 0 < β < 0.2. Thus our results call into serious question the widespread assumption that the ‘square-root’ model can be applied to estimate the kinetic fractionation of noble gas isotopes caused by diffusion in ambient liquid water. To illustrate the importance of this finding, we used the diffusion coefficients determined in our MD simulations to reconsider the geochemical modeling of ²⁰Ne/²²Ne and ³⁶Ar/⁴⁰Ar isotopic ratios in three representative hydrologic studies. Our new modeling results indicate that kinetic isotopic fractionation by diffusion may play a significant role in noble gas transport processes in groundwater.     

Activation energy for diffusion of helium in water-saturated, compacted Na-montmorillonite

It is important to clarify the migration behavior of hydrogen gas dissolved in water-saturated, compacted bentonite, which is a promising material for geologic disposal of high-level waste and TRU waste disposal. The diffusion coefficients of helium, which can be detected under extremely low background conditions, in water-saturated, compacted Na-montmorillonite were determined as a function of temperature by a transient diffusion method. The activation energies for diffusion of helium were then obtained. The activation energies were from 6.9 ± 4.8 to 19 ± 2.8 kJ mol^− 1 and were regarded to be independent of dry density. The activation energies of helium in water-saturated Na-montmorillonite were roughly equal to those in bulk water, 14.9 kJ mol^− 1, and in ice, from 11 to 13 kJ mol^− 1. It is possible that helium diffuses not only in pore water but also in interlayer water.     

Surface chemistry and dissolution kinetics of glassy rocks at 25°C

The weathering rates and mechanisms of three types of glassy rocks were investigated experimentally at 25 °C, pH 1.0 to 6.2, and reaction times as much as to 3 months. Changes in major element chemistry were monitored concurrently as a function of time in the aqueous solution and within the near surface region of the glass. Leach profiles, obtained by a HF leaching technique, displayed near-surface zones depleted in major cations. These zones increased in depth with increasing time and decreasing pH of reactions. Release rates into the aqueous solution were parabolic for Na and K and linear for Si and Al. A coupled weathering model, involving surface dissolution with concurrent diffusion of Na, K, and Al, produced a mass balance between the aqueous and glass phases. Steady state conditions are reached at pH 1.0 after approximately 3 weeks of reaction. Steady-state is not reached even after 3 months at pH 6.2.An interdiffusion model describes observed changes in Na diffusion profiles for perlite at pH 1.0. The calculated Na self-diffusion coefficient of 5 × 10^?19 cm²·s^?1 at 25°C approximates coefficients extrapolated from previously reported high temperature data for obsidian. The self-diffusion coefficient for H₃O⁺, 1.2 × 10^?20 cm²·s^?1, is similar to measured rates of water diffusion during hydration of obsidian to form perlite.     

Hydrogeochemistry of Lake Turkana,Kenya: Mass balance and mineral reactions in an alkaline lake

Lake Turkana, in northwestern Kenya, is a closed-basin, alkaline (pH = 9.2) lake of moderate salinity (TDS = 2500 ppm). Principal ions are Na⁺, HCO^?₃ and CI^?. The lake is essentially polymictic in the northern basin and little compositional variation occurs in surface waters. The Omo River is the principal influent, providing some 80–90% of water input to the lake. Chloride has an apparent accumulation time of about 2500 years after accounting for burial of interstitial water.The bottom sediments are predominantly detrital and fine-grained, yet mineral-water reactions are very important for the geochcmical budget. Ca²⁺ is precipitated as calcite; Na⁺ is removed as an exchangeable cation on smectite; Mg²⁺ is probably incorporated into a Mg-silicate phase, most likely poorlycrystalline smectite, as it enters the lake water; K⁺ may be used in illite regradation. Cation exchange is a very important process in the mass balance of this lake. Over 40% of incoming Na is removed as an exchangeable cation. After cation exchange and interstitial water burial, Na has a response time of 2650 years, which compares favorably with that of chloride. These processes seem to occur rapidly within the water mass of the lake: other reactions may be important in regulating interstitial water compositions.Several changes occur in the upper 3m of sediment: interstitial-water pH drops to 8.3 and alkalinity increases slightly with depth, SO^2?₄ decreases slightly, and amorphous silica saturation is approached. These changes are a response to organic matter oxidation and the dissolution of unstable silicates rather than a reversal of reactions occurring in the lake water. High rates of sedimentation (up to 1 cm per year) may minimize the effects of diffusion between the interstitial waters and the lake water, although burial of interstitial water assumes considerable importance.     

