Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep

Diffusion coefficients of Cr and Al in chromite spinel have been determined at pressures ranging from 3 to 7 GPa and temperatures ranging from 1,400 to 1,700°C by using the diffusion couple of natural single crystals of MgAl₂O₄ spinel and chromite. The interdiffusion coefficient of Cr–Al as a function of Cr# (=Cr/(Cr + Al)) was determined as D _Cr–Al = D ₀ exp {−(Q′ + PV*)/RT}, where D ₀ = exp{(10.3 ± 0.08) × Cr#^0.54±0.02} + (1170 ± 31.2) cm²/s, Q′ = 520 ± 81 kJ/mol at 3 GPa, and V* = 1.36 ± 0.25 cm³/mol at 1,600°C, which is applicable up to Cr# = 0.8. The estimation of the self-diffusion coefficients of Cr and Al from Cr–Al interdiffusion shows that the diffusivity of Cr is more than one order of magnitude smaller than that of Al. These results are in agreement with patterns of multipolar Cr–Al zoning observed in natural chromite spinel samples deformed by diffusion creep.     

Uphill diffusion,zero-flux planes and transient chemical solitary waves in garnet

Diffusion profiles in minerals are increasingly used to determine the duration of geological events. For this purpose, the distinction between growth and diffusion zoning is critical; it requires the understanding of complex features associated with multicomponent diffusion. Seed-overgrowth interdiffusion experiments carried out in the range 1,050–1,250°C at 1.3 GPa have been designed to quantify and better understand Fe–Mg–Ca interdiffusion in garnet. Some of the diffusion profiles measured by analytical transmission electron microscope show characteristic features of multicomponent diffusion such as uphill diffusion, chemical solitary waves, zero-flux planes and complex diffusion paths. We implemented three different methods to calculate the interdiffusion coefficients of the D matrix from the experimental penetration curves and determined that with Ca as the dependent component, the crossed coefficients of the D matrix are negative. Experiments and numerical simulations indicate that: (1) uphill diffusion in garnet can be observed indifferently on the three components Fe, Mg and Ca, (2) it takes the form of complementary depletion/repletion waves and (3) chemical waves occur preferentially on initially flat concentration profiles. Derived D matrices are used to simulate the fate of chemical waves in time, in finite crystals. These examples show that the flow of atoms in multicomponent systems is not necessarily unidirectional for all components; it can change both in space along the diffusion profile and in time. Moving zero-flux planes in finite crystals are transitory features that allow flux reversals of atoms in the diffusion zone. Interdiffusion coefficients of the D matrices are also analyzed in terms of eigenvalues and eigenvectors. This analysis and the experimental results show that depending on the composition of the diffusion couple, (1) the shape of chemical waves and diffusion paths changes; (2) the width of the diffusion zone for each component may or may not be identical; and (3) the width of diffusion calculated at a given D and duration may greatly vary. D matrices were retrieved from thirteen sets of diffusion profiles. Data were cast in Arrhenius relations. Linear regressions of the data yield activation energies equal to 368, 148, 394, 152 kJ mol⁻¹ at 1 bar and frequency factors D_o equal to 2.37 × 10⁻⁶, −4.46 × 10⁻¹⁶, −1.31 × 10⁻⁵, 9.85 × 10⁻¹⁵ m² s⁻¹ for [(D)\tilde]_FeFe^Ca \tilde{D}_{FeFe}^{Ca} , [(D)\tilde]_FeMg^Ca \tilde{D}_{FeMg}^{Ca} , [(D)\tilde]_MgFe^Ca \tilde{D}_{MgFe}^{Ca} , [(D)\tilde]_MgMg^Ca \tilde{D}_{MgMg}^{Ca} , respectively. These values can be used to calculate interdiffusion coefficients in Fe–Mg–Ca garnets and determine the duration of geological events in high temperature metamorphic or magmatic garnets.     

Multicomponent diffusion in garnets I: general theoretical considerations and experimental data for Fe–Mg systems

