Methane: An equation of state with application to the ternary system H2O-CO2-CH4

The following hardsphere modified Redlich-Kwong (HSMRK) equation of state was obtained by least squares fitting to available P-V-T data for methane (P in bars; T in Kelvins; v in cm³ mol^?1; b = 60.00 cm³ mol^?1; R = 83.14 cm³barmol^?1K^?1): $\text{P}\text{RT(1 + y + y}{}^2\text{?y}{}^3\text{v(1?y)}{}^3\text{)}\text{-}\text{c(T) + d(T)}\text{v}\text{+}\text{e(T)}\text{v}{}^2\text{/v(v + b)T}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$$\text{y =}\text{b}\text{4v}$c(T) = 13.403 × 10⁶ + (9.28 × 10⁴)T + 2.7 T²d(T) = 5.216 × 10⁹ ? (6.8 × 10⁶)T + (3.28 × 10³)T²e(T) = (?2.3322 × 10¹¹) + (6.738 × 10⁸)T + (3.179 × 10⁵)T² For the P-T range of experimental data used in the fit (50 to 8600 bars and from 320 to 670 K), calculated volumes and fugacity coefficients for CH₄ relative to experimentally determined volumes and fugacity coefficients have average percent deviations of 0.279 and 1.373, respectively. The HSMRK equation, which predicts linear isochores over a wide P-T range, should yield reasonable estimates of fugacity coefficients for CH₄ to pressures and temperatures well outside the P-T range of available P-V-T data. Calculations for the system H₂O-CO₂-CH₄, using the HSMRK equations for H₂O and CO₂ of Kerrick and Jacobs (1981) and the HSMRK equation for CH₄ of this study, indicate that compared to the binary H₂O-CO₂ system, small amounts of CH₄ in the ternary system H₂O-CO₂-CH₄ slightly increases the activity of H₂O, and significantly decreases the activity of CO₂.     

Transport properties of high albite crystals,near-endmember feldspar and pyroxene glasses,and their melts to high temperature

Thermal diffusivity (D) was measured using laser-flash analysis (LFA) from oriented single-crystal albite and glasses near LiAlSi₃O₈, NaAlSi₃O₈, CaAl₂Si₂O₈, LiAlSi₂O₆ and CaMgSi₂O₆ compositions. Viscosity measurements of the supercooled liquids, over 2.6 × 10⁸ to 8.9 × 10¹² Pa s, confirm strongly non-Arrhenian behavior for CaAl₂Si₂O₈, and CaMgSi₂O₆, and near-Arrhenian behavior for the others. As T increases, D _glass decreases, approaching a constant near 1,000 K. Upon crossing the glass transition, D decreases rapidly. For feldspars, D for the melt is ~15% below D of the bulk crystal, whereas for pyroxenes, this difference is ~40%. Thermal conductivity (k _lat = ρC _P D) of crystals decreases with increasing T, but k _lat of glasses increases with T because heat capacity (C _P ) increases with T more strongly than density (ρ) and D decrease. For feldspars, k _lat for the melt is ~10% below that of the bulk crystal or glass, whereas this decrease for pyroxene is ~50%. Therefore, melting substantially impedes heat transport, providing positive thermal feedback that could promote further melting.     

Thermodynamic data of the high-pressure phase Mg5Al5Si6O21(OH)7 (Mg-sursassite)

 Calorimetric and P–V–T data for the high-pressure phase Mg₅Al₅Si₆O₂₁(OH)₇ (Mg-sursassite) have been obtained. The enthalpy of drop solution of three different samples was measured by high-temperature oxide melt calorimetry in two laboratories (UC Davis, California, and Ruhr University Bochum, Germany) using lead borate (2PbO·B₂O₃) at T=700 ^∘C as solvent. The resulting values were used to calculate the enthalpy of formation from different thermodynamic datasets; they range from −221.1 to −259.4 kJ mol⁻¹ (formation from the oxides) respectively −13892.2 to −13927.9 kJ mol⁻¹ (formation from the elements). The heat capacity of Mg₅Al₅Si₆O₂₁(OH)₇ has been measured from T=50 ^∘C to T=500 ^∘C by differential scanning calorimetry in step-scanning mode. A Berman and Brown (1985)-type four-term equation represents the heat capacity over the entire temperature range to within the experimental uncertainty: C _P (Mg-sursassite) =(1571.104 −10560.89×T ^−0.5−26217890.0 ×T ⁻²+1798861000.0×T ⁻³) J K⁻¹ mol⁻¹ (T in K). The P V T behaviour of Mg-sursassite has been determined under high pressures and high temperatures up to 8 GPa and 800 ^∘C using a MAX 80 cubic anvil high-pressure apparatus. The samples were mixed with Vaseline to ensure hydrostatic pressure-transmitting conditions, NaCl served as an internal standard for pressure calibration. By fitting a Birch-Murnaghan EOS to the data, the bulk modulus was determined as 116.0±1.3 GPa, (K ^′=4), V _T,0 =446.49 ³ exp[∫(0.33±0.05) × 10⁻⁴ + (0.65±0.85)×10⁻⁸ T dT], (K _T/T) _P  = −0.011± 0.004 GPa K⁻¹. The thermodynamic data obtained for Mg-sursassite are consistent with phase equilibrium data reported recently (Fockenberg 1998); the best agreement was obtained with Δ_f H ⁰ ₂₉₈ (Mg-sursassite) = −13901.33 kJ mol⁻¹, and S ⁰ ₂₉₈ (Mg-sursassite) = 614.61 J K⁻¹ mol⁻¹. Received: 21 September 2000 / Accepted: 26 February 2001     

