Potassium and sodium self-diffusion in alkali feldspar

The rate of potassium self-diffusion in pure microcline was measured between 600° and 800° C using K⁴⁰ as a tracer. Transport of K⁴⁰ by processes other than volume diffusion was insignificant or minimal. Isotropic diffusion coefficients were calculated assuming spherical grains. The data are well fit by the Arrhenius relation and yield a pre-exponential factor (D₀) of 133.8 cm²/sec and an activation energy (Q) of 70 kcal/mole. Similar experiments on the self-diffusion of Na²² in a pure low-albite (exchanged microcline) yield D₀ of 2.31×10^–6 cm²/sec and Q of approximately 19 kcal/mole for the temperature interval from 200° to 600° C. The large difference in these activation energies suggests that the atomic mechanisms for sodium and potassium diffusion are different.     

Retention of ion-implanted-xenon in olivine: Dependence on implantation dose

The diffusion of Xe in olivine, a major mineral in both meteorites and lunar samples, was studied. Xe ions were implanted at 200 keV into single-crystal synthetic-forsterite targets and the depth profiles were measured by alpha particle backscattering before and after annealing for 1 hour at temperatures up to 1500°C. The fraction of implanted Xe retained following annealing was strongly dependent on the implantation dose. Maximum retention of 100% occurred for an implantion dose of 3 × 10¹⁵ Xe ions/cm². Retention was less at lower doses, with ≥ 50% loss at 1 × 10¹⁴ Xe ions/cm². Taking the diffusion coefficient at this dose as a lower limit, the minimum activation energy necessary for Xe retention in a 10 μm layer for 10⁷ years was calculated as a function of metamorphic temperature. For example, an activation energy of 50 kcal/mole implies Xe retention may be possible for metamorphic temperatures below 500°C.     

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.     

The dolomitization of CaCO3: an experimental study at 252–295°C

The results of experiments on the hydrothermal dolomitization of calcite (between 252 and 295°C) and aragonite (at 252°C) by a 2 M CaCl₂-MgCl₂ aqueous solution are reported and discussed. Dolomitization of calcite proceeds via an intermediate high (ca. 35 mole %) magnesian calcite, whereas that of aragonite is carried out through the conversion of the reactant into a low (5.6 mole %) magnesian calcite which in turn transforms into a high (39.6 mole %) magnesian calcite. Both the intermediate phases and dolomite crystallize through a dissolution-precipitation reaction. The intermediate phases form under local equilibrium within a reaction zone surrounding the dissolving reactant grains. The volume of the reaction zone solution can be estimated from Sr²⁺ and Mg²⁺ partitioning equations. In the case of low magnesian calcite growing at the expense of aragonite at 252°C, the total volume of these zones is in the range of 2 × 10^?5 to 2 × 10^?4 1., out of 5 × 10^?3 1., the volume of the bulk solution.The apparent activation energies for the initial crystallization of high magnesian calcite and dolomite are 48 and 49 kcal/mole, respectively.Calcite transforms completely into dolomite within 100 hr at 252°C. The overall reaction time is reduced to approximately 4 hr at 295°C. The transformation of aragonite to dolomite at 252°C occurs within 24 hr. The nature of the reactant dictates the relative rates of crystallization of the intermediate phases and dolomite. With calcite as reactant, dolomite growth is faster than that of magnesian calcite; this situation is reversed when aragonite is dolomitized.Coprecipitation of Sr²⁺ with dolomite is independent of temperature (within analytical error) between 252 and 295°C. Its partitioning, with respect to calcium, between dolomite and solution results in distribution coefficients in the range of 2.31 × 10^?2 to 2.78 × 10^?2.     

