Experimental determination of Mn-Mg mixing properties in garnet,olivine and oxide

We have measured the mixing properties of Mn-Mg olivine and Mn-Mg garnet at 1300° C from a combination of interphase partitioning experiments involving these phases, Pt-Mn alloys and Mn-Mg oxide solid solutions. Activity coefficients of Mn dilute in Pt-Mn alloys at 1300° C/1 atm were measured by equilibrating the alloy with MnO at known f _{O 2}. Assuming that the log f _{O 2} of the Mn-MnO equilibrium under these conditions is-17.80 (Robie et al. 1978), we obtain for _Mn: log_Mn = –5.25 + 3.67 X_Mn + 11.41X² _Mn Mixing properties of (Mn,Mg)O were determined by reversing the Mn contents of the alloys in equilibrium with oxide at known f _{O 2}. Additional constraints were obtained by measuring the maximum extent of immiscibility in (Mn,Mg)O at 800 and 750° C. The data are adequately described by an asymmetric (Mn,Mg)O solution with the following upper and lower limits on nonideality: (a) W_Mn = 19.9kj/Mol; W_Mg = 13.7kj/Mol; (b) W_Mn = 19.9kj/Mol; W_Mg = 8.2kj/Mol; Olivine-oxide partitioning was tightly bracketed at 1300° C and oxide properties used to obtain activity-composition relations for Mn-Mg olivine. Despite strong M2 ordering of Mn in olivine, the macroscopic properties are adequately described by a symmetric model with: W^ol = 5.5 ± 2.5 kj/mol (1-site basis) Using these values for olivine, garnet-olivine partitioning at 27 kbar/1300° C leads to an Mn-Mg interaction parameter in garnet given by: W^gt = 1.5 ± 2.5kJ/mol (1-site basis) Garnet-olivine partitioning at 9 kbar/1000° C is consistent with the same extent of garnet nonideality and the apparent absence of excess volume on the pyrope-spessartine join indicates that any pressure-dependence of W^Gt must be small. If olivine and garnet properties are both treated as unknown and the garnet-olivine partitioning data alone used to derive W^Ol and W^Gt, by multiple linear regression, best-fit values of 6.16 and 1.44 kJ/mol. are obtained. These are in excellent agreement with the values derived from metal-oxide, oxide-olivine and olivine-garnet equilibria.     

Thermodynamic properties of strontianite-witherite solid solution (Sr,Ba)CO3

Structural parameters and thermodynamic properties of strontianite — witherite solid solutions have been studied by X-ray powder diffraction, heat flux Calvet calorimetry and cation-exchange equilibria technique. X-ray study of the synthetic samples have shown linear and quadratic (for c-parameter) composition dependencies of the lattice constants in the carbonate solid solution. The thermodynamic energy parameters demonstrate the non-ideal character of strontianite — witherite solid solutions. Enthalpies of solution of the samples have been measured in 2PbO*B₂O₃ at 973 K. The new data on the enthalpy of formation H _f,298.15 ⁰ of SrCO₃ and BaCO₃ were obtained: -1231.4±3.2 and -1209.9±5.8 kJ*mol^-1 respectively. The enthalpy of mixing of the solid solution was found to be positive and asymmetric with maximum at X_Ba (carbonate)=0.35. The composition dependence of the enthalpy of mixing may be described by two — parametric Margules model equation: H _mix=X _BaX _Sr[(4.40±3.91)X _Ba+(28.13±3.91)X _Sr] kJmol^–1 Cation-exchange reactions between carbonates and aqueous SrCl₂-BaCl₂ supercritical solutions (fluids) were carried out at 973 and 1073 K and 2 kbar. Calculated Margules model parameters of the excess free energy are: for orthorhombic carbonate solid solutions W _Sr=W _Ba=11.51±0.40 kJmol^–1 (973 K) and W _Sr=W _Ba=12.09±0.95 kJmol^– (1073 K) for trigonal carbonate solid solutions W _Sr=W _Ba=13.55±0.40 kJmol^– (1073 K).     

