Diffusion Of Divalent Cations Research Articles

Forsteritic olivine in EH (enstatite) chondrite meteorites: A record of nebular, metamorphic, and crystal‐lattice diffusion effects

AbstractThe occurrence of forsteritic olivine in EH enstatite chondrites is indicative of bulk disequilibrium. In MgO‐rich magmatic systems, forsterite can either crystallize as a liquidus phase or be produced during peritectic melting of enstatite. Because diffusion of divalent cations through forsterite is relatively rapid, it records peak melting (i.e., chondrule‐forming events) and is also sensitive to subsequent metamorphism in the EH chondrite parent body. Here, we report the major and minor element geochemistry of olivine in EH chondrites across petrologic types 3 and 4. In all cases, olivine meets the technical definition of forsterite (>90 mole% Mg2SiO4). For unequilibrated EH chondrites, minor elements identify CaO‐Al2O3‐TiO2‐rich (refractory forsterite), MnO‐rich (“LIME” forsterite), and FeO‐bearing (forsteritic olivine) endmember components, the latter with Cr2O3‐rich and Cr2O3‐poor varieties. At higher petrologic type, minor element concentrations become restricted and compositions approach pure forsterite, while grain sizes reduce strongly with peak metamorphic temperatures. These changes reflect diffusive equilibration with enstatitic groundmass and dissolution reaction with free silica. The global geochemical distribution of forsteritic olivine in EH chondrites is, perhaps unexpectedly, more similar to those in low‐FeO type I chondrules and associated objects in carbonaceous chondrites (CCs), rather than equivalent objects in ordinary (H, L, LL), low‐FeO (or HH), or Kakangari (K) chondrites. Among achondrites, there is similarity between pure forsterite in aubrites and EH4 chondrites arising due to subsolidus equilibration in both settings, while Cr2O3‐poor forsteritic olivine in EH3 and CCs is similar to magnesian xenocrystic olivine in angrites. This might reflect CaO‐rich and SiO2‐poor magmatic sources across multiple early solar system reservoirs.

Bridging the Gap in Garnet Diffusion Models at Low Temperatures: Recalibration Using Western Tianshan Eclogitic Breccia

Abstract Models concerning the diffusion of divalent cations (Ca2+, Mg2+, Fe2+, and Mn2+) in garnet have been subject to extensive research and application over several decades, yet discrepancies among available models persist. Particularly the diffusion rate of Mn2+, which is the fastest in garnet, varies by more than two orders of magnitude for garnets in eclogite. In this study, we use an eclogitic breccia sample from the Western Tianshan (ultra-) high-pressure metamorphic belt for calibration. The thermobarometry indicates that the sample experienced exhumation from ~2.45 GPa, ~480°C to 1.85 GPa, ~515°C. Previous geochronological constraints estimate the exhumation duration to be a couple of million years to up to 15–20 Myr, with an average slab exhumation rate of ~3.5 mm/year. Although the estimates entail significant uncertainties, this range is still smaller than the discrepancy of Mn diffusion rate predicted among diffusion models. Thus, this natural sample provides valuable insights for calibrating the available diffusion models. Our analysis of garnet compositional profiles demonstrates that the diffusion rates (Di) at the pressure and temperature of interest are DCa:DFe:DMg:DMn = 0.2:0.4:1:2.4. By integrating garnet profiles, pressure–temperature–time information, and existing experimental data, we refine each diffusion model for Mn2+, thereby reducing the uncertainties associated with down-temperature extrapolation. Application of the newly calibrated models indicates that the oscillatory zoning of Mn2+ at the garnet rim is best described by a brief thermal excursion (~0.4 Myr, >20°C) at ~1.9 GPa. This minor thermal pulse punctuating the general exhumation path could be indicative of shear heating between nappes or momentary involvement in the mantle wedge, suggesting stacking or partial reactivation of the thrusts during exhumation.

Modeling diffusion in ionic, crystalline solids with internal stress gradients

Intracrystalline diffusion is an invaluable tool for estimating timescales of geological events. Diffusion is typically modeled using gradients in chemical potential caused by variations in composition. However, chemical potential is derived for uniform pressure and temperature conditions and therefore cannot be used to model diffusion when there are gradients in stress. Internal stress variations in minerals will create gradients in strain energy which, in addition to gradients in composition, will drive diffusion. Consequently, it is necessary to have a method that incorporates stress variations into diffusion models.To address this issue, we have derived a flux expression that allows diffusion to be modeled in ionic, crystalline solids under arbitrary stress states. Our approach is consistent with standard petrological methods but instead utilizes gradients in a thermodynamic potential called “relative chemical potential.” Relative chemical potential accounts for the lattice constraint in crystalline solids by quantifying changes in free energy due to the exchanges of constituents on lattice sites under arbitrary stress conditions. Consequently, gradients in relative chemical potential can be used to model diffusion when pressure is not uniform (i.e., under conditions of non-hydrostatic stress).We apply our derivation to the common quaternary garnet solid solution almandine–pyrope–grossular–spessartine. The rates and directions of divalent cation diffusion in response to stress are determined by endmember molar volumes or lattice parameters, elastic moduli, and non-ideal activity interaction parameters. Our results predict that internal stress variations of one hundred MPa or more are required to shift garnet compositions by at least a few hundredths of a mole fraction. Mineral inclusions in garnet present a potential environment to test and apply our stress-driven diffusion approach, as stress variations ranging from hundreds of MPa to GPa-level are observed or predicted around such inclusions. The ability to model stress-induced diffusion may provide new information about the magnitudes of both intracrystalline stresses and the timescales during which they occurred, imparting a better understanding of large-scale tectono-metamorphic processes.