Geothermochronology based on noble gases: II. Stability of the (U-Th)/He isotope system in zircon

The kinetics of He migration from zircon of variable degree of metamictization was investigated. The migration parameters of He were experimentally determined, the influence of radiation damage and the degree of metamictization on the stability of the (U-Th)/He isotope system was evaluated, the mechanisms of noble gas escape from zircon were investigated, new data on the kinetics of He migration were obtained and compared with previous results for the kinetics of Xe migration from zircon of the same geologic objects. It was shown that He occurs in two energy positions in the zircon lattice: the main position (more than 80% He) with an activation energy of ∼39 kcal/mol and k ₀ = 10¹¹ yr⁻¹ and the second position with an activation energy for migration of 5–10 kcal/mol and k ₀ ∼ 10⁶ yr⁻¹. It was concluded that He migration from the main energy position is better described by a single-jump mechanism. The migration of He from the second energy position is consistent with the diffusion mechanism. It was shown that deviations from the linear dependence in the lnln(He₀/He_t)-1/T coordinates are probably related to the destruction of volume defects containing He atoms at high temperatures (more than 1000°C on the experimental time scale) resulting in a change from the single-jump to diffusion mechanism and the presence of atoms migrating via the diffusion mechanism. It was shown that the peak width in the spectrum of radiogenic He release and the appearance of a second peak also depend on the fraction of atoms migrating in accordance with the diffusion mechanism. It was found that the low activation energy for He release from the second energy position indicates the existence of continuous He loss from the zircon lattice.     

Diffusion kinetics of proton-induced Ne, He, and He in quartz

A natural quartz sample free of mineral and fluid inclusions was irradiated with a 200 MeV proton beam to produce spallogenic ²¹Ne, ³He and ⁴He. Temperature-dependent diffusivities of these three nuclides were then determined simultaneously by high precision stepped-heating and noble gas mass spectrometry. The outward mobility of proton-induced nuclides reflects diffusion through the quartz lattice. In the studied range of 70 to 400°C the helium diffusion coefficients exceed those of neon by 5-7 orders of magnitude. The implied diffusion parameters E_a = 153.7 ± 1.5 (kJ/mol) and ln(D_o/a²) = 15.9 ± 0.3 (ln(s⁻¹)) and E_a = 84.5 ± 1.2 (kJ/mol) and ln(D_o/a²) = 11.1 ± 0.3 (ln(s⁻¹)) for proton-induced ²¹Ne and ³He, respectively, indicate that cosmogenic neon will be quantitatively retained in inclusion-free quartz at typical Earth surface temperatures whereas cosmogenic helium will not. However, the neon diffusion parameters also indicate that diffusive loss needs to be considered for small (<1 mm) quartz grains that have experienced elevated temperatures. Since natural quartz often contains fluid inclusions which may enhance noble gas retentivity, these parameters likely represent an end-member case of purely solid-state diffusion. The ∼70 kJ/mol higher activation energy for neon diffusion compared to helium diffusion likely represents an energy barrier related to its ∼13% greater diameter and provides a fundamental constraint with which to test theories of solid state diffusion. The diffusion parameters for proton-induced ⁴He are indistinguishable from those for ³He, providing no evidence for the commonly expected inverse square root of the mass diffusion relationship between isotopes. We also find preliminary indication that increased exposure to radiation may enhance neon and helium retentivity in quartz at low temperatures.     

Diffusion in single crystal of melilite: interdiffusion of Al + Al vs. Mg + Si

Interdiffusion coefficients of Al + Al vs. Mg + Si in the gehlenite–åkermanite system of melilite were determined by coupled annealing of synthesized end-member single crystals. The observed diffusion coefficients for a couple-annealed sample vary for about 2 orders of magnitude, showing strong dependence on the gehlenite–åkermanite composition: diffusion coefficient observed at 1350 °C, for example, is 3 × 10^?13 cm² s^?1 at 5 mol% åkermanite composition (Ak₅), increases to 2 × 10^?11 cm² s^?1 at Ak₈₀, and then decreases to 1 × 10^?12 cm² s^?1 at Ak₉₅. The diffusion coefficient–temperature relation indicates high activation energy of diffusion of about 420 kJ mol^?1 for gehlenite-rich melilite. The observed diffusion coefficient–composition relation may be explained by a combination of (1) the diffusion coefficient–melting temperature relation (Flynn's rule) and (2) the feasibility of local charge compensation, which can possibly be maintained more easily in the intermediate chemical composition. The high activation energy value for gehlenitic melilite appears to correspond to the complex diffusion mechanism. The observed highly variable diffusion coefficients suggest that gehlenite–åkermanite zoning in the melilite crystals in Ca, Al-rich inclusions in the carbonaceous meteorites may provide a sensitive indicator for the thermal history of the inclusions.     

