John R. Farver

Oxygen diffusion in quartz: Dependence on temperature and water fugacity

Abstract Oxygen self-diffusion coefficients (D) were determined in single crystals of Brazilian quartz by measuring 18O concentration profiles with an ion microprobe. In the α-quartz field at 450–590°C and 100-MPa confining pressure, for diffusion parallel to c, the Arrhenius relation is described by the parameters D0 = 2.9 · 10−5 m2 s−1 and Q = 243 ± 17 kJ (g-at. O)−1. The diffusion rate was also measured in β-quartz from 5- to 350-MPa confining pressure and at 700°C as a function of water, hydrogen and oxygen fugacities as well as for different proton activities. There is a good correlation of D with water fugacity, no correlation with oxygen nor hydrogen fugacities, and no correlation with proton activity over the range for which this parameter could be fixed independent of the water fugacity, The available evidence suggests that the oxygen-bearing species responsible for the rapid transport of oxygen under hydrothermal conditions is molecular water. The rate controlling step for oxygen diffusion may be either the rate of migration of water molecules, or the rate of oxygen exchange between the water molecules and the quartz structure.

Mg tracer diffusion in synthetic forsterite and San Carlos Olivine as a function of P, T and fO2

We present new experimental data on Mg tracer diffusion in oriented single crystals of forsterite (Fo100) and San Carlos olivine (Fo92) between 1000–1300° C. The activation energies of diffusion are found to be 400 (±60) kJ/mol (≈96 kcal/mol) and 275 (±25) kJ/mol (≈65 kcal/ mol) in forsterite and San Carlos olivine, respectively, along [001] at a fO2 of 10−12 bars. There is no change in activation energy of Mg tracer diffusion within this temperature range. Mg tracer diffusion in a nominally pure forsterite is found to be anisotropic (D∥c > D∥a > D ∥b) and a function of fO2. This fO2 dependence is different from that in olivine containing Fe as a major element, which suggests that the diffusion mechanism of Mg in forsterite is different from that in Fe-bearing olivine at least over some range of fO2. The diffusion mechanism in nominally pure forsterites may involve impurities present below the limits of detection or alternately, Si or Fe3+ interstitial defects, Fe being present as impurity (ppm level) in forsterite. Pressure dependence of Mg tracer diffusivity in forsterite measured to 10 GPa in a multianvil apparatus yields an activation volume of approximately 1–3.5 cm3/ mol. It is found that presence of small amounts of hydrogen bearing species in the atmosphere during diffusion anneal (fH2 ≈ 0.2 bars, fH20 ≈ 0.24 bars) do not affect Mg tracer diffusion in forsterite within the resolution of our measurement at a total pressure of 1 bar. The observed diffusion process is shown to be extrinsic; hence extrapolation of the diffusion data to lower temperatures should not be plagued by uncertainties related to change of diffusion mechanism from intrinsic to extrinsic.

Oxygen self-diffusion in diopside with application to cooling rate determinations

Abstract The kinetics of oxygen self-diffusion in a natural diopside have been measured over the temperature range 700–1250°C. Experiments were run under hydrothermal conditions using 18 O-enriched water. Profiles of 18 O/( 16 O+ 18 O) versus depth into the crystal were obtained using an ion microprobe. At 1000 bars (100 MPa) confining pressure, the Arrhenius relation for diffusion parallel to the c crystallographic direction yields a pre-exponential factor ( D 0 ) = 1.5 × 10 −6 cm 2 /s and an activation energy ( Q ) = 54 ± 5 kcal/g-atom O (226 kJ/g-atom O) over the temperature range of the experiments. Diffusion coefficients parallel to the c crystallographic direction are ≈ 100 times greater than perpendicular to c . The oxygen self-diffusion coefficient obtained for diopside is ≈ 1000 times less than that for diffusion in feldspars, and ≈ 100 times less than that for quartz at 800°C, transport parallel to the c axis. Closure temperatures calculated for oxygen diffusional exchange in natural diopside are significantly higher than for quartz or feldspars. Measurable oxygen isotope exchange in diopside by diffusion would require geological settings with very high temperatures maintained for very long durations. The oxygen diffusional exchange kinetics in diopside presented in this paper find important applications in studies of meteoric hydrothermal circulation systems and the time-temperature history of high-grade regionally metamorphosed terrains. Examples considered include the Outer Unlayered Gabbro, Cuillins Gabbro Complex, Isle of Skye, Scotland, and the granulite-grade Turpentine Hill Metamorphics near Einasleigh, Queensland, Australia.