Residence time of igneous garnet in Si-rich magmatic systems: Insights from diffusion modeling of major and trace elements

Although garnet is an important accessory phase in many granitic rocks, the petrogenetic history of such garnets is often debated. Explanations range from crystallization from (mostly) peraluminous melts to entrainment of peritectic or xenocrystic garnets originating from country rocks. Here we present a detailed microchemical study of a mid-crustal granodiorite from the Ivrea-Zone (N-Italy), which contains metapelitic enclaves and composite metamorphic-magmatic xeno-phenocryst garnet. Garnets from this locality exhibit high-phosphorus (∼800 ppm) metamorphic cores and multiple igneous overgrowth rims. The high-phosphorus cores appear to originate from granulite facies country-rock, while low-phosphorus rims indicate magmatic overgrowth in two main episodes. Zircon-bearing nanogranitoid inclusions are trapped along embayments between garnet cores and the first magmatic growth zones. Zirconium saturation thermometry indicates a temperature of 820 ± 5°C during the first magmatic overgrowth, and a temperature of 778 ± 10°C for the second overgrowth. The latter temperature agrees with garnet-biotite thermometry using the garnet rim composition, which yields a temperature of 773 ± 29 °C. In order to quantify the duration of the overgrowth episodes, we have numerically modeled Cr, Y, REEs and Hf trace element diffusion, as well as multicomponent major divalent cation diffusion within garnet using available experimental diffusion data and Cr diffusion data retrieved from natural garnets. All modeled diffusants conform to a single temperature-time path, in which the temperatures associated with the first and second magmatic overgrowths persisted for 5.4 and 6.3 kyr, respectively. Composite garnets in Si-rich magmatic systems have the potential to constrain magma transit rates in the continental crust.

Rapid reduction of basaltic glasses in piston-cylinder experiments: a XANES study

Graphite capsules are commonly used in high-temperature, high-pressure experiments, particularly for nominally anhydrous experiments and iron-bearing silicate samples. Due to the presence of graphite in the sample assembly, the oxygen fugacity for these experiments is thought to be relatively low, typically at or below the graphite-CO-CO2 buffer (CCO). The detailed mechanism and kinetics of redox control in graphite capsule experiments are, however, poorly understood. This is especially problematic for short duration experiments (e.g. kinetic experiments), because it is uncertain whether the experimental product will preserve its initial oxygen fugacity, or become reduced during the experiment. In this study, a set of basaltic glasses after high-temperature experiments in graphite capsules were analyzed by micro X-ray absorption near-edge structure (µ-XANES) to obtain their Fe3+/ΣFe profiles near the graphite–melt interface. The results show rapid reduction of ferric iron in the basaltic melt, reaching near-equilibrium in half an hour for samples of 2 mm diameter and 1.3–1.9 mm thickness. Even for a “time-zero” experiment, which was quenched immediately after reaching the target temperature, the reduction profile is over 100 µm in length. By comparing experiments at the same temperature and pressure but with different durations, the reduction reaction progress is found to be linear to the square root of duration, indicating that the reduction process is diffusion-controlled. Such a rapid reduction of the basaltic melt requires a mechanism that is significantly faster than divalent cation diffusion or oxygen diffusion, and is best explained by molecular hydrogen diffusion. It has been shown by previous studies that nominally anhydrous high-pressure experiments could contain significant amounts of water. Thousands of ppm of H2O could remain in the graphite capsule even after drying at 120 °C for an extended time period. At high temperatures, H2O reacts with graphite to produce molecular hydrogen, which then diffuses into the basaltic glass and causes reduction. This mechanism is also supported by a compensating H2O profile of equivalent length in the basaltic glass, showing evidence for H2O produced by molecular hydrogen reacting with ferric iron. A quantitative model is proposed and it successfully reproduces the Fe3+/ΣFe profiles in our experiments. The model helps explain the kinetics of the reduction process and demonstrates that for a basaltic glass with reasonable initial FeO* content, Fe3+/ΣFe ratios, and thicknesses, the equilibrium oxidation state can usually be reached in one hour at ~ 1300 °C and ~ 0.5 GPa. Although extrapolating our conclusion to the large range of graphite capsule experiments requires knowledge on how H2 solubility and diffusivity varies as a function of silicate composition, temperature, and pressure, the reduction process is expected to be rapid in general because H2 diffusivity is high in silicate melts. Our study elucidates the mechanism and rate of oxygen fugacity change in graphite capsule experiments. Based on thermodynamic calculations, the reaction between graphite capsule and H2O is expected to produce a C-O-H fluid with an intrinsic oxygen fugacity of CCO −0.9, which agrees well with the measured Fe3+/ΣFe ratios in the basaltic glasses and the estimated oxygen fugacity for graphite and Pt–graphite capsule experiments from a previous study. Future studies are needed to better constrain the kinetics of this process at different temperature, pressure, and in silicate melts of different compositions. The dynamic process of H2 diffusing and reducing Fe3+ to Fe2+ shown in our experiments also provides a potential way to determine the diffusivity and solubility of molecular hydrogen in silicate melts, which are crucial in understanding volatile behaviors on reducing planetary bodies, such as the Moon and Mercury.