Interdiffusion of Na,K,and Ca Between Granitic Melts and NaCl Liquid

This study is aimed at determining the diffusion coefficient of net-work modifiers (mainly Na, K, and Ca) in a two-phase melt-NaCl system, in which the melts are granitic and the system is NaCl-rich in composition. The diffusion coefficients of Na, K, and Ca were measured at the temperatures of 750 – 1400°C, pressures of 0.001 × 10⁸ – 2 × 10⁸ Pa, and initial H₂O contents of 0 wt% –6.9 wt% in the granitic melts. The diffusion coefficients of Fe and Mg were difficult to resolve. In all experiments a NaCl melt was present as well. In the absence of H₂O, the diffusion of net-work modifiers follows an Arrhanious equation at 1 × 10⁵ Pa: lgD_ca=−3. 88−5140/T, lgD_k =−3. 79−4040/T, and lgD_Na, =−4.99−3350/T, where D is in cm² /s andT is in K. The diffusion coefficients of Ca, Na, K, and Fe increase non-linearly with increasing H₂O content in the melt. The presence of about 2 wt% H₂O m the melt will lead to a dramatical increase in diffusivity, but higher H₂O content has only a minor effect. This change is probably the result of a change in the melt structure when H₂O is present. The diffusion coefficients measured in this study are significantly different from those in previous works. This may be understood in terms of the “transient two-liquid equilibrium” theory. Element interdiffusion depends not only on its concentration, but also on its activity co-efficient gradient, which is reflected by the distribution coefficient, of the two contacting melts.     

The petrogenesis of basic and ultrabasic alkaline rocks of western Makhtesh Ramon,Israel: geochemistry,melt and fluid inclusion study

The basic and ultrabasic alkaline rocks of western Makhtesh Ramon, Israel crop out in numerous lava flows and subvolcanic bodies. The rock suite is composed of tephrite, basanite, basanitic nephelinite, analcimite, olivine nephelinite, and melilite-olivine nephelinite and in many outcrops is represented by glass-bearing varieties. Melt and fluid inclusions have been studied in olivine, clinopyroxene, and plagioclase phenocrysts. The EP, SIMS and microthermometry methods were used for inclusion study. The geochemical data obtained on glasses of melt inclusions (major, REE, trace elements, volatiles) are compared with the data on whole-rock and groundmass glass compositions. The compositions of melt inclusions reflect the different stages of rock crystallization: the initial products of crystallization are similar to whole-rock compositions whereas final portions of melts are usually enriched in SiO₂, Al₂O₃, and alkalis, and depleted in mafic components. The data on contemporaneous melt and CO₂ inclusions were used for the evaluation of the P–T conditions of rock generation. The following parameters were obtained: tephrite: P = 6.3–7.7 kbar and T = 1,150–1,250°C; basanite: P = 6.6–9.2 kbar and T = 1,150–1,250°C; olivine and analcime-olivine nephelinite: P = 5.6–8.2 kbar and T = 1,150–1,250°C; melilite-olivine nephelinite: 4.0–5.4 kbar and T mainly between 1,150 and 1,200°C. Magma genesis was restricted to P–T conditions of spinel- and plagioclase-lherzolite fields. These data suggest the shallowest depth of magma genesis occurred in Makhtesh Ramon compared to other occurrences of Early Cretaceous magmatism at the Middle East. Differences in the degree of batch partial melting of the same source rocks best explain the diversity of the igneous suite in western Makhtesh Ramon.     

Stability of sapphirine-bearing mineral assemblages in the system FeO-MgO-Al2O3-SiO2 and metamorphic P-T parameters of aluminous granulites

Consistent thermodynamic data on the properties of pure mineral end members and the mixing properties of solid solutions in the system FeO-MgO-Al₂O₃-SiO₂ were employed to simulate phase relations of sapphirine, garnet, spinel, orthopyroxene, cordierite, quartz, Al silicates, and corundum. Compositional variations of the solid solutions with temperature notably modify the topology of the P-T diagrams, which differ from the petrogenetic grids widely used in the literature. It is worth noting that the evaluation of P-T metamorphic conditions based on reaction relations in sapphirine-bearing assemblages cannot be so far considered reliable enough. The lower stability limit of the sapphirine + quartz assemblage in the system in question is possibly located at much lower P-T parameters: at least 835°C and ∼6 kbar. The sapphirine + kyanite assemblage can be stable at temperatures below 860°C and a pressure of ∼11 kbar, and the stability field of the sapphirine + olivine assemblage is narrow and constrained to temperatures no higher than ∼800°C.     

