Saltation threshold on Earth, Mars and Venus

New formulations valid for wide ranges of particle diameter and density and gas density are presented for prediction of saltation threshold speed for small particles. A low-air-density wind tunnel was used to extend the range of previous investigations and to separate the effects of Reynolds number and interparticle forces of cohesion. The new formulations are used to predict saltation threshold for atmospheric conditions on the surface of the Earth, Mars, and Venus.     

The split fate of the early Earth,Mars, Venus,and Moon

Plate tectonics shaped the Earth, whereas the Moon is a dry and inactive desert, Mars probably came to rest within the first billion years of its history, and Venus, although internally very active, has a dry inferno for its surface. Here we review the parameters that determined the fates of each of these planets and their geochemical expressions. The strong gravity field of a large planet allows for an enormous amount of gravitational energy to be released, causing the outer part of the planetary body to melt (magma ocean), helps retain water on the planet, and increases the pressure gradient. The weak gravity field and anhydrous conditions prevailing on the Moon stabilized, on top of its magma ocean, a thick buoyant plagioclase lithosphere, which insulated the molten interior. On Earth, the buoyant hydrous phases (serpentines) produced by reactions between the terrestrial magma ocean and the wet impactors received from the outer solar system isolated the magma and kept it molten for some few tens of million years. The planets from the inner solar system accreted dry: foundering of wet surface material softened the terrestrial mantle and set the scene for the onset of plate tectonics. This very same process also may have removed all the water from the surface of Venus and added enough water to its mantle to make its internal dynamics very strong and keep the surface very young. Because of a radius smaller than that of the Earth, not enough water could be drawn into the Martian mantle before it was lost to space and Martian plate tectonics never began. The radius of a planet is therefore the key parameter controlling most of its evolutional features.     

动高压物理在地球与行星科学研究中的应用

综述了动高压物理应用于地球和行星科学研究中的一些最新进展,包括地球内部的物质组成与热力学状态,巨行星的物质组成模型,太阳系中的碰撞成坑与吸积相互作用等。依据铁的冲击波数据,结合其他热力学数据,可以得到一条统一的铁的熔化曲线,将动高压与静高压数据完全统一,初步解决了长期困扰高压界的动、静压关于铁的熔化温度存在系统偏差的诘难。外推到ICB处(330 GPa),铁的熔化温度(亦称锚定温度)约为(5 950±100) K。冲击Hugoniot 数据,结合地震学模型可以约束地幔与地核的物质组成。冲击压缩下钙钛矿型(Mg0 9,Fe0 1)SiO3的高压声速测量结果表明,1 770 km深度的不连续面不仅是一个相变界面而且是一个化学成分或矿物学分界面。低温可凝聚气体(H2、He)或冰(H2 O, CH4, CO2, NH3 和N2 )的冲击波数据,及Jeffrey 数等其他数据可以用来构建巨行星(如木星和土星)的物质组成模型。地球深部矿物的冲击温度测量可以用来研究它们的高压熔化行为,据此建立的高压相图可以为控制地幔对流的地幔物质的准静态蠕变提供约束条件。熔融硅酸盐在上地幔压力条件下的冲击压缩数据,可以约束地幔熔岩稳定存在的深度,在此深度地幔熔岩不会因固体围岩提供的浮力而向上运移到地表,从而在此深度形成稳定的低速带。冲击波数据在描写行?     

P-T-X conditions of calc-silicate formation: evidence from fluid inclusions and phase equilibria; Llano Uplift, central Texas, USA

Abstract The Llano Uplift in central Texas is a Grenville aged (c. 1.1 Ga) metamorphic terrane consisting predominantly of amphibolite facies mineral assemblages. The formation of these assemblages has been attributed to the emplacement of relatively late granite plutons throughout the area. Two types of granitic intrusion have previously been recognized: (1) Town Mountain Granites, which occur as relatively large, circular-shaped bodies of coarse-grained granite, and (2) Younger Granites which are present as smaller and more irregular bodies of finer-grained granite. In the central part of the uplift, wollastonite-bearing calc-silicate rocks occur within the Valley Spring Gneiss. The development of these calc-silicate rocks has been linked to infiltrating fluids presumably derived from spatially associated Younger Granites. The stability of coexisting quartz, calcite, wollastonite, grossular and anorthite and coexisting quartz, calcite, wollastonite, andradite and hedenbergite shows that the calc-silicate rocks equilibrated under H₂O-rich conditions with χCO₂ <0.10. Fluid inclusions present within the calc-silicate minerals are H₂O-rich with salinities of <17 wt% equivalent NaCl. The absence of any detectable CO₂ in the fluid inclusions may indicate entrapment of the inclusions at lower pressures and more H₂O-rich conditions compared to the stability of the peak metamorphic mineral assemblage. Homogenization temperatures, measured for texturally primary inclusions, range from 360 to 368° C corresponding to a density range from 0.53 to 0.82 g/cm³. Isochores for these fluid inclusions, when combined with the stability of the solid-solid equilibria Grs + Qtz = Wo + An, yield formation conditions of 500–550° C at 1–2 kbar. This indicates that the granitic intrusions involved in the formation of the Blount Mountain calc-silicates were emplaced at a pressure of at least 1–2 kbar.     