Oxygen self-diffusion in calcite: Dependence on temperature and water fugacity

Oxygen self-diffusion in natural calcite single crystals was studied hydrothermally at 400–800°C and 10–350 MPa confining pressure. Diffusion coefficients (D) were determined from18O concentration profiles measured with an ion microprobe. At 100 MPa confining pressure, the Arrhenius parameters yield an activation energy (Q) = 173 ± 6 kJ/mole and pre-exponential factor (D0) = 7 × 10−9 m2/s over the temperature range 400–800°C, and there is no measurable anisotropy. Constant temperature experiments at 700°C indicate that there is a strong linear correlation (slope = 0.9) of D with water fugacity over the range 4–240 MPa, consistent with the interpretation that, in the presence of water, the dominant oxygen-bearing transport species in calcite is molecular water. A sample containing 1180 ppm Mn shows a marked increase in observed D values at temperatures below ∼ 600°C. However, when pre-annealed at ⩾ 700°C the D values obtained at 550°C are within a factor of four of the value obtained for the low (100 ppm) Mn sample. The results of this study confirm that in contrast to carbon, oxygen diffusion rates in calcite are greatly enhanced when water is present. The difference in the effect of water on Doxygen and Dcarbon in calcite may provide valuable information for evaluating the role of fluids in the thermal histories of calcite-bearing rocks.

The effect of hydrogen, oxygen, and water fugacity on oxygen diffusion in alkali feldspar

Abstract Oxygen self-diffusion in adularia and albite single crystals was studied hydrothermally at 650°C from 5 to 1500 MPa confining pressure using a combination of hydrogen/oxygen buffers, a hydrogen ion buffer, and variable mole fractions of water (dilution with CO2). Diffusion coefficients (D) were determined from 18O concentration profiles measured with an ion microprobe. There is a good correlation of the D values with water fugacity but not with oxygen fugacity, hydrogen fugacity, hydrogen ion concentration, nor confining pressure over the range for which these parameters could be fixed independent of the water fugacity. Oxygen diffusion must involve the transport of an oxygen-bearing species, and the results of this study suggest that the transport species is molecular water. The rate-limiting step for oxygen diffusion could be either the rate of migration of the molecular water in the crystal or the rate of exchange of its oxygen with the feldspar structure. While protons may play a role in the mechanism of oxygen diffusion in feldspar, above the concentration supplied by pure water additional protons have no measurable effect on diffusion rates.

Oxygen diffusion in amphiboles

The kinetics of oxygen isotope self-diffusion in natural samples of hornblende, tremolite, and richterite have been measured. Samples were run under hydrothermal conditions using 18O enriched water. Profiles of 18O(16O + 18O)vs depth into the crystal were obtained using an ion microprobe; the depths of sputtered holes were measured using an optical interferometer. At 1000 bars (100 MPa) water pressure, the activation energies (Q) and pre-exponential factors (D0) for diffusion parallel to c are: D0(cm2/sec) Q (kcal/gm-atom) T (°C) Hornblende 1+20−1 × 10−741 ± 6 650–800 Tremolite 2+30−2× 10−8 39 ± 5 650–800 Richterite 3+5−2 × 10−4 57 ± 2 650–800 n nThe diffusion coefficient (D) for hornblende at 800°C and 1000 bars water pressure measured parallel to the c crystallographic direction is at least ten times greater than that parallel to the a or b directions. An increase in water pressure from 200 to 2000 bars increases D by a factor of 2.7 for diffusion parallel to c at 800°C. The D value for hornblende at 800°C is about 0.01 that for quartz and 0.001 that for anorthite. As a result, closure temperatures for oxygen exchange in natural primary amphiboles are significantly higher than for quartz or feldspars. It is unlikely that amphiboles will exchange oxygen isotopes by diffusion under most crustal conditions.

