Jibamitra Ganguly

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.

Diffusion closure temperature and age of a mineral with arbitrary extent of diffusion: theoretical formulation and applications

The commonly used expression of the closure temperature, TC, of a diffusing species in a mineral, as derived by M.H. Dodson [Contrib. Mineral. Petrol. 40 (1973) 259–264], is applicable only to systems which have undergone sufficient diffusion so that even the composition at the center of individual grains is significantly removed from that established at the onset of cooling. We have extended Dodsons formulation to include cases with arbitrarily small amount of diffusion, and applied it to calculate TC and age profiles, which would develop in single crystals of different geometries. These results permit evaluation of the extent of resetting of mineral age and of ion exchange geothermometers during cooling. The measured age profile of a mineral can also be used to constrain its cooling rate. These applications have been illustrated for the cases of garnet–biotite Fe–Mg exchange geothermometer, and the cooling age and closure temperatures of the Sm–Nd and Lu–Hf decay systems in garnet.

Garnet and clinopyroxene solid solutions, and geothermometry based on Fe-Mg distribution coefficient

The available thermodynamic mixing data of aluminosilicate garnet and clinopyroxene have been critically reviewed, and integrated with the thermochemical and selected experimental data to express the Fe-Mg distribution coefficient (KD) between these phases as function of pressure, temperature and composition. The predicted compositional dependence of KD agrees with the available experimental and observational data. Owing to the lack of adequate data on the mixing properties of Jadeite with diopside and hedenbergite, the geothermometric application of the model has to be currently restricted to the Na-poor bulk compositions. The temperature of a variety of rocks that have equilibrated under a wide range of P-T conditions have been estimated, and found to agree, on the average within 25°C, with other reliable temperature estimates of these rocks. The latter are, however, often in sharp disagreement with the temperatures determined on the basis of Raheim and Greens (1974, Contrib. Mineral. Petrol.48, 179–203) experimental calibration of KD as function of temperature and pressure on tholeiitic bulk composition.

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.

The energetics of natural garnet solid solution - I. Mixing of the aluminosilicate end-members

Approximate mixing properties of the dominant calcium silicate end-member components of natural garnets, namely grossularite, andradite and uvarovite, have been derived through theoretical thermodynamic and crystal chemical analysis, and appropriate reduction of the available experimental data. The stability of the solid solution with respect to phase separation in the ternary system has been analyzed. Finally, a general model is presented as to the approximate mixing properties of multicomponent natural garnet solid solution involving substitutions in both eight and six coordinated sites.

Exhumation history of a section of the Sikkim Himalayas, India: records in the metamorphic mineral equilibria and compositional zoning of garnet

The exhumation history of pelitic migmatite samples from the High Himalayan Crystalline Complex (HHC) near the South Tibetian Detachment System in the Sikkim-Darjeeling section has been determined on the basis of thermo-barometric analyses, retrograde breakdown reactions and compositional zoning of garnet. The peak metamorphic condition is estimated to be ∼10.4 kbar, 800°C from thermo-barometric and phase equilibrium constraints. The observed retrograde breakdown of garnet to spinel and cordierite requires near isothermal and, hence, extremely rapid (∼15 mm/yr) exhumation up to the depth of ∼15 km. Numerical modeling suggests that the initial rapid exhumation must have been followed by a much slower process, ∼2 mm/yr, up to at least ∼5 km depth, to lead to the development of the observed compositional zoning of garnet. The dramatic change of the exhumation velocity (Vz) might reflect a process of tectonic thinning followed by erosion and/or horizontal flow at shallow depth. Assuming that the Vz did not change significantly below 5 km depth, these results suggest that the HHC samples studied in this work exhumed from a depth of ∼34 km within ∼8 Ma.

Experimental determination of cation diffusivities in aluminosilicate garnets I. Experimental methods and interdiffusion data

We have carried out diffusion couple experiments using pairs of single crystals of natural garnet of dissimilar compositions in the range of 30–40 Kbar, 1,300–1,500° C, and measured the induced diffusion profiles by microprobe scanning across the interface. Significant modifications to, and experimentation with, the design of the pressure cell, furnace assembly and sample geometry were needed to obtain measurable volume diffusion at controlled P-T conditions.The diffusion profiles in the pyrope-almandine couples are short enough that retrieval of diffusion data from them must await deconvolution analysis to resolve the effect of spatial averaging of the microprobe beam. However, the profiles in the spessartine-almandine couples are sufficiently long to obviate convolution analysis. They yield interdiffusion coefficients (D) at 40 Kbar of D = 0.82×10−5 exp (−53.6±4.9 Kcal/RT) cm2/s and D=1.2×10−5 exp (−57.1±8.4 Kcal/RT) cm2/s for Fe-rich and Mn-rich compositions, respectively, and an activation volume of ∼4.7 cm3/mole. Preliminary analysis of profiles in a pyrope-almandine couple at ∼40 Kbar, 1,440°C suggests Fe-Mg interdiffusion to be an order of magnitude slower that Fe-Mn interdiffusion, and to increase with Fe/Mg ratio. The interdiffusion data reported here are in sharp disagreement with those of Freer (1979) and Duckworth and Freer (in Freer 1981) on Fe-Mn and Fe-Mg interdiffusion, respectively.

