Sumit Chakraborty

Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples, evaluation of effective binary diffusion coefficients, and applications

We present new experimental data on diffusion of divalent cations in almandine-spessartine diffusion couples in graphite capsules in the P-T range of 14–35 kb, 1100–1200° C. The tracer diffusion coefficients of the major divalent cations, viz. Fe, Mg and Mn, retrieved from the multicomponent diffusion profiles, have been combined with earlier data from our laboratory at 29–43 kb, 1300–1480° C (Loomis et al. 1985) to derive expressions of the P-T dependence of the diffusion coefficients at fO2 approximately corresponding to that defined by equilibrium in the system graphite-O2. We review the conditions, discussed earlier by Cooper, under which the flux of a component in a multicomponent system becomes proportional to its concentration gradient (Fickian diffusion), as if the entire solvent matrix behaves as a single component, and also suggest a method of incorporating the thermodynamic effect on diffusion in the same spirit. Regardless of the magnitude or sign of the off-diagonal terms of the D matrix, it is always possible to define an effective binary diffusion coefficient (EBDC) of a component in a semi-infinite multicomponent diffusion-couple experiment such that it has the property of the Fickian diffusion coefficient, provided that there is no inflection on the diffusion profiles. It is shown that the success of Elphick et al. in fitting the experimental diffusion profiles of all components over a limited concentration range by a single diffusion coefficient is due to fortuitous similarity of the EBDCs of the components (Fe, Mg, Mn and Ca) in their diffusion couple experiments. In common metapelitic garnets showing compositional zoning, the EBDCs of the divalent cations do not differ from each other by more than a factor of 2.5. However, the EBDC of a component changes from core to rim by a factor of 3 to 12, depending on the composition. We suggest a method of volume averaging of the EBDC which should prove useful in approximate calculations of diffusion flux during relaxation of compositional zoning. The EBDC of Mn is found to reduce essentially to DMnMn, the main diagonal term of the D matrix, and consequently can be calculated quite easily. Evaluation of EBDC of Fe, Mg and Mn in garnets from a prograde Barrovian sequence did not reveal any significant dependence on the extent of relaxation of garnet. The diffusion data have been applied to calculate the cooling rate of natural biotite-garnet diffusion couple from eastern Finland and diffusional modification of growth zoning in garnet in early Proterozoic Wopmay orogen, Canada. The results are in good agreement with geochronological and other independent constraints.

Compositional Zoning and Cation Diffusion in Garnets

Garnet is stable over a wide range of pressures, temperatures, and bulk compositions. The limited diffusion rates of cations in garnet enable it to retain compositional zoning which reflects its growth and reaction histories. Thus, compositional zoning in garnets is a major potential tool for obtaining quantitative information on the thermal and dynamic histories of a wide variety of rocks. The usefulness of garnet as a recorder of past conditions stems from the facts that it is physically resistant and abundant in many bulk compositions and its compositional profile can usually be measured with sufficient accuracy by step scanning in a microprobe.

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.

Multicomponent diffusion in ternary silicate melts in the system K2O-Al2O3-SiO2: I. Experimental measurements

Abstract We have measured the multicomponent diffusion coefficient matrix, D , for silica rich melts in the system K 2 O-Al 2 O 3 -SiO 2 between 1100–1600°C in air. Measurements were done in both peraluminous as well as peralkaline compositions at constant silica content (by weight). A previously untested method for retrieving the full diffusion coefficient matrix, D , from a single diffusion couple experiment was employed successfully. It is found that there is significant coupling between the different oxide components in the melt during diffusion. This coupling may lead to uphill diffusion of a component. Careful microprobe analysis revealed the occurrence of uphill diffusion of all components (not in the same experiment, however) in this study. The nature of coupling is quantitatively treated in a companion paper (Chakraborty et al., 1995). The nature of coupling is the same in peraluminous and peralkaline melts. However, diffusion rates are much faster in peralkaline melts at comparable conditions. The relationship between the elements of the D matrix, D;;, and the effective binary diffusion coefficients (EBDC) are discussed. It is shown that it is possible to describe diffusion in multicomponent melts in terms of EBDC, even if there is strong multicomponent interaction. However, if certain theoretical requirements are not fulfilled, then the EBDC obtained by fitting concentration profiles obtained in diffusion couple experiments may yield spurious results in mass transfer calculations.