We have carried out a combined theoretical and experimental study of multicomponent diffusion in garnets to address some unresolved issues and to better constrain the diffusion behavior of Fe and Mg in almandine–pyrope-rich garnets. We have (1) improved the convolution correction of concentration profiles measured using electron microprobes, (2) studied the effect of thermodynamic non-ideality on diffusion and (3) explored the use of a mathematical error minimization routine (the Nelder-Mead downhill simplex method) compared to the visual fitting of concentration profiles used in earlier studies. We conclude that incorporation of thermodynamic non-ideality alters the shapes of calculated profiles, resulting in better fits to measured shapes, but retrieved diffusion coefficients do not differ from those retrieved using ideal models by more than a factor of 1.2 for most natural garnet compositions. Diffusion coefficients retrieved using the two kinds of models differ only significantly for some unusual Mg–Mn–Ca-rich garnets. We found that when one of the diffusion coefficients becomes much faster or slower than the rest, or when the diffusion couple has a composition that is dominated by one component (>75 %), then profile shapes become insensitive to one or more tracer diffusion coefficients. Visual fitting and numerical fitting using the Nelder-Mead algorithm give identical results for idealized profile shapes, but for data with strong analytical noise or asymmetric profile shapes, visual fitting returns values closer to the known inputs. Finally, we have carried out four additional diffusion couple experiments (25–35 kbar, 1,260–1,400 °C) in a piston-cylinder apparatus using natural pyrope- and almandine-rich garnets. We have combined our results with a reanalysis of the profiles from Ganguly et al. (1998) using the tools developed in this work to obtain the following Arrhenius parameters in D = D ₀ exp{–[Q _1bar + (P–1)ΔV ⁺]/RT} for D _Mg^* and D _Fe^*: Mg: Q _1bar = 228.3 ± 20.3 kJ/mol, D ₀ = 2.72 (±4.52) × 10⁻¹⁰ m²/s, Fe: Q _1bar = 226.9 ± 18.6 kJ/mol, D ₀ = 1.64 (±2.54) × 10⁻¹⁰ m²/s. ΔV ⁺ values were assumed to be the same as those obtained by Chakraborty and Ganguly (1992).     

Ca–Mg diffusion in diopside: tracer and chemical inter-diffusion coefficients

We have experimentally determined the tracer diffusion coefficients (D*) of ⁴⁴Ca and ²⁶Mg in a natural diopside (~Di₉₆) as function of crystallographic direction and temperature in the range of 950–1,150 °C at 1 bar and f(O₂) corresponding to those of the WI buffer. The experimental data parallel to the a*, b, and c crystallographic directions show significant diffusion anisotropy in the a–c and b–c planes, with the fastest diffusion being parallel to the c axis. With the exception of logD*(²⁶Mg) parallel to the a* axis, the experimental data conform to the empirical diffusion “compensation relation”, converging to logD ~ −19.3 m²/s and T ~ 1,155 °C. Our data do not show any change of diffusion mechanism within the temperature range of the experiments. Assuming that D* varies roughly linearly as a function of angle with respect to the c axis in the a–c plane, at least within a limited domain of ~20° from the c-axis, our data do not suggest any significant difference between D*(//c) and D*(⊥(001)), the latter being the diffusion data required to model compositional zoning in the (001) augite exsolution lamellae in natural clinopyroxenes. Since the thermodynamic mixing property of Ca and Mg is highly nonideal, calculation of chemical diffusion coefficient of Ca and Mg must take into account the effect of thermodynamic factor (TF) on diffusion coefficient. We calculate the dependence of the TF and the chemical interdiffusion coefficient, D(Ca–Mg), on composition in the diopside–clinoenstatite mixture, using the available data on mixing property in this binary system. Our D*(Ca) values parallel to the c axis are about 1–1.5 log units larger than those Dimanov et al. (1996). Incorporating the effect of TF, the D(Ca–Mg) values calculated from our data at 1,100–1,200 °C is ~0.6–0.7 log unit greater than the experimental quasibinary D((Ca–Mg + Fe)) data of Fujino et al. (1990) at 1 bar, and ~0.6 log unit smaller than that of Brady and McCallister (1983) at 25 kb, 1,150 °C, if our data are normalized to 25 kb using activation volume (~4 and ~6 cm³/mol for Mg and Ca diffusion, respectively) calculated from theoretical considerations.     

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.     

New experimental determination of Li and B partition coefficients during upper mantle partial melting

Despite the growing interest for Li and B as geochemical tracers, especially for material transfer from subducting slabs to overlying peridotites, little is known about the behaviour of these two elements during partial melting of mantle sources. In particular, mineral/melt partition coefficients for B and to a lesser extent Li are still a matter of debate. In this work, we re-equilibrated a synthetic basalt doped with ~10 ppm B and ~6 ppm Li with an olivine powder from a spinel lherzolite xenolith at 1 GPa–1,330°C, and we analyzed Li and B in the run products by secondary ion mass spectrometry (SIMS). In our experiment, B behaved as a highly incompatible element with mineral/melt partition coefficients of the order of 10⁻² (D ^ol/melt = 0.008 (0.004–0.013); D ^opx/melt = 0.024 (0.015–0.033); D ^cpx/melt = 0.041 (0.021–0.061)), and Li as a moderately incompatible element (D ^ol/melt = 0.427 (0.418–0.436); D ^opx/melt = 0.211 (0.167–0.256); D ^cpx/melt = 0.246 (0.229–0.264)). Our partition coefficients for Li are in good agreement with previous determinations. In the case of B, our partition coefficients are equal within error to those reported by Brenan et al. (1998) for all the mineral phases analyzed, but are lower than other coefficients from literature for some of the phases (up to 5 times for cpx). Our measurements complement the data set of Ds for modelling partial melting of the upper mantle and basalt generation, and confirm that, in this context, B is more incompatible than previously anticipated.     