Reconciliation of discrepant U–Pb, Lu–Hf, Sm–Nd, Ar–Ar and U–Th/He dates in an amphibolite from the Cathaysia Block in Southern China

We present a combined garnet Lu–Hf and Sm–Nd, zircon and monazite U–Pb, hornblende Ar–Ar, and zircon U–Th/He geochronology study on a garnet-bearing amphibolite from the Cathaysia Block in Southern China. Pseudosection modeling and garnet–clinopyroxene thermometry indicate that the amphibolite attained peak metamorphic conditions of approximately 0.9 GPa and 780 °C. The Lu–Hf garnet date of 402.7 ± 1.0 Ma and Sm–Nd date of 331.6 ± 3.6 Ma define a ~ 70 Myr difference for the same garnet fractions. Reconciling the large discrepancies between these three geochronological systems with the observed major element diffusion profiles in garnet requires that REEs and Hf were fully re-equilibrated at peak temperatures and that subsequent rapid cooling prevented any disruption of the Lu–Hf or Sm–Nd systems throughout cooling from high temperatures. The Sm–Nd garnet age was partially reset during a thermal pulse associated with intrusion of leucocratic veins, which is inferred to have occurred at ca. 226 Ma based on the coinciding hornblende Ar–Ar (222.3 ± 0.9 Ma) and monazite U–Pb (226.2 ± 2.3 Ma) dates. The T–t path of a reheating event at 226 Ma necessary to produce both the major divalent cation diffusion profiles in garnet and partial resetting of the Sm–Nd garnet age, such that it records an apparent age of ~ 332 Ma, requires an effective diffusion radius of 45–60 μm in garnet during reheating, which is in agreement with the observation of pervasive chlorite-filled fractures within single garnet grains. Diffusion kinetics of Lu and Hf in garnet are sufficiently slow that this reheating episode would not impact the Lu–Hf system, and the 402.7 ± 1.0 Ma garnet age likely reflects the onset of rapid cooling from peak P–T conditions. The zircon U–Pb date of 434.8 ± 2.7 Ma predates the Lu–Hf garnet date by approximately 30 Myr and is interpreted to reflect zircon crystallization during prograde metamorphism. The ~ 226 Ma reheating event is contemporaneous with the intrusion and crystallization of the widespread Triassic A-type granites and alkaline syenites across the Cathaysia Block, indicating an extensional environment. We interpret the zircon U–Th/He date of 143.1 ± 4.2 Ma as reflecting a third thermal pulse based on the concurrence with the early Cretaceous volcanic rocks and granitoids, which overlies the amphibolite.

Piezoelectric and mechanical properties of CaO reinforced porous PZT ceramics with one-dimensional pore channels

The formation of capillaries in sodium alginate gels is a dissipative process driven by unidirectional diffusion of divalent cations into sodium alginate sols. In the present work, we have prepared 3-1 type porous lead zirconate titanate (PZT) ceramics with oxides (CaO) being doped on a molecular level from the dissipative process by incorporating PZT particles into the sodium alginate gel matrix. By varying the concentration of cation solutions (CaCl2) from 0.5mol/L to 2.5mol/L, both the microstructure, doping amount of oxides (CaO) and crystalline phase of the porous PZT ceramics were tailored. Accordingly, increase in the concentration of Ca2+ has led to a reduction in the relative permittivity (εr) first, and then an increase, while the piezoelectric coefficient (d33 and d31) demonstrated an opposite variation tendency. The prepared samples possessed a maximal HFOM value of 4755×10–15Pa−1 when the concentration of Ca2+ was 1.0mol/L. Addition of CaO was found to improve the compressive strength of porous PZT ceramics, which was preferential to promoting the stability and reliability for application.

Role of Reverse Divalent Cation Diffusion in Forward Osmosis Biofouling.