Chemical diffusion of fluorine in jadeite melt at high pressure

The chemical diffusion of fluorine in jadeite melt has been investigated from 10 to 15 kbars and 1200 to 1400°C using diffusion couples of Jadeite melt and fluorine-bearing jadeite melt (6.3 wt.% F). The diffusion profile data indicate that the diffusion process is concentration-independent, binary, F-O interdiffusion. The F-O interdiffusion coefficient ranges from 1.3 × 10^?7 to 7.1 × 10^?7 cm²/sec and is much larger than those obtained by Kushiro (1983) for Si-Ge and Al-Ga interdimision in jadeitic melts. The Arrhenius activation energy of diffusion is in the range of 36 to 39 kcal/mole as compared with 19 kcal/mole for fluorine tracer diffusion in a lime-aluminosilicate melt. The diffusivity and activation energy of F-O interdiffusion vary slightly with pressure, but the pressure dependence of F-O, Al-Ga and Si-Ge interdiffusion may be related to the relative volumes of the interdiffusing species for each pair. The magnitude of chemical diffusivity of fluorine is comparable to that of the chemical diffusivity of water in obsidian melts. The diffusivities of various cations are significantly increased by the addition of fluorine or water to a silicate melt. This fact, combined with the high diffusivity of fluorine, suggests that the F^? ion is the principal diffusing species in dry aluminosilicate melts and that dissolved fluorine will accelerate chemical equilibration in dry igneous melts.     

Oxygen chemical diffusion in three basaltic liquids at elevated temperatures and pressures

The diffusivity of oxygen has been measured in three basaltic liquids from 1280 to 1450°C and 4 to 21 kilobars using a solid media piston-cylinder apparatus. The measurements were done by monitoring the reduction of ferric iron in previously oxidized spheres of basalt melt. The compositions studied were olivine nephelinite, alkali basalt, and 1921 Kilauea tholeiite.The isobaric temperature dependence of oxygen diffusivity is adequately described by Arrhenius relationships for the three liquids studied. Arrhenius activation energies were determined at 12 kilobars for olivine nephelinite (62± 6 kcal/mole) and tholeiite (51 ± 4 kcal/mole) and at 4, 12, and 20 kilobars for alkali basalt (70 ± 7, 86 ± 6, and 71 ± 14 kcal/mole, respectively). The Arrhenius parameters for the three compositions define a compensation law which is indistinguishable from those for oxygen diffusion in simple silicate melts (DUNN, 1982) and for divalent cation diffusion in basaltic melts (Hofmann, 1980). These results suggest that the principal species contributing to the total diffusivity of oxygen is the oxide anion (O^2?).The isothermal pressure dependence of oxygen diffusion is complex and quite different from that observed for cationic diffusion in silicate melts. All three compositions show a sharp decrease in oxygen diffusivity at approximately the same pressure as the change in the liquidus phase from olivine to pyroxene, but otherwise the pressure dependence can be described by Arrhenius type equations. The equations yield negative activation volumes for the olivine nehpelinite and the alkali basalt. The activation volumes determined for the tholeiite are near zero at low pressure and positive at high pressure. A negative activation volume represents a decrease in the average size of the principal diffusing species.The results of this study are consistent with a melt model which includes both continuous changes in the relative proportions of the various anionic species in the melt with pressure and the occurrence of anionic disproportionation reactions within narrow pressure ranges.     

Interdiffusion of Mg–Fe in olivine at 1,400–1,600 °C and 1 atm total pressure

The interdiffusion coefficient of Mg–Fe in olivine (D _Mg–Fe) was obtained at 1,400–1,600 °C at the atmospheric pressure with the oxygen fugacity of 10^?3.5–10^?2 Pa using a diffusion couple technique. The D _Mg–Fe shows the anisotropy (largest along the [001] direction and smallest along the [100] direction), and its activation energy (280–320 kJ/mol) is ~80–120 kJ/mol higher than that estimated at lower temperatures. The D _Mg–Fe at temperatures of >1,400 °C can be explained by the cation-vacancy chemistry determined both by the Fe³⁺/Fe²⁺ equilibrium and by the intrinsic point defect formation with the formation enthalpy of 220–270 kJ/mol depending on the thermodynamical model for the Fe³⁺/Fe²⁺ equilibrium in olivine. The formation enthalpy of 220–270 kJ/mol for the point defect (cation vacancy) in olivine is consistent with that estimated from the Mg self-diffusion in Fe-free forsterite. The increase in the activation energy of D _Mg–Fe at >1,400 °C is thus interpreted as the result of the transition of diffusion mechanism from the transition metal extrinsic domain to the intrinsic domain at the atmospheric pressure.     