Experimental determination of cation diffusivities in aluminosilicate garnets - II. Multicomponent simulation and tracer diffusion coefficients

Data from experimentally-induced diffusion profiles at approximately 40 Kbar, 1,300–1,500° C in spessartine-almandine couples and a pyrope-almandine couple at ∼ 40 Kbar, 1,440° C, described in Part I, were used to derive tracer diffusion coefficients (D*) of Fe, Mn and Mg in garnet. The experimental data were fitted by numerical simulations that model multicomponent, compositionally-dependent difussion, including the effects of nonideal thermodynamic mixing. The simulations use the formalism of irreversible thermodynamics and an eigenvector technique of solution. We were able to fit the asymmetrical spessartine-almandine profiles using constant D* and either the Darken/Hartley-Crank or Manning-Lasaga models relating D* and interdiffusion coefficients, and both models yielded DMg*consistent with the direct measurement of DMg*in by Cygan and Lasaga (1985) at lower temperatures (750–900° C). The results (equations 4.1–4.3 and Table 1) indicate that DFe*≅DMg*<DMn*and QFe≅QMg>QMn, where Q is the activation energy. In contrast, the asymmetry of pyrope-almandine profiles is too great to fit with either tracer model assuming constant D* and indicates that DMg*is similar to its value in spessartine-almandine couples but DFe*is an order of magnitude less. The fit also suggests that DCa*< DFe*<DMg*in pyrope-almandine couples. Synthesis of data from the two types of diffusion couples suggests that DMg*is insensitive to compositional changes, whereas DFe*is affected by Mn/Mg and Fe/Mg ratios and probably by other factors. These compositional effects on tracer coefficients are compatible with those documented by Morioka (1983) for cation diffusion in olivine.

Sm^Nd dating of spatially controlled domains of garnet single crystals: a new method of high-temperature thermochronology

Ganguly and Tirone [Meteorit. Planet. Sci. 36 (2001) 167^175] recently presented a method of determining the cooling rates of rocks from the difference between the core and bulk ages of a crystal, as determined by a single decay system. Here we present the first application of the method using the core and bulk ages of garnet single crystals, according to the Sm^Nd decay system, in two rock samples with contrasting cooling rates, which can be constrained independently. The samples belong to the metamorphic core complex, Valhalla, British Columbia, and the mid-crustal magmatic arc exposure of the Salinian terrane, California. We have micro-sampled the garnet crystals over specific radial dimensions, and measured the Nd isotopes of these small sample masses, as NdO þ via solid source mass spectrometry, to determine the Sm^Nd age difference between the core and bulk crystals. Using a peak metamorphic P^T condition of 8 > 1 kbar, 820 > 30‡C [Spear and Parrish, J. Petrol. 37 (1996) 733^765], the core (67.3 > 2.3 Ma) and bulk (60.9 > 2.1 Ma) ages of the British Columbian garnet sample yield a cooling rate of 2^13‡C/Myr, which is in very good agreement with the cooling rates that we have derived by modeling the retrograde Fe^Mg zoning in the same garnet, and assuming the same peak metamorphic P^T condition. Considering earlier cooling rate data derived from closure temperature vs. age relation of multiple geochronological systems [Spear and Parrish, J. Petrol. 37 (1996) 733^ 765], a cooling rate of V15^20‡C/Myr seems most reasonable for the Valhalla complex. Diffusion kinetic analysis shows that the Sm^Nd core age of the selected garnet crystal could not have been disturbed during cooling. Consequently, the core age of the garnet crystal, 67.3 > 2.3 Ma, corresponds to the peak metamorphic age of the Valhalla complex. The Salinian sample, on the other hand, yields indistinguishable core (78.2 > 2.7 Ma) and bulk (77.9 > 2.9 Ma) ages, as expected from its fast cooling history, which can be constrained by the results of earlier studies. The Sm^Nd decay system in garnet has relatively high closure temperature (usually s 650‡C); therefore, the technique developed in this paper fills an important gap in thermochronology, since the commonly used thermochronometers are applicable only at lower temperatures. Simultaneous modeling of the retrograde Fe^Mg zoning in garnet, spatially resolved Sm^Nd ages of garnet single crystals, and resetting of the bulk garnet Sm^Nd age

Thermal history of mesosiderites: Quantitative constraints from compositional zoning and Fe-Mg ordering in orthopyroxenes

Abstract We have derived mathematical relations to calculate cooling rates from the extent of compositional zoning developed during cooling across the interface of a natural diffusion couple. These relations were used to calculate the high temperature cooling rates of the mesosiderites Lowicz and Clover Springs from the available data on compositional zoning across core-overgrowth interface of orthopyroxene grains. We have also determined the cation ordering in four selected orthopyroxene crystals from Bondoc and Estherville mesosiderites with very high precision, and used these data to calculate their low temperature cooling rates. The compositional zoning of orthopyroxene crystals reflects extremely rapid cooling rates, at least ~1°C/100 years in the temperature range 850–1150°C. However, simultaneous consideration of both metallographic and cation ordering data for Estherville, within the framework of either an asymptotic or an exponential cooling model, requires a cooling rate of ~l°C/Ma near 250°C. The cation ordering data for Bondoc, for which no metallographic data are yet available, are suggestive of even slower cooling rate, which implies excavation from a somewhat greater depth in the parent body. However, within the limits of their uncertainties, the measured site occupancies of the orthopyroxene crystals from Bondoc can be reconciled with a cooling rate similar to that of Estherville. The calculated cooling rates at both high- and low-temperatures have been used to develop a thermal evolution model of mesosiderites. The suggested model is not incompatible with an asteroidal parent body for these meteorites. Further, it is shown that the closure temperature of Ar-Ar age must be tied to the slow cooling rate below 500°C.