We investigated the role of reverse divalent cation diffusion in forward osmosis (FO) biofouling. FO biofouling by Pseudomonas aeruginosa was simulated using pristine and chlorine-treated thin-film composite polyamide membranes with either MgCl2 or CaCl2 draw solution. We related FO biofouling behavior-water flux decline, biofilm architecture, and biofilm composition-to reverse cation diffusion. Experimental results demonstrated that reverse calcium diffusion led to significantly more severe water flux decline in comparison with reverse magnesium permeation. Unlike magnesium, reverse calcium permeation dramatically altered the biofilm architecture and composition, where extracellular polymeric substances (EPS) formed a thicker, denser, and more stable biofilm. We propose that FO biofouling was enhanced by complexation of calcium ions to bacterial EPS. This hypothesis was confirmed by dynamic and static light scattering measurements using extracted bacterial EPS with the addition of either MgCl2 or CaCl2 solution. We observed a dramatic increase in the hydrodynamic radius of bacterial EPS with the addition of CaCl2, but no change was observed after addition of MgCl2. Static light scattering revealed that the radius of gyration of bacterial EPS with addition of CaCl2 was 20 times larger than that with the addition of MgCl2. These observations were further confirmed by transmission electron microscopy imaging, where bacterial EPS in the presence of calcium ions was globular, while that with magnesium ions was rod-shaped.

Analysis of experimental data on divalent cation diffusion kinetics in aluminosilicate garnets with application to timescales of peak Barrovian metamorphism, Scotland

We present a new statistical framework to analyze the diffusion data for divalent cations (Fe, Mg, Mn, and Ca) in aluminosilicate garnet using published experimental data and an Arrhenius relationship that accounts for dependence on temperature, pressure, garnet unit-cell dimension, and oxygen fugacity. The regression is based on Bayesian statistics and is implemented by the Markov chain Monte Carlo approach. All reported experimental uncertainties are incorporated, and the data are weighted by the precision of the experimental conditions. We also include a new term, the inter-experiment bias, to compensate for possible inconsistencies among experiments and to represent any experimental variability not explicitly presented in the Arrhenius relationship (e.g., water content, defect density). At high temperatures where most experiments were conducted, the diffusion coefficients calculated with the new parameters agree well with previous diffusion models (e.g., Chakraborty and Ganguly in Contrib Mineral Petrol, 111:74–86, 1992; Carlson in Am Mineral, 91:1–11, 2006). However, the down-temperature extrapolation leads to notable differences at lower temperatures for common petrological applications. For example, at 600 °C, the diffusion coefficients of Fe and Mn are one half-to-one order of magnitude faster and the diffusion coefficient of Ca is about one order of magnitude slower than calculated with parameters in Carlson (2006). Our statistical analysis also provides well-defined uncertainty bounds for timescale estimates based on garnet diffusion profiles. Application of the newly derived coefficients indicates that the timescale of the thermal peak of Barrovian metamorphism (Dalradian belt of Scotland) is about four to seven times longer than that estimated using previously published diffusion coefficients. The peak is still geologically brief, however—of the order of 106 years (0.75 Myr +0.70/−0.36 Myr; ±1σ). This brevity requires pulsed advective heat input, as provided by syn-orogenic mafic magmatism in these rocks.

Increasing capillary diameter and the incorporation of gelatin enhance axon outgrowth in alginate-based anisotropic hydrogels

Substantial recovery of function following peripheral and central nervous system (CNS) injury critically depends on longitudinally directed axon regeneration across the injury site, which requires a mechanical guidance providing scaffold. We have previously shown that anisotropic alginate-based hydrogels with a defined capillary diameter (25 μm), which form via a self-organizing process driven by unidirectional diffusion of divalent cations into sodium alginate sols, promoted longitudinally oriented elongation of CNS axons in vitro and in vivo. In the present study the influence of various capillary diameters and the incorporation of gelatin to promote directed axon outgrowth and Schwann cell migration were assessed in a dorsal root ganglion outgrowth assay in vitro. Superimposing an alginate sol with Cu 2+, Sr 2+, or Zn 2+ ion containing solutions allowed the creation of hydrogels with capillaries 18, 25 and 55 μm in diameter, respectively. Axon outgrowth and Schwann cell migration were analyzed in terms of axon length/density and Schwann cell density within the capillary structures. Axon ingrowth into capillary hydrogels, which was always accompanied by Schwann cells, was enhanced with increasing capillary diameter. The incorporation of gelatin did not influence overall axon density, but promoted the length of axon outgrowth within the hydrogels. The longitudinal orientation of axons decreased in wider capillaries, which suggests that medium-sized capillaries are the optimal substrate to elicit substantial axon growth and longitudinal orientation after axon injury.