Concentrations and behavior of oxygen and oxide ion in melts of composition CaO · MgO · xSiO2

The concentrations and behavior of oxygen and oxide ion were studied in silicate melts of composition CaO · MgO · xSiO₂ (1.25 ≤ x ≤ 3) in the temperature range 1425 to 1575°C by cyclic voltammetry and chronopotentiometry. Electroreduction of oxygen is a reversible, 2 electron process involving dissociated oxygen atoms. The Henry's Law constant for O₂ in molten diopside (CaO · MgO · 2SiO₂) is 0.023 ± 0.004 mole/l atm at 1450°C. The diffusion coefficient for molecular oxygen in diopside melt is 4.5 ± .5 × 10^?6 cm²/sec at 1450°C and the activation energy of diffusion is 80 ± 2 kcal/mole. Oxide ions produced by electroreduction of oxygen, rapidly dissociate silicate polymers, causing the concentration of free oxide ions in diopside melt to be buffered at a low level (4.7 ± .8 × 10^?5 mole/l). The concentration of free oxide ion increases at higher proportions of metal oxides but remains at this value in more silicic melts. The rate of formation of oxide ions by polymerization in diopside melt is 0.021 ± .007 mole/l sec. Thermodynamic parameters (the standard free energy, enthalpy and entropy) for the oxidation of Ni, Co, and Zn in diopside melt in equilibrium with gaseous oxygen agree with those for solid oxide systems. The platinum reference electrode in molten diopside is a reversible, oxygen electrode.     

Premelting and high-temperature diffusion of Ca in synthetic diopside: An increase of the cation mobility

A study of Ca self-diffusion along the b axis in synthetic (iron free) diopside single crystal was performed at temperatures ranging from 1273 K to 1653 K. Diffusion profiles of ⁴⁴Ca were measured using α-particles Rutherford Backscattering (α-RBS) micro analysis. We unambiguously find two distinct diffusional regimes, characterized by activation enthalpies H = 280 ± 26 kJ/mol and H = 951 ± 87 kJ/mol at temperatures lower and upper than 1515 K, respectively. This change of diffusion regime takes place near the onset of premelting as detected in calorimetric measurements and can be interpreted in terms of enhanced formation of Frenkel point defects with an activation enthalpy of formation of 1524 ± 266 kJ/mol (H _f/2 = 762 kJ/mol), in accordance with our high-temperature diffusion data. If premelting of diopside is actually related to Ca-Frenkel point defect concentration, this concentration could reach up to few mole percents close to the melting temperature.     

Exfoliation and diffusion following helium ion implantation in fluorapatite: implications for radiochronology and radioactive waste disposal

The properties of fluorapatite, both a useful radiochronometer and a potential storage matrix specific for minor actinides produced by the reprocessing of spent nuclear fuel, have been investigated with emphasis to its response to alpha decay. Exfoliation, which occurs after implantation of high doses of 1.6-MeV He-ions (>1.4×10¹⁷ ions cm⁻², corresponding to 5% atomic proportion), could set an upper limit to the concentration of imbedded actinides (about 2 atoms % corresponding to 20 wt. %) or storage age unless significant diffusion of radiogenic He intervenes. This process has been studied by combining He implantation, thermal treatments in the temperature range 124–250°C and measurement of the resulting He profile by an ion beam technique (ERDA) using 8.5-MeV C ions. The diffusion coefficient follows an Arrhenius' law with an activation energy of 120 (±2) KJ/mole and a frequency factor of 14.5 (±7)×10⁻³ cm² sec⁻¹ in agreement with literature data. The inferred closure temperature which validates the U,Th–He radiochronological method also fits previous values: 97 (±10)°C for grain size 165 μm. With respect to radwaste disposal. He volume diffusion is too small to exclude the occurrence of exfoliation unless diffusion at grain boundary is much higher and a fine-grain matrix is deliberately chosen.     

