Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples,evaluation of effective binary diffusion coefficients,and applications   总被引：9，自引：1，他引：8  

Sumit Chakraborty  Jibamitra Ganguly 《Contributions to Mineralogy and Petrology》1992,111(1):74-86

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 D _MnMn, 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.Symbols and abbreviations a Radius of a spherical garnet crystal - BSE Back-scattered electron imaging - C Column vector of (n-1) independent components - D Diffusion coefficient matrix - D _ij An element of the diffusion matrix on the i th row and j th column - D _* ⁱ Tracer diffusion coefficient of component i - D(i) Effective interdiffusion coefficient (EIC) of various components in a multicomponent solution rich in the component i - D(i-j) Interdiffusion coefficient of components i and j in a binary solution - D _i (EB) Effective binary diffusion coefficient of component i in a multicomponent solution - D _i (EB:Ideal) D _i (EB) under condition of ideal thermodynamic mixing of the diffusing species - D _i (EB:thermo) Thermodynamic component of D _i(EB) - D _O ^A Interdiffusion coefficient at peak temperature T ₀ in the phase A - D ₀ Pre-exponential factor in an Arrhenius relation - EBDC Effective binary diffusion coefficient between a solute and a multicomponent solvent matrix - FEC Fixed edge composition model - EIC Effective interdiffusion coefficient - f _i Fugacity of component i - HM Hematite-magnetite oxygen fugacity buffer - kb Kilobars - P Pressure - Q Activation energy (enthalpy) of diffusion - Extent of relaxation defined as the difference between core and rim compositions normalized to the same difference in the initial zoning profile - R Gas constant - s Cooling rate - T ₀, T _Ch Peak temperature and characteristic temperature, respectively - t Time - VEC Variable edge composition model - V ⁺ Activation volume - W _ij Simple mixture interaction parameter between i and j - W _i(EB) Effective simple mixture interaction parameter of a component i in a multicomponent solution - _ij Margules interaction parameter between i and j - X _i Mole fraction of component i - _i Activity coefficient of component i - A dimensionless variable =D t/a ² - _ij Kronecker delta (i=j, _ij =1; ij, _ij =0) - Z_i Charge on the ion i  相似文献   

Thermophysical properties of the α–β–γ polymorphs of Mg<Subscript>2</Subscript>SiO<Subscript>4</Subscript>: a computational study     

G. Ottonello  B. Civalleri  J. Ganguly  M. Vetuschi Zuccolini  Y. Noel 《Physics and Chemistry of Minerals》2009,36(2):87-106

Thermophysical properties of the various polymorphs (i.e. α-, β- and γ) of Mg₂SiO₄ were computed with the CRYSTAL06 code within the framework of CO-LCAO-GTF approach by using the hybrid B3LYP density functional method. Potential wells were calculated through a symmetry preserving, variable cell-shape structure relaxation procedure. Vibrational frequencies were computed at the long-wavelength limit corresponding to the center of the Brillouin zone (k → 0). Thermodynamic properties were estimated through a semiclassical approach that combines B3LYP vibrational frequencies for optic modes and the Kieffer’s model for the dispersion relation of acoustic modes. All computed values except volume (i.e. electronic energy, zero point energy, optical vibrational modes, thermal corrections to internal energy, standard state enthalpy and Gibbs free energy of reaction, bulk modulus and its P and T derivatives, entropy, C _V, C _P) are consistent with available experimental data and/or reasonable estimates. Volumes are slightly overestimated relative to those determined directly by X-ray diffraction. A set of optimized volumetric properties that are consistent with the other semiclassical properties of the phases α, β and γ have been derived by optimization procedure such that the calculated boundaries for the α/β and β/γ equilibria have the best overall agreement with the experimental data for these transitions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

G. OttonelloEmail:

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A comparison between thomson scatter and meteor radar wind measurements in the 65–105 km altitude region at Arecibo     

J.D. Mathews  M.P. Sulzer  C.A. Tepley  R. Bernard  J.L. Fellous  M. Glass  M. Massebeuf  S. Ganguly  R.M. Harper  R.A. Behnke  J.C.G. Walker 《Planetary and Space Science》1981,29(3):341-348