Diffusion and partition coefficients of minor and trace elements in San Carlos olivine at 1,300°C with some geochemical implications

Lattice diffusion coefficients have been determined for 19 elements (Li, Be, Na, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Y, Zr, Eu, Gd, Lu and Hf) in a single crystal of San Carlos olivine as a function of crystallographic orientation, at 1,300°C, 1 bar and fO2 = 10−8.3 bars, by equilibration with a synthetic silicate melt. Results for Li, Na, V, Cr, Fe and Zn are from diffusion of these elements out of the olivine, starting from their indigenous concentrations; those for all other elements are from diffusion into the olivine, from the silicate melt reservoir. Our 25-day experiment produced diffusion profiles 50 to > 700 μm in length, which are sufficiently long that precise analyses could be achieved by scanning laser ablation inductively coupled plasma mass spectrometry, even at concentration levels well below 1 μg g−1. For the divalent cations Ca, Mn, Fe and Ni, profiles were also obtained by electron microprobe analysis. The results of the two methods agree well with each other, and are consistent with divalent cation diffusion coefficients previously determined using different experimental methodologies. Olivine/melt partition coefficients retrieved from the data are also consistent with other published partitioning data, indicating that element incorporation and transport in olivine in our experiment occurred via mechanisms appropriate to natural conditions. Most of the examined trace elements diffuse through olivine at similar rates to the major octahedral cations Fe and Mg, showing that cation charge and radius have little direct influence on diffusion rates. Aluminium and P remain low and constant in the olivine, implying negligible transport at our analytical scale, hence Al and P diffusion rates that are at least two orders of magnitude slower than the other cations studied here. All determined element diffusivities are anisotropic, with diffusion fastest along the [001] axis, except Y and the REEs, which diffuse isotropically. The results suggest that element diffusivity in olivine is largely controlled by cation site preference, charge balance mechanisms and point-defect concentrations. Elements that are present on multiple cation sites in olivine (e.g. Be and Ti) and trivalent elements that are charge-balanced by octahedral site vacancies tend to diffuse at relatively fast rates.

Fe–Mg interdiffusion in wadsleyite: The role of pressure, temperature and composition and the magnitude of jump in diffusion rates at the 410 km discontinuity

The limited stability range of wadsleyite seriously impedes our ability to constrain kinetic parameters (e.g. activation energy, activation volume) using experiments carried out over a wide range of temperature and pressure. We have carried out a new measurement to extend the experimental temperature range of the dataset of Chakraborty et al. [Chakraborty, S., Knoche, R., Schulze, H., Rubie, D.C., Dobson, D., Ross, N.L., Angel, R.J., 1999. Enhancement of cation diffusion rates across the 410-kilometer discontinuity in Earth’s mantle. Science 283, 362–365] to the maximum possible limit for that experimental setup. This result allows us to (i) obtain a better constrained value for activation energy for Fe–Mg diffusion in wadsleyite at 15 GPa (∼230 kJ/mol), and (ii) characterize the compositional dependence of Fe–Mg diffusion in wadsleyite. Evaluation of all data available in the literature [i.e. this study; Chakraborty et al., 1999; Farber, D.L., Williams, Q., Ryerson, F.J., 2000. Divalent cation diffusion in Mg 2SiO 4 spinel (ringwoodite), β-phase (wadsleyite), and olivine: implications for the electrical conductivity of the mantle. J. Geophys. Res. 105, 513–529; Kubo, T., Shimojuko, A., Ohtani, E., 2004. Fe–Mg interdiffusion rates in wadsleyite and the diffusivity jump at the 410 km discontinuity. Phys. Chem. Miner. 31, 456–464] reveals that there is a strong pressure dependence of the diffusion coefficient (activation volume ≈14 cm 3/mol). The expression D ( m 2 /s ) = 1.24 × 10 − 6 exp [ 11.8 ( 0.86 − X Mg ) ] exp − 229,000 + ( P − 15 ) × 13.9 × 10 3 J/mol R T is an excellent description of all experimentally measured diffusion coefficients in wadsleyite and points to consistency between the various studies from different laboratories that used different methods. This expression should provide a robust basis for extrapolation of diffusion data for wadsleyite to conditions removed from the experimental ones, e.g. for modeling processes in the interiors of cold subducting slabs. Moreover, characterization of fO 2 and water contents of wadsleyites in the current study and consideration of the pressure dependence of diffusion rates in olivines confirms that the jump in diffusion rates at the olivine–wadsleyite boundary in the transition zone is at least six orders of magnitude; increased water contents in wadsleyite can cause the actual enhancement [Kubo et al., 2004] to be as much as seven orders of magnitude. Taken together with the observation that diffusive mixing is practically impossible in the lower mantle [Holzapfel, C., Rubie, D.C., Frost, D.J., Langenhorst, F., 2005. Fe–Mg interdiffusion in (Mg,Fe)SiO 3 perovskite and lower mantle reequilibration. Science 309, 1707–1710] has a maximum at the lithosphere–asthenosphere boundary in the olivine-bearing upper mantle [Holzapfel, C., Chakraborty, S., Rubie, D.C., Frost, D.J., 2007. Effect of pressure on Fe–Mg, Ni and Mn diffusion in (Fe x Mg 1− x ) 2SiO 4 olivine. Phys. Earth Planet. Int. 162, 186–198], and decreases with depth within the transition zone (this work), these results establish the base of the lithosphere and the top of the mantle transition zone as the key regions for mixing and erasure of chemical heterogeneities in the mantle.