The behavior of apatite during crustal anatexis: Equilibrium and kinetic considerations

The solubility and dissolution kinetics of apatite in felsic melts at 850°–1500°C have been examined experimentally by allowing apatite crystals to partially dissolve into apatite-undersaturated melts containing 0–10 wt% water. Analysis of P and Ca gradients in the crystal/melt interfacial region enables determination of both the diffusivities and the saturation levels of these components in the melt. Phosphorus diffusion was identified as the rate-limiting factor in apatite dissolution. Results of four experiments at 8 kbar run in the virtual absence of water yield an activation energy (E) for P diffusion of 143.6 ± 2.8 kcal-mol^?1 and frequency factor (D₀) of 2.23^+2.88_?1.26 × 10⁹cm²-sec^?1. The addition of water causes dramatic and systematic reduction of both E and D₀ such that at 6 wt% H₂O the values are ~25 kcal-mol^?1 and 10^?5 cm²-sec^?1, respectively. At 1300°C, the diffusivity of P increases by a factor of 50 over the first 2% of water added to the melt, but rises by a factor of only two between 2 and 6%, perhaps reflecting the effect of a concentration-dependent mechanism of H₂O solution. Calcium diffusion gradients do not conform well to simple diffusion theory because the release of calcium at the dissolving crystal surface is linked to the transport rate of phosphorus in the melt, which is typically two orders of magnitude slower than Ca. Calcium chemical diffusion rates calculated from the observed gradients are about 50 times slower than calcium tracer diffusion.Apatite solubilities obtained from these experiments, together with previous results, can be described as a function of absolute temperature (T) and melt composition by the expression: In D^apatite/melt_P = [(8400 + ((SiO₂ ? 0.5)2.64 × 10⁴))/T] ? [3.1 + (12.4(SiO₂ ? 0.5))] where SiO₂ is the weight fraction of silica in the melt. This model appears to be valid between 45% and 75% SiO₂, 0 and 10% water, and for the range of pressures expected in the crust.The diffusivity information extracted from the experiments can be directly applied to several problems of geochemical interest, including I) dissolution times for apatite during crustal anatexis, and 2) pileup of P, and consequent local saturation in apatite, at the surfaces of growing major-mineral phases.     

Lithospheric flexural modelling of the seaward and trenchward of the subducting oceanic plates

ABSTRACT

Based on a two-segment plate flexural modelling, we investigated the effective elastic thickness of global subducting oceanic lithosphere. Our results show that for the plate age of 0 to 50 Ma, the seaward effective elastic thickness T _e ^M values are located between 600 and 900°C isotherms, and do not track any isotherm, while the majority of the trenchward effective elastic thickness T _e ^m values are located between 300 and 600°C isotherms. For the plate age older than 50 Ma, T _e ^M values basically matches the 600°C isotherm with some fluctuations for the age older than 110 Ma, while T _e ^m values mainly fall between 200 and 400°C isotherms. The reduction in effective elastic thickness (T _e ^M-T _e ^m) varies from 2.6 to 30.1 km, or 11–68% of seaward T _e ^M. Thus, the absolute value of the decrease in the effective elastic thicknesses (T _e ^M-T _e ^m) increases with the plate age, while the percentage reduction in the effective elastic thickness (1-T _e ^m/T _e ^M) has no obvious relationship with the age, but more related to the curvature of bending plate. Almost all bending-related earthquakes occurred above the T _e ^M line, but many normal-faulting earthquakes are deeper than the T _e ^M-T _e ^m line, implying that the plate may still retain some thickness of an elastic property core in the areas (depth) where earthquakes occur.     

Estimating Influence of Crystallizing Latent Heat on Cooling-Crystallizing Process of a Granitic Melt and Its Geological Implications

Based on the theory of thermal conductivity, in this paper we derived a formula to estimate the prolongation period （AtL） of cooling-crystallization process of a granitic melt caused by latent heat of crystallization as follows：△tL=QL×△tcol/（TM-TC）×CP where TM is initial temperature of the granite melt, Tc crystallization temperature of the granite melt, Cp specific heat, △tcol cooling period of a granite melt from its initial temperature （TM） to its crystallization temperature （Tc）, QL latent heat of the granite melt.
The cooling period of the melt for the Fanshan granodiorite from its initial temperature （900℃） to crystallization temperature （600℃） could be estimated -210,000 years if latent heat was not considered. Calculation for the Fanshan melt using the above formula yields a AtL value of -190,000 years, which implies that the actual cooling period within the temperature range of 900°-600℃ should be 400,000 years. This demonstrates that the latent heat produced from crystallization of the granitic melt is a key factor influencing the cooling-crystallization process of a granitic melt, prolongating the period of crystallization and resulting in the large emplacement-crystallization time difference （ECTD） in granite batholith.     

