F-OH exchange equilibria between mica-amphibole mineral pairs

Fluoride-hydroxyl exchange equilibria between phlogopite-pargasite and phlogopite-tremolite mineral pairs were experimentally determined at 1,173K, 500 bars and 1,073–1,173 K, 500 bars respectively. The distribution of fluorine between phlogopite and pargasite was found to favor phlogopite slightly, G _ex ^. (1,173 K)=–1.71 kJ anion^–1, while in the case of phlogopite-tremolite, fluorine was preferentially incorporated in the mica, G _ex ^. (1,073)=– 5.67 kJ anion^–1 and G _ex ^. (1,173K)=–5.84 kJ anion^–1. These results have yielded new values of entropy and Gibbs energy of formation for fluortremolite, S _f =–2,293.4±16.0JK^–1 mol^–1 and G _f = –11,779.3±25.0 kJ mol^–1, respectively. In addition, F-OH mineral exchange equilibria support a recent molten oxide calorimetric value for the Gibbs energy of fluorphlogopite, G _f =–6,014.0±7.0 kJ mol^–1, which is approximately 40 kJ mol^–1 more exothermic than the tabulated value.This work performed in part at Sandia National Laboratories supported by the U.S. Department of Energy, DOE, under contract number DE-AC04-76DP00789     

Thermodynamic properties,low-temperature heat-capacity anomalies,and single-crystal X-ray refinement of hydronium jarosite, (H<Subscript>3</Subscript>O)Fe<Subscript>3</Subscript>(SO<Subscript>4</Subscript>)<Subscript>2</Subscript>(OH)<Subscript>6</Subscript>

Crystals of hydronium jarosite were synthesized by hydrothermal treatment of Fe(III)–SO₄ solutions. Single-crystal XRD refinement with R₁=0.0232 for the unique observed reflections (|F_o| > 4_F) and wR₂=0.0451 for all data gave a=7.3559(8) Å, c=17.019(3) Å, V^o=160.11(4) cm³, and fractional positions for all atoms except the H in the H₃O groups. The chemical composition of this sample is described by the formula (H₃O)_0.91Fe_2.91(SO₄)₂[(OH)_5.64(H₂O)_0.18]. The enthalpy of formation (H^o_f) is –3694.5 ± 4.6 kJ mol^–1, calculated from acid (5.0 N HCl) solution calorimetry data for hydronium jarosite, -FeOOH, MgO, H₂O, and -MgSO₄. The entropy at standard temperature and pressure (S^o) is 438.9±0.7 J mol^–1 K^–1, calculated from adiabatic and semi-adiabatic calorimetry data. The heat capacity (C_p) data between 273 and 400 K were fitted to a Maier-Kelley polynomial C_p(T in K)=280.6 + 0.6149T–3199700T^–2. The Gibbs free energy of formation is –3162.2 ± 4.6 kJ mol^–1. Speciation and activity calculations for Fe(III)–SO₄ solutions show that these new thermodynamic data reproduce the results of solubility experiments with hydronium jarosite. A spin-glass freezing transition was manifested as a broad anomaly in the C_p data, and as a broad maximum in the zero-field-cooled magnetic susceptibility data at 16.5 K. Another anomaly in C_p, below 0.7 K, has been tentatively attributed to spin cluster tunneling. A set of thermodynamic values for an ideal composition end member (H₃O)Fe₃(SO₄)₂(OH)₆ was estimated: G^o_f= –3226.4 ± 4.6 kJ mol^–1, H^o_f=–3770.2 ± 4.6 kJ mol^–1, S^o=448.2 ± 0.7 J mol^–1 K^–1, C_p (T in K)=287.2 + 0.6281T–3286000T^–2 (between 273 and 400 K).     