Calcium diffusivity in alumino-silicate garnets: an experimental and ATEM study

Concentration gradients in calcium are common in metamorphic or magmatic garnets and can be used to determine the timescales of geological processes. However, the kinetics of Ca diffusion in garnet is poorly constrained and experimental studies have to date yielded widely varying diffusion coefficients. In this paper, we describe a new method for generating diffusion profiles in garnet. We incorporated polished and compositionally homogeneous garnet seeds in a finely ground powder of clinopyroxene and garnet. During the experiments (1.3 GPa, 1,050–1,250°C, and ƒO₂ ≤ the graphite-O₂ buffer), the mineral powder partially melted, recrystallized, and formed a 10–50 μm wide overgrowth zone of compositionally distinct garnet around the seeds. Long duration experiments generated measurable relaxation profiles at these seed/overgrowth interfaces. We performed analytical transmission electron microscope traverses across the interfaces in each experiment. Thirteen usable compositional profiles were obtained with characteristic distances of diffusion ranging from 300 to 1,000 nm. From these profiles, Ca–(Fe, Mg) interdiffusion coefficients were retrieved using an analytical solution for the diffusion equation and the data were cast in an Arrhenius relation. Linear regression of the data yields an activation energy Q _{Ca–(Fe, Mg)} equal to 188 ± 48 kJ mol⁻¹ and a frequency factor D ₀ equal to 6.6 × 10⁻¹⁴ m² s⁻¹. Within the compositional range studied, the composition of garnet has no major effect on the Ca–(Fe, Mg) interdiffusion coefficient. The very slow diffusion rate of Ca is in agreement with natural observations indicating that Ca diffuses more slowly than Fe and Mg. The Ca diffusion coefficients derived from this study are not model-dependent and can be used to determine the durations of geological events from Ca relaxation profiles in natural garnets.

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The mechanisms of water diffusion in polymerized silicate melts

Diffusion of water was experimentally investigated for melts of albitic (Ab) and quartz-orthoclasic (Qz₂₉Or₇₁, in wt %) compositions with water contents in the range of 0 to 8.5 wt % at temperatures of 1100 to 1200 °C and at pressures of 1.0 and 5.0 kbar. Apparent chemical diffusion coefficients of water (D _water) were determined from concentration-distance profiles measured by FTIR microspectroscopy. Under the same P-T condition and water content the diffusivity of water in albitic, quartz-orthoclasic and haplogranitic (Qz₂₈Ab₃₈ Or₃₄, Nowak and Behrens, this issue) melts is identical within experimental error. Comparison to data published in literature indicates that anhydrous composition only has little influence on the mobility of water in polymerized melts but that the degree of polymerization has a large effect. For instance, D_water is almost identical for haplogranitic and rhyolitic melts with 0.5–3.5 wt % water at 850 °C but it is two orders of magnitude higher in basaltic than in haplogranitic melts with 0.2–0.5 wt % water at 1300 °C. Based on the new water diffusivity data, recently published in situ near-infrared spectroscopic data (Nowak 1995; Nowak and Behrens 1995), and viscosity data (Schulze et al. 1996) for hydrous haplogranitic melts current models for water diffusion in silicate melts are critically reviewed. The NIR spectroscopy has indicated isolated OH groups, pairs of OH groups and H₂O molecules as hydrous species in polymerized silicate melts. A significant contribution of isolated OH groups to the transport of water is excluded for water contents above 10 ppm by comparison of viscosity and water diffusion data and by inspection of concentration profiles from trace water diffusion. Spectroscopic measurements have indicated that the interconversion of H₂O molecules and OH pairs is relatively fast in silicate glasses and melts even at low temperature and it is inferred that this reaction is an active step for migration of water. However, direct jumps of H₂O molecules from one cavity within the silicate network to another one can not be excluded. Thus, we favour a model in which water migrates by the interconversion reaction and, possibly, small sequences of direct jumps of H₂O molecules. In this model, immobilization of water results from dissociation of the OH pairs. Assuming that the frequency of the interconversion reaction is faster than that of diffusive jumps, OH pairs and water molecules can be treated as a single diffusing species having an effective diffusion coefficient . The shape of curves of D_water versus water content implies that increases with water content. The change from linear to exponential dependence of D_water between 2 and 3 wt % water is attributed to the influence of the dissociation reaction at low water content and to the modification of the melt structure by incorporation of OH groups. Received: 26 March 1996 / Accepted: 23 August 1996     