Mg tracer diffusion in aluminosilicate garnets at 750-850° C, 1 atm. and 1300° C, 8.5 GPa

 Tracer diffusion coefficients of Mg in natural aluminosilicate garnets of composition Alm₃₈Pyr₅₀Gr₁₀Sp₂ and Alm₇₃Pyr₂₁Gr₅Sp₁ have been measured at 1 bar, 750-850° C and at 8.5 GPa, 1300° C by chemically depositing a salt layer enriched in ²⁶Mg on the specially prepared surface of a garnet single crystal. Diffusion anneals at 1 atmosphere (101325 Pa) were carried out at a controlled f _{O 2} of ∼10^−17.5 bars maintained by a flowing gas mix of CO-CO₂. Annealing conditions were carefully chosen to avoid decomposition of garnet by redox reactions. High pressure anneals were carried out in a multianvil apparatus. Induced diffusion profiles (0.1–0.6 μm) were measured by an ion-microprobe with SIMS attachment. Diffusion coefficients at 1 atmosphere are in excellent agreement with extrapolation of data from high P-T experiments (Loomis et al. 1985; Chakraborty and Ganguly 1992) and also with the low temperature (750–900° C) dataset of Cygan and Lasaga (1985) if the diffusion coefficients are assumed to be proportional to f _{O 2} ^1/6. Such an f _{O 2} dependence, however, makes this dataset inconsistent with the recent dataset of Schwandt et al. (1995) on garnets of composition (Alm₁₅Pyr₇₂Gr₁₃Sp₀) unless a strong compositional dependence of Mg tracer diffusivity for Mg-rich garnets is invoked. The present experimental results show that such a compositional dependence is weak to non-existent for garnets with >38 mole percent almandine component. It is emphasized that the temperature dependence of diffusion coefficients at constant oxygen fugacities (activation energy ≈54 kcal/mol) are different from that along an oxygen fugacity buffer (activation energy ≈64.5 kcal/mol), as already pointed out by Chakraborty and Ganguly (1991). This distinction is of importance for modelling natural processes. The measurements at low temperatures either eliminate the need for, or greatly reduce the uncertainty of, extrapolation of laboratory data for modelling metamorphic processes. The high pressure results combined with those from Chakraborty and Ganguly (1992) and Loomis et al. (1985) indicate that pressure dependence of Mg tracer diffusivity in garnets is much stronger than that in forsterite (Chakraborty et al. 1994). This difference in pressure dependence of diffusivity may be caused by the difference in compressibility of the coordination polyhedra of Mg between olivines and garnets. Activation volumes of Mg tracer diffusion as high as 8 cm³/mol may be estimated using the present data in combination with earlier results. These data suggest that at a temperature of 1300° C, Mg tracer diffusion rates in garnets will decrease by an order of magnitude for every 100 km depth. The pressure effect will be stronger at lower temperatures. For calculations involving diffusion coefficients of garnets at high pressures (e.g. mantle xenoliths, eclogites) the pressure dependence of diffusivity must be taken into account. Received: 21 December 1994 / Accepted: 22 September 1995     

Diffusion control of quartz and forsterite dissolution rates

An established engineering model is used to identify conditions where diffusion controls the dissolution of quartz and forsterite in packed beds. The model shows that diffusion control is favored at low advection flux, large grain size, high temperature, and high pH (if the reaction consumes H⁺). Quartz dissolution is chemical reaction controlled for most geochemically reasonable combinations of temperature, grain size, and flow rate. On the other hand, forsterite dissolution rates can be diffusion controlled for typical advection fluxes, grain sizes, temperatures, and pH’s. The apparent activation energy for diffusion-controlled reactions in a packed bed is much higher than the <∼20 kJ/mol value that is often used to identify diffusion controlled reactions. The models are quite general and can be adapted to deal with other mineral dissolution and precipitation reactions.     