The upper stability limit of the assemblage paragonite + quartz and its natural occurrences

The assemblage paragonite + quartz is encountered frequently in low- to medium-grade metamorphic rocks. With rising grade of metamorphism they react mutually to yield the condensed assemblage albite + Al₂SiO₅.The univariant curve pertaining to the equilibrium paragonite + quartz=albite + andalusite + H₂O has been located experimentally. The reversed P _{H 2 O}-T data are: 1 kb: 470–490° C 2 kb: 510–530° C 3 kb: 540–560° C 4 kb: 560–580° C 5 kb: 590–600° C The univariant curve pertaining to the equilibrium paragonite + quartz=albite + kyanite + H₂O runs through the following P _{H 2 O}-T-intervals: 5 kb: 570–625° C 6 kb: 600–630° C 7 kb: 620–640° C Thermodynamic calculations of S ₂₉₈ ⁰ , H _f,298 ⁰ and G _f,298 ⁰ of the phase paragonite from the experimental data presented above and those obtained from the equilibria of the reaction paragonite=albite + corundum + H₂O (Chatterjee, 1970), agree within the limits of uncertainty. This prompts the idea that Zen's (1969) suggestion of a possible error of approximately 7 kcal in G _f,298 ⁰ of the Al₂SiO₅ polymorphs may in fact be due to an error of similar magnitude in G _f,298 ⁰ of corundum.A best estimate of S ₂₉₈ ⁰ , H _f,298 ⁰ and G _f,298 ⁰ of paragonite based on these considerations yield: S ₂₉₈ ⁰ : 67.61±3.9 cal deg^–1 gfw^–1 H _f,298 ⁰ : –1411.4±2.7 kcal gfw^–1 G _f,298 ⁰ : –1320.9±4.0 kcal gfw^–1 These numbers will be subject to change when better thermochemical data on corundum and albite are available.In medium-grade metamorphic rocks the assemblage paragonite + quartz is commonly found in stable coexistence with such other phases as muscovite, staurolite, andalusite, kyanite, but not with cordierite or sillimanite. However, the assemblage paragonite-sillimanite has been reported to be stable in the absence of quartz. All these petrologic observations can be explained on the basis of the stability data of the phases and phase assemblages concerned.     

Gibbs energy of aluminous minerals

The discrepancy between the tabulated Gibbs Energies of Formation for Al₂SiO₅ and corundum relative to muscovite and kaolinite is considered to lie principally with the latter two minerals. New values for heat of formation of gibbsite [Gbs] will affect the tabulated H _f ⁰ , G _f(298,1) ⁰ for the other aluminous minerals which are referred to gibbsite as calorimetric aluminum reference. Gibbs Energy Difference Functions, calculated from phase equilibria in the system CaO-Al₂O₃-SiO₂-(H₂O-CO₂), can be used to estimate consistent H _f ⁰ , G _f(298,1) ⁰ values for aluminous minerals. A self consistent data set is presented referred to G _f(298,1) ⁰ [Corundum]=–378.08 kcal mol^–1. Two independent values for G _f(298,1) ⁰ [Anorthite]=–961.52 and –960.29 kcal, from a recalculation of the H _f ⁰ [Anor] based upon the revised H _f(298,1) ⁰ [Gbs]=–309.325 kcal mol^–1 and from measurement of silica activity on the anorthite-saturated part of the CaO-Al₂O₃-SiO₂ liquidus, respectively, are considered to show the magnitude of the discrepancy and are used in the calculations.     

APL computer programs for thermodynamic calculations of equilibria in P-T-X CO 2 space