Local structural heterogeneity,mixing behaviour and saturation effects in the grossular–spessartine solid solution

Local structural heterogeneities in crystals of the binary grossular–spessartine solid solution have been analyzed using powder IR absorption spectroscopy. Wavenumber shifts of the highest energy Si–O stretching mode in spectra collected at room temperature are consistent with variations in Si–O bond length from structural data. They show a smaller positive deviation from linearity across the join than is seen for the grossular–pyrope and grossular–almandine binaries. The effective line widths, corr, of three selected wavenumber regions all deviate positively from linear behaviour. An empirical calibration of this excess spectroscopic property, obtained by comparison with calorimetric enthalpy of mixing data, gives an estimate for the symmetric Margules parameter of W^H_spec = 14.4(7) kJ mol^–1 in H^mix = W^H_specX_GrX_Sp. W^H_spec values derived on the same basis for four aluminosilicate garnet solid solutions analyzed by IR spectroscopy vary with V², where V represents the difference in molar volume between the end members of each binary system. Measurements of lattice parameters and IR spectra were made over a range of temperatures for seven samples with different compositions. Positive excess molar volumes of mixing at low temperature (30 K) may be larger than the excess molar volumes at room temperature. The saturation temperatures of the molar volumes show no correlation with composition, however, in contrast with what had been expected on the basis of data for the grossular–pyrope binary. Saturation temperatures for spectroscopic parameters and lattice parameters of samples with compositions Gr15Sp85 and Gr60Sp40 seem to be outliers in all experiments. It is concluded that the data hint at systematic changes in saturation temperatures across the solid solution, with implications for both the excess entropy of mixing and the excess volume of mixing, but more precise data or further sample characterization are needed to prove that this composition dependence is real in garnet solid solutions.     

Mixing behavior in quaternary garnet solid solution and an extended Ellis and Green garnet-clinopyroxene geothermometer

Applications of the different formulations of garnet-clinopyroxene geothermometers to crustal granulites and particularly to metamorphosed manganese formations show a wide scatter of estimates. This is primarily related to the uncertainty associated with the formulation of the activity-composition relationship in garnet solid solution besides that in the clinopyroxene solid solution. The largest uncertainty appears to have resulted from the adopted Mg-Mn interaction parameter in garnet which is yet to be experimentally determined. A fresh statistical regression of eleven pairs of garnet and clinopyroxene equilibrated at identical P-T conditions from a manganese formation in India yields W _Mg-Mn ^Gt (=W_Mn-Mg) value of 1600±500 cal/mols. An extension of the Ellis and Green (1979) geothermometer, known to work well in normal granulites, incorporating terms associated with the activity coefficients of the exchangeable cations, now yields consistent temperature estimation from normal granulites as well as from metamorphosed manganese formations. The geothermometer, however, will not work well for garnet having X_Fe0.65 and clinopyroxenes containing appreciable Na, Al and/or Fe³⁺.     

A refined garnet - biotite Fe−Mg exchange geothermometer and its application in amphibolites and granulites

A new formulation of garnet-biotite Fe–Mg exchange thermometer has been developed through statistical regression of the reversed experimental data of Ferry and Spear. Input parameters include available thermo-chemical data for quaternary Fe–Mg–Ca–Mn garnet solid solution and for excess free energy terms, associated with mixing of Al and Ti, in octahedral sites, in biotite solid solution. The regression indicates that Fe–Mg mixing in biotite approximates a symmetrical regular solution model showing positive deviation from ideality withW _FeMg ^bi =1073±490 cal/mol. H _r and S _r for the garnet-biotite exchange equilibrium were derived to be 4301 cal and 1.85 cal respectively. The resultant thermometer gives consistent results for rocks with a much wider compositional range than can be accommodated by earlier formulations.     

Garnet-cordierite-biotite equilibria in the Steinach aureole,Bavaria

Three garnet-biotite pairs and eleven garnet-cordierite-biotite triplets from the Steinach aureole (Oberpfalz, North-East Bavaria) were analyzed using an electron probe microanalyzer.The regional metamorphic muscovite-biotite schists contain garnets strongly zoned with Mn-Ca-rich centers and Fe-rich edges, the average composition being almandine 67 — spessartine 4 — pyrope 4 — grossular (+andradite) 25.The first contact garnet that is formed in mica schists of the outermost part of the aureole is small, virtually unzoned, and has an average composition of almandine 52 — spessartine 37 — pyrope 8 — grossular (+andradite) 3. With increasing metamorphic grade, there is a consistent trend to form garnets richer in Fe ending up with a composition almandine 84.5 — spessartine 5.5 — pyrope 7.5 — grossular (+andradite) 2.5. This trend is accompanied by a general increase in grain size and modal amount of garnet. Associated cordierites and biotites also become richer in Fe with increasing grade. While the garnets in the highest grade sillimanite hornfelses are poorly zoned, the transitional andalusite-sillimanite hornfelses contain garnets with distinct but variable zonation profiles.These facts can possibly be explained by the time-temperature relationships in the thermal aureole. In a phase diagram such as the Al-Fe-Mg-Mn tetrahedron, the limiting mineral compositions of a four-phase volume or a three-phase triangle are fixed by T and P (the latter remaining effectively constant within a thermal aureole). Thus, in garnet-cordierite-biotite assemblages, garnet zonation should be controlled by temperature variation rather than by a non-equilibrium depletion process. Taking into account the experimental data of Dahl (1968), a zoned garnet from a transitional andalusite-sillimanite hornfels would reflect a temperature increase of about 40° C during its growth. A hypothetical P-X diagram is proposed to show semi-quantitatively the compositional variation of garnet-cordierite pairs with varying pressures (T constant).     