Molecular dynamics simulations of pressure and temperature effects on MgSiO3 and Mg2SiO4 melts and glasses

Ab-initio interionic potentials for Mg²⁺, Si⁴⁺, and O^2– have been used in molecular dynamics (MD) simulations to investigate diffusivity changes, pressure-induced structural transitions, and temperature effects on polymerization in MgSiO₃ and Mg₂SiO₄ melts and glasses. The potential gives reasonable agreement with the 0.1 MPa radial distribution function of MgSiO₃ glass. Maxima in the diffusion coefficients of Si⁴⁺ and O^2– occur as pressure is increased on the MgSiO₃ melt. The controlling structural mechanism for this behavior is the Q¹ species of SiO₄ tetrahedra. Mg²⁺ diffusion coefficients decrease monotonically with pressure in both melt compositions. Increasing Mg²⁺ coordination number and population of 3- and 4-membered SiO₄ rings with pressure combine to hinder translation of the Mg²⁺ ions. The dominant changes in structure with pressure are a decrease in the intertetrahedral (Si-O--Si) angle up to approximately 4 g/cm³ and coordination changes of the ions above this density. Temperature effects on viscosity in these simulated melts are indirectly studied by analyzing polymerization changes with temperature. Polymerization and coordination numbers increase with decreasing temperature and a small quench rate effect is observed. Fair agreement is found between the MD simulations and experimental equation of state for Mg₂SiO₄, but the equation of state predictions for MgSiO₃ melts are much less accurate. The zero pressure volume, V ₀, is significantly higher and K ₀ is lower in the simulations than empirical values. The inadequacies reflect error in using the ionic approximation for polymerized systems and a need to collect more data for a variety of molecular configurations in the development of ab-initio potentials.     

Self-diffusion of water and its dependence on temperature and ionic strength in highly compacted montmorillonite, illite and kaolinite

The effect of temperature and ionic strength on the diffusion of HTO parallel to the direction of compaction through 5 highly compacted clay minerals (bulk dry density, ρ_b,d = 1.90 ± 0.05 Mg/m³), namely montmorillonite (Na- and Ca-form), illite (Na- and Ca-form), and kaolinite, was studied. The diffusion experiments were carried out at temperatures between 0 °C and 60 °C and at ionic strengths of 0.01 M and 1 M NaCl for the Na-form clays and kaolinite, and of 0.005 M and 0.5 M CaCl₂ for the Ca-form. The ionic strength had an insignificant influence on the values of the effective diffusion coefficient (variation by less than 10%) for the clays under study at this degree of compaction. The effective diffusion coefficients followed the order Na-montmorillonite < Ca-montmorillonite < Ca-illite < Na-illite  kaolinite. It is thought that the differences between Na- and Ca-montmorillonite originate from the larger size particles, and thus the lower tortuosity of the latter; whereas the differences between Na- and Ca-illite are related to the different degree of solvation of the Na and Ca cations. The activation energies were successfully calculated using the Arrhenius law. Swelling clays (Na- and Ca-montmorillonite) had slightly larger activation energy values (20 kJ/mol) compared to bulk water (17 kJ/mol); Ca-illite (16 kJ/mol), Na-illite (13 kJ/mol) and kaolinite (14.4 kJ/mol) lower values than that of bulk water. The low activation energies of the last three clays may be related to weaker H-bonds between water and the clay surfaces compared to those in bulk water.     

Kinetics of zircon dissolution and zirconium diffusion in granitic melts of variable water content

The experimental dissolution of zircon into a zircon-undersaturated felsic melt of variable water content at high pressure in the temperature range 1,020° to 1,500° C provides information related to 1) the solubility of zircon, 2) the diffusion kinetics of Zr in an obsidian melt, and 3) the rate of zircon dissolution. Zirconium concentration profiles observed by electron microprobe in the obsidian glass adjacent to a large, polished zircon face provide sufficient information to calculate model diffusion coefficients. Results of dissolution experiments conducted in the virtual absence of water (<0.2% H₂O) yield an activation energy (E) for Zr transport in a melt ofM=1.3 [whereM is the cation ratio (Na+K+2Ca)/(Al·Si)] of 97.7±2.8 kcal-mol^?1, and a frequency factor (D ₀) of 980 _?580 ^+1,390 cm²-sec^?1. Hydrothermal experiments provide an E=47.3±1.9 kcal-mol^?1 andD ₀=0.030 _?0.015 ^+0.030 cm²-sec^?1. Both of these results plot close to a previously defined diffusion compensation line for cations in obsidian. The diffusivity of Zr at 1,200° C increases by a factor of 100 over the first 2% of water introduced into the melt, but subsequently rises by only a factor of five to an apparent plateau value of ～2×10^?9 cm²-sec^?1 by ～6% total water content. The remarkable contrast between the wet and dry diffusivities, which limits the rate of zircon dissolution into granitic melt, indicates that a 50 μm diameter zircon crystal would dissolve in a 3 to 6% water-bearing melt at 750° C in about 100 years, but would require in excess of 200 Ma to dissolve in an equivalent dry system. From this calculation we conclude that zircon dissolution proceeds geologically instantaneously in an undersaturated, water-bearing granite. Estimates of zircon solubility in the obsidian melt in the temperature range of 1,020° C to 1,500° C confirm and extend an existing model of zircon solubility to these higher temperatures in hydrous melts. However, this model does not well describe zircon saturation behavior in systems with less than about 2% water.     