APL computer programs for the thermodynamic calculation of devolatilization and solid-solid equilibria operate using stored values for the molar volume and entropy of solids, the free energies of H₂O and CO₂, and the free energies of formation for 110 geologically-important phases. P-T-X _{CO 2} calculations of devolatilization equilibria can be made at pressures from 0.2 through 10 kb, and temperatures from 200 through 1,000° C. P-T-X calculations of solid-solid equilibria may be accomplished at pressures to 30 kb and temperatures to 1,000° C. Calculations can be extrapolations from experimental points, or direct calculations from thermochemical data alone. Options are available in these programs to consider effects of: real vs. ideal gas mixing, thermal expansion and compressibility, solid solution, fluid pressure differing from solid pressure, and uncertainties in high-temperature entropies.A collection of thermodynamic data programs accompanies the programs for calculating P-T-X _{CO 2} equilibria. Over a wide range of physical conditions, the data functions report free energies, entropies, fugacities of H₂O and CO₂, high temperature entropies of solids, and activities of components in H₂O-CO₂ mixtures.List of Symbols Activity of H₂O and CO₂ - G_f Free energy of formation of a phase from elements - G_r Free energy change of reaction - G _r ^o Standard state free energy change of a reaction - Free energies of pure H₂O and CO₂ - H _r ^o Standard state enthalpy change for a reaction - K Equilibrium constant - R Gas constant - S _r ^o Standard state entropy change of reaction - S _s ^o Standard state entropy change of solids in a reaction - V_s ^o Standard state volume change of a reaction - V_s ^o Standard state volume change of solids in a reaction - Mole fraction of H₂O and CO₂ - Activity coefficient of H₂O and CO₂     

Synthesis and upper stability of paragonite

The mineral paragonite, NaAl₂[AlSi₃O₁₀ (OH)]₂, has been synthesized on its own composition starting from a variety of different materials. Indexed powder data and refined cell parameters are given for both the 1M and 2M₁ polymorphs obtained. The upper stability limit of paragonite is marked by its breakdown to albite + corundum + vapour. The univariant equilibria pertaining to this reaction have been established by reversing the reaction at six different pressures, the equilibrium curve running through the following intervals: 1 kb: 530°–550° C 2 kb: 555°–575° C 3 kb: 580°–600° C 5kb: 625°–640° C 6 kb: 620°–650° C 7 kb: 650°–670° C.Comparison with the upper stability limit of muscovite (Velde, 1966) shows that paragonite has a notably lower thermal stability thus explaining the field observation that paragonite is absent in many higher grade metamorphic rocks in which muscovite is still stable.The enthalpy and entropy of the paragonite breakdown reaction have been estimated. Since intermediate albites of varying structural states are in equilibrium with paragonite, corundum and H₂O along the univariant equilibrium curve, two sets of data pertaining to the entropy of paragonite (S ₂₉₈ ⁰ ) as well as the enthalpy ( H _f,298 ⁰ ) and Gibbs free energy ( G _f,298 ⁰ ) of its formation were computed, assuming (1) high albite and (2) low albite as the equilibrium phase. The values are: (1) (2) S ₂₉₈ ⁰ 67.8±3.9 cal deg^–1 gfw^–1 63.7±3.9 cal deg^–1 gfw^–1 H _f,298 ⁰ –1417.9±2.7 kcal gfw^–1 –1420.2±2.6 kcal gfw^–1 G _f,298 ⁰ –1327.4±4.0 kcal gfw^–1 –1328.5±4.0 kcal gfw^–1.Adapted from a part of the author's Habilitationsschrift accepted by the Ruhr University, Bochum (Chatterjee, 1968).     

Cation distribution in pentlandites (Fe,Ni)9S8: Dependence on pressure and temperature and kinetics of the cation exchange reaction

This paper describes the distribution of Fe and Ni between the octahedral and tetrahedral sites in pentlandite (Fe,Ni)₉S₈. The dependence of the distribution on pressure and temperature and the activation energy of the cation exchange reaction were determined through annealing experiments. Synthetic crystals were annealed at 433–723 K and pressures up to 4 GPa, and natural crystals were annealed at 423, 448 and 473 K in evacuated silica capillary tubes for various durations. The cation distributions in the synthetic crystals were determined with an X-ray powder method employing the anomalous dispersion effect of CuK. and FeK radiations, while those of natural crystals were calculated from the cell dimensions. The values of U, S and V for the Fe/Ni exchange reaction are –6818 J mol^–1, 20.52 J K^–1 mol^–1, and 6.99 × 10^–6 m³ mol^–1, respectively. The dependence of the Fe/Ni distribution on pressure (Pa) and temperature (Kelvin) was determined as lnK = 2.47+8.20 × 10² T ^–1+8.41 x 10^–7 T ^–1 P, where K = (Fe/Ni)_octahedral /(Fe/Ni)_tetrahedral. The activation energy of the cation exchange reaction was 185 kJ mol^–1.     

