Bruno J. Giletti

Diffusion effects on oxygen isotope temperatures of slowly cooled igneous and metamorphic rocks

Recently obtained data on oxygen diffusion in feldspars, quartz, and hornblende permit the prediction of the apparent18O16O temperatures that would be measured in a rock that consisted only of those three minerals, and cooled slowly from high temperature. The computed temperatures would be based on the differences in the18O16O ratios between coexisting pairs of minerals. The present calculation takes into account the diffusion rates for oxygen as a function of temperature, the cooling rate of the rock, the mineral grain sizes, and the mode of the rock. For mineral grains 1 mm in radius, and a cooling rate of 10°C/m.y., the minimum difference in apparent temperature between quartz-feldspar and feldspar-hornblende pairs will be 115°C, despite the assumption of a normal, uneventful, slow cooling history to room temperature. Further, the apparent quartz-hornblende temperature will range over 30°C (590–620°C) depending on the mode of the rock. For a cooling rate of 1000°C/m.y., the apparent difference in temperature can be as much as 400°C. Consequently, consistency in temperatures obtained by oxygen isotope analysis should not be expected in most high-grade metamorphic rocks or igneous rocks which are cooled slowly. Departures from the pattern of temperatures obtained in this model would imply a very rapid quench from high temperature, or a complex history for the rock. For some minerals, including hornblende, the relation between temperature and the equilibrium fractionation of oxygen isotopes between coexisting phases has been derived from observed relations in natural specimens. The choice of the specimens used for such calibrations needs to be re-evaluated in light of these findings. This may result in a change in the equilibrium equation constants. An example from the literature, the San Jose tonalite, Baja California, Mexico, was modelled and yieldsδ18O concentrations in the minerals that correspond closely with the measured values. This suggests that the model used is appropriate, that the rock has had a simple thermal history, and that it cooled at 100–200°C/m.y. over the temperature range 800–500°C. The set of paleotemperatures obtained for a rock will, in general, yield neither the mineral closure temperatures nor the formation or crystallization temperatures. On the other hand, the cooling rate of the rock may be derived from the data. This, in turn, may have important tectonic implications with regard to denudation and uplift rates.

Studies in diffusion—III. Oxygen in feldspars: an ion microprobe determination

Abstract Self-diffusion of oxygen in adularia, anorthite, albite, oligoclase and labradorite has been measured by isotope exchange of oxygen between natural feldspars and hydrothermal water enriched in 18 O. The analysis consisted of measuring the 18 O/ 16 O gradient inward from the feldspar surface using an ion microprobe, and fitting a solution of the diffusion equation to the data. Depth of the sputtered hole was measured with an optical interferometer. Linear Arrhenius plots were obtained: d 0 ( cm 2 /sec ) Q ( kcal/g-atom O ) T(°C) Adularia (Or 98 ) 4.51 × 10 −8 25.6 350–700 Albite (Ab 97 , Ab 99 ) 2.31 × 10 −9 21.3 350–800 Anorthite (An 96 ) 1.39 × 10 −7 26.2 350–800 The results for two intermediate plagioclases (Ab 82.5 and Ab 35.7 ) between 550 and 800°C are similar to these, and hence all the feldspars have very similar oxygen exchange behavior. Diffusion coefficients for albite at 800°C measured normal to the (001), (010), ( 1 11), and (130) faces are the same within a factor of four. Owing to the low activation energy, there is no single “closure temperature” for exchange of oxygen. The feldspars are susceptible to diffusional exchange of oxygen in geological settings to comparatively low temperatures.

