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 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     

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

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.

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

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.     

Interacting system NGC 7805/6 (Arp 112) and its tidal dwarf galaxy candidate

We present results from our Giant Metrewave Radio Telescope(GMRT)HⅠ,Himalayan Chandra Telescope(HCT)Hα,1 m Sampurnanand Telescope(ST)and 1.3 m Devasthal Fast Optical Telescope(DFOT)deep optical observations of the NGC 7805/6(Arp 112)system to test KUG 2359+311’s tidal dwarf galaxy(TDG)candidacy and explore the properties of the interacting system.Our GMRT HⅠmap shows no HⅠdetection associated with KUG 2359+311,nor any HⅠtail or bridge-like structure connecting KUG 2359+311 to the NGC 7805/6 system.Our HCT Hαimage,on the other hand,displays strong detections in KUG 2359+311,with net SFR0.035±0.009 M_⊙yr^-1.The Hαdata constrain the redshift of KUG 2359+311 to 0.00≤z≤0.043,compared to the redshift of NGC 7806 of0.015.TDGs detected to date have all been HⅠrich,and displayed HⅠ,ionised gas and stellar tidal debris trails(bridges or tails)linking them to their parent systems.However,neither our HⅠdata nor our optical imaging,while three magnitudes deeper than SDSS,reveals a tidal trail connecting KUG 2359+311 to NGC 7805/6.Lack of HⅠ,presence of an old stellar population,ongoing star formation and reasonably high SFR compared to normal dwarf galaxies suggest that KUG 2359+311 may not be an Arp 112 TDG.It is most likely a case of a regular gas-rich dwarf galaxy undergoing a morphological transformation after having lost its entire gas content to an interaction with the Arp 112 system.Redshift and metallicity from future spectroscopic observations of KUG 2359+311 would help clarify the nature of this enigmatic structure.     

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

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.     

Incorporation of water into olivine during nebular condensation: Insights from density functional theory and thermodynamics,and implications for phyllosilicate formation and terrestrial water inventory

Using density functional theory, we have examined the hydration mechanism of olivine with the objective of understanding the reaction pathways toward the formation of crystalline serpentine and brucite. It is found that further supply of water beyond saturation of the adsorption sites on olivine surfaces leads to the formation of amorphous brucite and serpentine molecules, with the latter forming in the subsurface domain. The calculated activation energy for this process is ~25 kJ mol^?1, which permits formation of the amorphous materials well within the life span of the solar nebula. In addition, molecular dynamic simulations show that the adsorbed water in olivine is stable at least up to 900 K—a finding that is in accord with independent experimental studies. Thus, adsorption plus subsurface reaction of H₂O in olivine could have taken place at temperatures considerably higher than the stability limit of hydrous minerals in the nebular condition. Using the DFT derived enthalpy of adsorption data, and reasonable approximation for the entropy of adsorption, we have calculated the fractional coverage of the reactive surface sites of olivine grains of spherical geometry by adsorbed water, and the corresponding ocean equivalent water (OEW) that could have been accreted into the Earth. These results suggest that adsorption and the associated subsurface hydroxylation of olivine grains might have been responsible for a significant fraction of the Earth's water budget. The adsorption of water into olivine crystals in the solar nebula might also have led to the delivery of water to other planetary bodies.     

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

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     

Neodymium diffusion in orthopyroxene: Experimental studies and applications to geological and planetary problems