Kinetics and mechanisms of iron redox reactions in silicate melts: The effects of temperature and alkali cations

The kinetics and the mechanisms of iron redox reactions in molten Fe-bearing pyroxene compositions have been investigated by Raman spectroscopy and X-ray absorption Near Edge Structure (XANES) experiments at the iron K-edge. The former experiments have been made only near the glass transition whereas the latter have also been performed from about 1300 to 2100 K. The same kinetics are observed with both techniques. They are described by characteristic times that depend primarily on temperature and not on the initial redox state. At high temperatures, where both kinds of reactions could be investigated, these times are similar for oxidation and reduction. From these characteristic times we have calculated as a function of temperature and composition a parameter termed effective redox diffusivity. For a given melt, the diffusivities follow two distinct Arrhenius laws, which indicate that the mechanisms of the redox reaction are not the same near the glass transition and at high temperatures. As is now well established, diffusion of divalent cations is the dominant mechanism at low temperatures but the enhanced kinetics observed for alkali-bearing melts indicate that Li + and Na + also participate in ionic transport. At superliquidus temperatures, in contrast, diffusion of oxygen represents the dominant mechanism.

Uranium and manganese diffusion in apatite

Diffusion of manganese and uranium has been characterized by Rutherford Backscattering Spectrometry (RBS) in fluorapatite. The following Arrhenius relation is obtained for Mn diffusion in natural Durango fluorapatite, for diffusion parallel to c: D Mn = 5.4 × 10 − 7 exp ( − 288 kJ mol − 1 / R ⁢ T ) m 2 s − 1 . Mn diffusion normal to c appears to be similar to diffusion parallel to c, and diffusivities in natural and synthetic (free of significant amounts of REE or other minor constituents) apatites are the same within experimental uncertainties. Experiments run in air, where Mn is in a more oxidized state, yield diffusivities similar to those for experiments run in sealed silica capsules, which the above Arrhenius relation represents. Uranium diffusion experiments over the temperature range 1000–1300 °C yield the following Arrhenius relation for diffusion parallel to c: D U = 1.3 × 10 − 6 exp ( − 394 kJ mol − 1 / R ⁢ T ) m 2 s − 1 . Diffusion coefficients for transport normal to c are quite similar to those parallel to c. U diffusion experiments run in air, where U is most likely hexavalent, yield diffusivities about an order of magnitude slower than the Ni–NiO buffered experiments. Diffusivities of Mn are comparable to those established previously for Sr and are slightly slower than Pb in apatite. The similar diffusion rates for Sr and Mn, despite their significant differences in cationic radii, suggest that cation size does not exert strong influence on diffusion of divalent cations in apatite, a finding consistent with that previously observed for the trivalent REE. In contrast, cation charge does seem to influence diffusivities strongly in apatite (although Mn appears perhaps something of an exception). U diffusion (buffered at NNO) is about 4 orders of magnitude slower than Mn diffusion, and about 2 orders of magnitude slower than REE diffusion. The differences between U diffusivities in experiments run with the NNO buffer, when U is more likely in the tetravalent state, and in air, where U is hexavalent, are also consistent with this observation.

Rare earth element diffusion in a natural pyrope single crystal at 2.8 GPa

Volume diffusion rates of Ce, Sm, Dy, and Yb have been measured in a natural pyrope-rich garnet single crystal (Py71Alm16Gr13) at a pressure of 2.8 GPa and temperatures of 1,200–1,450 °C. Pieces of a single gem-quality pyrope megacryst were polished, coated with a thin layer of polycrystalline REE oxide, then annealed in a piston cylinder device for times between 2.6 and 90 h. Diffusion profiles in the annealed samples were measured by SIMS depth profiling. The dependence of diffusion rates on temperature can be described by the following Arrhenius equations (diffusion coefficients in m2/s): \(\)\(\matrix{ {\log _{10} D_{{\rm Yb}} = ( - 7.73 \pm 0.97) - \left( {343 \pm 30\;{\rm kJ}\;{\rm mol}^{{\rm - 1}} /2.303RT} \right)} \cr {\log _{10} D_{{\rm Dy}} = ( - 9.04 \pm 0.97) - \left( {302 \pm 30\;{\rm kJ}\;{\rm mol}^{{\rm - 1}} /2.303RT} \right)} \cr {\log _{10} D_{{\rm Sm}} = ( - 9.21 \pm 0.97) - \left( {300 \pm 30\;{\rm kJ}\;{\rm mol}^{{\rm - 1}} /2.303RT} \right)} \cr {\log _{10} D_{{\rm Ce}} = ( - 9.74 \pm 2.84) - \left( {284 \pm 91\;{\rm kJ}\;{\rm mol}^{{\rm - 1}} /2.303RT} \right)} \cr } \) . There is no significant influence of ionic radius on diffusion rates; at each temperature the diffusion coefficients for Ce, Sm, Dy, and Yb are indistinguishable from each other within the measurement uncertainty. However, comparison with other diffusion data suggests that there is a strong influence of ionic charge on diffusion rates in garnet, with REE3+ diffusion rates more than two orders of magnitude slower than divalent cation diffusion rates. This implies that the Sm–Nd isotopic chronometer may close at significantly higher temperatures than thermometers based on divalent cation exchange, such as the garnet–biotite thermometer. REE diffusion rates in pyrope are similar to Yb and Dy diffusion rates in diopside at temperatures near the solidus of garnet lherzolite (~1,450 °C at 2.8 GPa), and are an order of magnitude faster than Nd, Ce, and La in high-Ca pyroxene at these conditions. At lower temperatures relevant to the lithospheric mantle and crust, REE diffusion rates in garnet are much faster than in high-Ca pyroxene, and closure temperatures for Nd isotopes in slowly-cooled garnets are ~200 °C lower than in high-Ca pyroxene.