Petrogenesis of Hawaiian tholeiites: 1, phase equilibria constraints

The most magnesian olivine phenocrysts [Mg no.=100 Mg/(Mg+Fe)=90.5] in Hawaiian tholeiites provide evidence for the earliest stages of differentiation of Hawaiian magmas. Based on the correction of olivine fractionation effects, the primitive melt compositions which have crystallised these olivines are picritic with 16 wt% MgO. They are excellent primary-melt candidates. An experimental study on a new Hawaiian picritic primary-melt estimate demonstrates multiple saturation with peridotite (harzburgite) at 2.0 GPa and 1450° C. Garnet is not a liquidus phase at pressures below 3.5 GPa, and garnet peridotite is not a liquidus phase assemblage at any pressure or temperature. This result confirms previous experimental studies on Hawaiian primary-melt estimates and conflicts with trace-elementgeochemistry-based interpretations, which claim that melt generation occurs in the presence of residual garnet. If Hawaiian tholeiite primary magmas are picritic and have equilibrated with garnet-absent peridotite residues, the geochemical and isotopic characteristics of Hawaiian tholeiites (i.e. Sm/Nd chondrites and Nd>0) are consistent with their source recently having been enriched in incompatible elements. Previous modelling shows that such characteristics are consistent with source enrichment through the migration of small melt fractions generated at depth in the presence of garnet. This may be effected either at the time of Hawaiian magma genesis through dynamic melt segregation processes or, by melting of a previously enriched mantle source; possibly oceanic lithospheric mantle which has been infiltrated by melt fractions from the underlying asthenosphere prior to Hawaiian magmatism. Alternatively, if Hawaiian primary magmas are ultramafic in composition (20 wt% MgO) they may be generated in the presence of garnet peridotite at pressures 3.0 GPa.     

Heat capacity,entropy, and phase equilibria of dmitryivanovite

The heat capacity (C _p ) of dmitryivanovite synthesized with a cubic press was measured in the temperature range of 5–664 K using the heat capacity option of a physical properties measurement system and a differential scanning calorimeter. The entropy of dmitryivanovite at standard temperature and pressure (STP) was calculated to be 110.1 ± 1.6 J mol⁻¹ K⁻¹ from the measured C _p data. With the help of new phase equilibrium experiments done at 1.5 GPa, the phase transition boundary between krotite and dmitryivanovite was best represented by the equation: P (GPa) = −2.1825 + 0.0025 T (K). From the temperature intercept of this phase boundary and other available thermodynamic data for krotite and dmitryivanovite, the enthalpy of formation and Gibbs free energy of formation of dmitryivanovite at STP were calculated to be −2326.7 ± 2.1 and −2,208.1 ± 2.1 kJ mol⁻¹, respectively. It is also inferred that dmitryivanovite is the stable CaAl₂O₄ phase at STP and has a wide stability field at high pressures whereas the stability field of krotite is located at high temperatures and relatively low pressures. This conclusion is consistent with natural occurrences (in Ca–Al-rich inclusions) of dmitryivanovite and krotite, where the former is interpreted as the shock metamorphic product of originally present krotite.     