Stability of titanian clinohumite: Experiments and thermodynamic analysis

Reversed hydrothermal experiments on a natural titanoclinohumite [Ti-Cl; approximate formula Mg_7.5FeTi_0.5O₁₆(OH)] show that it breaks down at 475°±11° C (3.5 kbar), 620°±11° C (14 kbar) and 675°±8° C (21 kbar) to the assemblage olivine +ilmenite+vapor. An internal-consistency analysis of the data yields _r G _s ^/0 (298 K, 1 bar)=36,760±3,326 cal (mole Ti-Cl)^–1. _r S _s ^/0 (298 K, 1 bar)=34.14±5.91 cal deg^–1(mole Ti-Cl)^–1. Linear correlation coefficient r _G–S 1.0. A solution model that accounts for TiO₂-M(OH)₂ and F-OH substitution shows that the results for our nearly F-free Ti-Cl are in reasonable agreement with the unreversed breakdown experiments of Mer-rill et al. (1972) on a F-bearing Ti-Cl.Because fluorine is necessary to stabilize Ti-Cl under mantle conditions, we suggest that Ti-Cl is much more likely to be a storage device for fluorine than for water in the mantle.     

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.     

Pd-oxide equilibration: a new experimental method for the direct determination of oxide activities in melts and minerals

We have developed a new technique for the experimental determination of the activities of oxide components in melts and minerals using the equilibrium between Pd alloy, oxygen, and the oxide component in the sample of interest. If a melt or mineral sample is equilibrated with Pd metal at fixed P, T, and f _{O 2}, a small amount of each constituent oxide will reduce to metal and dissolve into the Pd, forming an alloy. Due to the extraordinary stability of dilute alloys of Pd with Mg, Al, and Si, these metals dissolve into the Pd in amounts easily measured with the electron microprobe at f _{O 2} s that can be achieved with conventional gas-mixing techniques. We determined the activity-composition relations for Pd–Mg, –Al, and –Si alloys by equilibrating Pd at fixed f _{O 2}and T with periclase, corundum, and cristobalite (a _oxide1). Because Mg, Al, and Si have constant activity coefficients in Pd at low concentrations, the activity of the oxide of each metal is a simple function of the ratio of the concentration of the metal in Pd in equilibrium with the sample to that in Pd in equilibrium with the pure oxide. Therefore, if Pd plus a melt or mineral and Pd plus pure oxide standards are equilibrated simultaneously at fixed T and f _{O 2}, the precision of the analytical technique is the major limitation on the determination of oxide activities. We used Pd-oxide equilibration to explore activities in silicate melts analogous to Type B Ca–Al-rich inclusions (CAIs) from carbonaceous chondrites; the measured activities deviate systematically from model valves but agree to within 1–30%. The activities imply that Type B CAIs did not condense as liquids from a gas of solar composition, and that only very aluminous compositions are potential liquid condensates from the solar nebula. We also used Pd-oxide equilibration to determine the free energy of formation from the oxides, G _f ^/O , of the spinel end-member MgAl₂O₄ at 1150 to 1400°C to a precision of 2–19% (1). Because the technique reflects equilibration at high temperature, the G _f ^/O _s accurately represent the mineral with equilibrium Mg–Al disorder at temperature, a feature not true of drop calorimetric results because of partial reordering during quenching. Our results indicate more negative G _f ^Emphasis>/O and hence higher entropy of formation, S _f ^Emphasis>/O , than given in most compilations of thermodynamic data for spinel.Division of Geological and Planetary Sciences Contribution #5278     