Systematic study of hydrogen incorporation into Fe-free wadsleyite

The H₂O content of wadsleyite were measured in a wide pressure (13–20 GPa) and temperature range (1,200–1,900°C) using FTIR method. We confirmed significant decrease of the H₂O content of wadsleyite with increasing temperature and reported first systematic data for temperature interval of 1,400–1,900°C. Wadsleyite contains 0.37–0.55 wt% H₂O at 1,600°C, which may be close to its water storage capacity along average mantle geotherm in the transition zone. Accordingly, water storage capacity of the average mantle in the transition zone may be estimated as 0.2–0.3 wt% H₂O. The H₂O contents of wadsleyite at 1,800–1,900°C are 0.22–0.39 wt%, indicating that it can store significant amount of water even under the hot mantle environments. Temperature dependence of the H₂O content of wadsleyite can be described by exponential equation C_{\textH2 \textO} = 6 3 7.0 7 \texte ^{- 0.00 4 8T} , C_{{{\text{H}}_{2} {\text{O}}}} = 6 3 7.0 7 {\text{e}}^{ - 0.00 4 8T} , where T is in °C. This equation is valid for temperature range 1,200–2,100°C with the coefficient of determination R ² = 0.954. Temperature dependence of H₂O partition coefficient between wadsleyite and forsterite (D _wd/fo) is complex. According to our data apparent D_wd/fo decreases with increasing temperature from D _wd/fo = 4–5 at 1,200°C, reaches a minimum of D _wd/fo = 2.0 at 1,400–1,500°C, and then again increases to D _wd/fo = 4–6 at 1,700–1,900°C.     

Empirical constraints on closure temperatures from a single diffusion coefficient

The elucidation of thermal histories by geochronological and isotopic means is based fundamentally on solid-state diffusion and the concept of closure temperatures. Because diffusion is thermally activated, an analytical solution of the closure temperature (T _c ^*) can only be obtained if the diffusion coefficient D of the diffusion process is measured at two or more different temperatures. If the diffusion coefficient is known at only one temperature, however, the true closure temperature (T _c ^*) cannot be calculated analytically because there exist an infinite number of possible (apparent) closure temperatures (Tˉ _c ) which can be generated by this single datum. By introducing further empirical constraints to limit the range of possible closure temperatures, however, mathematical analysis of a modified form of the closure temperature equation shows that it is possible to make both qualitative and quantitative estimates of T _c ^* given knowledge of only one diffusion coefficient D _M measured at one temperature T _M . Qualitative constraints of the true closure temperature T _c ^* are obtained from the shapes of curves on a graph of the apparent T _c (Tˉ _c ) vs. activation energy E, in which each curve is based on a single diffusion coefficient measurement D _M at temperature T _M . Using a realistic range of E, the concavity of the curve shows whether T _M is less than, approximately equal to, or greater than T _c ^*. Quantitative estimates are obtained by considering two dimensionless parameters [ln êRT^ _c vs. T _c ^*/T _M ] derived from these curves. When these parameters are plotted for known argon diffusion data and for a given diffusion size and cooling rate, it is found that the resultant curves are almost identical for all of the commonly dated K–Ar minerals – biotite, phlogopite, muscovite, hornblende and orthoclase – in spite of differences in their diffusion parameters. A common curve for Ar diffusion can be derived by least-squares fitting of all the Ar diffusion data and provides a way of predicting a “model” closure temperature T _cm from a single diffusion coefficient D _M at temperature T _M . Preliminary diffusion data for a labradorite lead to a T _cm of 507 ± 17 °C and a corresponding activation energy of about 65 kcal/mol, given a grain size of 200 μm and a cooling rate of 5 °C/Ma. Curves for He diffusion in silicates (augite, quartz and sanidine) also overlap to a significant degree, both among themselves and with the Ar model curve, suggesting that a single model curve may be a good representation of noble gas closure temperatures in silicates. An analogous model curve for a selection of ¹⁸O data can also be constructed, but this curve differs from the Ar model curve. A single model curve for cationic species does not appear to exist, however, suggesting that chemical bonding relationships between the ionic size/charge and crystal structure may influence the closure temperatures of diffusing cations. An indication of the degree of overlap among the various curves for Ar, He, ¹⁸O and cations is also obtained by considering the dimensionless parameter E/RT _c ^*; for the noble gases and ¹⁸O, E/RT _c ^* values for the respective minerals are very similar, whereas for cations, there is significant dispersion. Given these constraints, this may be a potential method of estimating closure temperatures for certain diffusing species when there are limited diffusion data. Received: 1 July 1999 / Accepted: 24 March 2000     