The results of simultaneous meteor and Thomson scatter radar wind measurements in the 65–105 km altitude region are presented. The two radars are located in Puerto Rico where the 430-MHz Thomson scatter radar at Arecibo Observatory is employed along with the French (CNET) portable meteor radar which is at a 40-km distance. The two sets of wind measurements compare quite favorably during periods of coincident observation. The meteor radar yields continuous results while the Thomson scatter radar is usable only during daylight hours. The Thomson scatter results, on the other hand, extend down to 65 km altitude and are available with better height and time resolutions than the meteor radar results. The two measurement techniques are therefore complementary.  相似文献   

Cooling history of lunar Mg-suite gabbronorite 76255, troctolite 76535 and Stillwater pyroxenite SC-936: The record in exsolution and ordering in pyroxenes     

I. Stewart McCallum  M. Chiara Domeneghetti  Jeffrey M. Schwartz  Emily K. Mullen  Michele Zema  Fernando Cmara  Catherine McCammon  Jibamitra Ganguly 《Geochimica et cosmochimica acta》2006,70(24):6068-6078

We have determined cooling rates of orthopyroxene crystals from two Mg-suite lunar samples (gabbronorite 76255 and troctolite 76535) and one terrestrial sample (orthopyroxenite SC-936 from the Stillwater Complex), on the basis of their Fe–Mg ordering states. In addition, a cooling rate of 76255 was determined by modeling the formation of exsolution lamellae in pyroxenes. The M1–M2 site occupancies of the orthopyroxene crystals were determined by single crystal X-ray diffraction and the rate constant for the ordering reaction was used along with calibrations of the equilibrium intracrystalline fractionation of Fe and Mg as a function of temperature to calculate cooling rates. The closure temperatures (T_C) of cation ordering are 525 °C for 76255, 500 °C for 76535 and 350 °C for SC-936 corresponding to cooling rates of 4 × 10⁻² °C/year at the closure temperature for the lunar samples and 10⁻⁶ °C/year for the Stillwater sample. A cooling rate for 76255, determined by simulating the exsolution process, is 1.7 × 10⁻² °C/year at a closure temperature for exsolution of 700 °C. The Fe–Mg ordering cooling rate determined for 76535 reflects a complex thermal history superimposed on the initial plutonic provenance established for this sample [McCallum, I.S., Schwartz, J.M., 2001. Lunar Mg suite: thermobarometry and petrogenesis of parental magmas. J. Geophys. Res. 106, 27969–27983]. The preservation of a crystallization age of 4.51 Ga and a metamorphic age of 4.25 Ga for 76535 is consistent with a model in which excavation of this sample from the lower lunar crust took place while the sample was at a temperature above the closure temperatures for the Sm–Nd, U–Pb and Ar–Ar isotopic systems. Temperatures in excess of the isotopic closure temperatures (i.e., >600 °C) in the lower lunar crust were maintained by heat diffusing from concentrations of U- and Th-rich KREEP material at the base of the crust. On the other hand, 76255 formed at a much shallower depth in the lunar crust (2 km) and was well below its isotopic closure temperatures at the time of excavation, most likely during the Serenitatis basin-forming impact event. Both lunar samples were reheated during transport to the surface and deposition in hot ejecta blankets. The reheating was short lived but apparently sufficient to redistribute Fe and Mg in M sites in orthopyroxenes. For the lunar samples, the cooling rates based on Fe–Mg ordering represent final stage cooling within an ejecta blanket.  相似文献   

Thermodynamics of the oxygen isotope fractionation involving plagioclase     

Jibamitra Ganguly 《Earth and Planetary Science Letters》1982,61(1):123-126

The thermodynamic relationship between the oxygen isotope fractionation properties of plagioclase and its composition has been derived by treating plagioclase as a “reciprocal solution” consisting of independent cationic and anionic substitutions, namely (NaAl)⁵⁺?(CaSi)⁵⁺and¹⁸O?¹⁶O. The results show that the logarithm of the oxygen isotope fractionation factor, α, between plagioclase and a coexisting phase varies linearly with the anorthite content of plagioclase. The proportionality constant is given by the oxygen isotope fractionation factor between albite and anorthite, and has been derived from the experimental data of two groups of workers, O'Neil and Taylor [2] and Matsuhisa et al. [3], on the isotopic fractionation between each plagioclase end-member and aqueous solutions. It is found that O'Neil and Taylor's data on isotopic exchange of plagioclase end-members with only 2–3 M chloride solution, rather than with both pure water and the chloride solution, lead essentially to zero intercept of the ln α(Ab-An) vs. 1/T² relation, in accord with Bottinga and Javoy's [10] conclusion about the oxygen isotope fractionation between two anhydrous silicates at T<500°C.  相似文献   