Heat capacity,entropy and phase equilibria of stishovite

The low-temperature heat capacity (C _P) of stishovite (SiO₂) synthesized with a multi-anvil device was measured over the range of 5–303 K using the heat capacity option of a physical properties measurement system (PPMS) and around ambient temperature using a differential scanning calorimeter (DSC). The entropy of stishovite at standard temperature and pressure calculated from DSC-corrected PPMS data is 24.94 J mol⁻¹ K⁻¹, which is considerably smaller (by 2.86 J mol⁻¹ K⁻¹) than that determined from adiabatic calorimetry (Holm et al. in Geochimica et Cosmochimica Acta 31:2289–2307, 1967) and about 4% larger than the recently reported value (Akaogi et al. in Am Mineral 96:1325–1330, 2011). The coesite–stishovite phase transition boundary calculated using the newly determined entropy value of stishovite agrees reasonably well with the previous experimental results by Zhang et al. (Phys Chem Miner 23:1–10, 1996). The calculated phase boundary of kyanite decomposition reaction is most comparable with the experimental study by Irifune et al. (Earth Planet Sci Lett 77:245–256, 1995) at low temperatures around 1,400 K, and the calculated slope in this temperature range is mostly consistent with that determined by in situ X-ray diffraction experiments (Ono et al. in Am Mineral 92:1624–1629, 2007).     

No water, no plate tectonics: convective heat transfer and the planetary surfaces of Venus and Earth

We consider the influence of water on the near-surface rheology of Venusian and terrestrial rocks and hence the way their heat transfer processes have been able to shape their planetary surfaces. We suggest that Earth is now unique in having plate-like surface movements at velocities characteristic of ‘deep’ material in self-regulating convective states (～ few cm/year) only because liquid water is there available to facilitate mechanical failure of its lithosphere (sic). The relative absence of free water on Venus is thought to more than compensate for the effect of higher temperatures on the deformability of its surface rocks and is interpreted as the reason for an absence of Earth-like platetectonics and the distinctive distributions of volcanism and seismicity accompanying such a process for > 109 years. The characteristics of Venusian volcanism in its post plate-tectonic era are now expected to be similar to Earth's intraplate (‘hotspot’) volcanism.     

Low temperature phase equilibria in the Fe-Ni and Fe-Ni-P systems: application to the thermal history of metallic phases in meteorites

The solubility limits of the α (kamacite) and γ (taenite) phases in the Fe-Ni and Fe-Ni-P phase diagrams have been measured at low temperatures, 700-300°C. The predicted $\text{α}\text{α}\text{+ γ}$ retrograde solubility below 500°C was demonstrated experimentally for the first time in the Fe-Ni system. The minimum solubility of Ni in γ at the $\text{γ}\text{α}\text{+γ}$ boundary increases with decreasing temperature to as much as 54 wt% at 300°C. The addition of P increases the maximum solubility of Ni in α by as much as 1.6 wt% and decreases the minimum solubility of Ni in γ by as much as 7 wt% at 300°C.The solubility limits of kamacite and taenite were also obtained from heat-treated samples of the Grant and Cape York iron meteorites. The data indicate that in iron meteorites minor and trace elements other than P do not significantly shift the Ni solubility limits of the Fe-Ni and Fe-Ni-P phase diagrams. The measured phase diagrams can be used to explain the Agrell effect and the differences in maximum Ni content of taenite among irons and chondrites. The formation of plessite and the influence of the measured solubility limits on the cooling rate simulation method are also considered.     

The application of ionic equilibria to metamorphic differentiation: An example

Mineral segregations formed by metamorphic differentiation are an important source of information on diffusion processes in metamorphism. Segregations consisting of andalusite-biotite-quartz cores surrounded by a quartz-feldspar mantle in sillimanite-biotitefeldspar-quartz gneiss near Västervik, Sweden (Loberg, 1963) formed by core-to-mantle migration of K, and mantle-to-core migration of Fe, Mg and Ca. These migrations can be represented by a set of interconnected ionic equilibria involving reaction of microcline and Fe(OH)⁺ in the core to form andalusite plus biotite, and reaction of K⁺, sillimanite and biotite in the mantle to form microcline. Equilibrium constants for these reactions, calculated for conditions inferred from the mineral assemblage and biotite composition, indicate gradients of K⁺ activity (higher in core) and Fe(OH)⁺ activity (higher in mantle). These gradients result simply from the free energy difference between andalusite and sillimanite, without invoking pre-existing megascopic inhomogeneities in the rock or surface energy effects. Although small, these gradients appear to be capable of driving the segregation process.     