Oxygen and strontium diffusion kinetics in apatite and potential applications to thermal history determinations

The kinetics of oxygen and strontium diffusion in natural fluorapatite (Durango, Mexico) have been measured under hydrothermal conditions using an ion microprobe. Diffusion coefficients were obtained at temperatures from 550 to 1200°C for oxygen, and 650 to 1200°C for strontium. All experiments were run at 1000 bars (100 MPa) water pressure except those designed to measure the water pressure dependence, which were at 200 to 2000 bars. The Arrhenius relations obtained for diffusion parallel to the c axis at 1000 bars water pressure are: Element D0(cm2/sec) Q(kcal/mol) T(°C) Oxygen 9·10−5 49 ± 3 550–1200 Strontium 2·10−11 25 ± 4 650–1000 Strontium 1· 105 120 ± 22 1100–1200. n nThe diffusion coefficient for oxygen transport parallel to the c axis is approximately three orders of magnitude greater than that perpendicular to the c axis over the temperature range of the experiments. No anisotropy was observed for strontium diffusion in apatite. An increase in water pressure from 200 to 2000 bars yields an increase in D of approximately a factor of three for oxygen diffusion parallel to the c axis at 800°C. n nThe Arrhenius relation for strontium diffusion in the temperature range 1100 to 1200°C is in good agreement with the Watsonet al. (1985) data for dry 1 atm experiments at 1050 to 1250°C. Strontium diffusion coefficients obtained in the temperature range 650 to 1000°C yield significantly greater D values than predicted by extrapolation of the high-temperature Arrhenius relation. The new data show that closure temperatures calculated for strontium diffusion in apatite are significantly lower than the hightemperature studies would predict. Thus, apatite crystals would remain open to strontium diffusional exchange well below the solidus temperature of most igneous rocks. This could result in higher 87Sr86Sr values in the apatite than the whole-rock initial value. Measurable enrichment in 87Sr86Sr values in apatite could also be produced by a later thermal disturbance at moderate geologic temperatures and durations.

Measurement of oxygen grain boundary diffusion in natural, fine-grained, quartz aggregates

Grain boundary diffusion measurements using fine-grained, natural, monomineralic aggregates offer several distinct advantages over techniques previously employed. Pure quartz aggregates (Arkansas novaculite), with 1.2 and 4.9 μm diameter grains, were annealed at 450–800°C and 100 MPa confining pressure in 18O-enriched water. Profiles of 18O(18O + 16O) with depth from the surface were measured using an ion microprobe, and data were collected from an area 68 μm in diameter in order to obtain a well-averaged value for many grain boundaries. Using graphical solutions appropriate to the boundary conditions employed, the product of the average grain boundary diffusion coefficient (D′) and effective boundary width (δ) is obtained and is independent of the grain size, geometry, and grain boundary tortuosity. Arrhenius parameters for the 1.2 and 4.9 μm grain size samples are: D′0δ = 2.6 and 3.4 × 10−17 m3/sec, and Q = 27 ± 1 and 26 ± 3 kcal/mol, respectively. Measured values of D′δ were about three times greater for the 4.9 μm aggregate, although this might be due in part to thermal cracking while going to temperature. The activation energy of both samples, ~ 27 kcal/mol ( 113 kJ/mol), is significantly less than that for volume diffusion of oxygen in quartz, but greater than that for ionic diffusion in a static fluid. Measured D′δ values are within the range of most previous estimates. For a representative effective grain boundary width of 1 nm, the oxygen grain boundary diffusion coefficients are 4 to 6 orders of magnitude greater than oxygen volume diffusion coefficients in quartz single crystals, and ~6 orders of magnitude less than ionic diffusion coefficients in a static fluid, over the temperature range of the experiments.

