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.     

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.     

Laboratory simulation of meteoritic noble gases. I. Sorption of xenon on carbon: Trapping experiments

We have studied trapping of radioactive ¹²⁷Xe in three types of carbon: carbon black (lamp black  LB), pyrolyzed polyvinylidene chloride (PVDC), and pyrolyzed acridine (C₁₃H₉N). A total of 86 samples were exposed to Xe at T between 100 and 1000°C, for times between 5 min and 240 hours, at p_xe ~ 5 × 10^?7 atm. Excess gas phase and loosely sorbed Xe were pumped away and the remaining, tightly bound Xe was measured by γ-spectrometry.At 100°C,× >90% of the Xe desorbs within a few minutes' pumping but a small amount remains even after 4000 min. Distribution coefficients for this tightly bound Xe are ~1 × 10^?2, 1 and 10 ccSTP/g atm for LB, acridine and PVDC carbons. The tightly bound Xe consists of two components. One occurs over the entire range 100–1000°C, becoming less abundant at high T; it appears to be physisorbed. The other occurs only at T > 500°C and is probably due to volume diffusion. The adsorbed component in LB has an apparent ΔH between ?2.3 and ?5.7 kcal/mole. The diffused component, which occurs in LB and possibly in acridine carbon, has an activation energy Q = 27 ± 8 kcal/mole and a diffusion coefficient D = 1.3 × 10^?17 cm²/sec at 1000°C. These values are comparable to those found for other types of amorphous carbon (Morrisonet al., 1963; Nakai et al., 1960).The low-T component displays two paradoxical features: low ΔH_ads, in the range for Xe physisorbed on carbon, but exceedingly long adsorption or desorption times (~10³ min at 100–400 or 1000°C). Although these long times seem to suggest a high energy process such as chemisorption, our results are best explained by a model that invokes physisorption within a labyrinth of micropores—of atomic dimensions—known to exist in amorphous carbons. The long adsorption/desorption times reflect either the long distances (~5 cm) Xe atoms must migrate by random walk to enter or leave the labyrinth, or the long times needed for Xe atoms to traverse tight spots or constricted pores that connect interior and exterior surfaces of the carbon (activated entry). Both variants of this model predict long equilibration times for the observed ΔH_ads of ?2 to ?6 kcal/mole. Apparently, xenon can be tightly trapped in carbon without resorting to high-energy bonding or to exotic mechanisms.These results suggest that “planetary” type noble gases in meteorites, located at or near grain surfaces of amorphous carbon, may be trapped by adsorption in micropores, whereas components such as CCFXe, which are uniformly distributed in their carrier phases, may be trapped by mechanisms such as volume diffusion or ion implantation.     

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.     

Cation diffusion in olivine—I. Cobalt and magnesium

Cobalt and magnesium interdiffusion coefficients in synthetic crystals of olivine have been determined by a method of couple annealing. These coefficients increase with temperature and Co concentration. The coefficients in forsterite along the c crystallographic axis range from 1.13 × 10^?12 to 6.85 × 10^{?11 cm2sec?1} at temperatures ranging from 1150 to 1400°C. The calculated activation energies for Co-Mg interdiffusion in forsterite are 526 kJmol^?1 above approximately 1300°C and 196 kJmol^?1 at lower temperatures. These results indicate that the Co-Mg mobility in olivine is relatively low compared to published results for Fe-Mg interdiffusion.     

Laboratory simulation of meteoritic noble gases. II. Sorption of xenon on carbon: Etching and heating experiments

Sixteen amorphous carbon (lampblack) samples that had been exposed to Xe¹²⁷ and pumped for >9 hrs to remove the most labile gas were examined by etching with HNO₃, for comparison with the release pattern of meteoritic xenon. Samples originally exposed at 100–200°C lost 90% of their Xe very readily, when the surface had been etched to a mean depth of only ~0.2 Å. This suggests that the Xe is adsorbed mainly at rare sites that are unusually reactive to HNO₃. The adsorbed Xe survived several months' storage in vacuum, but on exposure to air, part of it was lost within a few hours, while the remainder persisted without measurable exchange. Samples exposed at 800–1000°C had a similar adsorbed component, as well as a second, tightly bound component extending to a mean depth of up to 30 Å; this component had apparently diffused into the carbon during exposure. The (microscopic) diffusion coefficient for graphitic crystallites is 5 × 10^?20 cm²/sec at 1000°C.PVDC carbon lost its adsorbed Xe at about the same rate as lampblack on exposure to air or HNO₃, though it differs from lampblack in being non-graphitizable and more porous. It had only a small diffused component, however.The most tightly bound part of the Xe adsorbed on lampblack resembles planetary Xe in most characteristics: surface siting, etchability, persistence in vacuum, and lack of exchange with atmospheric Xe. The Xe concentrations—if interpreted as equilibrium distribution coefficients—are some 10⁶× too small to account for meteoritic Xe, but it appears that equilibrium had not been reached by any of the samples, even after 1 day's exposure to Xe. If the uptake of Xe is controlled by rate rather than equilibrium, then the high noble gas concentrations in meteorites may simply reflect the much longer uptake times in the solar nebula. It seems likely that the trapping mechanisms discussed here can also explain two other features: elemental fractionations of noble gases, and the close correlation between planetary Xe and CCFXe.     