Garnet-pyroxene equilibria in the system CaO-MgO-Al2O3-SiO2 (CMAS): prospects for simplified (‘T-independent’) lherzolite barometry and an eclogite-barometer

New experimental data on compositions of garnets in two-pyroxene — garnet assemblages in the system CaO –MgO –Al₂O₃ –SiO₂ (CMAS) are presented for conditions between 1,100 and 1,570° C and 30 to 50 kb. Garnets in these assemblages become less calcic with increasing pressure. Garnet-orthopyroxene barometry (Al-solubility-barometry) pertinent to geobarometry for garnet lherzolites has been evaluated with a set of experimental data covering the range 900 to 1,570° C and 15 to 100 kb. Various formulations of this barometer work well to 75 kb. Phase equilibria are not sufficient to positively verify the thermodynamic validity of any of such models. Empirical garnet-orthopyroxene barometry at least in the system CMAS can be formulated to obtain a pressure estimate without previous temperature estimation (P(kb)=34.4-19.175 1n X _Al ^M1 +17.702 1n X _Ca ^M2 ). The potential application of an analogous garnetclinopyroxene equilibrium is limited because the amount of Ca-Tschermaks in natural clinopyroxenes is usually quite small in garnet lherzolites and many eclogites. The Ca-Mg exchange between garnet and clinopyroxene appears however sufficiently sensitive to pressure to allow calibration of a CMAS barometer. The reaction 3CaMgSi₂O₆+Mg₃Al₂Si₃O₁₂=3Mg₂Si₂O₆+Ca₃Al₂Si₃O₁₂ has a V ^o of 3.5 cm³. The total pressure dependency of this reaction is however closer to a theoretical V ^o of about 5 cm³ when excess volume properties of the phases involved are taken into account. We have calibrated such a barometer (mean error of estimate 2.8 kb) for assemblages with pyrope-rich (py>80) garnets and orthopyroxenes. This may provide the basis for a geobarometer for eclogites from kimberlites.Abbreviations Used in the Text CaTs Ca-tschermak's molecule, CaAl₂SiO₆ - cpx clinopyroxene - di diopside, CaMgSi₂O₆ - en enstatite, Mg₂Si₂O₆ - gr grossular, Ca₃Al₂Si₃O₁₂ - gt garnet - MgTs Mg-Tschermak's molecule, MgAl₂SiO₆ - opx orthopyroxene - px pyroxene - py pyrope, Mg₃Al₂Si₃O₁₂ - a _i ^j activity of component i in phase j - activity coefficient - G(I) molar Gibbs free energy difference of reaction (I) at standard state unless specified otherwise - H(I), (H _I) molar enthalpy (difference) of phase (reaction) (I) at standard state unless specified otherwise - S (I), (S _I) molar entropy (difference) of phase (reaction) (I) at standard state unless specified otherwise - V ^o, (V _I ^o) molar volume (difference) of phase (reaction) (I) at standard state - X _i ^j mole fraction of component i in phase j     

Oxygen isotope variations in granulite-grade iron formations: constraints on oxygen diffusion and retrograde isotopic exchange