The ZnSiO3 clinopyroxene-ilmenite transition: Heat capacity,enthalpy of transition,and phase equilibria

ZnSiO₃ clinopyroxene stable above 3 GPa transforms to ilmenite at 10–12 GPa, which further decomposes into ZnO (rock salt) plus stishovite at 20–30 GPa. The enthalpy of the clinopyroxene-ilmenite transition was measured by high-temperature solution calorimetry, giving ΔH⁰=51.71 ±3.18 kJ/mol at 298 K. The heat capacities of clinopyroxene and ilmenite were measured by differential scanning calorimetry at 343–733 and 343–633 K, respectively. The C _p of ilmenite is 3–5% smaller than that of clinopyroxene. The entropy of transition was calculated using the measured enthalpy and the free energy calculated from the phase equilibrium data. The enthalpy, entropy and volume changes of the pyroxene-ilmenite transition in ZnSiO₃ are similar in magnitude to those in MgSiO₃. The present thermochemical data are used to calculate the phase boundary of the ZnSiO₃ clinopyroxene-ilmenite transition. The calculated boundary,

Phlogopite: High temperature solution calorimetry,thermodynamic properties,Al-Si and stacking disorder,and phase equilibria

Methods have been developed for solution calorimetry of hydrous phases in molten lead borate near 700°C. These involve thermochemical cycles using dissolution and decomposition reactions of hydrous silicates and hydroxides. Preliminary results suggest that H₂O derived from the decomposition of hydroxides dissolves in molten 2PbO-B₂O₃ with an exothermic enthalpy of solution of −5.7 ±0.7 kcal mol⁻¹. Hydroxyphologopite persists metastably at 714°C and its heat of solution in 2PbO·B₂O₃ has been measured. From these new data, the standard enthalpy of formation of phlogopite from the elements at 25°C is −1485.5 ±1.5 kcal mol⁻¹. The standard free energy of formation is -1394.6 ±1.5 kcal mol⁻¹, assuming complete tetrahedral Al-Si disorder.Two structural features complicate the thermodynamics of synthetic and natural micas. The first is a varying degree of tetrahedral Al-Si disorder. Raman spectroscopic study of phlogopite synthesized above 600°C suggests a disordered Al-Si distribution. Calculations of the P-T locus of the geologically important equilibrium: Phl + 3Qtz = 3En + Sa + H₂O, using our thermochemical data, agree within experimental error with the results of calculations based on the best available phase equilibrium data only if a tetrahedrally disordered phlogopite is assumed. Such calculations are very sensitive to uncertainties in ΔH° and ΔG°, and reversed phase equilibrium experiments remain essential to obtaining reliable estimates of thermodynamic properties. In contrast to these Al-Si disordered phlogopites, some biotites of low temperature parageneses (<600°C) may have substantial Al-Si order. A variable Al-Si distribution has a substantial effect on the configurational entropy and therefore on the free energy of the mica in question. Because of these and other questions, applications of biotite equilibria to determining volatile fugacities in igneous and metamorphic petrogenesis are subject to large uncertainties.The second structural complication is stacking disorder, which is present in phlogopite synthesized at 650°C but not in the 850°C sample. The enthalpy difference between these two samples, determined by solution calorimetry, is smaller than the experimental uncertainty of ±1.0 kcal mol⁻¹. Thus there appears to be little driving force for ordering, and micas with disordered stacking sequences may persist in many geologic environments. The effect of stacking disorder on thermodynamic properties is probably very small.     

Phase equilibria in carbonic systems,and their application to freezing studies of fluid inclusions

Addition of CH₄ to CO₂ lowers the temperatures at which phase changes occur with respect to those in the unary system CO₂. At high density and high a melting interval of solid CO₂ can be expected. Rearrangement of currently available theoretical and experimental data permits bulk compositions of carbonic fluid inclusions to be determined from the final melting temperature of CO₂ and the degree of filling at that temperature. Homogenization temperatures of CO₂-CH₄ inclusions can be expressed in terms of equivalent CO₂-densities, permitting estimates of P-T relations using isochores in the unary system CO₂.     

Ultrahigh-temperature mafic granulites from Panrimalai,south India: Constraints from phase equilibria and thermobarometry