Experimental investigation of zoisite–clinozoisite phase equilibria in the system CaO–Fe2O3–Al2O3–SiO2–H2O

The system Ca₂Al₃Si₃O₁₁(O/OH)-Ca₂Al₂FeSi₃O₁₁(O/OH), with emphasis on the Al-rich portion, was investigated by synthesis experiments at 0.5 and 2.0 GPa, 500-800 °C, using the technique of producing overgrowths on natural seed crystals. Electron microprobe analyses of overgrowths up to >100 µm wide have located the phase transition from clinozoisite to zoisite as a function of P-T-X_ps and a miscibility gap in the clinozoisite solid solution. The experiments confirm a narrow, steep zoisite-clinozoisite two-phase loop in T-X_ps section. Maximum and minimum iron contents in coexisting zoisite and clinozoisite are given by X_ps^zo (max) = 1.9*10 ^{- 4} T+ 3.1*10 ^{- 2} P - 5.36*10 ^{- 2}{\rm X}_{{\rm ps}}^{{\rm zo}} {\rm (max) = 1}{\rm .9*10}^{ - 4} T{\rm + 3}{\rm .1*10}^{ - 2} P - {\rm 5}{\rm .36*10}^{ - 2} and X_ps^czo (min) = (4.6 * 10 ^{- 4} - 4 * 10 ^{- 5} P)T + 3.82 * 10 ^{- 2} P - 8.76 * 10 ^{- 2}{\rm X}_{{\rm ps}}^{{\rm czo}} {\rm (min)} = {\rm (4}{\rm .6} * {\rm 10}^{ - {\rm 4}} - 4 * {\rm 10}^{ - {\rm 5}} P{\rm )}T + {\rm 3}{\rm .82} * {\rm 10}^{ - {\rm 2}} P - {\rm 8}{\rm .76} * {\rm 10}^{ - {\rm 2}} (P in GPa, T in °C). The iron-free end member reaction clinozoisite = zoisite has equilibrium temperatures of 185ᇆ °C at 0.5 GPa and 0ᇆ °C at 2.0 GPa, with (H_r⁰=2.8ǃ.3 kJ/mol and (S_r⁰=4.5ǃ.4 J/mol2K. At 0.5 GPa, two clinozoisite modifications exist, which have compositions of clinozoisite I ~0.15 to 0.25 X_ps and clinozoisite II >0.55 X_ps. The upper thermal stability of clinozoisite I at 0.5 GPa lies slightly above 600 °C, whereas Fe-rich clinozoisite II is stable at 650 °C. The schematic phase relations between epidote minerals, grossular-andradite solid solutions and other phases in the system CaO-Al₂O₃-Fe₂O₃-SiO₂-H₂O are shown.     

Thermal equations of state of dioctahedral micas on the join muscovite–paragonite

 Powder diffraction measurements at simultaneous high pressure and temperature on samples of 2M1 polytype of muscovite (Ms) and paragonite (Pg) were performed at the beamline ID30 of ESRF (Grenoble), using the Paris-Edinburgh cell. The bulk moduli of Ms, calculated from the least-squares fitting of V–P data on each isotherm using a second-order Birch–Murnaghan EoS, were: 57.0(6), 55.1(7), 51.1(7) and 48.9(5) GPa on the isotherms at 298, 573, 723 and 873 K, respectively. The value of (∂K _T /∂T) was −0.0146(2) GPa K⁻¹. The thermal expansion coefficient α varied from 35.7(3) × 10⁻⁶ K⁻¹ at P ambient to 20.1(3) × 10⁻⁶ K⁻¹ at P = 4 GPa [(∂α/∂P) _T = −3.9(1) × 10⁻⁶ GPa⁻¹ K⁻¹]. The corresponding values for Pg on the isotherms at 298, 723 and 823 K were: bulk moduli 59.9(5), 55.7(6) and 53.8(7) GPa, (∂K _T /∂T) −0.0109(1) GPa K⁻¹. The thermal expansion coefficient α varied from 44.1(2) × 10⁻⁶ K⁻¹ at P ambient to 32.5(2) × 10⁻⁶ K⁻¹ at P = 4 GPa [(∂α/∂P) _T = −2.9(1) × 10⁻⁶ GPa⁻¹ K⁻¹]. Thermoelastic coefficients showed that Pg is stiffer than Ms; Ms softens more rapidly than Pg upon heating; thermal expansion is greater and its variation with pressure is smaller in Pg than in Ms. Received: 28 January 2002 / Accepted: 5 April 2002     

Transport properties of low-sanidine single-crystals, glasses and melts at high temperature