Point defects and cation tracer diffusion in (Ti<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> Fe<Subscript><Emphasis Type="Italic">1−x</Emphasis></Subscript>)<Subscript>3−δ</Subscript>O<Subscript>4</Subscript>. II. Cation tracer diffusion

 Cation tracer diffusion coefficients, D_Me ^*, for Me=Fe, Mn, Co and Ti, were measured using radioactive isotopes in the spinel solid solution (Ti _x Fe _1−x )_3−δO₄ as a function of the oxygen activity. Experiments were performed at different cationic compositions (x=0, 0.1, 0.2 and 0.3) at 1100, 1200, 1300 and 1400 °C. The oxygen activity dependence of all data for D_Me ^* at constant temperature and cationic composition can be described by equations of the type D_Me ^*=D^∘ _Me[V]. C_V·a _O2 ^2/3+D_Me[I] ^∘·a _O2 ^−2/3·D_Me[V] ^∘ and D_Me[I] ^∘ are constants and C_V is a factor of the order of unity which decreases with increasing δ. All log D_Me ^* vs. loga _O2 curves obtained for different values of x and for different temperatures go through a minimum due to a change in the type of point defects dominating the cation diffusion with oxygen activity. Cation vacancies prevail for the cation diffusion at high oxygen activities while cation interstitials become dominant at low oxygen activities. At constant values of x, D_Me[V] ^∘ decreases with increasing temperature while D_Me[I] ^∘ increases.     

Fluid transfer of gold,palladium, and rare earth elements and genesis of ore occurrences in the Subpolar Urals

To estimate the behavior of Au, Pd, REE, and Y in magmatic and postmagmatic processes, a series of experimental studies on the solubility of noble metals and REE in magma, magmatic fluid, and hydrothermal solutions has been performed in wide temperature and pressure ranges (300–400°C, 860–1350°C; 1–14 kbar). The coefficients of Au and Pd partitioning (D ^F/L) between fluid and tholeiitic melt have been determined. Depending on P, T, and the composition of the system, they vary from 1 to 11 for Au and 0.02 to 1 for Pd. The phase solubility technique was used to determine Au and Pd solubility in hydrothermal fluid. The effects of temperature, composition, and fluid acidity on Au and Pd solubility have been estimated. The high solubility of these metals in aqueous chloride solutions has been established for both Au (28–803 mg/kg at T = 300°C, 305–1123 mg/kg at T = 350°C, and 330–1400 mg/kg at T = 400°C) and Pd (40–126 mg/kg at T = 300°C, 62–152 mg/kg at T = 350°C, and 20–210 mg/kg at T = 400°C). The coefficients of REE and Y partitioning (D ^F/L) between fluid and tholeiitic or alkaline melts have been determined. They vary from 0.00n to 2 depending on P, T, and fluid composition. The experimental data on Au and Pd solubility in solutions and magmatic fluids and the wide variation of REE D ^F/L between fluid and melt show that magmatic and hydrothermal fluids are efficient agents of Au, Pd, and REE transfer and fractionation. The obtained experimental data were used for elucidating sources of fluids and their role in the genesis of Au-Pd-REE occurrences in the Subpolar Urals.     

Variation of illite/muscovite <Superscript>40</Superscript>Ar/<Superscript>39</Superscript>Ar age spectra during progressive low-grade metamorphism: an example from the US Cordillera