Thermodynamic data from redox reactions at high temperatures. III. Activity-composition relations in Ni-Pd alloys from EMF measurements at 850–1250 K,and calibration of the NiO+Ni-Pd assemblage as a redox sensor

The assemblage NiO+Ni-Pd alloy has been calibrated as a precise oxygen fugacity sensor in the temperature range 850–1250 K at 1 bar, using an electrochemical technique with oxygen-specific CSZ electrolytes, and Ni+NiO and Cu+Cu₂O as the reference electrodes. Nine compositions were studied, ranging from 0.12 to 0.83 X _Ni ^alloy . Steady EMFs, implying equilibrium, were rapidly achieved in all cells, and were found to be reversible on increasing and decreasing temperature with a precision approaching 0.1 mV. The estimated accuracy of the measurements on each cell is ±0.2 mV (1, corresponding to ±0.003 log-bar units in fo₂ at 1273 K). Compositions of the Ni-Pd alloys were measured after each run by electron microprobe, and these compositions were then checked for internal consistency by measuring the lattice parameter by X-ray diffraction. Nickel-rich alloys show positive deviations from ideality and endothermic enthalpies of mixing, but palladium-rich compositions have exothermic enthalpies of mixing and strong negative deviations from ideality. The excess entropies of mixing are positive for all compositions, and correlate approximately with the excess volumes of mixing. The highly asymmetrical deviations from ideality are well described by a polynomial expression of the Redlich-Kister form, with three terms for the enthalpies, and two for the excess entropies and volumes of mixing. The experimental data from this study have been used to re-formulate the Ni-Pd oxygen fugacity sensor to give an expression; _O2 ^ss = _O2 ^NNO – 2RT ln X _Ni ^alloy – [2 · (1 – X _Ni ^alloy )² · [(–2165–7.958 · T) + (9409 – 0.888 · T) · (4 X _Ni ^alloy – 1) + 2089 · (6 X _Ni ^alloy – 1) · (2 X _Ni ^alloy – 1)]](850<T<1300) where _O2 ^ss is in J mol^-1, T is in kelvins, and the expression for _O2 ^NNO is that given by O'Neill and Pownceby (1993). Values in terms of log fo₂ may be obtained from the above by dividing by RT ln 10. The estimated standard error in _O2 ^ss is on the order of ±200 J mol^-1, which is approximately ±0.01 log-bar units in fo₂ at 1273 K.     

A revision of the garnet-clinopyroxene Fe2+-Mg exchange geothermometer

A comprehensive experimental dataset was used to analyse the compositional dependence of the garnet-clinopyroxene Fe²⁺/Mg partition coefficient (K _d). The Mg no. of garnet was found to have a significant effect on the K _d, in addition to calcium content of garnet. An empirical model was developed to relate these effects with equilibrium temperature and pressure in the form of a conventional geothermometer, T(K) = { – 1629[X^Gt _Ca]² + 3648.55[X^Gt _Ca] – 6.59[Mg no. (Gt)] + 1987.98 + 17.66P (kbar)}/(In k_d + 1.076). Application of this thermometer produced reasonable temperature estimates for rocks from the lower crust (garnet amphibolites, granulites and eclogites) and the upper mantle (eclogite and lherzolite xenoliths in kimberlites, mineral inclusions in diamonds).     

