Thermodynamic data from redox reactions at high temperatures. II. The MnO-0Mn3O4 oxygen buffer,and implications for the thermodynamic properties of MnO and Mn3O4

The \(\mu _{O_2 } \) defined by the reaction 6 MnO+O₂ =2 Mn₃O₄ has been determined from 917 to 1,433 K using electrochemical cells (with calcia-stabilized zirconta, CSZ) of the type: Steady emfs were achieved rapidly at all temperatures on both increasing and decreasing temperature, indicating that the MnO-Mn₃O₄ oxygen buffer equilibrates relatively easily. It therefore makes a useful alternative choice in experimental petrology to Fe₂O₃-Fe₃O₄ for buffering oxygen potentials at oxidized values. The results are (in J/mol, temperature in K, reference pressure 1 bar); \(\mu _{O_2 } \) (±200)=-563,241+1,761.758T-220.490T inT+0.101819T ² with an uncertainty of ±200 J/mol. Third law analysis of these data, including a correction for the deviations in stoichiometry of MnO, impliesS _298.15 for Mn₃O₄ of 166.6 J/K · mol, which is 2.5 J/K · mol higher than the calorimetric determination of Robie and Hemingway (1985). The low value of the calorimetric entropy may be due to incomplete ordering of the magnetic spins. The third law value of Δ _r H _298.15 ⁰ is-450.09 kJ/mol, which is significantly different from the calorimetric value of-457.5±3.4 kJ/mol, calculated from Δ _f H _298.15 ⁰ of MnO and Mn₃O₄, implying a small error in one or both of these latter.     

Thermodynamic properties of glaucophane new data from calorimetric and spectroscopic measurements

New data concerning glaucophane are presented. New high temperature drop calorimetry data from 400 to 800 K are used to constrain the heat capacity at high temperature. Unpublished low temperature calorimetric data are used to estimate entropy up to 900 K. These data, corrected for composition, are fitted for C _p and S to the polynomial expressions (J · mol^?1 · K^?2) for T> 298.15 K: $$\begin{gathered} C_p = 11.4209 * 10^2 - 40.3212 * 10^2 /T^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - 41.00068 * 10^6 /T^2 \hfill \\ + 52.1113 * 10^8 /T^3 \hfill \\ \end{gathered} $$ $$\begin{gathered} S = 539 + 11.4209 * 10^2 * \left( {\ln T - \ln 298.15} \right) - 80.6424 * 10^2 \hfill \\ * \left( {T^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - 1/\left( {298.15} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right) + 20.50034 * 10^6 \hfill \\ * \left( {T^{ - 2} - 1/\left( {298.15} \right)^2 } \right) - 17.3704 * 10^8 * \left( {T^{ - 3} - \left( {1/298.15} \right)^3 } \right) \hfill \\ \end{gathered} $$ IR and Raman spectra from 50 to 3600 cm^?1 obtained on glaucophane crystals close to the end member composition are also presented. These spectroscopic data are used with other data (thermal expansion, acoustic velocities etc.) in vibrational modelling. This last method provides an independent way for the determination of the thermodynamic properties (C_p and entropy). The agreement between measured and calculated properties is excellent (less than 2% difference between 100 and 1000 K). It is therefore expected that vibrational modelling could be applied to other amphiboles for which spectroscopic data are available. Finally, the enthalpy of formation of glaucophane is calculated.     

Thermodynamic properties of Zn(Al,Cr)2O4 spinels at high temperatures and pressures

Three Al-Cr exchange isotherms between Zn(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 900°, 1100°, and 1300° C, at a total pressure of 25 kbar. Employing data on the equation of state of corundum (Chatterjee et al. 1982), the experimental results were evaluated thermodynamically. It was found that the thermodynamic mixing properties of Zn(Al, Cr)₂O₄ spinels are best described in terms of a symmetric Margules equation. The T- and P- dependence of the Margules Parameter, W _G ^Sp , and of ΔG^* of the exchange reaction, 1/2 ZnAl₂O₄ + 1/2 Cr₂O₃ = 1/2 ZnCr₂O₄+1/2 A1₂O₃, are found to be ΔG ^*=1493?2.869·T+0.0081·P and W _G ^Sp (J/mol)=23456+0.0386·P, with T given in K and P in bar.     