A Subwaveform-Based Retracker for Multipeak Waveforms: A Case Study over Ukai Dam/Reservoir     

Debojyoti Ganguly  Shard Chander  Shruti Desai  Prakash Chauhan 《Marine Geodesy》2015,38(3):581-596

Retracking altimeter waveforms over inland water bodies is a challenging task as a wide range of waveform is encountered while the retracking algorithms are available only for a handful of echo shapes. One such waveform shape widely encountered in lakes and reservoirs is the multipeak echo. These echoes are produced when the interacting surface in the altimeter footprint is not homogeneous and a number of different types of surfaces contribute to the resulting waveform. The widely used conventional retrackers, namely the Brown, Beta-5, Ice-2, OCOG, and threshold, can retrack a number of different waveform shapes such as the Brown like waveforms, specular waveforms, and rectangular waveforms but may not perform well for multipeak waveforms. In this article, a technique has been demonstrated to identify the different subwaveforms within a multipeak waveform and identify the subwaveform corresponding to the target at nadir. The subwaveform that is reflected from the nadir surface is identified from apriory information about the surface topography of the area. The subwaveform is then retracked using the 50% threshold to find the correct retracked range and water height. This technique has been tested for nine cycles of SARAL SIGDR data on Ukai reservoir, Gujarat, India, and found to perform much better than the other retrackers, particularly for multipeak waveforms.  相似文献   

Analytical solutions for transient temperature distribution in a geothermal reservoir due to cold water injection     

Sayantan Ganguly  M. S. Mohan Kumar 《Hydrogeology Journal》2014,22(2):351-369

An analytical solution to describe the transient temperature distribution in a geothermal reservoir in response to injection of cold water is presented. The reservoir is composed of a confined aquifer, sandwiched between rocks of different thermo-geological properties. The heat transport processes considered are advection, longitudinal conduction in the geothermal aquifer, and the conductive heat transfer to the underlying and overlying rocks of different geological properties. The one-dimensional heat transfer equation has been solved using the Laplace transform with the assumption of constant density and thermal properties of both rock and fluid. Two simple solutions are derived afterwards, first neglecting the longitudinal conductive heat transport and then heat transport to confining rocks. Results show that heat loss to the confining rock layers plays a vital role in slowing down the cooling of the reservoir. The influence of some parameters, e.g. the volumetric injection rate, the longitudinal thermal conductivity and the porosity of the porous media, on the transient heat transport phenomenon is judged by observing the variation of the transient temperature distribution with different values of the parameters. The effects of injection rate and thermal conductivity have been found to be profound on the results.  相似文献   

Fe2+-Mg order-disorder in orthopyroxene: equilibrium fractionation between the octahedral sites and thermodynamic analysis     

M. Stimpfl  J. Ganguly  G. Molin 《Contributions to Mineralogy and Petrology》1999,136(4):297-309

The equilibrium intracrystalline distribution coefficient, k _D ^*, of Fe^* (i.e. Fe²⁺ + Mn) and Mg between the M1 and M2 sites of three natural nearly binary Fe²⁺-Mg orthopyroxene crystals (Fs₁₄, Fs₁₅ and Fs₄₉) were determined by annealing experiments at several temperatures between 550 and 1000 °C and single crystal X-ray structure refinements. In addition, the X-ray data of an orthopyroxene crystal (Fs₂₃), which were collected earlier by Molin et al. (1991) between 700 and 1000 °C, were re-refined. The data were processed through two different refinement programs (SHELXL-93 and RFINE90) using both unit and individual weights and also both ionic and atomic scattering factors. The calculated site occupancies were found to agree within their estimated standard errors. However, the use of ionic scattering factors led to significantly better goodness of fit and agreement index, and smaller standard deviations of the site occupancies than those obtained from the use of atomic scattering factors. Furthermore, the weighted refinements yielded significantly smaller standard deviations of the site occupancies than the unweighted refinements even when the same set of reflections was used in the two procedures. The site occupancy data from this study were combined with selected published data to develop expressions of k _D ^* as a function of temperature and composition. Calculation of the excess configurational entropy, ΔS ^XS, suggests that orthopyroxene should be treated as a two parameter symmetric solution instead of as a “simple mixture”. The calculated ΔS ^XS values and the excess Gibbs free energy of mixing suggested by available cation exchange data lead to a slightly negative enthalpy of mixing in the orthopyroxene solid solution. Received: 25 August 1998 / Accepted: 10 March 1999  相似文献