The Panrimalai area constitutes part of the granulite-facies rocks of the Madurai block in the Southern Granulite Terrain (SGT), India. Garnet-bearing mafic granulites in Panrimalai occur as small enclaves within charnockite. The common stable assemblage during peak metamorphism contains hornblende, garnet, orthopyroxene, clinopyroxene, quartz and plagioclase. The resorption of garnet in various reaction textures and the development of spectacular orthopyroxene–plagioclase and hornblende–plagioclase symplectites characterize the subsequent stages of metamorphism. Application of multi-equilibrium calculation procedures for mineral core compositions of the early assemblage yields near peak conditions at  ≥ 900 °C at 9 kbar. These estimates are the highest yet reported in mafic granulites from the Madurai block. The post-peak P–T path is constructed for the mafic granulites based on observed microstructural relations and thermobarometric results is characterized by a steep clockwise decompressional P–T segment from  ≥ 9 to  < 4.5 kbar. Constraints from model Nd ages provide evidence for Paleoproterozoic magmatism restricted to the Madurai block in the Southern Granulite Terrain. The early part of the crustal evolution of the Panrimalai granulites could be coeval with the Paleoproterozoic event. Subsequent development of symplectitic assemblages via near-isothermal decompression can be ascribed to a distinctly later tectonic event. Available U–Pb and Sm–Nd mineral dates suggest a widespread Pan-African tectonothermal event in the SGT. Given the general recognition of ultrahigh-temperature (UHT) and isothermal decompression (ITD) in Pan-African age metamorphism in the East-African–Antarctic Orogen (EAAO) , the Panrimalai UHT history is considered to be part of this record.     

Petrogenesis of Al-rich chondrules: Evidence from bulk compositions and phase equilibria

We measured major, minor, and trace-element compositions for eleven Al-rich chondrules from unequilibrated ordinary chondrites to investigate the relationships between Al-rich chondrules, ferromagnesian chondrules, Ca-, Al-rich inclusions (CAIs), and amoeboid olivine aggregates (AOAs). Phase equilibrium considerations show that, for the most part, mineral assemblages in Al-rich chondrules are those expected from melts of the observed compositions. The diversity of mineral assemblages and Al-rich chondrule types arises mainly from the fact that the array of compositions spans both the spinel-saturated anorthite-forsterite reaction curve and a thermal divide defined by where the anorthite-forsterite join crosses the reaction curve. The reaction curve accounts for the two principal varieties of Al-rich chondrule, plagioclase-phyric and olivine-phyric, with or without aluminous spinel. The thermal divide influences the subsequent evolution of each variety. A third variety of Al-rich chondrule contains abundant sodium-rich glass; trace-element fractionation patterns suggest that these glassy Al-rich chondrules could have been derived from the other two by extensive alteration of plagioclase to nepheline followed by remelting. The bulk compositions of Al-rich chondrules (except sodium-rich ones) are intermediate in a volatility sense between ferromagnesian chondrules and type C CAIs. The combined trend of bulk compositions for CAIs, Al-rich chondrules, and ferromagnesian chondrules mirrors, but does not exactly match, the trend predicted from equilibrium condensation at P_T ∼ 10^-3 atm; the observed trend does not match the trend found for evaporation from a liquid of chondritic composition. We thus infer that the bulk compositions of the precursors to CAIs, Al-rich chondrules, were ferromagnesian chondrules were controlled primarily by vapor-solid reactions (condensation or sublimation) in the solar nebula. Some Al-rich chondrules are consistent with an origin by melting of a compound CAI-ferromagnesian chondrule hybrid; others cannot be so explained. Any hybrid model is restricted by the constraint that the CAI precursor consisted dominantly of pyroxene + plagioclase + spinel; melilite cannot have been a significant component. Amoeboid olivine aggregates also have the inferred mineralogical characteristics of Al-rich chondrule precursors—they are mixtures of olivine with plagioclase-spinel-pyroxene-rich CAIs—but the few measured bulk compositions are more olivine-rich than those of Al-rich chondrules.     

Mercury deposition and methylmercury formation in Narraguinnep Reservoir,southwestern Colorado,USA