Divalent cation diffusion in Mg2SiO4 spinel (ringwoodite), β phase (wadsleyite), and olivine: Implications for the electrical conductivity of the mantle

Mg‐Fe and Mg‐Ni interdiffusion coefficients have been measured in single‐crystal olivine (α‐(Mg,Ni,Fe)2SiO4), polycrystalline β phase (β‐(Mg,Ni,Fe)2SiO4), and silicate spinel (γ‐(Mg,Ni,Fe)2SiO4) at 1473 K between 1 and 14 GPa under controlled thermodynamic conditions. In olivine, DMg‐Niα ranges from 10−17 m2 s−1 at 1 GPa to 4×10−18 m2 s−1 at 9 GPa, and DMg‐Feα ranges from 3×10−15 m2 s−1 at 1 GPa to 10−15 m2 s−1 at 4 GPa. At 9 GPa the cation diffusion rates in γ spinel are ∼3 orders of magnitude higher than those in olivine; between 9 and 14 GPa, DMg‐Niγ decreases from 8×10−15 to 9×10−16 m2 s−1, and DMg‐Feγ decreases from 2×10−13 to 5×10−14 m2 s−1. Between 10 and 14 GPa the diffusion coefficients for both Fe and Ni are similar in magnitude and pressure dependence between β phase and γ spinel. The activation volumes for Mg‐Ni diffusion are 3.2 and 6.7 cm3 mol−1 in the α and γ(β) phases, respectively, and for Mg‐Fe diffusion are 5.4 and 6.1 cm3 mol−1 in the α and γ(β) phases, respectively. Our results demonstrate that extreme differences in transport properties are expected to occur across the 400 km discontinuity. A model for electrical conductivity in the upper mantle involving two mechanisms for electrical conduction, with one mechanism being associated with a hydrogen or defect‐related conduction process and the other involving a straightforward application of the Nernst‐Einstein equation to our cationic diffusion data, reproduces geomagnetic sounding results for the upper mantle and shallow transition zone. This modeling yields an order of magnitude increase in electrical conductivity across the 400 km discontinuity, with little or no change in conductivity occurring near 520 km depth. Our modeling suggests that divalent cation diffusion is the dominant mechanism of charge transport between 400 and 670 km depth and that the high‐pressure olivine polymorphs dominate the electrical behavior of the deep upper mantle. Comparison between field‐based deep‐mantle conductivity profiles derived from magnetotelluric studies and extrapolation of our model suggests that a discontinuity in electrical transport properties exists at the base of the transition zone as well. Similarly, given the dramatic differences in chemical diffusion between different polymorphs of olivine, it is possible that other transport property‐mediated processes, such as viscous flow, could dramatically change across the 400 and 670 km discontinuities; such changes are less likely to occur at 520 km depth.

Diffusion of Ca and Mg in calcite

The self-diffusion of Ca and the tracer diffusion of Mg in calcite have been measured experimentally using isotopic tracers of 25 Mg and 44 Ca. Natural single crystals of calcite were coated with a thermally sputtered oxide thin film and then annealed in a CO 2 gas at 1 atm total pressure and temperatures from 550 to 800 °C. Diffusion coefficient values were derived from the depth profiles obtained by ion microprobe analysis. The resultant activation energies for Mg tracer diffusion and Ca self-diffusion are, respectively: E a (Mg) = 284 ± 74 kJ/mol and E a (Ca) = 271 ± 80 kJ/mol. For the temperature ranges in these experiments, the diffusion of Mg is faster than Ca. The results are generally consistent in magnitude with divalent cation diffusion rates obtained in previous studies, and provide a means of interpreting the thermal histories of carbonate minerals, the mechanism of dolomitization, and other diffusion-controlled processes. The results indicate that cation diffusion in calcite is relatively slow and cations are the rate-limiting diffusing species for the deformation of calcite and carbonate rocks. Application of the calcite-dolomite geothermometer to metamorphic assemblages will be constrained by cation diffusion and cooling rates. The direct measurement of Mg tracer diffusion in calcite indicates that dolomitization is unlikely to be accomplished by Mg diffusion in the solid state but by a recrystallization process.