Strontium diffusion kinetics in plagioclase feldspars

Abstract A pronounced, systematic variation, by a factor of 104, in strontium tracer diffusion kinetics has been measured in four feldspar specimens that span the range of plagioclase compositions. The experiments were carried out in air, using isotopically enriched 86Sr, and analyzed with an ion microprobe. The Arrhenius relations for strontium diffusion are: Plagioclase [Ab]% D 0 ( m 2 /s ) Q ( kj g - atom Sr) Temperature Range °C Albite 98 1.05e 279 550–1080 Oligoclase 73 7.4e-7 261 750–1100 Labradorite 36 1.1e-6 295 800–1300 Anorthite 4 5.7e-9 267 900–1300 No difference was found, within the measurement uncertainty, between these results and those for albite under hydrothermal conditions at one kbar (100 MPa). Strontium diffusion rates parallel to, and normal to the albite twin lamellae are the same. There is no effect on the strontium diffusion rate in albite between an oxygen partial pressure of 0.2 bar (air) and ~ 10−19 bar (graphite buffer). A relation is developed that permits calculation of the strontium diffusion Arrhenius parameters for any normal plagioclase composition. The large variation in diffusion rate with composition has a major effect on the ease of strontium isotope exchange at high temperatures between plagioclases and coexisting phases in rocks, which may prove useful in determining thermal histories.

An Empirical Model for Predicting Diffusion Coefficients in Silicate Minerals

An empirical model describing the diffusion kinetics of oxygen in silicate minerals under hydrothermal conditions has been established for temperatures between 773 and 1073 Kelvin at 100 megapascals of water pressure. The equation, log D = α + (β/T) + [(γ + (δ/T))Z], where D is the diffusion coefficient, α, β, γ, and δ are constants, T is the Kelvin temperature, and Z is the total ionic porosity, may be used to predict diffusion coefficients, in most cases to within the reported experimental reproducibility of a factor of 2. For oxygen diffusion, α = -2, β = -3.4 x 104K, γ = -0.13, and δ = 6.4 x 102K, for D in square centimeters per second. Limited data for the diffusion of argon in silicates suggest that the model describes this system as well.

Lead diffusion in monazite

Abstract We have measured the tracer diffusion rate of Pb in natural, annealed, gem-quality monazite from Alexander Co., NC, USA, and Riverside Co., CA, USA. Observations from the literature concerning low T annealing in monazite suggest the possibility that Pb diffusion at geologic conditions occurs, in effect, within a similarly annealed lattice. Our experiments were performed by evaporating an aqueous solution containing 204 Pb onto a crystal face and then heating the charge to 1000–1200°C for 4 to 36 days. To the extent that the compositions of the two samples differed, we observed no effect of composition upon the rate of Pb diffusion. We do find that transport parallel to the c -axis is ∼2–5 times slower than that measured perpendicular to c . For Pb diffusion perpendicular to c , the Arrhenius parameters are Q = 180 ± 48 kJ/mol and log D 0 = −14.18 ± 1.54 (for D 0 in m 2 /s). While these parameters now allow for a direct calculation of closure temperatures for monazite, we believe a more useful form of our data for geochronologists is the fraction of Pb lost from crystals, expressed as a function of T , time, and crystal size. We have applied this formalism to discordant monazite UPb ages from the recent literature and find that Pb diffusion at rates extrapolated from our experiments can account for the observed degree of discordancy. We suggest that, rather than employing the concept of closure temperature to evaluate possible Pb loss in monazite, the diffusion data presented here be used in Pb loss models based upon T and duration conditions appropriate for a given geological setting.

Rb and Sr diffusion in alkali feldspars, with implications for cooling histories of rocks

Volume diffusion of Sr and Rb have been measured in orthoclase feldspar as well as Sr diffusion in albite, using isotope exchange, hydrothermal solutions, and analysis by ion microprobe. For water pressures of 1000 bars, the kinetics of diffusion parallel to the c-axis are given by the Arrhenius relations Strontium transport in the Or is isotropic to within a factor of four. The measurements use a new procedure in which only the elements in question are present in the starting fluid. Cooling rates of igneous rocks can now be determined from closure temperatures, material balance, and the Rb-Sr dating method, based on the departures of the mineral data from the whole-rock isochron, for cooling rates less than approximately 100°C/my.