The oxygen isotope ratios of various minerals were measured in a granulite-grade iron formation in the Wind River Range, Wyoming. Estimates of temperature and pressure for the terrane using well calibrated geothermometers and geobarometers are 730±50° C and 5.5±0.5 kbar. The mineral constraints on fluid compositions in the iron formation during retrogression require either very CO₂-rich fluids or no fluid at all. In the iron formation, isotopic temperature estimates from quartz-magnetite fractionations are controlled by the proximity to the enclosing granitic gneiss, and range from 500° C ( _{qz – mt}=10.0) within 2–3 meters of the orthogneiss contact to 600° C ( _{qz – mt}=8.0) farther from the contact. Temperature estimates from other isotopic thermometers are in good agreement with those derived from the quartz-magnetite fractionations.During prograde metamorphism, the isotopic composition of the iron formation was lowered by the infiltration of an external fluid. Equilibrium was achieved over tens of meters. Closed-system retrograde exchange is consistent with the nearly constant whole-rock ¹⁸O_wr value of 8.0±0.6. The greater _qz-mt values in the iron formation near the orthogneiss contact are most likely due to a lower oxygen blocking temperature related to greater exchange-ability of deformed minerals at the contact. Cooling rates required to preserve the quartz-magnetite fractionations in the central portion of the iron formation are unreasonably high (800° C/Ma). In order to preserve the 600° C isotopic temperature, the diffusion coefficient D (for -quartz) should be two orders of magnitude lower than the experimentally determined value of 2.5×10^–16 cm²/s at 833 K. There are no values for the activation energy (Q) and pre-exponential diffusion coefficient (D ₀), consistent with the experimentally determined values, that will result in reasonable cooling rates for the Wind River iron formation. The discrepancy between the diffusion coefficient inferred from the Wind River terrane and that measured experimentally is almost certainly due to the enhancement of exchange by the presence of water in the laboratory experiments. Cooling rate estimates were also determined for iron formation retrograded under water-rich conditions. Application of the experimentally determined data to these rocks results in a reasonable cooling rate estimate, supporting the conclusion that the presence of water greatly enhances oxygen diffusion.Contribution 441 from the Mineralogical Laboratory, University of Michigan     

High-temperature enthalpy at the orientational order-disorder transition in calcite: implications for the calcite/aragonite phase equilibrium

The enthalpy of calcite has been measured directly between 973 K and 1325 K by transposed-temperature- drop calorimetry. The excess enthalpy has been analysed in terms of Landau theory for this tricritical phase transition. The zero-point enthalpy and entropy allow estimates of the parameters a and C in the Landau expansion for free energy which expresses excess free energy G as a function of the order parameter Q and temperature T: G 1/2a(T _2c–T)Q ²+1/6CQ ⁶ with a=24 J·K·mol^-1, C = 30 kJ·mol^– T _c = 1260 ±5 K. The entropy of disorder below the transition has been formulated as a function of temperature allowing the calculation of the calcite/aragonite phase boundary when taking this extra entropy into account. There is remarkable agreement between the calculated equilibrium curve and previous experimental observations. The Landau theory predicts behaviour which fully accounts for the change in slope of the calcite/aragonite phase boundary, which is thus wholly due to the R¯3c –R¯3m transition in calcite.     

Basaltic glass with high-temperature equilibrated immiscible sulphide bodies with native iron from disko,central West Greenland

Immiscible sulphide bodies show eutectic quench textures in a basaltic glass rock (mg=66) from a native iron-bearing dyke chilled at T=1,200° C and P=250 bars. The sulphide bodies are composed of troilite (90–91%), iron (9–10%) and very scarce vanadium-rich chromite and approach a ternary cotectic in the Ni-poor part of the system Fe-Ni-S. Transition element partition between olivine (mg=83), silicate glass (mg=59) and sulphide blebs indicate that the phases were equilibrated at 1,200° C. D _{vanadium(olivine/glass)} is close to unity and reflect the reducing nature of the rock, for which estimates of f _O210^{–12 to –13} and f _S210^–5 have been made. D _{nickel, cobalt, copper (sulphide/glass)}=4,300, 230 and 380 respectively, are much higher than reported experimentally determined D's on_{monosulphide/basalt glass} at the same temperature and show increasing positive deviation (Ni>Co>Cu) with the increasingly siderophile character of the elements. K _{Dnickel-iron (sulphide/olivine)}=63 is much higher than an experimentally reported value (33) and comparison with published thermodynamic data on Ni-partition between olivine and iron metal suggests that the positive deviation is roughly proportional to the excess metal component in the sulphide melt. The occurrence of strongly Ni-depleted reduced basalts on Disko shows that fractionation of metal and sulphides was a common and geologically important process.     