The energetics of natural garnet solid solution

Approximate mixing properties of the end-member components of the quarternary garnet solid solution, (Fe,Mg,Ca,Mn)₃Al₂Si₃O₁₂, have been derived through theoretical analysis of observational data, combined with certain experimental results and crystal chemical considerations. The results suggest that the mixing of pyrope with grossularite, spessartite, and almandine would involve significant positive excess free energies of mixing leading to the critical mixing temperatures of 694±55, 535±140, and 479±63 °C respectively. Spessartite would mix with almandine nearly ideally, and with grossularite with small positive deviation from ideality. The quarternary solution reduces essentially to a ternary mixture of pyrope, grossularite, and almandine + spessartite. The solid solubility relation, and tie line coordinates in this ternary system has been calculated as a function of temperature; the solid solution is found to be intrinsically stable for practically all ternary compositions at 600 °C.     

Internally consistent recalibrations of mineral equilibria for geothermobarometry involving garnet–orthopyroxene–plagioclase–quartz assemblages and their application to the South Indian granulites

Abstract Three reactions are calibrated as geothermobarometers for garnet–orthopyroxene–plagioclase–quartz assemblages, namely: 1/2 ferrosilite + 1/3 pyrope ± 1/2 enstatite + 1/3 almandine (A): ferrosilite + anorthite ± 2/3 almandine + 1/3 grossularite + quartz (B); and enstatite + anorthite ± 2/3 pyrope + 1/3 grossularite + quartz (C). The internally consistent geothermobarometers based on reactions (A), (B) and (C) are calibrated from experimental data only. The thermodynamic parameters of reaction (A) are derived from published experimental data in the FMAS system (n= 104) in the range 700–1400°C and 5–50 kbar, while those for reaction (B) are derived by summation of the existing reversed experimental data of the mineral equilibria: ferrosilite ± fayalite + quartz (D) and anorthite + fayalite ± 2/3 almandine + 1/3 grossularite (E). The retrieved thermodynamic parameters for reactions (A), (B) and (C) are, respectively: (ΔH⁰, cal) -3367 ± 209, -2749 ± 350 and +3985 ± 545; (ΔS⁰, cal K^?1) -1.634 ± 0.163, -8.644 ± 0.298 and -5.376 ± 0.391; and (ΔV⁰_1,298, cal bar^?1) -0.024, -0.60946 and -0.5614. On a one-cation basis, the derived Margules parameters of the ternary Ca–Fe–Mg in garnet are: W_Fe–Mg= -1256 + 1.0 (～0.23) T(K), W_Mg–Fe= 2880 -1.7 (～0.13) T(K), W_Ca–Mg= 4047 (～77) -1.5 T(K), W_Mg–Ca= 1000 (～77) -1.5 T(K), W_Ca–Fe= -723 + 0.332 (～0.02) T(K), W_Fe–Ca= 1090, (cal) and the ternary constant C₁₂₃= -4498 + 1.516 (～0.265) T(K) cal (subregular solution model of non-ideal mixing); and Fe–Mg–Al in orthopyroxene: W_Fe–Mg= 948 (～200) -0.34 (～0.10) T(K), W_Fe–Al= -1950 (～500) and W_Mg–Al= 0 (cal) (regular solution model of non-ideal mixing). The anorthite activity in plagioclase is calculated by the ‘Al-avoidance’model of subregular Ca–Na mixing commonly used for geobarometry based on reactions (B) and (C). When the geothermobarometers are applied to garnet–orthopyroxene–plagioclase–quartz assemblages (n= 45) of wide compositional range from the Precambrian South Indian granulites, temperature ranges of 690–860°C (X= 760 ± 45°C) and pressure ranges of 5–10 kbar were obtained. The P–T values were estimated simultaneously and there is no difference in the pressure calculated from P_Mg (reaction C) and P_Fe (reaction B). In the existing calibrations this difference is 1 kbar or more. Furthermore, there is no compositional dependence of the ln K of the experimental data in the FMAS (n= 104) and the CFMAS (n= 78) systems at different temperatures and the estimated temperatures of the South Indian granulites.     