Thermodynamic mixing properties of Mg(Al,Cr)2O4 spinel crystalline solution at high temperatures and pressures

Three Al-Cr exchange isotherms at 1,250°, 1,050°, and 796° between Mg(Al, Cr)₂O₄ spinel and (Al, Cr)₂O₃ corundum crystalline solutions have been studied experimentally at 25 kbar pressure. Starting from gels of suitable bulk compositions, close approach to equilibrium has been demonstrated in each case by time studies. Using the equation of state for (Al, Cr)₂O₃ crystalline solution (Chatterjee et al. 1982a) and assuming that the Mg(Al, Cr)₂O₄ can be treated in terms of the asymmetric Margules relation, the exchange isotherms were solved for Δ G ^*, and . The best constrained data set from the 1,250° C isotherm clearly shows that the latter two quantities do not overlap within three standard deviations, justifying the choice of asymmetric Margules relation for describing the excess mixing properties of Mg(Al, Cr)₂O₄ spinels. Based on these experiments, the following polybaric-polythermal equation of state can be formulated: , P expressed in bars, T in K, G _m ^ex and W _G,i ^Sp in joules/mol. Temperature-dependence of G _m ^ex is best constrained in the range 796–1,250° C; extrapolation beyond that range would have to be done with caution. Such extrapolation to lower temperature shows tentatively that at 1 bar pressure the critical temperature, T _c, of the spinel solvus is 427° C, with dT_c/dP≈1.3 K/kbar. The critical composition, X _c, is 0.42 , and changes barely with pressure. Substantial error in calculated phase diagrams will result if the significant positive deviation from ideality is ignored for Al-Cr mixing in such spinels.     

The thermodynamics of substances at very high pressures and temperatures and some mineral reactions in the earth's mantle

The thermodynamic properties of 25 substances (elements, compounds, modifications) are calculated on the basis of an extrapolation of their caloric values and compressibilities into the region of pressures up to 2mbar and temperatures up to 4,000K. The extrapolation methods are described. The ratio of molar volumes is used to predict the thermodynamic properties of the high pressure modifications. It is inferred that water vapour and oxides of Mg, Fe, and Si ought to be stable in the entire mantle. In the lower mantle garnet should be more stable than the perovskite-type phase of MgSiO₃ (in presence of Al₂O₃ or Fe₂O₃). ‘Perovskite’ phase plus MgO are more stable here than forsterite, Mg₂SiO₄. Pyrrhotite, FeS, reveals astonishing stability in the entire mantle and in the outer core as well. Carbon dioxide, CO₂, may exist only in the upper mantle, whereas methane, CH₄, remains stable in the entire mantle.     

Fugacities of gases and some mineralogical reactions at very high pressures and temperatures (an extrapolation)

Fugacities of H₂, N₂, O₂, CH₄, H₂O, H₂S, NH₃, CO, and CO₂ are calculated on the basis of the extrapolation of the caloric properties, and those of the compressibility of substances into the region of pressures up to 2 Mbar and of temperatures up to 4000K. Several equilibrium mineralogical reactions are calculated. The most probable sequence of decreasing the magnitudes of the equilibrium molar fractions (masses) of these gases in the lower mantle of the earth is predicted.     

The effect of chemical composition and oxygen fugacity on the electrical conductivity of dry and hydrous garnet at high temperatures and pressures

The in situ electrical conductivity of hydrous garnet samples (Py₂₀Alm₇₆Grs₄–Py₇₃Alm₁₄Grs₁₃) was determined at pressures of 1.0–4.0 GPa and temperatures of 873–1273 K in the YJ-3000t apparatus using a Solartron-1260 impedance/gain-phase analyzer for various chemical compositions and oxygen fugacities. The oxygen fugacity was controlled by five solid-state oxygen buffers (Fe₂O₃ + Fe₃O₄, Ni + NiO, Fe + Fe₃O₄, Fe + FeO, and Mo + MoO₂). Experimental results indicate that within a frequency range from 10⁻² to 10⁶ Hz, electrical conductivity is strongly dependent on signal frequency. Electrical conductivity shows an Arrhenius increase with temperature. At 2.0 GPa, the electrical conductivity of anhydrous garnet single crystals with various chemical compositions (Py₂₀Alm₇₆Grs₄, Py₃₀Alm₆₇Grs₃, Py₅₆Alm₄₃Grs₁, and Py₇₃Alm₁₄Grs₁₃) decreases with increasing pyrope component (Py). With increasing oxygen fugacity, the electrical conductivity of dry Py₇₃Alm₁₄Grs₁₃ garnet single crystal shows an increase, whereas that of a hydrous sample with 465 ppm water shows a decrease, both following a power law (exponents of 0.061 and −0.071, respectively). With increasing pressure, the electrical conductivity of this hydrous garnet increases, along with the pre-exponential factors, and the activation energy and activation volume of hydrous samples are 0.7731 ± 0.0041 eV and −1.4 ± 0.15 cm³/mol, respectively. The results show that small hopping polarons ( \textFe_\textMg ^· ) \left( {{\text{Fe}}_{\text{Mg}}^{ \cdot } } \right) and protons ( \textH ^· {\text{H}}^{ \cdot } ) are the dominant conduction mechanisms for dry and wet garnet single crystals, respectively. Based on these results and the effective medium theory, we established the electrical conductivity of an eclogite model with different mineral contents at high temperatures and high pressures, thereby providing constraints on the inversion of field magnetotelluric sounding results in future studies.     