Relationships among Gibbs free energies and enthalpies of formation of phosphates,oxides and aqueous ions

Two parameters _GO^2– and _HO^2– are defined as the differences between respectively the Gibbs free energies and the enthalpies of formation of an oxide and its corresponding aqueous cation. The Gibbs free energies and enthalpies of formation of phosphates from their consituent oxides are shown to be linear functions of respectively _GO^2– and _HO^2– of their constituent cations.     

The P-T-fO 2 stability of deerite,Fe 12 2+ Fe 6 3+ [Si12O40](OH)10

New equilibrium experiments have been performed in the 20–27 kbar range to determine the upper thermal stability limit of endmember deerite, Fe ₁₂ ²⁺ Fe ₆ ³⁺ [Si₁₂O₄₀](OH)₁₀. In this pressure range, the maximum thermal stability limit is represented by the oxygen-conserving reaction: deerite(De)=9 ferrosilite(Fs)+3 magnetite(Mag)+3 quartz(Qtz)+5 H₂O(W) (1). Under the oxygen fugacities of the Ni-NiO buffer the breakdown-reduction reaction: De=12 Fs+2 Mag+5 W+1/2 O₂ (10) takes place at lower temperatures (e.g. T=63° at 27 kbar). The experimental brackets can be fitted using thermodynamic data for ferrosilite, magnetite and quartz from Berman (1988) and the following 1 bar, 298 K data for deerite (per gfw): V^o=55.74 J.bar^-1, S^o=1670 J.K^-1, H _f ^o =-18334 kJ, =2.5x10^-5K^-1, =-0.18x10^-5 bar^-1. Using these data in conjunction with literature data on coesite, grunerite, minnesotaite, and greenalite, the P-T stability field of endmember deerite has been calculated for P _s=P _{H 2}O. This field is limited by 6 univariant oxygenconserving dehydration curves, from which three have positive dP/dT slopes, the other three negative slopes. The lower pressure end of the stability field of endmember deerite is thus located at an invariant point at 250±70°C and 10+-1.5 kbar. Deerite rich in the endmember can thus appear only in environments with geothermal gradients lower than 10°C/km and at pressures higher than about 10 kbar, which is in agreement with 4 out of 5 independent P-T estimates for known occurrences. The presence of such deerite places good constraints on minimum pressure and maximum temperature conditions. From log f _{O 2}-T diagrams constructed with the same data base at different pressures, it appears that endmember deerite is, at temperatures near those of its upper stability limit, stable only over a narrow range of oxygen fugacities within the magnetite field. With decreasing temperatures, deerite becomes stable towards slightly higher oxygen fugacities but reaches the hematite field only at temperatures more than 200°C lower than the upper stability limit. This practically precludes the coexistence deerite-hematite with near-endmember deerite in natural environments.     

A redox profile of the Slave mantle and oxygen fugacity control in the cratonic mantle

The authors report a redox profile based on Mössbauer data of spinel and garnet to a depth of 210 km from mantle xenoliths of the northern (N) and southeastern (SE) Slave craton (northern Canada). The profile transects three depth facies of peridotites that form segments of different bulk composition, represented by spinel peridotite, spinel–garnet peridotite, low-temperature garnet peridotite, high-temperature garnet peridotite, and pyroxenite. The shallow, more depleted N Slave spinel peridotite records lower oxygen fugacities compared to the deeper, less depleted N Slave spinel–garnet peridotite, consistent with their different spinel Fe³⁺ concentrations. Garnet peridotites show a general reduction in log fO₂ (FMQ)s with depth, where values for garnet peridotites are lower than those for spinel–garnet peridotites. There is a strong correlation between depletion and oxygen fugacity in the spinel peridotite facies, but little correlation in the garnet peridotite facies. The strong decrease in log fO₂ (FMQ) with depth that arises from the smaller partial molar volume of Fe³⁺ in garnet, and the observation of distinct slopes of log fO₂ (FMQ) with depth for spinel peridotite compared to spinel–garnet peridotite strongly suggest that oxygen fugacity in the cratonic peridotitic mantle is intrinsically controlled by iron equilibria involving garnet and spinel.