Narraguinnep Reservoir in southwestern Colorado is one of several water bodies in Colorado with a mercury (Hg) advisory as Hg in fish tissue exceed the 0.3 μg/g guideline to protect human health recommended by the State of Colorado. Concentrations of Hg and methyl-Hg were measured in reservoir bottom sediment and pore water extracted from this sediment. Rates of Hg methylation and methyl-Hg demethylation were also measured in reservoir bottom sediment. The objective of this study was to evaluate potential sources of Hg in the region and evaluate the potential of reservoir sediment to generate methyl-Hg, a human neurotoxin and the dominant form of Hg in fish. Concentrations of Hg (ranged from 1.1 to 5.8 ng/L, n = 15) and methyl-Hg (ranged from 0.05 to 0.14 ng/L, n = 15) in pore water generally were highest at the sediment/water interface, and overall, Hg correlated with methyl-Hg in pore water (R² = 0.60, p = 0007, n = 15). Net Hg methylation flux in the top 3 cm of reservoir bottom sediment varied from 0.08 to 0.56 ng/m²/day (mean = 0.28 ng/m²/day, n = 5), which corresponded to an overall methyl-Hg production for the entire reservoir of 0.53 g/year. No significant point sources of Hg contamination are known to this reservoir or its supply waters, although several coal-fired power plants in the region emit Hg-bearing particulates. Narraguinnep Reservoir is located about 80 km downwind from two of the largest power plants, which together emit about 950 kg-Hg/year. Magnetic minerals separated from reservoir sediment contained spherical magnetite-bearing particles characteristic of coal-fired electric power plant fly ash. The presence of fly-ash magnetite in post-1970 sediment from Narraguinnep Reservoir indicates that the likely source of Hg to the catchment basin for this reservoir has been from airborne emissions from power plants, most of which began operation in the late-1960s and early 1970s in this region.     

Fictive component model of pyroxenes and multicomponent phase equilibria

Pyroxenes are considered as ideal solid solutions of some real components (e.g. diopside or orthoenstatite) and some fictive or hypothetical components (e.g. orthodiopside or orthohedenbergite). Using the reversed experimental data in the CaO-MgO-SiO₂ system, the Gibbs free energy of formation of fictive orthodiopside and of fictive clinoenstatite have been determined in the temperature range of 1,000 to 1,600 °K. The data on free energies of components in the binary system can be used to extend the fictive component model to the ternary CaSiO₃-MgSiO₃-FeSiO₃ system. Using published phase diagrams on the pyroxene quadrilateral, Gibbs free energy of formation of fictive orthohedenbergite has been calculated. Application of the ideally mixing fictive component model to computation of phase equilibria leads to the determination of compositions of coexisting Fe-Mg-Ca pyroxenes at different temperatures.Abbreviations and symbols G _f ⁰ Gibbs free energy of formation from the elements at 1 bar and temperature - G ^Ex excess free energy of mixing in a solution - G molar Gibbs free energy - R gas constant - H enthalpy - S entropy - T absolute temperature - P pressure - KJ/M kilojoules per mole - j joules - Opx orthopyroxene - Cpx clinopyroxene - H hedenbergite - D diopside - E enstatite - F ferrosilite - X mole fraction - K equilibrium constant     

Hydrate phase equilibria in porous media: effect of pore size and salinity

ABSTRACT Considering the ever-increasing importance of marine gas hydrates, it is crucial to gain a better understanding of clathrate formation and decomposition in porous media. It is well established that, due to capillary effects, small-diameter pores – similar to those found in natural sediments – act to inhibit hydrate stability. However, accurate data constraining these effects are still lacking. Here, we present experimental methane clathrate dissociation data for 3.5 mass% methanol aqueous solutions in confined silica glass pores of narrow distribution (30.6, 15.8, and 9.2 nm mean diameters). These data have been used to validate a thermodynamic model for clathrate stability porous media. Experimental data show a marked improvement on literature data – which we attribute to the experimental and interpretative methods used – and are in good agreement with the model predictions. Results suggest that mass transfer of inhibitors (methanol) and dissolved gas during clathrate formation/dissociation within the porous network plays an important role in controlling gas hydrate equilibria.     

Experimental investigation and application of garnet granulite equilibria

Two mineralogic geobarometers based on the assemblages olivine-plagioclase-garnet and orthopyroxeneplagioclase-garnet-quartz have been calibrated from the reaction (1) fayalite+anorthite?garnet (Gr₁Alm₂). The reaction boundary has been determined to within 0.2 kbar using piston-cylinder apparatus. It is located at 4.7, 5.1, 5.5, 5.8, 6.2, 6.6, and 7.0 kbar at 750, 800, 850, 900, 950, 1,000, and 1,050° C, respectively. Summation of ΔG for reaction (1) and fayalite +quartz?ferrosilite locates to within 0.3 kbar the following model garnet-forming reaction for quartz-saturated granulites: (2) ferrosilite+ anorthite?garnet(Gr₁ Alm₂) + quartz. Geobarometers based on (1) and (2) are widely applicable in granulite terranes and yield precise pressures that are in agreement with other well-calibrated barometers. Pressures of 7–10 kbar are inferred for many granulite terranes requiring the widespread development of 60–70 km thick continental crust by mid-Proterozoic.