Uranotungstit,ein neues sekundäres Urnmineral aus dem Schwarzwald

Zusammenfassung Uranotungstit kommt als Sekundärbildung in der Uranlagerstätte von Menzenschwand im südlichen Schwarzwald und in der Grube Clara bei Oberwolfach im mittleren Schwarzwald vor. Er bildet Krusten auf Quarz, Meta-Uranocircit und Meta-Heinrichit. Zu den weiteren Begleitmineralien gehören Bergenit, Meta-Torbernit, Meta-Zeunerit und Schoepit.Das Mineral bildet sphärolithische Aggregate, deren Durchmesser 0,3 mm erreicht. Die rhombischen Kristalle sind lattenförmig ausgebildet mit (010) als Tafelfläche. Farbe gelb, orange oder bräunlich. Strich gelb. Etwas durchscheinend, Glanz stumpf, zum Teil perlmutterartig, Spaltbarkeit nach (010) vollkommen, Bruch unregelmäßig, Härte ungefähr 2, Dichte (gem.)>4,03 (ber.) 4,27 g/cm³. Optische Eigenschaften:n =1,682,n =1,845,n =1,855 (jeweils±0,005), negativ, 2V=42^o,r>v, Pleochroismus:X ± farblos,Y, Z gelb,X=b.Gitterkonstanten:a ₀=9,22,b ₀=13,81,c ₀=7,17 Å,Z=2. Stärkste Linien des Pulver-diagramms: 6,96 (10) 020; 4,60 (6) 200, 030; 3,46 (5) 012, 040; 3,21 (7) 140, 022. Die Analyse des Minerals von Menzeschwand ergab. FeO 2,3, BaO 4,9, PbO 6,9, UO₃ 45,1, WO₃ 19,8, H₂O 22,5, Summe 101,5, was auf der Basis von 24 Sauerstoffatomen zur Formel (Fe_0,38Ba_0,37Pb_0,36) _1,11U_1,82W_0,99H_28,94O₂₄ führt oder, idealisiert, (Fe,Ba,Pb)(UO₂)₂(WO₄) (OH)₄·12H₂O.Das Mineral ist das erste in der Natur nachgewiesene Uranylwolframat.

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Uranotungstite, a new secondary uranium mineral from the Black Forest

Summary Uranotungstite has been found as secondary mineral at the uranium deposit of Menzenschwand in the Southern Black Forest and at the Clara Mine near Oberwolfach in the Central Black. Forest (Germany). It forms crusts on quartz, meta-uranocircite and meta-heinrichite. Other associated secondary minerals are bergenite, meta-torbernite, meta-zeunerite and schoepite.The mineral forms spherulitic aggregates reaching 0.3 mm in diameter. The orthorhombic crystals are lath-like with (010) as plane of flattening. Colour yellow, orange or brownish. Streak yellow. Somewhat translucent, luster dull, in part pearly, perfect cleavage (010), fracture irregular, hardness about 2, density (meas.)>4.03, (calc.) 4.27 g/cm³. Optical properties:n =1.682,n =1.845,n =1.855 (±0.005 each), negative, 2V=42^o,r>v, pleochroism:X ± colourless,Y, Z yellow,X=b.Unit-cell dimensions:a ₀=9.22,b ₀=13.81,c ₀=7.17 Å,Z=2. Strongest lines of the powder pattern: 6.96 (10) 020; 4.60 (6) 200, 030; 3.46 (5) 012, 040; 3.21 (7) 140, 022. The analysis of the mineral from Menzenschwand, FeO 2.3, BaO 4.9, PbO 6.9, UO₃ 45.1, WO₃ 19.8, H₂O 22.5, total 101.5, yields the following formula on the basis of 24 oxygen atoms: (Fe_0.38Ba_0.37Pb_0.36) _1.11U_1.82W_0.99H_28.94O₂₄ or, idealized, (Fe,Ba,Pb) (UO₂)₂ (WO₄) (OH)₄·12H₂O.The mineral is the first uranyl tungstate discovered in nature.

     

A thermodynamic model of Fe–Cr spinels

A new thermodynamic model for multi-component spinel solid solutions has been developed which takes into account thermodynamic consequences of cation mixing in spinel sublattices. It has been applied to the evaluation of thermodynamic functions of cation mixing and thermodynamic properties of Fe₃O₄–FeCr₂O₄ spinels using intracrystalline cation distribution in magnetite, lattice parameters and activity-composition relations of magnetite–chromite solid solutions. According to the model, cation distribution in binary spinels, (Fe_1-x²⁺ Fe_x³⁺)[Fe_x²⁺Fe_2-2y-x³⁺Cr_2y]O₄, and their thermodynamic properties depend strongly on Fe²⁺–Cr³⁺ cation mixing. Mixing of Fe²⁺–Fe³⁺ and Fe³⁺–Cr³⁺ can be accepted as ideal. If Fe²⁺, Fe³⁺ and Cr are denoted as 1, 3 and 4 respectively, the equation of cation distribution is –RT ln(x²/((1–x)(2–2y–x)))= G₁₃^* + (1–2x)W₁₃+y(W₁₄–W₁₃–W₃₄) where G₁₃^* is the difference between the Gibbs energy of inverse and normal magnetite, W_ij is a Margules parameter of cation mixing and G₁₃^*, J/mol =–23,000+13.4 T, W₁₄=36 kJ/mol, W₁₃=W₃₄=0. The positive nonconfigurational Gibbs energy of mixing is the main reason for changing activity–composition relations with temperature. According to the model, the solvus in Fe₃O₄–FeCr₂O₄ spinel has a critical temperature close to 500°C, which is consistent with mineralogical data.     