Constraint on the time scale of biotite-grade metamorphism during Acadian Orogeny from a natural garnet-garnet diffusion couple

Abstract We have determined the concentration profiles across the interface of a natural garnetgarnet couple in a biotite-grade rock from eastern Vermont. The couple consists of a grossular-spessartine garnet that had formed during regional metamorphism associated with the Acadian orogeny on an almandine core, which had crystallized during an earlier episode of metamorphism related to the intrusion of Fairlee granite at 411 ± 5 Ma. The concentration profiles were measured by both electron microprobe and analytical transmission electron microscope, and they were modeled to retrieve the value of ∫D(t)dt through the time that diffusion was effective but without recourse to any diffusion data. The length of the concentration profiles measured in microprobe is barely resolvable from that resulting from a convolution effect from the spatial averaging in the spot analyses. Deconvolution of the microprobe profiles yields a value of ∫D(t)dt = 0-3.4 × 10-11 cm2, suggesting very little or no diffusion. TEM analyses of the concentration profiles, which are not subject to any significant convolution effect, show a very small but definitive diffusion zone across the interface of the garnet-garnet couple, which yields a value of ∫D(t)dt = 7.6 × 10-12 cm2. Because D is a function of time through its dependence on temperature, this value of ∫D(t)dt provides an important constraint on the thermal history during the regional metamorphism. As an example, we used it in conjunction with the available diffusion data for garnet to derive ∼40-50 Ma as the probable time scale for the biotite-grade metamorphism, taking into account the effects of the off-diagonal terms and thermodynamic nonideality on the diffusion process.

Solid-solid reactions mediated by a gas phase; an experimental study of reaction progress and the role of surfaces in the system olivine+iron metal

Abstract The intergranular fluid involved in solid-solid reactions is tacitly assumed to be a melt or a (C-O-H-S-Cl-F)-bearing phase. We have studied the system olivine+metal using diffusion couple experiments, in situ reaction progress monitoring using Knudsen-cell mass spectrometry, and thermodynamic-kinetic analysis to show that a dry vapor phase coexisting with solids (silicates, oxides, metals) has all the characteristics of a classical petrologic ‘‘intergranular fluid,’’ and it is a viable transport agent for major rock-forming elements such as Mg, Fe, or Si in many petrologic situations. Some of the major conclusions of the work are: (1) ignoring the vapor phase leads to incorrect estimation of degrees of freedom and consequently, incorrect interpretations of mineral assemblages and zonation; (2) normally refractory elements such as Mg may in some cases be more volatile than O2; and (3) reaction modeling using free-energy minimization allows the main parameters controlling reaction progress, pathway, and products (assemblage, abundance of phases, and composition) to be identified. These parameters include: available reactive surface area; volume of the reaction system; diffusion rates in the product solid; temperature; and relative rates of reaction to transport (in/out of the system). Components other than those appearing explicitly in the mass-balance equations (e.g., ƒO₂ in the olivine+metal system) O2 may play an important role. Transport of Mg in the vapor phase away from local reaction sites explains the compositional zoning of olivine around FeNi-metal inclusions and simultaneously provides a mechanism for the growth of at least some of the fayalite-rich rims in Allende and other meteorites of the CV3-class. Similar considerations may play a role in terrestrial problems where metal and silicate coexist, e.g., the primitive terrestrial magma ocean and the ‘‘D’’ layer.

Multicomponent diffusion in ternary silicate melts in the system K2O-A12O3-SiO2: II. Mechanisms, systematics, and geological applications

Diffusion coefficient matrices (D) for ternary silicate melts have been analysed in terms of eigenvalues and eigenvectors of these matrices. We have used experimental data from our laboratory on melts in the system K2O-Al2O3-SiO2 (Chakraborty et al., 1995), as well as data from the literature. It is found that the eigenvectors, which determine the stoichiometry of homogeneous melt reactions in the melts during diffusion, are relatively insensitive to composition in a given system and temperature. In contrast, the rates of these reactions, given by the eigenvalues of the [D] matrices are strong functions of both composition and temperature. Analysis of diffusion in terms of eigenvalues and eigenvectors helps us to explain observed diffusion paths in the ternary systems and rationalize the difference in behavior of alkalis vs. non alkalis in multicomponent systems, found earlier in the literature (Watson, 1982; Watson and Jurewicz, 1984). A method for predicting the occurrence of uphill diffusion during diffusion in multicomponent systems is discussed and tested experimentally. n nThe concentration profiles obtained during interdiffusion experiments (Chakraborty et al., 1995) are fitted to theoretical models to retrieve tracer diffusion coefficients of Si and Al in these melts. For peraluminous melts in the silica rich part of the K2O-Al2O3-SiO2 system the activation energies for both Si and Al tracer diffusion are found to be 290–318 kJ/mol (70–76 kcal), for corresponding peralkaline compositions the energies are 125–146 kJ/mol (30–35 kcal). The retrieved tracer diffusivities are then used to constrain structural relaxation timescales and viscosities of these melts. n nCompositions that develop during mixing of multicomponent melts are determined by the nature of diffusion paths that develop during the mixing process. It is discussed that anomalous compositions may develop in the mixing zone due to both weak and strong coupling during diffusion which may make interpretation of chemical signatures of melt inclusions difficult. On the other hand, the peculiarities of diffusion paths in a multicomponent system may help understand complex geochemical mixing arrays and some features of anomalous alkali enrichment/ depletion during magmatic evolution.