⁴⁰Ar/³⁹Ar step-heating data were collected from micron to submicron grain-sizes of correlative illite- and muscovite-rich Cambrian pelitic rocks from the western United States that range in metamorphic grade from the shallow diagenetic zone (zeolite facies) to the epizone (greenschist facies). With increasing metamorphic grade, maximum ages from ⁴⁰Ar/³⁹Ar release spectra decrease, as do total gas ages and retention ages. Previous studies have explained similar results as arising dominantly or entirely from the dissolution of detrital muscovite and precipitation/recrystallization of neo-formed illite. While recognizing the importance of these processes in evaluating our results, we suggest that the inverse correlation between apparent age and metamorphic grade is controlled, primarily, by thermally activated volume diffusion, analogous to the decrease in apparent ages with depth observed for many thermochronometers in borehole experiments. Our results suggest that complete resetting of the illite/muscovite Ar thermochronometer occurs between the high anchizone and epizone, or at roughly 300 °C. This empirical result is in agreement with previous calculations based on muscovite diffusion parameters, which indicate that muscovite grains with radii of 0.05–2 μm should have closure temperatures between 250 and 350 °C. At high anchizone conditions, we observe a reversal in the age/grain-size relationship (the finest grain-size produces the oldest apparent age), which may mark the stage in prograde subgreenschist facies metamorphism of pelitic rocks at which neo-formed illite/muscovite crystallites typically surpass the size of detrital muscovite grains. It is also approximately the stage at which neo-formed illite/muscovite crystallites develop sufficient Ar retentivity to produce geologically meaningful ⁴⁰Ar/³⁹Ar ages. Results from our sampling transect of Cambrian strata establish a framework for interpreting illite/muscovite ⁴⁰Ar/³⁹Ar age spectra at different stages of low-grade metamorphism and also illuminate the transformation of illite to muscovite. At Frenchman Mtn., NV, where the Cambrian Bright Angel Formation is at zeolite facies conditions, illite/muscovite ⁴⁰Ar/³⁹Ar data suggest a detrital muscovite component with an apparent age ≥967 Ma. The correlative Carrara Fm. is at anchizone conditions in the Panamint and Resting Spring Ranges of eastern California, and in these locations, illite/muscovite ⁴⁰Ar/³⁹Ar data suggest an early Permian episode of subgreenschist facies metamorphism. The same type of data from equivalent strata at epizone conditions (greenschist facies) in the footwall of the Bullfrog/Fluorspar Canyon detachment in southern Nevada reveals a period of slow-to-moderate Late Cretaceous cooling.     

Hydroxyl in mantle olivine xenocrysts from the Udachnaya kimberlite pipe

The incorporation of hydrogen in mantle olivine xenocrysts from the Udachnaya kimberlite pipe was investigated by Fourier-transform infrared spectroscopy and secondary ion mass spectrometry (SIMS). IR spectra were collected in the OH stretching region on oriented single crystals using a conventional IR source at ambient conditions and in situ at temperatures down to −180°C as well as with IR synchrotron radiation. The IR spectra of the samples are complex containing more than 20 strongly polarized OH bands in the range 3,730–3,330 cm⁻¹. Bands at high energies (3,730–3,670 cm⁻¹) were assigned to inclusions of serpentine, talc and the 10 Å phase. All other bands are believed to be intrinsic to olivine. The corresponding point defects are (a) associated with vacant Si sites (3,607 cm⁻¹ E || a, 3,597 E || a, 3,571 cm⁻¹ E || c, 3,567 E || c, and 3,556 E || b), and (b) with vacant M1 sites (most of the bands polarized parallel to a). From the pleochroic behavior and position of the OH bands associated with the vacant M1 sites, we propose two types of hydrogen—one bonded to O1 and another to O2, so that both OH vectors are strongly aligned parallel to a. The O2–H groups may be responsible for the OH bands at higher wavenumbers than those for the O1–H groups. The multiplicity of the corresponding OH bands in the spectra can be explained by different chemical environments and by slightly different distortions of the M1 sites in these high-pressure olivines. Four samples were investigated by SIMS. The calculated integral molar absorption coefficient using the IR and SIMS results of 37,500±5,000 L mol H₂O cm⁻² is within the uncertainties slightly higher than the value determined by Bell et al. (J Geophys Res 108(B2):2105–2113, 2003) (28,450±1,830 L mol H₂O cm⁻²). The reason for the difference is the different distributions of the absorption intensity of the spectra of both studies (mean wavenumber 3,548 vs. 3,570 cm⁻¹). Olivine samples with a mean wavenumber of about 3,548 cm⁻¹ should be quantified with the absorption coefficient as determined in this study; those containing more bands at higher wavenumber (mean wavenumber 3,570 cm⁻¹) should be quantified using the value determined by Bell et al. (J Geophys Res 108(B2):2105–2113, 2003).