An experimental study of Fe-Mg partitioning between garnet and olivine and its calibration as a geothermometer

The partitioning of Fe and Mg between coexisting garnet and olivine has been studied at 30 kb pressure and temperatures of 900 ° to 1,400 °C. The results of both synthesis and reversal experiments demonstrate that K _D (= (Fe/Mg)_gt/(Fe/Mg)_OI) is strongly dependent on Fe/Mg ratio and on the calcium content of the garnet. For example, at 1,000 °C/30 kb, K _D varies from about 1.2 in very iron-rich compositions to 1.9 at the magnesium end of the series. Increasing the mole fraction of calcium in the garnet from 0 to 0.3 at 1,000 ° C increases K _D in magnesian compositions from 1.9 to about 2.5.The observed temperature and composition dependence of K _D has been formulated into an equation suitable for geothermometry by considering the solid solution properties of the olivine and garnet phases. It was found that, within experimental error, the simplest kind of nonideal solution model (Regular Solution) fits the experimental data adequately. The use of more complex models did not markedly improve the fit to the data, so the model with the least number of variables was adopted.Multiple linear regression of the experimental data (72 points) yielded, for the exchange reaction: 3Fe₂SiO₄+2Mg₃Al₂Si₃O₁₂ olivine garnet 2Fe₂Al₂Si₃O₁₂+3Mg₂SiO₄ garnet olivine H ° (30kb) of –10,750 cal and S ° of –4.26 cal deg^–1 mol^–1. Absolute magnitudes of interaction parameters (W _ij ) derived from the regression are subject to considerable uncertainty. The partition coefficient is, however, strongly dependent on the following differences between solution parameters and these differences are fairly well constrained: W _FeMg ^ol -W _FeMg ^gt 800 cal W _CaMg ^gt -W _CaFe ^gt 2,670 cal.The geothermometer is most sensitive in the temperature and composition regions where K _D is substantially greater than 1. Thus, for example, peridotitic compositions at temperatures less than about 1,300 ° C should yield calculated temperatures within 60 °C of the true value. Iron rich compositions (at any temperature) and magnesian compositions at temperatures well above 1,300 °C could not be expected to yield accurate calculated temperatures.For a fixed K _D the influence of pressure is to raise the calculated temperature by between 3 and 6 °C per kbar.     

Study on the compositional dependence of the apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene solid solution

Compositional dependence of apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene from Mt. Higasiakaisi is studied by means of a multicomponent regular solution model. It is shown that garnet and clinopyroxene solid solutions are positively non-ideal, and the non-ideal parameters according to the symmetric regular solution model are 2.58 kcal and 2.39 kcal, respectively, assuming the equilibration temperature of the mass to be 550° C.Notations a _i ^h activity of component i in phase h - _ij interaction parameter of component i and j in a solid solution - _i activity coefficient of component i - X _i mole fraction of component i - K partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - K apparent partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - G ⁰ difference in free energy of the partition reaction - H ⁰ difference in enthalpy of the partition reaction - S ⁰ difference in entropy of the partition reaction - R gas constant - G garnet - Alm almandine component - Py pyrope component - Gr grossular component - Sp spessartine component - CPx clinopyroxene - Hd hedenbergite component - Di diopside component - Jd jadeite component - Ts Tschermac's molecule component Deceased on April 17, 1974.     