Closed system behaviour of argon in osumilite records protracted high‐T metamorphism within the Rogaland–Vest Agder Sector,Norway

Here, we present results of the first ⁴⁰Ar/³⁹Ar dating of osumilite, a high‐T mineral that occurs in some volcanic and high‐grade metamorphic rocks. The metamorphic osumilite studied here is from a metapelitic rock within the Rogaland–Vest Agder Sector, Norway, an area that experienced regional granulite facies metamorphism and subsequent contact metamorphism between 1,100 Ma and 850 Ma. The large grain size (~1 cm) of osumilite in the studied rock, which preserves a nominally anhydrous assemblage, increases the potential for large portions of individual grains to have remained essentially unaffected by the effects of diffusive argon loss, potentially preserving prograde ages. Step‐heating diffusion experiments yielded a maximum activation energy of ~461 kJ/mol and a pre‐exponential factor of ~8.34 × 10⁸ cm²/s for Ar diffusion in osumilite. These parameters correspond to a relatively high closure temperature of ~620°C for a cooling rate of 10°C/Ma in an osumilite crystal with a 175 µm radius. Fragments of osumilite separated from the sample preserve a range of ages between c. 1,070 and 860 Ma. The oldest ages are inferred to date the growth of coarse‐grained osumilite during prograde granulite facies regional metamorphism, which pre‐date contact metamorphism that has historically been ascribed to the growth of osumilite in the region. The majority of fragments record ages between c. 920 and 860 Ma, inferred to reflect the growth of osumilite and/or diffusive argon loss during contact metamorphism. The retention of old ⁴⁰Ar/³⁹Ar dates was facilitated by the low diffusivity of Ar in osumilite (i.e. a closed system), large grain sizes, and anhydrous metamorphic conditions. The ability to date osumilite with the ⁴⁰Ar/³⁹Ar method provides a valuable new thermochronometer that may constrain the timing and duration of high‐T magmatic and metamorphic events.     

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.     

Radio-colouration of diamond: a spectroscopic study

We have undertaken a study of the common green or orange-brown spots at the surface of rough diamond specimens, which are caused by alpha particles emanating from radioactive sources outside the diamond. Richly coloured haloes represent elevated levels of structural damage, indicated by strong broadening of the main Raman band of diamond, intense strain birefringence, and up-doming of spots due to their extensive volume expansion. Green radio-colouration was analogously generated through the irradiation of diamond with 8.8 MeV helium ions. The generation of readily visible radio-colouration was observed after irradiating diamond with ≥10¹⁵ He ions per cm². The accumulation of such a high number of alpha particles requires irradiation of the diamond from a radioactive source over long periods of time, presumably hundreds of millions of years in many cases. In the samples irradiated with He ions, amorphisation was observed in volume areas where the defect density exceeded 5 × 10^?3 Å^?3 (or 0.03 dpa; displacements per target atom). In contrast, graphitisation as a direct result of the ion irradiation was not observed. The green colouration transformed to brown at moderate annealing temperatures (here 450 °C). The colour transformation is associated with only partial recovery of the radiation damage. The colour change is mainly due to the destruction of the GR1 centre, explained by trapping of vacancies at A defects to form the H3 centre. An activation energy of ~2.4 ± 0.2 eV was determined for the GR1 reduction. The H3 centre, in turn, causes intense yellowish-green photoluminescence under ultraviolet illumination. Radio-colouration and associated H3 photoluminescence are due to point defects created by the ions irradiated, whereas lattice ionisation is of minor importance. This is concluded from the depth distribution of the colouration and the photoluminescence intensity (which corresponds to the defect density but not the ionisation distribution pattern). The effect of the implanted He ions themselves on the colour and photoluminescence seems to be negligible, as radio-colouration and H3 emission were analogously produced through irradiation of diamond with C ions. The photoluminescence emission becomes observable at extremely low defect densities on the order of 10^?6 Å^?3 (or 0.000006 dpa) and is suppressed at moderate defect densities of ~5 × 10^?4 Å^?3 (or ~0.003 dpa). Intensely brown-coloured diamond hence does not show the H3 emission anymore. Anneals up to 1,600 °C has reduced considerably irradiation damage and radio-colouration, but the structural reconstitution of the diamond (and its de-colouration) was still incomplete.     