Thermal expansion and dehydroxylation of phengite micas

Phengite samples (2M ₁ and 3T politypes) and a synthetic end-member muscovite specimen were studied by in situ high-temperature synchrotron radiation X-ray diffraction. The measured volume thermal expansion of 2M ₁ phengite (<α _V> ≈ 36.6 × 10⁻⁶ K⁻¹) was systematically greater than <α _V> of the 3T polytype (≈33.3 × 10⁻⁶ K⁻¹). A positive linear correlation between the average thermal expansion on (001) plane and the mean tetrahedral rotation angle at ambient condition is proposed on the ground of new measurements and literature data. Dehydroxylation processes were observed in 2M ₁, starting at 1,000 K in 3T at 800 and 945 K in synthetic muscovite. Rietveld refinements allowed a determination of structural variations upon heating of phengite samples and their dehydroxylate phases. The phengite structure expands by regularizing the tetrahedral sheet and by reducing the bond length differences between the outer and inner coordination shell of the interlayer site. The dehydroxylate phase derived from 2M ₁ is characterized by fivefold polyhedra in the low temperature form as a consequence of two OH groups reacting to form H₂O + O (residual). The dehydroxylate exhibits an increase of the cation–cation distances along the M–Or–M bonds with respect to low-temperature phengite structures. For the 3T phase, we were unable to achieve completion of dehydroxylation. The refined structural model of the dehydroxylate phase shows two hydroxyl sites, but at a short distance from one another. This result suggests that the dehydroxylation reaction did not proceed to completion. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Neoarchean high-pressure margarite–phengitic muscovite–chlorite corona mantled corundum in quartz-free high-Mg,Al phlogopite–chlorite schists from the Bundelkhand craton,north central India

In quartz-free Fe, Na-poor and high-Mg, Al schists from the Bundelkhand craton in north central India, corundum porphyroblasts in finely interleaved phlogopite–chlorite aggregates with rare clinozoisite are mantled by fine-grained (<3 μm) intergrowths of outer collars (>200 μm wide) of phengitic-muscovite and chlorite (phlogopite + corundum + H₂O → phengitic-muscovite + chlorite), and <100 μm wide inner collars of margarite–muscovite (corundum + clinozoisite + phengitic muscovite → margarite + muscovite + H₂O). Wide-beam electron probe microanalyses indicate Mg in the bi-layered corona increases from corundum outwards, with a complementary decrease in Al and K. Si and Ca increase and then decrease to matrix values. The sharp chemical gradients across the highly structured bi-layered corona are inferred to suggest that the corona-forming reactions were promoted by local grain-boundary-controlled thermodynamic instability as opposed to element transport by advective diffusion. The P–T convergence of KMASH reactions and NCKMASH pseudosection phase relations computed using micro-domain compositions indicate the chlorite–phengitic muscovite outer collar formed at 18–20 kbar and ca. 630°C. The NCKMASH margarite–muscovite inner collar yielded lower metamorphic P–T conditions of 11 ± 3 kbar, ca. 630°C. U–Th–Pb chemical dating of metamorphic monazite and LA-ICPMS U–Pb isotope dating of re-equilibrated zircon yield ca. 2.78 Ga ages, which are interpreted to date corona formation and Neoarchean high-P metamorphism in the Bundelkhand craton, hitherto unknown in the Indian Precambrian. (220)     

Diffusion of tetravalent cations in zircon

Diffusion rates for the three tetravalent cations U, Th and Hf have been measured in synthetic zircon. Diffusant sources included oxide powders and ground pre-synthesized silicates. Rutherford backscattering spectrometry (RBS) was used to measure depth profiles. Over the temperature range 1400–1650 °C, the following Arrhenius relations were obtained (diffusion coefficients in m²sec⁻¹): log D _Th = (1.936 ± 0.9820) + (− 792 ± 34 kJ mol⁻¹ /2.303 RT) log D _U = (0.212 ± 2.440) + (− 726 ± 83 kJ mol⁻¹ /2.303 RT) log D _Hf = (3.206 ± 1.592) + (− 812 ± 54 kJ mol⁻¹ /2.303 RT) The data show a systematic increase in diffusivity with decreasing ionic radius (i.e., faster diffusion rates for Hf than for U or Th), a trend also observed in our earlier study of rare earth diffusion in zircon. Diffusive fractionation may be a factor in the Lu-Hf system given the much slower diffusion rates of tetravalent cations when compared with the trivalent rare earths. The very slow diffusion rates measured for these tetravalent cations suggest that they are essentially immobile under most geologic conditions, permitting the preservation of fine-scale chemical zoning and isotopic signatures of inherited cores. Received: 12 July 1996 / Accepted: 2 December 1996     

Volume and grain boundary diffusion of calcium in natural and hot-pressed calcite aggregates