DIffusion of Eu and Gd in basalt and obsidian

Tracer diffusion coefficients of ¹⁵³Gd and ¹⁵²Eu in olivine tholeiite have been determined at temperatures between 1150 and 1440°C. The results are identical for both tracers within experimental error. Between 1440 and 1320°C the diffusion coefficients are given by D(Eu, Gd) = 0.058 exp(?40,600/ RT). Between 1320 and 1210°C, the diffusion coefficients are constant at D = (1.4 ± 0.4) × 10^?7 cm²s^?1 and between 1210 and 1150°C, the D values drop irregularly to 4 × 10^?9 cm²s^?1. The liquidus temperature (1270°C) lies within the region of constant D. Such anomalous behavior has not been encountered in previous studies of Ca, Sr, Ba and Co diffusion in basalt. To explain the constant D value near the liquidus, we speculate that the structure of the melt changes as a function of temperature in such a way that the normal temperature dependence of the diffusivity is compensated. For example, the rare earth ions may be displaced from their (high temperature) octahedral coordination sites to other sites where they are more readily dissociated and therefore become progressively more mobile. The behavior below 1210°C may be the result of relatively stable complexes or molecules in the melt or of the formation of a REE bearing crystalline phase that has so far escaped detection. Preliminary results for Eu diffusion in obsidian are D (Eu, 800°C) = 5 × 10^?13 cm² s^?1 and D (Eu, 950°C) = 1.5 × 10^?11 cm² s^?1. These data are consistent with an activation energy of 59 Kcal mole^?1. These low diffusivities indicate that the partitioning of REE in crystallizing intermediate and acidic melts may be controlled by diffusion in the melt rather than equilibrium between the crystal surface and the bulk melt.The diffusion data are applied to partial melting in the mantle, in an attempt to explain how LREE enriched tholeiites may be derived from a LREE depleted mantle source. In this model LREE diffuse from garnet bearing regions that have small melt fractions into garnet free regions that have relatively large melt fractions. REE diffusion is so slow that this process is quantitatively significant only in small partially molten bodies (diameter ～1 km or less) or in larger, but strongly flattened bodies. Internal convective motion during diapiric rise would also increase the efficiency of the process.     

Fe–Mg diffusion in olivine I: experimental determination between 700 and 1,200<Emphasis Type="Bold">°</Emphasis>C as a function of composition,crystal orientation and oxygen fugacity

We have determined Fe–Mg diffusion coefficients in olivines from different sources (Nanga Parbat, Pakistan and San Carlos, Arizona, USA) at atmospheric pressure as a function of composition, oxygen fugacity (10⁻⁵–10⁻¹² Pa) and temperature (700–1200°C) using thin films produced by pulsed laser deposition and RBS to analyze the concentration profiles. We have characterized the nano-scale structure and composition of the thin films annealed at various conditions and shown that the nature of the film (e.g. crystallinity, wetting behavior) depends strongly on the annealing conditions. If these variations are not taken into account in the form of boundary conditions for modeling the diffusion profiles, artifacts would result in the diffusion data. The diffusion coefficients obtained from 75 experiments reveal that (i) between fO₂ of 10⁻⁵ and 10⁻¹⁰ Pa, diffusion along all three principal crystallographic directions in olivine, [100], [010] and [001], are described by a constant activation energy of ∼200 kJ/mol, precluding any temperature dependence of diffusion anisotropy and change of mechanism of diffusion at temperatures between 950 and 1200°C, (ii) diffusion coefficients increase with oxygen fugacity at fO₂ > 10⁻¹⁰ Pa, with an fO₂ exponent that lies between 1/4 and 1/7, and (iii) at fO₂ below 10⁻¹⁰ Pa, and consequently at temperatures below ∼900°C, diffusion becomes weakly dependent/independent of fO₂, indicating a change of diffusion mechanism. Activation energy of diffusion at these conditions is slightly higher, ∼220 kJ/mol. The data, including the change of mechanism, are analyzed in terms of point defect chemistry in Part II of this work to derive an equation that allows calculation of diffusivities in olivine over its entire field of stability. Availability of directly measured data at temperatures down to 700°C imply that for the first time diffusion coefficients can be interpolated, rather than extrapolated, for modeling most natural systems.     