Thermal diffusivity (D) was measured using laser-flash analysis from oriented single-crystal low-sanidine (K_0.92Na_0.08Al_0.99Fe³⁺ _0.005Si_2.95O₈), and three glasses near KAlSi₃O₈. Viscosity measurements of the three supercooled liquids, in the range 10^6.8 to 10^12.3 Pa s, confirm near-Arrhenian behavior, varying subtly with composition. For crystal and glass, D decreases with T, approaching a constant near 1,000 K: D _sat ∼ 0.65 ± 0.3 mm² s⁻¹ for bulk crystal and ∼0.53 ± 0.03 mm² s⁻¹ for the glass. A rapid decrease near 1,400 K is consistent with crossing the glass transition. Melt behavior is approximated by D = 0.475 ± 0.01 mm² s⁻¹. Thermal conductivity (k _lat) of glass, calculated using previous heat capacity (C _P) and new density data, increases with T because C _P strongly increases with T. For melt, k _lat reaches a plateau near 1.45 W m⁻¹ K⁻¹, and is always below k _lat of the crystal. Melting of potassium feldspars impedes heat transport, providing positive thermal feedback that may promote further melting in continental crust.     

The effect of halogens on Zr diffusion and zircon dissolution in hydrous metaluminous granitic melts

Diffusion of Zr and zircon solubility in hydrous, containing approximately 4.5 wt% H₂O, metaluminous granitic melts with halogens, either 0.35 wt% Cl (LCl) or 1.2 wt% F (MRF), and in a halogen-free melt (LCO) were measured at 1.0 GPa and temperatures between 1,050 and 1,400 °C in a piston-cylinder apparatus using the zircon dissolution technique. Arrhenius equations for Zr diffusion in each hydrous melt composition are, for LCO with 4.4ǂ.4 wt% H₂O: % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacqWGebarcqGH9aqpcq % aIYaGmcqGGUaGlcqaI4aaocqaI4aaocqGHXcqScqaIWaamcqGGUaGl % cqaIWaamcqaIZaWmcqWG4baEcqaIXaqmcqaIWaamdaahaaWcbeqaai % abgkHiTiabiIda4aaakiGbcwgaLjabcIha4jabcchaWnaabmaabaWa % aSaaaeaacqGHsislcqaIXaqmcqaI0aancqaIWaamcqGGUaGlcqaIXa % qmcqGHXcqScqaIZaWmcqaIZaWmcqGGUaGlcqaI5aqoaeaacqWGsbGu % cqWGubavaaaacaGLOaGaayzkaaaaaa!571F! D = 2.88 ±0.03x10 ^{- 8} exp( [( - 140.1 ±33.9)/(RT)] )D = 2.88 \pm 0.03x10^{ - 8} \exp \left( {{{ - 140.1 \pm 33.9} \over {RT}}} \right) , for LCl with 4.5ǂ.5 wt% H₂O: % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacqWGebarcqGH9aqpcq % aIYaGmcqGGUaGlcqaIZaWmcqaIZaWmcqGHXcqScqaIWaamcqGGUaGl % cqaIWaamcqaI1aqncqWG4baEcqaIXaqmcqaIWaamdaahaaWcbeqaai % abgkHiTiabisda0aaakiGbcwgaLjabcIha4jabcchaWnaabmaabaWa % aSaaaeaacqGHsislcqaIYaGmcqaI1aqncqaI0aancqGGUaGlcqaI4a % aocqGHXcqScqaI2aGncqaI0aancqGGUaGlcqaIXaqmaeaacqWGsbGu % cqWGubavaaaacaGLOaGaayzkaaaaaa!5719! D = 2.33 ±0.05x10 ^{- 4} exp( [( - 254.8 ±64.1)/(RT)] )D = 2.33 \pm 0.05x10^{ - 4} \exp \left( {{{ - 254.8 \pm 64.1} \over {RT}}} \right) and for MRF with 4.9ǂ.3 wt% H₂O: % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacqWGebarcqGH9aqpcq % aIYaGmcqGGUaGlcqaI1aqncqaI0aancqGHXcqScqaIWaamcqGGUaGl % cqaIWaamcqaIZaWmcqWG4baEcqaIXaqmcqaIWaamdaahaaWcbeqaai % abgkHiTiabiwda1aaakiGbcwgaLjabcIha4jabcchaWnaabmaabaWa % aSaaaeaacqGHsislcqaIYaGmcqaIYaGmcqaIZaWmcqGGUaGlcqaI4a % aocqGHXcqScqaIXaqmcqaI1aqncqGGUaGlcqaI1aqnaeaacqWGsbGu % cqWGubavaaaacaGLOaGaayzkaaaaaa!5715! D = 2.54 ±0.03x10 ^{- 5} exp( [( - 223.8 ±15.5)/(RT)] )D = 2.54 \pm 0.03x10^{ - 5} \exp \left( {{{ - 223.8 \pm 15.5} \over {RT}}} \right) . Solubilities