Transport of perfluorocarbon tracers and carbon dioxide in sediment columns – Evaluating the application of PFC tracers for CO2 leakage detection

Perfluorocarbon compounds (PFCs) have high chemical and thermal stability, low background levels in natural systems, and easy detectability. They are proposed as tracers for monitoring potential CO₂ leakage associated with geological carbon sequestration (GCS). The fate of the PFCs in porous media, and in particular, the transport of these compounds relative to CO₂ gas in geological formations, has not been thoroughly studied. We conducted column tests to study the transport of perfluoro-methylcyclo-pentane (PMCP), perfluoro-methylcyclo-hexane (PMCH), ortho-perfluoro-dimethylcyclo-hexane (ortho-PDCH), and perfluoro-trimethylcyclo-hexane (PTCH) gas tracers in a variety of porous media. The influence of water content and sediment minerals on the retardation of the tracers was tested. The transport of PFC tracers relative to ¹³CO₂ and the conservative tracer sulfur hexafluoride (SF₆) was also investigated. Results show that at high water content, the PFCs and SF₆ transported together. In dry and low-water-content sediments, however, the PFCs were retarded relative to SF₆ with the degree of retardation increasing with the molecular weight of the PFC. When water was present in the medium, the transport of CO₂ was greatly retarded compared to SF₆ and the PFC tracers. However, in dry laboratory sediments, the migration of CO₂ was slightly faster than all the tracers. The type of minerals in the sediments also had a significant impact on the fate of the tracers. In order to use the PFC tracer data obtained from the ground surface or shallow subsurface in a GCS site to precisely interpret the extent and magnitude of CO₂ leakage, the retardation of the tracers and the interaction of CO₂ with the reservoir overlying formation water should be carefully quantified.     

Hydrogeochemical Characteristics and Groundwater Inrush Source Identification for a Multi‐aquifer System in a Coal Mine

Correct identification of water inrush sources is particularly important to prevent and control mine water disasters. Hydrochemical analysis, Fisher discriminant analysis, and geothermal verification analysis were used to identify and verify the water sources of the multi‐aquifer groundwater system in Gubei coal mine, Anhui Province, North China. Results show that hydrochemical water types of the Cenozoic top aquifer included HCO₃–Na+K–Ca, HCO₃–Na+K–Mg and HCO₃–Na+K, and this aquifer was easily distinguishable from other aquifers because of its low concentration of Na⁺+K⁺ and Cl^–. The Cenozoic middle and bottom aquifers, the Permian fissure aquifer, and the Taiyuan and Ordovician limestone aquifers were mainly characterized by the Cl–Na+K and SO₄–Cl‐Na+K or HCO₃–Cl–Na+K water types, and their hydrogeochemistries were similar. Therefore, water sources could not be identified via hydrochemical analysis. Fisher model was established based on the hydrogeochemical characteristics, and its discrimination rate was 89.19%. Fisher discrimination results were improved by combining them with the geothermal analysis results, and this combination increased the identification rate to 97.3 % and reasonably explained the reasons behind two water samples misjudgments. The methods described herein are also applicable to other mines with similar geological and hydrogeological conditions in North China.     