Fugacities and free energies of CO2 at high pressures and temperatures

Fugacity and free-energy values have been calculated from p-v-t data for CO₂ in the temperature range from 50 to 1000°C, at pressures from 25 to 1400 bars.     

The influence of H2O-H2 fluids and redox conditions on melting temperatures in the haplogranite system

Solidus temperatures of quartz–alkali feldspar assemblages in the haplogranite system (Qz-Ab-Or) and subsystems in the presence of H₂O-H₂ fluids have been determined at 1, 2, 5 and 8 kbar vapour pressure to constrain the effects of redox conditions on phase relations in quartzofeldspathic assemblages. The hydrogen fugacity (f _H2) in the fluid phase has been controlled using the Shaw membrane technique for moderately reducing conditions (f _H2 < 60 bars) at 1 and 2 kbar total pressure. Solid oxygen buffer assemblages in double capsule experiments have been used to obtain more reducing conditions at 1 and 2 kbar and for all investigations at 5 and 8 kbar. The systems Qz-Or-H₂O-H₂ and Qz-Ab-H₂O-H₂ have only been investigated at moderately reducing conditions (1 and 5 kbar) and the system Qz-Ab-Or-H₂O-H₂ has been investigated at redox conditions down to IW (1 to 8 kbar). The results obtained for the water saturated solidi are in good agreement with those of previous studies. At a given pressure, the solidus temperature is found to be constant (within the experimental precision of ± 5°C) in the f _H2 range of 0–75 bars. At higher f _H2, generated by the oxygen buffers FeO-Fe₃O₄ (WM) and Fe-FeO (IW), the solidus temperatures increase with increasing H₂ content in the vapour phase. The solidus curves obtained at 2 and 5 kbar have similar shapes to those determined for the same quartz - alkali feldspar assemblages with H₂O-CO₂- or H₂O-N₂-bearing systems. This suggests that H₂ has the behaviour of an inert diluent of the fluid phase and that H₂ solubility in aluminosilicate melts is very low. The application of the results to geological relevant conditions [HM (hematite-magnetite) > f _O2 > WM] shows that increasing f _H2 produces a slight increase of the solidus temperatures (up to 30 °C) of quartz–alkali feldspar assemblages in the presence of H₂O-H₂ fluids between 1 and 5 kbar total pressure. Received: 4 March 1996 / Accepted: 22 August 1996     

Experimental measurements of the graphite C−O equilibrium and CO2 fugacities at high temperature and pressure

Thef _{o 2} of the equilibrium between graphite and C−O fluid has been determined from 15–30 kbar and 1100–1400°C using a sliding redox sensor consisting of (Ni, Mn) O+Ni metal. The equilibrium composition of oxide coexisting with metal was approached from both directions in each experiment with convergence to within 1 mol% NiO. Since, in theP−T range of the experiments, C−O fluids are >90% CO₂ our measurements off _{o 2} translate into determinations of CO₂ fugacity with an uncertainty of ±0.1 log units. These new determinations of theP−T−f _{o 2} plane of GCO equilibrium are in excellent agreement with the mainly unreversed measurements of Ulmer and Luth (1991) using pure metal-metal oxide sensors and with the equation of state of Saxena and Fei (1987). Modified forms of the Redlich-Kwong (MRK) equation of state (Holloway 1977; Flowers 1979; Kerrick and Jacobs 1981) predict higher values off _{o 2} for the GCO equilibrium than determined experimentally. This implies that CO₂ is more compressible than the MRK predicts. Editorial responsibility: V. Trommsdorff     