determined by the dissolution technique were reversed for LCO +4.5ǂ.5 wt% H₂O by crystallization of a Zr-enriched glass of LCO composition at 1,200 and 1,050 °C at 1.0 GPa. The solubility data were used to calculate partition coefficients of Zr between zircon and hydrous melt, which are given by the following expressions: for LCO % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacyGGSbaBcqGGUbGBcq % WGebardaqhaaWcbaGaemOwaOLaemOCaihabaGaemOEaONaemyAaKMa % emOCaiNaem4yamMaem4Ba8MaemOBa4Maei4la8IaemyBa0Maemyzau % MaemiBaWMaemiDaqhaaOGaeyypa0JaeGymaeJaeiOla4IaeGOnayJa % eG4mamZaaeWaaeaadaWcaaqaaiabigdaXiabicdaWiabicdaWiabic % daWiabicdaWaqaaiabdsfaubaaaiaawIcacaGLPaaacqGHsislcqaI % 1aqncqGGUaGlcqaI4aaocqaI3aWnaaa!5924! lnD_Zr^zircon/melt = 1.63( [10000/(T)] ) - 5.87\ln D_{Zr}^{zircon/melt} = 1.63\left( {{{10000} \over T}} \right) - 5.87 , for LCl % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacyGGSbaBcqGGUbGBcq % WGebardaqhaaWcbaGaemOwaOLaemOCaihabaGaemOEaONaemyAaKMa % emOCaiNaem4yamMaem4Ba8MaemOBa4Maei4la8IaemyBa0Maemyzau % MaemiBaWMaemiDaqhaaOGaeyypa0JaeGymaeJaeiOla4IaeGinaqJa % eG4naCZaaeWaaeaadaWcaaqaaiabigdaXiabicdaWiabicdaWiabic % daWiabicdaWaqaaiabdsfaubaaaiaawIcacaGLPaaacqGHsislcqaI % 0aancqGGUaGlcqaI3aWncqaI1aqnaaa!5920! lnD_Zr^zircon/melt = 1.47( [10000/(T)] ) - 4.75\ln D_{Zr}^{zircon/melt} = 1.47\left( {{{10000} \over T}} \right) - 4.75 and, for MRF by % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavP1wzZbItLDhis9wBH5garm % Wu51MyVXgaruWqVvNCPvMCG4uz3bqee0evGueE0jxyaibaieYlf9ir % Veeu0dXdh9vqqj-hEeeu0xXdbba9ev6pc9fs0-rqaqpepmKs4qpepe % I8kaL8kuc9pgc9q8qqaq-dhH6hb9hs0dXdHu6deP0u0-vr0-vr0db8 % meaabaqaciGacaGaaeaabaWaaeaaeaaakeaacyGGSbaBcqGGUbGBcq % WGebardaqhaaWcbaGaemOwaOLaemOCaihabaGaemOEaONaemyAaKMa % emOCaiNaem4yamMaem4Ba8MaemOBa4Maei4la8IaemyBa0Maemyzau % MaemiBaWMaemiDaqhaaOGaeyypa0JaeGymaeJaeiOla4IaeGinaqJa % eG4naCZaaeWaaeaadaWcaaqaaiabigdaXiabicdaWiabicdaWiabic % daWiabicdaWaqaaiabdsfaubaaaiaawIcacaGLPaaacqGHsislcqaI % 0aancqGGUaGlcqaI5aqocqaIXaqmaaa!591C! lnD_Zr^zircon/melt = 1.47( [10000/(T)] ) - 4.91\ln D_{Zr}^{zircon/melt} = 1.47\left( {{{10000} \over T}} \right) - 4.91 . Experiments on the same compositions, but with water contents down to 0.5 wt%, demonstrated reductions in both the diffusion coefficient of Zr and zircon solubility in the melt. The addition of halogens at the concentration levels studied to metaluminous melts has a small effect on either the diffusion of Zr in the melt, or the solubility of zircon at all water concentrations and temperatures investigated. At 800 °C, the calculated diffusion coefficient of Zr is lowest in LCl, 9᎒^-17 m² s^-1, and is highest in LCO, 4᎒^-15 m² s^-1. Extrapolation of the halogen-free solubility data to a magmatic temperature of 800 °C yields solubilities of approximately one-third of those directly measured in similar compositions, predicted by earlier studies of zircon dissolution and based upon analyses of natural rocks. This discrepancy is attributed to the higher oxygen fugacity of the experiments of this study compared with previous studies and nature, and the effect of oxygen fugacity on the structural role of iron in the melt, which, in turn, affects zircon solubility, but does not significantly affect Zr diffusion.     