Impregnation-induced memory effect of thermally activated layered double hydroxides

The memory effect of calcined Cu–Co–Zn–Al layered double hydroxides (LDH) upon impregnation with K-containing solutions was studied. A sample of nominal composition CuCoZn 2Al 4O x was prepared by coprecipitation at controlled pH. The resulting hydrotalcite-like (HT) precipitate was calcined at 673, 773, or 873 K. The products were impregnated with different K-containing solutions [K 2CO 3(aq), KOH (aq) and KOH (alc)]. Reconstruction of the HT phase upon impregnation was followed by X-ray diffraction. The HT recrystallization was favored by impregnating calcined LDH samples with K 2CO 3(aq) by wet impregnation. The memory effect was reduced by increasing the calcination temperature of the parent layered double hydroxide. It is proposed that the reconstruction of the HT phase occurs via a retro-topotactic transformation from the Al 3+ and divalent cations located both in the octahedral sites of the oxide matrix. The increase of the calcination temperature causes the solid-state diffusion of divalent cations into tetrahedral positions which results in the progressive formation of stable normal spinels. After calcination at 873 K, all the divalent cations occupy tetrahedral sites and the memory effect disappears.

The restriction of diffusion of cations at the external surface of cardiac myocytes varies between species

In cardiac muscle sarcolemmal structures such as T-tubules, caveolae and negatively charged protein-polysaccharides may affect the rate of cation exchange on the external surface of the cells. To test this hypothesis, we examined the rate of external cation exchange in adult rabbit and rat ventricular myocytes using a rapid solution switcher to change the bulk external solution within 4 ms. To assess the rate of diffusion of monovalent cations, we increased [K+]o from 4.4 to 6.6 or 8.8 mM and measured the time required to achieve a stable membrane depolarization. In rat myocytes, the mean time to 90% depolarization (t90) was significantly longer than that in rabbit myocytes (137 and 64 ms, respectively) and the difference in t90 was not associated with the cell size. To assess the time course of exchange of external Ca2+, we rapidly exposed the myocytes to 0 Ca2+-2 mM EGTA solution at specific time points before action potentials or voltage clamp steps, and measured the rate of alteration of the normalized peak [Ca2+]i transient (Flux-3) or Ca2+ current. Exposure to 0 Ca2+-2 mM EGTA solution caused a decline in the intracellular calcium transient. In rat myocytes, the rate of decline in the [Ca2+]i transient was much slower (t90 > 1500 ms, the time required for 90% decline) than for the rabbit (t90 = 295 ms). Also, the rate of decline in the Ca2+ current was prolonged in rat myocytes (t90 = 910 ms) compared with rabbit myocytes (t90 = 241 ms). These data indicate that there is a restricted space on the external surface of sarcolemma which limits diffusion of divalent cations more markedly than monovalent cations. The extent of this limitation of cation diffusion varies between species, and may have functional significance.

The mechanism of oxidation of a basaltic glass: Chemical diffusion of network-modifying cations

Rutherford backscattering spectroscopy, in conjunction with optical and scanning electron microscopy, has been used to characterize the oxidation process in a homogeneous, well-annealed glass prepared from a nepheline-normative olivine basalt. Initially melted and annealed at an oxygen fugacity substantially below the quartz-fayalite-magnetite (QFM) buffer, the glasses were oxidized in air under the time and temperature ranges 1–100 h and 550–600°C, respectively. Oxidation causes (1) formation of crystalline CaO and MgO that partially covers the free surface of the glass and (2) an internal reaction zone that is depleted of Ca2+ and Mg2+ but enriched in Na+ The reaction morphology is uniquely consistent with a model in which oxidation occurs by the outward diffusion (to the free surface) of Ca2+ and Mg2+ that is charge compensated by an inward flux of electron holes (polarons): oxidation of the glass occurs as the oxygen/cation ratio increases, not by addition of oxygen, but rather by removal of cations. The flux of Na+ from depth in the glass to the oxidizing region, which is also charge compensated by a counterflux of electron holes, is a response to the thermodynamic driving force seeking to stabilize Fe3+ as a network former, consistent with equilibrium thermodynamic and spectroscopic studies. Growth of the oxidized/transformed glass follows parabolic (chemical-diffusion-limited) kinetics. Using a first-order, Wagnerian approach, the diffusion coefficient and driving force terms of the parabolic reaction-rate constant are separated, giving an average divalent cation diffusion coefficient of D̄A2+(cm2·s−1) = 9.9 × 10−2exp−210kJ·mol−1RT. The oxidation mechanism seen for the glass, that is, one dominated by diffusion of network modifying cations and not an oxygen species, is anticipated to also occur in iron-bearing aluminosilicate melts: the discrepancy between the kinetics of redox reactions and of oxygen tracer diffusion noted in the literature for melts is most likely explained in this way.