Compositional zoning in garnet and kinetics of metamorphic crystallization

The kinetics of zoned garnet porphyroblast growth is exemplified in a sample of garnet-staurolite-biotite schist from the northern Ladoga region. The diffusion-controlled porphyroblast growth was accompanied by a decrease in the kinetic coefficient during phase reactions. Even at insignificant (1–2°C) thermal overstepping, the leading role of diffusion as a factor that controls kinetics of porphyroblast growth in medium-grade metapelites is consistent with the parameters of metamorphic crystallization: T = 500–650°C, t = 1 Ma; D _A1 ^app = 10^?14 cm²/s, L = 0.2–0.6 cm, r = 1–3 mm, ΔC _Al = 1.5 × 10^?4–1.5 × 10^?3 mol/cm³.     

Helium measurements of pore fluids obtained from the San Andreas Fault Observatory at Depth (SAFOD, USA) drill cores

⁴He accumulated in fluids is a well established geochemical tracer used to study crustal fluid dynamics. Direct fluid samples are not always collectable; therefore, a method to extract rare gases from matrix fluids of whole rocks by diffusion has been adapted. Helium was measured on matrix fluids extracted from sandstones and mudstones recovered during the San Andreas Fault Observatory at Depth (SAFOD) drilling in California, USA. Samples were typically collected as subcores or from drillcore fragments. Helium concentration and isotope ratios were measured 4?C6 times on each sample, and indicate a bulk ⁴He diffusion coefficient of 3.5?±?1.3?×?10^?C8 cm²?s^?C1 at 21°C, compared to previously published diffusion coefficients of 1.2?×?10^?C18 cm²?s^?C1 (21°C) to 3.0?×?10^?C15 cm²?s^?C1 (150°C) in the sands and clays. Correcting the diffusion coefficient of ⁴He_water for matrix porosity (??3%) and tortuosity (??6?C13) produces effective diffusion coefficients of 1?×?10^?C8 cm^2?s^?C1 (21°C) and 1?×?10^?C7 (120°C), effectively isolating pore fluid ⁴He from the ⁴He contained in the rock matrix. Model calculations indicate that <6% of helium initially dissolved in pore fluids was lost during the sampling process. Complete and quantitative extraction of the pore fluids provide minimum in situ porosity values for sandstones 2.8?±?0.4% (SD, n?=?4) and mudstones 3.1?±?0.8% (SD, n?=?4).     

Experimental study of silica diffusion during metasomatic reactions in the presence of water at 550°C and 1000 bars

Metasomatic reactions between quartz and incompatible oxides or hydroxides were experimentally studied at 550°C and 1000 bars water pressure. Two porous pellets of the initial reagents pressed one against the other were used. Reaction rims in the millimeter range develop at the initial boundary in the oxide pellet. All the experiments show that an important transfer of silica occurs by diffusion in the stationary intergranular solution.The chemical transfer of silica through the intergranular fluid is quantitatively determined by studying the kinetics of growth of the forsterite rim in the system quartz-brucite. The kinetics limiting stage being silica transfer, the experiments allow the determination of the diffusion coefficient of silica through the solution. At 550°C and 1000 bars, a value of 2.4 × 10^?1cm² s¹ is found.This high value shows the importance of chemical diffusion in the intergranular fluid of rocks during metamorphic processes.     