Back transformation and oxidation of (Mg,Fe)2SiO4 spinels at high temperatures

Based on the in situ and temperature-quench X-ray measurements, the back transformation in the (Mg, Fe)₂SiO₄-spinels has been characterized in terms of the transformation temperature (T _r ),mechanism and kinetics of the transformation, and of the end product(s), with specific emphasis on the effect of oxygen on this transformation. The in situ measurements were conducted to 900° C in vacuum (10^-4 to 10^-5 torr) and to 600° C in air using synchrotron radiation (SR) at Stanford Synchrotron Radiation Laboratory (SSRL). In the quench-type measurements, samples were heated in air to 1100° C, quenched and examined at ambient conditions using the conventional X-ray diffraction facilities. Important results are (1) in vacuum, all the spinels convert back into the olivine phase, with their T _r decreasing with increasing iron content; (2) the spinel olivine back transformation is a nucleation and growth type of transformation and can be described quantitatively using the Avrami equation; (3) in air, the (Mg, Fe)₂SiO₄-spinels with 0.2 mole fraction Fe or more are all oxidized, and the composition and phase of the end products depend upon the temperature and the starting composition; and (4) the oxidation of the iron-rich (Mg, Fe)₂SiO₄-spinels in air occurs at 350–400° C, which is significantly lower than its T _r ( 300° C) in vacuum.     

Effect of dehydration on the electrical conductivity of phyllite at high temperatures and pressures

Mineralogy and Petrology - The electrical conductivity of phyllite (measured in situ at 0.5–2.5&nbsp;GPa and 773–1173&nbsp;K) increases with increasing temperature, satisfying...     

中地壳温度压力条件下的水-岩作用化学动力学实验

为模拟中地壳条件下水.岩相互作用,本文作者重点做了大于300℃,在水的近临界区至超临界区条件下的硅酸盐矿物与水反应的化学动力学实验。矿物(钠长石(Ab)、透辉石(Di)、阳起石(Act))的溶解反应动力学实验是使用流体通过叠层反应器的开放体系在25℃～400℃和22MPa下完成的。实验发现矿物在300至400℃范围内,在跨越水临界点时出现反应速率的涨落。多金属氧化物硅酸盐与水反应时的各个元素溶解到溶液里的释放速率一般不一样。硅酸盐矿物的最大溶解反应速率多是在300℃,如,硅的最大释放速率是在300℃。其余元素如Na、K、Mg、Ca、Fe、Al等释放速率在<300℃、22MPa时都高于硅的释放速率,在>300℃时硅的释放速率要高于其它元素的释放速率。我们还完成了玄武岩与水在25℃～400℃条件下的反应动力学实验。实验发现,硅的最大释放反应速率也多是在300℃。中地壳的流体处于由亚临界态进入超临界流体的演化过程,这时流体的性质会有剧烈变化。这一变化会引起水/岩相互作用的反应动力学涨落。流体性质的突变和水岩相互作用涨落会导致中地壳岩层的许多性质变化,硅酸盐矿物格架的解体,岩石被淋失,岩层的崩塌。     

Intrinsic oxygen fugacity measurements on seven chondrites,a pallasite,and a tektite and the redox state of meteorite parent bodies

Intrinsic oxygen-fugacity (fO₂) measurements were made on five ordinary chondrites, a carbonaceous chondrite, an enstatite chondrite, a pallasite, and a tektite. Results are of the form of linear log $\text{f}\text{O}{}_2\text{?}\text{1}\text{T}$ plots. Except for the enstatite chondrite, measured results agree well with calculated estimates by others.The tektite produced fO₂ values well below the range measured for terrestrial and lunar rocks. The lowpressure atmospheric regime that is reported to follow large terrestrial explosions, coupled with a very high temperature, could produce glass with fO₂ in the range measured.The meteorite Salta (pallasite) has low fO₂ and lies close to Hvittis (E6). Unlike the other samples, results for Salta do not parallel the iron-wüstite buffer, but are close to the fayalite-quartz-iron buffer in slope.Minor reduction by graphite appears to have taken place during metamorphism of ordinary chondrites. fO₂ values of unequilibrated chondrites show large scatter during early heating suggesting that the constituent phases were exposed to a range of fO₂ conditions. The samples equilibrated with respect to fO₂ in relatively short time on heating. Equilibration with respect to fO₂ in ordinary chondrites takes place between grades 3 and 4 of metamorphism. Application of P ? T ? fO₂ relations in the system C-CO-CO₂ indicates that the ordinary chondrites were metamorphosed at pressures of 3–20 bars, as it appears that they lay on the graphite surface.A steep positive thermal gradient in a meteorite parent body lying at the graphite surface will produce thin reduced exterior, an oxidized near-surface layer, and an interior that is increasingly reduced with depth; a shallow thermal gradient will produce the reverse. A body heated by accretion on the outside will have a reduced exterior and oxidized interior. Meteorites from the same parent body clearly are not required to have similar redox states.     