Proton migration in portlandite inferred from activation energy of self-diffusion and potential energy curve of OH bond

A fundamental mechanism on the atomic level for self-diffusion in the proton layer of portlandite, Ca(OH)₂, was investigated by conducting hydrogen–deuterium (H–D) exchange diffusion experiments and by deriving potential energy curves of OH vibrations from optical absorption measurements. Synthetic single crystals of portlandite were used in H–D experiments between 250 and 450°C at 150 MPa. Arrhenius parameters for proton diffusion perpendicular to the c-axis gave a frequency factor of 1.0 × 10⁻¹⁰ m²/s and activation energy of 0.61 eV (58.5 kJ/mol). The activation energy corresponds to the height of the potential barrier between two oxygen atoms across an interlayer. The potential barrier height was also theoretically estimated using the OH potential energy curve (OH-PEC) determined by optical absorption measurements. Experimental and theoretical results suggest that the potential barrier height cannot be simply determined by overlapping two OH-PECs. The potential barrier derived theoretically was 3.11 eV. This is too high for the activation energy of the proton diffusion. It implies that the interaction between a diffusing proton and the vacancy of a proton site, and the shortening of interlayer oxygen distance by thermal vibration reduce the potential barrier.     

Electrical conductivity of K-feldspar at high temperature and high pressure

Electrical conductivity measurements on dry polycrystalline K-feldspar were performed at 1.0 to 3.0 GPa and 873 to 1,173 K with a multi-anvil high-pressure apparatus and the Solartron-1260 Impedance/Gain Phase Analyzer in the frequency range of 10^?1 to 10⁶ Hz. At each temperature the complex impedance displays a perfect semi-circular arc that represents the grain-interior conduction. Under the experimental conditions, electrical conductivity exponentially increases with increasing temperature and slightly decreases with increasing pressure; however, the effect of pressure on the conductivity is less pronounced than that of temperature. The activation enthalpy decreases slightly from 0.99 to 1.02 eV with increasing pressure, and the activation energy and activation volume for K-feldspar are 0.98 eV and 1.46?±?0.17 cm³/mol, respectively. According to these Arrhenius parameters, ionic conduction is proposed to be the dominant conduction mechanism in K-feldspar at high temperatures and pressures, and potassium ions are the charge carriers transporting by an interstitial mechanism. The diffusion coefficient of potassium at high temperatures was calculated from our conductivity data on K-feldspar using Nernst–Einstein equation, and the results were compared with the previous experimental results.     

Ar40 diffusion in homogenous orthoclase and an interpretation of Ar diffusion in K-feldspars

Ar⁴⁰ diffusion in a natural, non-perthitic orthoclase has been studied isothermal heating experiments between 500° and 800°C under both vacuum and hydrothermal (2 kbar) conditions. The sample is a one-phase K-feldspar without detectable chemical of structural inhomogeneities as verified by heating experiments, chemical and microprobe analyses, and cell refinements. The orthoclase does not disorder detectably and is stable for the duration of the heating interval. Diffusion coefficients were calculated using an isotropic model for spherical grains. Agreement of diffusion coefficients obtained on grain-sizes which differed by a factor of four indicate that the effective dimension for Ar⁴⁰ diffusion is the actual particle size. A series of experiments at 700°C show that Ar⁴⁰ loss may be described by the ideal spherical model and that the diffusion coefficient does not change with time. The Arrhenius relation is obeyed with a single activation energy and the diffusion coefficients are described by: D = (0·00982) exp — (43800/RT). Agreement of experiments conducted under vacuum and hydrothermally (up to 2 kbar) indicate that pressure and H₂O do not significantly affect Ar⁴⁰ loss. Relatively small amounts of alkali exchange between the feldspar and hydrothermal salt solutions do not affect the loss behavior.The simple behavior obtained for this orthoclase is attributed of the use of a simple technique within the region of sample stability and to the homogeneous nature of the feldspar. Effects due to sample instability and to the use of perthites are discussed. The new data are compared to those for homogeneous feldspars showing that the orthoclase gives diffusion coefficients which are as low as those sanidine. It is suggested that perthitization of feldspars in nature may reduce the effective grain size for diffusion and thereby allow diffusional loss of Ar⁴⁰ at relatively low temperatures.