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Annite stability revised. 1. Hydrogen-sensor data for the reaction annite = sanidine + magnetite + H2

In P - T - logfO₂ space, the stability of annite (ideally KFe ₃ ²⁺ (OH)₂AlSi₃O₁₀) at high fO₂ (low fH₂) is limited by the reaction: annite = sanidine + magnetite + H₂. Using the hydrogen-sensor technique, the equilibrium fH₂ of this reaction was measured between 500 and 800° C at 2.8 kbar in 50° C intervals. Microbrobe analyses of the reacted annite+sanidine+magnetite mixtures show that tetrahedral positions of annite have a lower Si/Al ratio than the ideal value of 3/1. Silicon decreases from 2.9 per formula unit at low temperatures to 2.76 at high temperatures. As determined by Mössbauer spectroscopy in three experimental runs, the Fe³⁺ content of annite in the equilibrium assemblage is 11%±3. A least squares fit to the hydrogensensor data gives H _R ⁰ = 50.269 ± 3.987 kJ and S _R ⁰ = 83.01 ± 4.35 J/K for equilibrium (1). The hydrogene-sensor data are consistent with temperature half brackets determined in the classical way along the nickel-nickel oxide (NNO) and quartz-fayalite-magnetite (QFM) buffers with a mixture of annite+sanidine+magnetite for control. Compared to published oxygen buffer reversals, agreement is only found at high temperature and possible reasons for that discrepancy are discussed. The resulting slope of equilibrium (1) in logfO₂ – T dimensions is considerably steeper than previously determined and between 400 and 800°C only intersects with the QFM buffer curve. Based on the hydrogen-sensor data and on the thermodynamic dataset of Berman (1988, and TWEEQ data base) for sanidine, magnetite and H₂, the deduced standard-state properties of annite are: H _f ⁰ =-5127.376±5.279 kJ and S ⁰=422.84±5.29 J/(mol K). From the recently published unit cell refinements of annites and their Fe³⁺ contents, determined by Mössbauer spectroscopy (Redhammer et al. 1993), the molar volume of pure annite was constrained as 15.568±0.030 J/bar. A revised stability field for annite is presented, calculated between 400 and 800°C.     

The enthalpy of fusion of anorthite

The high-temperature enthalpies of liquid and glassy CaAl₂Si₂O₈ were measured by drop calorimetry using a diphenyl ether drop calorimeter. These data are combined with published values of the high-temperature enthalpy of crystalline anorthite and the enthalpy of vitrification of anorthite to obtain the enthalpy of fusion of anorthite. Analysis of the data yields the following preferred values (enthalpy in kcal/mol, uncertainty limits correspond to two standard deviations):enthalpy of vitrification at 985 K, _v H _{v 985}=18.6±0.6; enthalpy of the liquid at 1,830 K, H ₁₈₃₀ ^l ₃₀₀ ^g =130.4±1.2; enthalpy of the glass at 985 K, H ₉₈₅ ^g -H ₃₀₀ ^g =46.7±0.4; enthalpy of crystalline anorthite between 985 and 1,830 K, H ₁₈₃₀ ^c -H ₉₈₅ ^c =69.9±1.4; calculated enthalpy of fusion of anorthite at 1,830 K, _f H ₁₈₃₀= 32.4±2.1.The average heat capacity of supercooled liquid CaAl₂Si₂O₈ between the glass transition (T _g 1,086 K) and the melting point (T _f7=1,830 K) is 102 ± 2 cal/mol/K. The large difference between the enthalpy of fusion and the enthalpy of vitrification for the minerals anorthite and diopside is emphasized. The practice of assuming _fH _vH should be discontinued for silicate compounds for which T _f T _g.     

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.