Modeling the thermodynamic parameters of six endmember garnets at ambient and high pressures from vibrational data

Raman and infrared spectroscopic data at ambient and high pressures were used to compute the lattice contribution to the heat capacities and entropies of six endmember garnets: pyrope, almandine, spessartine, grossular, andradite and uvarovite. Electronic, configurational and magnetic contributions are obtained from comparing available calorimetric data to the computed lattice contributions. For garnets with entropy in excess of the computed lattice contribution, the overwhelming majority is found in the subambient temperature regime. At room temperature, the non-lattice entropy is approximately 11.5 J/mol-K for pyrope, 49 J/mol-K for almandine, and 19 J/mol-K for andradite. The non-lattice entropy for pyrope and some for almandine cannot be accounted for by magnetic or electronic contributions and is likely to be configurational in nature. Estimates of low temperature non-lattice entropies for both spessartine and uvarovite are made in absence of calorimetric measurements and are based on low temperature calorimetry of other minerals containing the Mn²⁺ and Cr³⁺ cations as well as on solid solution garnets containing these cations. The estimate for uvarovite non-lattice entropy is approximately 18 J/mol-K, while for spessartine, approximately 45 J/mol-K. Neither of these cations is expected to provide electronic contributions to the entropy. For both iron-bearing garnets, a small electronic or magnetic entropy contribution continues above ambient temperatures. High pressure data on pyrope, grossular and andradite permit calculation of the thermodynamic parameters at high pressures, which are important for computation of processes in the Earth’s mantle. Thermal expansion coefficients of these materials were found to be 1.6, 1.5, 1.6×10⁻⁵ K⁻¹ at 298 K, respectively, using a Maxwell relation. These closely match the literature values at ambient conditions.     

冲绳海槽浮岩的高温高压纵波速度

对采自冲绳海槽中部海底的浮岩样品和邻近陆地樱岛火山的安山岩样品进行了温度 (常温 - 15 0 0℃ )与压力 (常压 - 2 .4 GPa)实验 ,测得在较低温度 -压力条件下 (<1GPa,<80 0℃ )浮岩样品的纵波速度小于安山岩样品的纵波速度 ,在较高温度 -压力条件下 (>1GPa,>80 0℃ )二者的纵波速度接近一致 (5 .9km /s)。 1GPa/80 0℃是浮岩样品和安山岩样品的热动力相变点 ,推测该点的深度大于 18km。     

Solid solubility of Al2O3 in enstatite at high temperatures and 1–5 kb water pressure

Solid solubility of Al₂O₃ in orthorhombic enstatite by the substitution AlAl=MgSi is, in the range studied, mainly a function of temperature and not strongly pressure-dependent. Even at 1 kb up to 9 wt.-% Al₂O₃ can be substituted at 1200° C. The thermal stability of the orthorhombic pyroxene phase is strongly increased by the incorporation of Al.In crustal rocks the alumina content of orthopyroxene might be used as a geothermometer but not, as sometimes suggested, as a barometer.     

Experimental study of the stability of cordierite and garnet in pelitic compositions at high pressures and temperatures

The stability of cordierite and garnet has been studied experimentally in complex, silica oversaturated compositions (in the systems MgO-FeO-Al₂O-CaO₃-Na₂O-K₂OSiO₂) in which the molecular ratio Al₂O₃/FeO+MgO<1. Compositions with 100 Mg/Mg+Fe²⁺ ratios (X) of 0, 30, 50, 70 and 100 have been used to investigate the role of this ratio in determining phase assemblages and P, T coordinates of reactions. The minimum pressure for appearance of garnet at a given temperature is strongly dependent on X _{total rock}.The X-values of co-existing phases (chiefly garnet, cordierite, hypersthene) in divariant equilibrium are a function of temperature and pressure and have been experimentally determined at 900° C, 1000° C and 1100° C. At high temperature (>1050° C) the phases sapphirine and spinel are stable with quartz in Mg-rich and Fe-rich compositions respectively. Experiments in the system MgO-FeO-Al₂O₃-SiO₂ show that for a given X-value and temperature the pressure required to produce Ca-free garnet from hypersthene-cordierite assemblages is 1–2 kb greater than that required to produce garnet containing 6±2 mol percent grossular solid solution in the more complex Ca-bearing system.