Alkali diffusion in plagioclase feldspar

Tracer diffusion kinetics at 1 atm pressure under ‘dry’ conditions using 6Li, 41K, and 87Rb in four plagioclase feldspars have been determined. Diffusion profiles were measured using an ion microprobe (SIMS). The Arrhenius parameters and ± 2σ uncertainties for Li, K, and Rb, respectively, in albite, are: pre-exponential factor (log Do) = - 3.8 ± 1.0; −3.4 ± 1.4; and −5.8 ± 3.8 (in m2/s) and activation energies = 146 ± 14; 296 ± 30; and 283 ± 85 kJ/mol. The diffusion rate of K in albite at 700°C and 100 MPa water pressure equals that at 1 atm ‘dry’, suggesting that diffusion of K is not dependent on water fugacity between ∼ 0.004 and 100 MPa. The K diffusion rate depends on plagioclase anorthite content and is approximately 20 times slower in labradorite than albite. Li diffusion rates in albite and anorthite are identical. A linear relation between log D for the alkalis measured and their ionic radius squared, permits an estimate of Cs diffusion kinetics. Diffusion rates are isotropic or nearly so in albite.

Volume self-diffusion of oxygen in biotite, muscovite, and phlogopite micas

The kinetics of oxygen self-diffusion have been measured in natural samples of biotite, muscovite, and phlogopite micas under hydrothermal conditions using both bulk exchange and profiling analyses. All experiments were run at 1000 bars (100 MPa) water pressure except those designed to measure water pressure dependence, which ranged from 200 to 2000 bars. The Arrhenius relations obtained for layer-parallel diffusive transport in the three micas by bulk exchange experiments, fit to an infinite cylinder model, are Mineral biotite muscovite phlogopite 34 ±2 39 ± 5 42 +- 3 9.1 × 10−6 7.7 × 10−5 1.4 × 10−4 T(°C) 500–800 512–700 600–900. The results of ion microprobe (SIMS) depth profiling perpendicular to the layers (parallel to c-axis) yield diffusion coefficients 3 to 4 orders of magnitude lower than for transport parallel to the layers. A single layer-parallel step profiling experiment yields a diffusion coefficient identical, within uncertainty, to those obtained from bulk exchange experiments. A slight dependence of diffusion rate on water pressure may obtain in phlogopite; however, the difference is approximately within the uncertainty of the measurement. Diffusion rates are similar, within about a half an order of magnitude, for a range of biotite composition from annite4 to annite63, as well as for muscovite. Comparison of oxygen diffusion rates in biotite from this study with Ar, K, and Rb diffusion from published data supports the idea that water is the oxygen-bearing species in hydrothermal diffusion experiments. The implication of these results for natural systems is that the micas, especially biotite, will continue to exchange oxygen isotopes via volume diffusion down to temperatures as low as 300 °C. The rapid diffusion kinetics may explain biotite oxygen isotope disequilibrium, which is commonly observed even in rocks where other mineral phases preserve equilibrium compositions. Full-size table Table options View in workspace Download as CSV

Carbon and oxygen diffusion in calcite: Effects of Mn content and PH2O

AbstractThe diffusion rates of carbon and oxygen in two calcite crystals of different Mn contents have been studied between 500° and 800° C in a CO2-H2O atmosphere (PCO2=1−5 bars, PH2O=0.02−24 bars) labeled with 13C and 18O. Isotope concentration gradients within annealed specimens were measured using a secondary ion microprobe by depth profiling parallel and perpendicular to the c axis. Despite the anisotropic structure of calcite, the diffusion of carbon and oxygen are both very nearly isotropic. Least-squares fitting of the carbon data to an Arrhenius relation gives an activation energy of 87±2 kcal/mole, with D0 terms dependent only slightly upon direction: 1