In search of the mixed derivative ?2 M /? P ? T ( M = G , K ): joint analysis of ultrasonic data for polycrystalline pyrope from gas- and solid-medium apparatus

Elastic wave velocities for dense (99.8% of theoretical density) isotropic polycrystalline specimens of synthetic pyrope (Mg₃Al₂Si₃O₁₂) were measured to 1,000 K at 300 MPa by the phase comparison method of ultrasonic interferometry in an internally heated gas-medium apparatus. The temperature derivatives of the elastic moduli [(∂Ks/∂T) _P = −19.3(4); (∂G/∂T) _P = −10.4(2) MPa K⁻¹] measured in this study are consistent with previous acoustic measurements on both synthetic polycrystalline pyrope in a DIA-type cubic anvil apparatus (Gwanmesia et al. in Phys Earth Planet Inter 155:179–190, 2006) and on a natural single crystal by the rectangular parallelepiped resonance (RPR; Suzuki and Anderson in J Phys Earth 31:125–138, 1983) method but |(∂Ks/∂T) _P | is significantly larger than from a Brillouin spectroscopy study of single-crystal pyrope (Sinogeikin and Bass in Phys Earth Planet Inter 203:549–555, 2002). Alternative approaches to the retrieval of mixed derivatives of the elastic moduli from joint analysis of data from this study and from the solid-medium data of Gwanmesia et al. in Phys Earth Planet Inter 155:179–190 (2006) yield ∂² G/∂P∂T = [0.07(12), 0.20(14)] × 10⁻³ K⁻¹ and ∂² K _S /∂P∂T = [−0.20(24), 0.22(26)] × 10⁻³ K⁻¹, both of order 10⁻⁴ K⁻¹ and not significantly different from zero. More robust inference of the mixed derivatives will require solid-medium acoustic measurements of precision significantly better than 1%.     

Heat capacity of wadeite-type K2Si4O9 and the pressure-induced stable decomposition of K-feldspar

The heat capacity of synthetic, stoichiometric wadeite-type K₂Si₄O₉ has been measured by DSC in the 195≤T(K)≤598 range. Near the upper temperature limit of our data, the heat capacity observed by DSC agrees with that reported by Geisinger et al. (1987) based on a vibrational model of their infrared and Raman spectroscopic data. However, with decreasing temperature, the Cp observed by DSC is progressively higher than that predicted from the vibrational model, suggesting that the standard entropy of K₂Si₄O₉ is likely to be larger than 198.9 ± 4.0 J/K · mol computed from the spectroscopic data. A fit to the DSC data gave: Cp(T) = 499.13 (±1.87) − 4.35014 · 10³(±3.489 · 10¹) · T ^−0.5, with T in K and average absolute percent deviation of 0.37%. The room-temperature compressibilities of kalsilite and leucite, hitherto unknown, have been measured as well. The data, fitted to the Murnaghan equation of state, gave K _o = 58.6 GPa, K _o ^′ = 0.1 for kalsilite and K _o = 45 GPa, K _o ^′ = 5.7 for α-leucite. Apart from the above mentioned data on the properties of the individual phases, we have also obtained reaction-reversals on four equilibria in the system K₂O-Al₂O₃-SiO₂. The Bayesian method has been used simultaneously to process the properties of 13 phases and 15 reactions between them to derive an internally consistent thermodynamic dataset for the K₂O-Al₂O₃-SiO₂ ternary. The enthalpy of formation of K₂Si₄O₉ wadeite is in perfect agreement with its revised calorimetric value, the standard entropy is 232.1 ± 10.4 J/K · mol, ∼15% higher than that implied by vibrational modeling. The phase diagram, generated from our internally consistent thermodynamic dataset, shows that for all probable P-T trajectories in the subduction regime, the stable pressure-induced decomposition of K-feldspar will produce coesite + kalsilite rather than coesite + kyanite + K₂Si₄O₉ (cf. Urakawa et al. 1994). Received: 11 June 1997 / Accepted: 2 December 1997     

Osumilite–melt interactions in ultrahigh temperature granulites: phase equilibria modelling and implications for the P–T–t evolution of the Eastern Ghats Province,India