Chemical diffusivity of boron in melts of haplogranitic composition

Abstract Chemical diffusivities of B in synthetic melts of haplogranitic composition have been measured by the diffusion couple technique at 1 atm between 1200–1600°C. The compositional profiles were measured by ion microprobe and modelled using the Boltzmann-Matano formalism to retrieve compositionally dependent interdiffusion coefficients. At the experimental conditions, B 2 O 3 is found to exchange primarily with SiO 2 and the interdiffusion coefficient increases with increasing replacement of Si by B in the melt. No isotopic fractionation of boron was observed in the diffusion zone at the experimental conditions. The compositional dependence of diffusivity increases with decreasing temperature. The activation energy of diffusion (~70 kcal) is similar to that for viscous flow in melts of the same composition and is relatively insensitive to B content between 1–10 wt% B 2 O 3 in the melt. However, the addition of the initial 1 wt% B 2 O 3 to a haplogranitic melt appears to dramatically lower the activation energy for these processes from ~ 100 kCal to ~70 kCal. Thus, common geochemical concentrations of B may affect petrogenesis of granitic rocks by their influence on these transport properties. Some implications of these results for crystal growth and dissolution in B-bearing melts and boron isotopic variation of granitic melts have been discussed. If diffusion is the rate-limiting process, boron isotopic heterogeneity may be maintained in granitic melts at magmatic temperatures on time scales of millions of years on a millimeter scale. The influence of small amounts of B on transport properties may also contribute toward resolution of an enigma regarding emplacement mechanisms of peraluminous granites.

Quantitative measurement of short compositional profiles using analytical transmission electron microscopy

Abstract X-ray absorption fine structure spectroscopy (XAFS) was used to determine arsenic (As) oxidation state, local coordination (to a radius of ≈7 Å around As), and the relative proportion of different As species in model compounds and three California mine wastes: fully oxidized tailings (Ruth Mine), partially oxidized tailings (Argonaut Mine), and roasted sulfide ore (Spenceville Mine). Mineralogy was characterized by Rietveld refinement of X-ray powder diffraction patterns. The spatial distribution of As in the mine wastes (at several micrometers spatial resolution) was determined by electron microprobe analyses. X-ray absorption near edge structure (XANES) analysis indicates that As5+ is the dominant oxidation state in the mine samples, but mixed oxidation states (nominally As0 and As5+) were observed in the Argonaut Mine waste. Non-linear, least-squares fits of mine waste EXAFS (Extended XAFS) spectra indicate variable As speciation in each of the three mine wastes: As5+ in the Ruth Mine sample is sorbed on ferric oxyhydroxides and aluminosilicates (probably clay) in roughly equal portions. Tailings from the Argonaut Mine contain ≈20% As bound in arsenopyrite (FeAsS) and arsenical pyrite (FeS2-xAsx) and ≈80% As5+ in a precipitate such as scorodite (FeAsO4·2H20); however, no precipitate was detected by X-ray diffraction or microprobe analysis, suggesting that the phase is poorly crystalline or has low abundance (total As in sample = 262 ppm). Roasted sulfide ore of the Spenceville Mine contains As5+ substituted for sulfate in jarosite [KFe3(SO4)2(OH)6] or incorporated in the structure of an unidentified Ca- or K-bearing phase, and As5+ sorbed to the surfaces of hematite or ferric oxyhydroxide grains. Detemiination of solid-phase As speciation in mine wastes by XAFS spectroscopy is a valuable first step in the evaluation of its bioavailability, because the mobility and toxicity of As compounds vary with oxidation state. As bound in precipitates, as in the Argonaut mine sample, is considered to be less available for uptake by organisms than when sorbed on mineral surfaces or coprecipitated with poorly crystalline phases, as found for the Ruth and Spenceville mine wastes.