Structure and dynamics of water on Li-, Na-, K-, Cs-, H3O-exchanged muscovite surfaces: A molecular dynamics study

The distribution and dynamics of water molecules and monovalent cations (Li⁺, Na⁺, K⁺, Cs⁺, and H₃O⁺) on muscovite surfaces were investigated by molecular dynamics (MD) simulations. The direct comparison of calculated X-ray reflectivity profiles and electron density profiles with experiments revealed the precise structure at the aqueous monovalent electrolyte solutions/muscovite interface. To explain the experimentally observed electron density profiles for the CsCl solution-muscovite interface, the co-adsorption of Cs⁺ and Cl⁻ ion pairs would be necessary. Two types of inner-sphere complexes and one type of outer-sphere complex were observed for hydrated Li⁺ ions near the muscovite surface. For Na⁺, K⁺, Cs⁺, and H₃O⁺ ions, the inner-sphere complexes were stable on the muscovite surface. The density oscillation of water molecules was observed to approximately 1.5 nm from the muscovite surface. The number of peaks and the locations for the density of water oxygen atoms were almost similar among the water molecules coordinated to Li⁺, Na⁺, K⁺, and H₃O⁺ ions adsorbed on the muscovite surfaces. The water molecules around Cs⁺ ions that were adsorbed to muscovite surfaces seemed to avoid coordinating with Cs⁺ ions on the surface, and the density of water oxygen near the muscovite surface decreased relative to that in a bulk state. There was no significant difference in self-diffusion, viscosity, retention time, and reorientation time of water molecules among different cations adsorbed to muscovite surfaces. These translational and rotational motions of water molecules located at less than 1 nm from the muscovite surfaces were slower than those in a bulk state. A significant difference was observed for the exchange times of water molecules around monovalent cations. The exchange time of water molecules was long around Li⁺ ions and decreased with an increase in the ionic radius.     

The determination of SO42-, NaSO4-, and MgSO40 tracer diffusion coefficients and their application to diagenetic flux calculations

Sulfur-35 was used to monitor the non-steady-state tracer diffusion of the free sulfate ion and sulfate ion-pairs in aqueous solutions of MgSO₄ and Na₂SO₄. Diffusion coefficients were derived from radiotracer flux measurements taken over ionic strengths ranging from 0.001 to 0.7. The experimental tracer diffusion coefficient is a function of the diffusion coefficients of the free sulfate ion and the sulfate ion-pairs as well as the ion pair equilibrium constant. The free sulfate ion tracer diffusion coefficient was determined independently from both the MgSO₄ and Na₂SO₄, experiments and found to be 1.11 and 1.08 (in units of 10^-5cm²sec^-1, ± 10%, respectively. These values closely agree with that calculated from the Nernst expression, 1.07 sx 10^-5cm²sec^-1. The tracer diffusion coefficients of MgSO₄⁰ and NaSO₄^- were determined to be 0.85 and 1.23 sx 10^-5cm²sec^-1, respectively. These numbers are in reasonable agreement with the earlier work on mutual diffusion coefficients by Rard and Miller (1979b) (D_MgSO4^o = 0.65, D_naso4^- = 1.19) and Harned and Hudson (1951)D_MgSO4⁰ = (0.70). A modified version of the theoretical equation developed by Pikal (1971) is proposed for predicting the tracer diffusion coefficients of many ion-pairs relevant to seawater. Many of these predicted values are found to be within 10–20% of the empirical values extracted from mutual diffusion data. The experimental and theoretical diffusion coefficient data are used to calculate revised coupled diffusion coefficients, D^g, according to the model of Lasaga (1979).     

O and H diffusion in uraninite: Implications for fluid-uraninite interactions, nuclear waste disposal, and nuclear forensics