We have determined the Nd³⁺ diffusion kinetics in natural enstatite crystals as a function of temperature, f(O₂) and crystallographic direction at 1 bar pressure and applied these data to several terrestrial and planetary problems. The diffusion is found to be anisotropic with the diffusion parallel to the c-axial direction being significantly greater than that parallel to a- and b-axis. Also, D(//a) is likely to be somewhat greater than D(//b). Diffusion experiments parallel to the b-axial direction as a function of f(O₂) do not show a significant dependence of D(Nd³⁺) on f(O₂) within the range defined by the IW buffer and 1.5 log unit above the WM buffer. The observed diffusion anisotropy and weak f(O₂) effect on D(Nd³⁺) may be understood by considering the crystal structure of enstatite and the likely diffusion pathways. Using the experimental data for D(Nd³⁺), we calculated the closure temperature of the Sm-Nd geochronological system in enstatite during cooling as a function of cooling rate, grain size and geometry, initial (peak) temperature and diffusion direction. We have also evaluated the approximate domain of validity of closure temperatures calculated on the basis of an infinite plane sheet model for finite plane sheets showing anisotropic diffusion. These results provide a quantitative framework for the interpretation of Sm-Nd mineral ages of orthopyroxene in planetary samples. We discuss the implications of our experimental data to the problems of melting and subsolidus cooling of mantle rocks, and the resetting of Sm-Nd mineral ages in mesosiderites. It is found that a cooling model proposed earlier [Ganguly J., Yang H., Ghose S., 1994. Thermal history of mesosiderites: Quantitative constraints from compositional zoning and Fe-Mg ordering in orthopyroxene. Geochim. Cosmochim. Acta 58, 2711-2723] could lead to the observed ∼90 Ma difference between the U-Pb age and Sm-Nd mineral age for mesosiderites, thus obviating the need for a model of resetting of the Sm-Nd mineral age by an “impulsive disturbance” [Prinzhoffer A, Papanastassiou D.A, Wasserburg G.J., 1992. Samarium-neodymium evolution of meteorites. Geochim. Cosmochim. Acta 56, 797-815].     

Methane flux dynamics in relation to methanogenic and methanotrophic populations in the soil of Indian Sundarban mangroves

The dynamics of methane (CH₄) flux in relation to populations of methanogenic and methanotrophic bacteria was studied under the different biophysical conditions of the Indian Sundarban mangrove ecosystem. Soil depth profile analysis (up to 60 cm) in the lower littoral zone (LLZ) revealed that a methanogenic population of 6.45 ± 0.19 × 10⁴ cells/g dry weight (dry wt) of soil accounted for a CH₄ production rate of 6.23 ± 3.53 × 10³ µmol m^?2 day^?1, whereas in the surface soil, a methanogenic population of 3.34 ± 0.37 × 10⁴ cells/g dry wt of soil accounted for a CH₄ production rate of 31.6 ± 0.57 µmol m^?2 day^?1. The CH₄ oxidation rate at 60 cm depth in the LLZ was 24.42 ± 1.28 µmol m^?2 day^?1, with an average methanotrophic population of 1.33 ± 0.43 × 10⁴ cells/g dry wt of soil, whereas in the surface soil, the oxidation rate and average population were 3.38 ± 1.43 × 10³ µmol m^?2 day^?1 and 12.80 ± 2.54 × 10⁴ cells/g dry wt of soil, respectively. A similar soil profile in terms of CH₄ dynamics and the populations of methanogenic and methanotrophic bacteria was found in the mid‐littoral and upper littoral zones of the studied area. The results demonstrate that most of the produced CH₄ (approximately 60%) was oxidized by methanotrophic bacteria present in the soil, thus revealing their principal role in regulating the CH₄ flux from this unique ecosystem.     

Type IIP supernova SN 2004et: a multiwavelength study in X-ray, optical and radio

We present X-ray, broad-band optical and low-frequency radio observations of the bright type IIP supernova SN 2004et. The Chandra X-ray Observatory observed the supernova at three epochs, and the optical coverage spans a period of ∼470 d since explosion. The X-ray emission softens with time, and we characterize the X-ray luminosity evolution as   L _X∝ t ^−0.4  . We use the observed X-ray luminosity to estimate a mass-loss rate for the progenitor star of  ∼2 × 10⁻⁶ M_⊙ yr⁻¹  . The optical light curve shows a pronounced plateau lasting for about 110 d. Temporal evolution of photospheric radius and colour temperature during the plateau phase is determined by making blackbody fits. We estimate the ejected mass of ⁵⁶Ni to be  0.06 ± 0.03 M_⊙  . Using the expressions of Litvinova & Nadëzhin we estimate an explosion energy of  (0.98 ± 0.25) × 10⁵¹ erg  . We also present a single epoch radio observation of SN 2004et. We compare this with the predictions of the model proposed by Chevalier, Fransson & Nymark. These multiwavelength studies suggest a main-sequence progenitor mass of  ∼20 M_⊙  for SN 2004et.