Fe-Mn partitioning between garnet and ilmenite: experimental calibration and applications

A new mineralogic geothermometer based on the partitioning of Fe and Mn between garnet and ilmenite has been calibrated by reversal experiments in the P-T range 600–900° C, 2 and 5 kbars and for fO₂=QFM. The results constitute a sensitive geothermometer applicable over a broad range of composition and conditions. Garnetilmenite thermometry has advantages relative to existing geothermometers because of its accurate calibration, marked temperature sensitivity and the chemical and structural simplicity of the crystalline solutions involved. Application to natural assemblages reveals that the garnet-ilmenite geothermometer yields temperatures that agree well with other estimates. The reactivity of, and relatively rapid Fe-Mn diffusion in ilmenite may lead to retrograde resetting of high temperature partition values, but these factors may be useful for estimating rock cooling rates. Analysis of the experimental data indicates minor positive deviations from ideality for Fe-Mn garnets and ilmenites. Absolute magnitudes of interaction parameters (W _AB) derived from a regression analysis are subject to considerable uncertainty. The partition coefficient is, however, strongly dependent on the difference between solution parameters. These differences are well constrained with a magnitude of W _FeMn ^ilm –W _FeMn ^gar 300 cal mol^–1. The accuracy and applicability of garnet-ilmenite thermometry will improve with the availability of better thermodynamic data for garnet crystalline solutions.Abbreviations and symbols used in text R universal gas constant (cal/mol/°K) - T absolute temperature (°K or °C) - P pressure (kbars) - V ⁰ volume change of reaction (1) - H _{1, T} ⁰ standard state enthalpy change of reaction (1) at 1 bar and the T of interest, in cal/mole - S _T ⁰ entropy change of reaction (1) at T of interest, in cal/mole/°K - G _P,T ⁰ standard free energy change of reaction (1) at the T and P of interest, in cal/mole - distribution coefficient for Fe-Mn partitioning between garnet and ilmenite - K apparent equilibrium coefficient for reaction (1) - _i ^j activity of component i in phase j - W _A-B binary A-B interaction (Margules) parameter - gar garnet - ilm ilmenite - biot biotite - ol olivine - opx orthopyroxene     

Correlation by Rb-Sr geochronology of garnet growth histories from different structural levels within the Tauern Window,Eastern Alps

In order to evaluate rates of tectonometamorphic processes, growth rates of garnets from metamorphic rocks of the Tauern Window, Eastern Alps were measured using Rb-Sr isotopes. The garnet growth rates were determined from Rb-Sr isotopic zonation of single garnet crystals and the Rb-Sr isotopic compositions of their associated rock matrices. Garnets were analyzed from the Upper Schieferhülle (USH) and Lower Schieferhülle, (LSH) within the Tauern Window. Two garnets from the USH grew at rates of 0.67 _–0.13 ^+0.19 mm/million years and 0.88 _–0.19 ^+0.34 mm/million years, respectively, indicating an average growth duration of 5.4±1.7 million years. The duration of growth coupled with the amount of rotation recorded by inclusion trails in the USH garnets yields an average shear-strain rate during garnet growth of 2.7 _–0.7 ^+1.2 ×10^-14 s^-1. Garnet growth in the sample from the USH occurred between 35.4±0.6 and 30±0.8 Ma. The garnet from the LSH grew at a rate of 0.23±0.015 mm/million years between 62±1.5 Ma and 30.2±1.5 Ma. Contemporaneous cessation of garnet growth in both units at 30 Ma is in accord with previous dating of the thermal peak of metamorphism in the Tauern Window. Correlation with previously published pressure-temperature paths for garnets from the USH and LSH yields approximate rates of burial, exhumation and heating during garnet growth. Assuming that theseP — T paths are applicable to the garnets in this study, the contemporaneous exhumation rates recorded by garnet in the USH and LSH were approximately 4 _–2 ⁺³ mm/year and 2±1 mm/year, respectively.     

Activity-composition relationships for pyrope-grossular garnet

Activity coefficients () for grossular in pyrope-grossular garnet have been determined experimentally using the divariant assemblage garnet-anorthite-sillimanite (kyanite)-quartz. Values of for garnets with 10–12 mole % grossular have been obtained at 1000 °, 1100 °, 1200 ° and 1300 ° C at pressures between 15 and 21 Kb. The data are consistent with a symmetrical regular solid model for grossular-pyrope solid solutions. The interaction parameter (W) increases linearly with decreasing temperature and is given by W = 7460-4.3 T cals (T in °K). A solvus in the pyrope-grossular solid solution is predicted with a temperature of critical mixing of 629°C±90 ° C.     