Diffusion coefficients for oxygen and hydrogen were determined from a series of natural uraninite-H₂O experiments between 50 and 700 °C. Under hydrous conditions there are two diffusion mechanisms: (1) an initial extremely fast-path diffusion mechanism that overprinted the oxygen isotopic composition of the entire crystals regardless of temperature and (2) a slower volume-diffusive mechanism dominated by defect clusters that displace or eject nearest neighbor oxygen atoms to form two interstitial sites and two partial vacancies, and by vacancy migration. Using the volume diffusion coefficients in the temperature range of 400-600 °C, diffusion coefficients for oxygen can be represented by D = 1.90e⁻⁵ exp (−123,382 J/RT) cm²/s and for temperatures between 100 and 300 °C the diffusion coefficients can be represented by D = 1.95e⁻¹⁰ exp (−62484 J/RT) cm²/s, where the activation energies for uraninite are 123.4 and 62.5 kJ/mol, respectively. Hydrogen diffusion in uraninite appears to be controlled by similar mechanisms as oxygen. Using the volume diffusion coefficients for temperatures between 50 and 700 °C, diffusion coefficients for hydrogen can be represented by D = 9.28e⁻⁶ exp (−156,528 J/RT) cm²/s for temperatures between 450 and 700 °C and D = 1.39e⁻¹⁴ exp (−34518 J/RT) cm²/s for temperatures between 50 and 400 °C, where the activation energies for uraninite are 156.5 and 34.5 kJ/mol, respectively.Results from these new experiments have implications for isotopic exchange during natural UO₂-water interactions. The exceptionally low δ¹⁸O values of natural uraninites (i.e. −32‰ to −19.5‰) from unconformity-type uranium deposits in Saskatchewan, in conjunction with theoretical and experimental uraninite-water and UO₃-water fractionation factors, suggest that primary uranium mineralization is not in oxygen isotopic equilibrium with coeval clay and silicate minerals. The low δ¹⁸O values have been interpreted as resulting from the low temperature overprinting of primary uranium mineralization in the presence of relatively modern meteoric fluids having δ¹⁸O values of ca. −18‰, despite petrographic and U-Pb isotope data that indicate limited alteration. Our data show that the anomalously low oxygen isotopic composition of the uraninite from the Athabasca Basin can be due to meteoric water overprinting under reducing conditions, and meteoric water or groundwater can significantly affect the oxygen isotopic composition of spent nuclear fuel in a geologic repository, with minimal change to the chemical composition or texture. Moreover, the rather fast oxygen and hydrogen diffusion coefficients for uraninite, especially at low temperatures, suggest that oxygen and hydrogen diffusion may impart characteristic isotopic signals that can be used to track the route of fissile material.     

Diffusion and retention of sodium and strontium in Opalinus clay: Comparison of sorption data from diffusion and batch sorption measurements, and geochemical calculations

The retention of ²²Na and ⁸⁵Sr on Opalinus clay from Benken and the Mont Terri Rock Laboratory (Switzerland) was measured by through- and out-diffusion measurements on intact rock samples, and by batch sorption on crushed material. The sorption values obtained from these measurements were compared with one another and with ones calculated from a selectivity coefficient/geochemical modelling approach. One of the main aims of the work was to test to what extent sorption values deduced from diffusion experiments on intact rock were compatible with those measured in batch tests on crushed material and with sorption values calculated from geochemical modelling. This is an important consideration in repository performance assessment studies because apparent diffusion coefficients are often calculated from batch R_d values and effective diffusion coefficients measured using tritiated water.In general, there was excellent agreement between the distribution ratios for Na obtained by all 3 approaches for both sources of Opalinus clay. For Sr the agreement was also good, but the calculations based on selectivity coefficients in the case of Benken, and the batch sorption data in the case of Mont Terri material were a factor of 2 different from the values found in the other two cases. Nevertheless, a factor of 2 difference in the worst case is not considered to be significant when the errors associated with the different methods are considered realistically.The uptake mechanism for both elements in the Opalinus clay system is cation exchange and the results strongly indicate that there is no significant difference between the exchange capacity available in the dispersed and in the intact rock systems i.e. reduced site accessibility in intact Opalinus clay is not an issue where sorption by cation exchange is occurring.     

Anion exclusion effects in compacted bentonites: Towards a better understanding of anion diffusion

Diffusion of ³⁶Cl⁻ in compacted bentonite was studied using through-diffusion, out-diffusion and profile analysis techniques. Both the bulk dry density of the bentonite and the composition of the external solution were varied. Increasing the bulk dry density of the bentonite resulted in a decrease of both the effective diffusion coefficient and the Cl-accessible porosity. Increasing the ionic strength of the external solutions resulted in an increase of both the effective diffusion coefficient and the Cl-accessible porosity. This can be explained by anion exclusion effects (Donnan exclusion). At high ionic strength values (I ? 1 M NaCl) the Cl-accessible porosity approaches the interparticle porosity. This interparticle porosity is the difference between the total and interlayer porosity of the bentonite. The interlayer porosity was found to depend on the degree of compaction. Up to a bulk dry density of 1300 kg m⁻³ the interlayer is built up of 3 water layers. Between 1300 and 1800 kg m⁻³ the interlayer water is reduced from 3 to 2 layers of water. Above 1800 kg m⁻³ evidence for a further decrease to 1 layer of water was found. These findings are in agreement with X-ray data found in the literature showing a decrease of the basal spacing of montmorillonite (the main clay mineral in bentonite) with increasing degree of compaction. The relationship between the effective diffusion coefficient of Cl⁻ and the diffusion-accessible porosity can be described by an empirical relationship analogous to Archie’s law. To predict the effective diffusion coefficient of Cl⁻ in compacted bentonite, the diffusion coefficient of Cl⁻ in water, the bulk dry density and the ionic strength of the pore water have to be known.