About possibility of isotope dating of native gold by the (U-Th)/He method

For investigation of helium in native gold, a new measuring complex was created and used: the high sensitivity mass spectrometer MSU-G (ZAO SKB “SPECTRON”). The sensitivity of measuring ⁴He was 5.3 × 10^?13 cm³/g per impulse. Experiments in stepwise heating of samples have been carried out, and the kinetics of radiogenic ⁴He emanation from native gold was investigated. Migration parameters (activation energy and frequency factor) were determined. Model calculations of stability (closure temperature) of radiogenic ⁴He in the native gold structure with a given time and temperature of thermal influences were made using the data received. The concentration of ⁴He in native gold from the original deposit Nesterovskoe is (4.7 ± 0.1) × 10^?5 cm³/g in the sample from the placer; from Chudnoe deposit, it is (3.8 ± 0.1) × 10^?5 cm³/g; from sulfide deposits of Kitoiskii knot of Eastern Sayani, it is (1.9 ± 0.1) × 10^?5 cm³/g; and from the South Muiskii ore region it is (8.7 ± 0.5) × 10^?7 cm³/g. The received curve lines of kinetics of ⁴He emanation from native gold show that radiogenic helium is well bonded in the native gold structure: in all the examined samples, most ⁴He emanates only by reaching the temperature of 950–1000°C. A specific feature of the kinetics of radiogenic ⁴He emanation in all examined samples is an outburstlike emanation in the form of a peak of large amplitude in the area of temperatures near the melting temperature point of gold. This is stipulated by the existence of helium bubbles released by metals only while they melt. The spectrum of helium thermal desorption from native gold has a complicated form and is a result of superposition of several peaks. This proves the migration of groups of atoms located in the gold structure in different energy states. Very large values of the activation energy of helium migration from native gold were received: up to 161–176 kcal/mol. Extremely large values of the frequency factor, from 2 × 10¹⁸ to 3 × 10³², correspond to such values of activation energies. This is caused probably by helium migration in the form of gas bubbles. The received data indicate the very high stability of the (U-Th)/He isotope system in native gold. Using the (U-Th)/He method of isotope geochronology seems to be very promising for isotope dating of these strategic raw materials.     

Diffusion of 40Ar in biotite: Temperature,pressure and compositional effects

The measured radiogenic ⁴⁰Ar loss from sized biotite (56% annite) samples following isothermalhydrothermal treatment have provided model diffusion coefficients in the temperature interval 600°C to 750°C, calculated on the assumption that Ar transport proceeds parallel to cleavage. These data yield an array on an Arrhenius plot with a slope corresponding to an activation energy 47.0 ± 2 kcal-mol^?1 and a frequency factor of 0.077^+0.21_?0.06 cm²-sec^?1. Together with previous diffusion data for micas in the annitephlogopite series, our results indicate a strong compositional effect, with increasing $\text{Fe}\text{Mg}$ ratio corresponding to an increase in diffusivity. An effective diffusion radius of about 150 μm for biotite is inferred from the experimental data which compares favorably with that estimated from geological studies. A pressure effect on activation energy corresponding to an activation volume of about 14 cm³-mol^?1 is observed. These data yield closure temperature estimates for this biotite composition cooling at rates of 100°C-Ma^?1, 10°C-Ma^?1 and 1°C-Ma^?1 of 345°C, 310°C and 280°C, respectively. ${}^{40}\text{Ar}{}^{39}\text{Ar}$ age-spectrum analysis of a hydrothermally treated biotite yields a complex release pattern casting doubt on the general usefulness of such measurements for geochronological purposes.     

Comparison of low-temperature with high-temperature diffusion of sodium in albite

Diffusion of sodium in albite from Amelia County, Virginia, was examined at high and intermediate temperatures by means of the sectioning technique and at low temperatures by means of an exchange technique. These studies indicate that diffusion is heterogeneous at low and intermediate temperatures, but goes to volume diffusion at high temperatures. Apparent diffusion coefficients of the order of magnitude of 10⁻¹⁸ cm²/sec and an activation energy of approximately 3000 cal/mole sodium are determined for the low-temperature movement. An activation energy of approximately 35 kcal/mole sodium is determined for the high-temperature movement.     

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.     

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.     

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.     

Dislocation-assisted diffusion of oxygen in albite

Oxygen diffusion in albite has been determined by the integrating (bulk ¹⁸O) method between 750° and 450° C, for a P _H2O of 2 kb. The original material has a low dislocation density (<10⁶ cm^?2), and its lattice diffusion coefficient (D ₁), given below, agrees well with previous determinations. A sample was deformed at high temperature and pressure to produce a uniform dislocation density of 5 × 10⁹ cm^?2. The diffusion coefficient (D _a) for this deformed material, given below, is about 0.5 and 0.7 orders of magnitude larger than D ₁ at 700° and 450° C, respectively. This enhancement is believed due to faster diffusion along the cores of dislocations. Assuming a dislocation core radius of 4 Å, the calculated pipe diffusion coefficient (D _p), given below, is about 5 orders of magnitude larger than D ₁. These results suggest that volume diffusion at metamorphic conditions may be only slightly enhanced by the presence of dislocations. $$\begin{gathered} D_1 = 9.8 \pm 6.9 \times 10^{ - 6} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 33.4 \pm 0.6(kcal/mole)/RT] \hfill \\ \end{gathered} $$ $$\begin{gathered} D_a = 7.6 \pm 4.0 \times 10^{ - 6} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 30.9 \pm 1.1(kcal/mole)/RT] \hfill \\ \end{gathered} $$ $$\begin{gathered} D_p \approx 1.2 \times 10^{ - 1} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 29.8(kcal/mole)/RT]. \hfill \\ \end{gathered} $$      

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.