Interphase boundary diffusion of oxygen and potassium in K-feldspar/quartz aggregates

Abstract Interphase boundary diffusion rates of oxygen and potassium in fine-grained K-feldspar/ quartz aggregates were determined experimentally at 450–700°C and 100 MPa (hydrothermal). The starting materials were hot-pressed and crystallized using equal weights of natural quartz fragments and orthoclase (KAlSi 3 O 8 ) composition glass. The technique employed isotopic tracers ( 18 O, 41 K) in an aqueous solution surrounding the sample, and depth profiling using an ion microprobe (SIMS). From the depth profiles, the product of the average boundary diffusion coefficient ( D ′) and average effective boundary width (δ) was calculated using numerical solutions to the appropriate diffusion equation. Potassium and oxygen profiles measured in the same samples are different, confirming a diffusional transport mechanism. Potassium diffusion in the K-feldspar/quartz aggregate has a greater activation energy than oxygen (218 vs. 75 kJ/mol), and the Arrhenius relations cross at ∼600°C. The D ′ δ values in the K-feldspar/quartz aggregates are about a factor of four greater than both oxygen and potassium D ′ δ values previously determined in monomineralic K-feldspar aggregates, and a factor of 20–40 greater than oxygen D ′ δ values in monomineralic quartz aggregates. The Arrhenius relations show the activation energies for both oxygen and potassium are similar for the K-feldspar/quartz and monomineralic K-feldspar aggregates, and significantly lower for oxygen in K-feldspar/quartz versus monomineralic quartz aggregates.

Patterns and processes of oxygen isotope exchange in a fossil meteoric hydrothermal system, Cuillins Gabbro Complex, Isle of Skye, Scotland

Oxygen isotope compositions of whole rock specimens and mineral separates from the Cuillins Gabbro Complex, Isle of Skye, Scotland, are employed to determine the patterns and processes of18O depletion in the Outer Unlayered Gabbro (OUG) and associated dikes. Whole rockδ18O values range from +4.8 to −1.1‰ (SMOW) and dikeδ18O values range from +4.7 to −2.8‰ Mineral separates from three OUG samples yieldδ18O values from +5.3 to +4.8‰ for augite and +4.1 to +0.8‰ for plagioclase. An early, small-scale hydrothermal circulation system was initiated by the OUG prior to the large-scale hydrothermal convection established by the later Layered Cuillins Complex (LCC). Dikes were emplaced in the OUG after intrusion of the LCC and had only a minor effect on hydrothermal circulation in the OUG. There is evidence of enhanced fluid flow along dike/gabbro contacts. Isotopic compositions of augite separates demonstrate a normalδ18O value for the OUG magma with all18O depletion in the OUG due to subsolidus exchange processes including diffusion and surface reaction. The mineral separates yield a pattern of18O depletion consistent with a diffusion mechanism, the bulk of the exchange having occurred in the plagioclase. Secondary mineral formation played a subordinate role in the18O depletion of the OUG. The calculated water to rock mass ratio necessary to effect the observed18O depletion in the OUG is on the order of 0.2, although a much greater amount of water circulation probably occurred. The cooling duration required to explain the measured18O depletion in the OUG by diffusion is very short (140 years at 750° C, 2400 years at 550° C) compared to the duration necessary for pure conductive cooling (105 to 106 years). Rapid local cooling rates in the OUG due to meteoric water convection are consistent with the observed18O depletion in OUG samples.