 Calcium self-diffusion rates in natural calcite single crystals were experimentally determined at 700 to 900° C and 0.1 MPa in a stream of CO₂. Diffusion coefficients (D) were determined from ⁴²Ca concentration profiles measured with an ion microprobe. The Arrhenius parameters yield an activation energy (Q)=382±37 kJ/mol and pre-exponential factor (D₀)=0.13 m²/s, and there is no measurable anisotropy. Calcium grain boundary diffusion rates were experimentally determined in natural (Solnhofen) limestone and hot-pressed calcite aggregates at 650° to 850° C and 0.1 to 100 MPa pressure. The Solnhofen limestone was first pre-annealed for 24 h at 700° C and 100 MPa confining pressure under anhydrous conditions to produce an equilibrium microstructure for the diffusion experiments. Values for the product of the grain boundary diffusion coefficient (D′) and the effective grain boundary diffusion width (δ) were determined from ⁴²Ca concentration profiles measured with an ion microprobe. The results show that there is no measurable difference between D′δ values obtained for pre-annealed Solnhofen samples at 0.1 and 100 MPa or between hot-pressed calcite aggregates and pre-annealed Solnhofen samples. The temperature dependence for calcium grain boundary diffusion in Solnhofen samples annealed at 0.1 MPa is described by the Arrhenius parameters D^′ ₀δ=1.5×10⁻⁹ m³/s and Q=267±47 kJ/mol. Comparison of the results of this study with previously published data show that calcium is the slowest volume diffusing species in calcite. The calcium diffusivities measured in this study place constraints on several geological processes that involve diffusive mass transfer including diffusion-accommodated mechanisms in the deformation of calcite rocks. Received: 19 December 1994/Accepted: 30 June 1995     

Experimental study of migration of potassium ion through a two-layer soil system

A barrier system based on the hydraulic trap design concept for a landfill was proposed. To study the field scenario in which a clay liner is underlain by a granular layer functioning as a secondary leachate drain layer, a laboratory advection–diffusion test was performed to investigate factors controlling the transport of contaminants in a two-layer soil system. The soils used for this study were Ariake clay and, the underlying layer, Shirasu soil from the Kyushu region of Japan. Potassium (K⁺) was selected as the target chemical species with an initial concentration of 905 mg L⁻¹. The effective diffusion coefficients (D _e) of K⁺ for Ariake clay and Shirasu soil were back-calculated using an available computer program, Pollute V 6.3. Values of D _e derived from this experiment are consistent with previously published ones. The Ariake clay has lower D _e than the Shirasu soil. The hypothesis that mechanical dispersion can be considered negligible is reasonable based on both the observation that the predicted values well fit the experimental data and the analyses of two dimensionless parameters. Parametric analyses show that transport of K⁺ through soils is controlled by advection–diffusion rather than diffusion only, whereas at low Darcy velocity (i.e., ≤10⁻⁹ m s⁻¹), transport of K⁺ will be controlled by diffusion. Applications of the test results and parametric analysis results in practical situations were reviewed.     

Characterization of non-equilibrium and equilibrium occurrences of paragonite/muscovite intergrowths in an eclogite from the Sesia–Lanzo Zone (Western Alps, Italy)

 Coexisting muscovite and paragonite have been observed in an eclogite from the Sesia–Lanzo Zone (Western Alps, Italy). The P-T conditions of this eclogite reached 570–650 °C and 19–21 kbar and the rocks show several stages of mineral growth during their retrograde path, ranging from the subsequent lower-P eclogite facies to the blueschist facies and then the greenschist facies. Muscovite and paragonite are very common in these rocks and show two texturally different occurrences indicating equilibrium and non-equilibrium states between them. In one mode of occurrence they coexist in equilibrium in the lower-P eclogite facies. In the same rock muscovite ± albite also replaced paragonite during a greenschist-facies overprint, as evidenced by unique across – (001) layer boundaries. The chemical compositions of the lower-P eclogite-facies micas plot astride the muscovite – paragonite solvus, whereas the compositions of the greenschist-facies micas lie outside the solvus and indicate disequilibrium. The TEM observations of the textural relations of the greenschist-facies micas imply structural coherency between paragonite and muscovite along the layers, but there is a sharp discontinuity in the composition of the octahedral and tetrahedral sheets across the phase boundary. We propose that muscovite formed through a dissolution and recrystallization process, since no gradual variations toward the muscovite – paragonite interfaces occur and no intermediate, homogeneous Na-K phase has been observed. Because a solid-state diffusion mechanism is highly unlikely at these low temperatures (300–500 °C), especially with respect to octahedral and tetrahedral sites, it is assumed that H₂O plays an important role in this process. The across-layer boundaries are inferred to be characteristic of such non-equilibrium replacement processes. The characterization of these intergrowths is crucial to avoiding erroneous assumptions regarding composition and therefore about the state of equilibrium between both micas, which in turn may lead to misinterpretations of thermometric results. Received: 3 February 1999 / Accepted: 19 October 1999