Elastic properties of pyrope

Brillouin spectroscopy was used to measure the single crystal elastic properties of a pure synthetic pyrope and a natural garnet containing 89.9 mol% of the pyrope end member (Mg₃Al₂Si₃O₁₂). The elastic moduli, c _ij , of the two samples are entirely consistent and agree with previous estimates of the elastic properties of pyrope based upon the moduli of solid solutions. Our results indicate that the elastic moduli of pyrope end-member are c ₁₁=296.2±0.5, c ₁₂=111.1±0.6, c ₄₄=91.6±0.3, K_s=172.8±0.3, =92.0±0.2, all in units of GPa. These results differ by several percent from those reported previously for synthetic pyrope, but are based upon a much larger data set. Although the hydrous components of the two samples from the present study are substantially different, representing both dry and saturated samples, we find no discernable effect of structurally bound water on the elastic properties. This is due to the small absolute solubility of water in pyrope, as compared with other garnets such as grossular.     

Thermodynamic data from redox reactions at high temperatures. V. Thermodynamic properties of NiO−MnO solid solutions from emf measurements

Divariant oxide plus metal assemblages potentially make useful redox sensors for use in hydrothermal and other high pressure experiments. Here we report the calibration of the (Ni, Mn)O/Ni redox sensor in which the Ni/NiO (NNO) oxygen buffer is displaced to lower oxygen chemical potentials (O₂), by the solid solution of MnO in the oxide phase. This assemblage was chosen because: (1) it covers a useful range of O₂; (2) the system can be calibrated very accurately. Values of O₂ defined by the (Ni, Mn)O/Ni assemblage were determined electrochemically, from 900 to 1300 K, using calcia-stabilized zirconia solid electrolytes. The oxide compositions (8 in total, ranging from 0.1X _NiO0.8) were analysed afterwards by electron microprobe, and were checked for internal consistency by measuring the lattice parameters (a₀), using powder XRD. The accuracies of the measurements, both assessed theoretically and established empirically, are (1): ±80J/mol in O₂, ±0.0002 Å in a₀ and ±0.002 to 0.005 in X _NiO. Activity-composition relations were fitted to the Redlich-Kister formalism. There is a slight asymmetry (corresponding to a subregular model) across the solution with A ₀ ^G =9577(±45) J/mol, and A ₁ ^G =–477(±80) J/mol. The experimental data were also used to derive the parameters V^ex, H^ex and S^ex. There is no obvious relationship between excess volumes and enthalpies of mixing, nor between excess volumes and excess entropies. The experimental data from this study have been used to formulate the (Ni, Mn)O/Ni redox sensor expression: O₂ = ₂(NNO) + 2RTlnX _NiO + 2(1 – X _NiO)²[11483 – 1.697T] – 477(4X _NiO – 1)(900 < T(K) < 1300) where O₂(NNO)=–478967+248.514T–9.7961 T In T, from O'Neill and Pownceby(1993a).     

Thermochemistry of the tremolite-edenite amphiboles using fluorine analogues,and applications to amphibole-plagioclase-quartz equilibria

Heats of mixing of synthetic C2/m fluortremolite-fluoredenite amphiboles measured at 985 K show a systematic deviation from ideal mixing consistent with a subregular solution model. The deviations from ideal mixing are interpreted in terms of Na ordering in the A-site and Na-Al interactions in edenite-poor compositions. Enthalpies of edenite substitution reactions in amphiboles and in SiO₂-NaAlO₂ glasses and framework silicates are comparable. Gibbs free energies of formation of fluortremolite and fluoredenite at 298K are -2,821.07±3.34 kcal mol^–1 and -2,889.59±2.40 kcal mol^–1 respectively. The former value is in good agreement with values calculated from both F-OH exchange experiments and from a natural fluortremolite-bearing metamorphic rock. Least-squares fitted sub-regular heat-of-mixing parameters are poorly constrained and unrealistically high, but estimated subregular mixing parameters consistent with 95% confidence interval uncertainties in the calorimetric data and with TEM constraints give activity-composition relations in good agreement with the A-site compositions of natural metamorphic and igneous hornblendes. These relations predict unmixing in edenite-rich compositions over a wide range of temperature, but lend no support to the existence of a hornblende-actinolite miscibility gap. Calibration of the reaction tremolite+ albite=edenite+4 quartz as a function ofP,T andX _ed ^amph indicates negativedP/dT slopes and a limited range of X _ed ^amph (0.3 to 0.5) in equilibrium with plagioclase and quartz over a wide range of pressure and temperature, consistent with metamorphic hornblende-plagioclase assemblages. The energetics of this reaction suggest, however, that amphibole-plagioclase disequilibrium may be common.