The exposed residual crust in the Eastern Ghats Province records ultrahigh temperature (UHT) metamorphic conditions involving extensive crustal anatexis and melt loss. However, there is disagreement about the tectonic evolution of this late Mesoproterozoic–early Neoproterozoic orogen due to conflicting petrological, structural and geochronological interpretations. One of the petrological disputes in residual high Mg–Al granulites concerns the origin of fine‐grained mineral intergrowths comprising cordierite + K‐feldspar ± quartz ± biotite ± sillimanite ± plagioclase. These intergrowths wrap around porphyroblast phases and are interpreted to have formed by the breakdown of primary osumilite in the presence of melt trapped in the equilibration volume by the melt percolation threshold. The pressure (P)–temperature (T) evolution of four samples from three localities across the central Eastern Ghats Province is constrained using phase equilibria modelling in the chemical system Na₂O–CaO–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O–TiO₂–Fe₂O₃ (NCKFMASHTO). Results of the modelling are integrated with published geochronological results for these samples to show that the central Eastern Ghats Province followed a common P–T–t history. This history is characterized by peak UHT metamorphic conditions of 945–955 °C and 7.8–8.2 kbar followed by a slight increase in pressure and close‐to‐isobaric cooling to the conditions of the elevated solidus at 940–900 °C and 8.5–8.3 kbar. In common with other localities from the Eastern Ghats Province, the early development of cordierite before osumilite and the peak to immediate post‐peak retrograde reaction between osumilite and melt to produce the intergrowth features requires that the prograde evolution was one of contemporaneous increasing pressure with increasing temperature. This counter‐clockwise (CCW) evolution is evaluated for one sample using inverse phase equilibria modelling along a schematic P–T path of 150 °C kbar^?1 starting from the low P–T end of the prograde P–T path as constrained by the phase equilibria modelling. The inverse modelling is executed by step‐wise down temperature reintegration of sufficient melt into the residual bulk chemical composition at the P–T point of the 1 mol.% melt isopleth at each step, representing the melt remaining on grain boundaries after each prograde drainage event, to reach the melt connectivity transition (MCT) of 7 mol.%. The procedure is repeated until a plausible protolith composition is recovered. The result demonstrates that clastic sedimentary rocks that followed a CCW P–T evolution could have produced the observed mineral assemblages and microstructures preserved in the central Eastern Ghats Province. This study also highlights the role of melt during UHT metamorphism, particularly its importance to both chemical and physical processes along the prograde and retrograde segments of the P–T path. These processes include: (i) an increase in diffusive length scales during the late prograde to peak evolution, creating equilibration volumes larger than a standard thin section; (ii) the development of retrograde mineral assemblages, which is facilitated if some melt is retained post‐peak; (iii) the presence of melt as a weakening mechanism and the advection of heat by melt, allowing the crust to thicken; and (iv) the effect of melt loss, which makes the deep crust both denser and stronger, and reduces heat production at depth, limiting crustal thickening and facilitating the transition to close‐to‐isobaric cooling.     

Fluid influence on mineral reactions in ultrahigh-pressure granulites: a case study in the Śnieżnik Mts. (West Sudetes, Poland)

Small tectonic slices of undeformed eclogites and ultrahigh-pressure granulites occur in three tectonic units of the Śnieżnik Mts. (SW Poland). Ultrahigh-pressure granulite/eclogite transitions with peak metamorphic conditions between 21 and 28 kbar at 800 to 1000 °C occur only in the Złote unit. Conventional U-Pb multigrain analyses of zircons from a mafic granulite provided ²⁰⁷Pb/²⁰⁶Pb ages between 360 to 369 Ma which are interpreted to approximate timing of original crystallisation from a melt. Diffusion kinetics and the restricted availability of a fluid phase mainly controlled the conversion from granulite to eclogite, although some bulk-chemical differences were also recognised. The ultrahigh-pressure granulites from the Złote unit exclusively contain H₂O-rich inclusions with variable salinities which distinguishes them from high-temperature (HT)-granulites world-wide. This is also in contrast to the fluid regime (H₂O-N₂-CO₂) recognised in the lower-temperature eclogites (600–800 °C) from the closely associated Międzygórze and Śnieżnik units. The variation in fluid composition between the lower-temperature eclogites and ultrahigh-pressure granulites on the one hand and ultrahigh-pressure granulites and HT-granulites on the other hand probably indicates contrasting P-T-t paths as a result of different tectonic environments. Received: 15 June 1998 / Accepted: 2 March 1999     

Phase equilibria modelling of kyanite‐bearing anatectic paragneisses from the central Grenville Province

Kyanite‐bearing paragneisses from the Manicouagan Imbricate Zone and its footwall (high‐P belt of the central Grenville Province) preserve evidence of partial melting with development of metamorphic textures involving biotite–garnet ± kyanite ± plagioclase ± K‐feldspar–quartz. Garnet in these rocks displays a variety of zoning patterns with respect to Ca. Pseudosection modelling in the Na₂O–CaO–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O–TiO₂–O (NCKFMASHTO) system using measured bulk rock compositions accounts for the textural evolution of two aluminous and two sub‐aluminous samples from the presumed thermal peak to conditions at which retained melt solidified. The prograde features are best explained by pseudosections calculated with compositions to account for melt loss. The intersection of isopleths of grossular content and Fe/(Fe + Mg) relating to large porphyroblasts of garnet provide constraints on the P–T conditions of the metamorphic peak. These P–T estimates are considered to be minima because of the potential for diffusional modification of the composition of garnet at high‐T and during the early stages of cooling. However, they are consistent with textural observations and pseudosection topology, with peak assemblages best preserved in rocks for which the calculated pseudosections predict only small changes in mineral proportions in the P–T interval, in which retrograde reactions are inferred to have occurred between the thermal peak and the solidus. Maximum P–T conditions (14.5–15.5 kbar and 840–890 °C) and steep retrograde P–T paths inferred for rocks from the Manicouagan Imbricate Zone are comparable with those determined for mafic rocks from the same area. In contrast, maximum P–T conditions of 12.5–13 kbar and 815–830 °C and flatter P–T paths are inferred for the rocks of the footwall to the Manicouagan Imbricate Zone. The general consistency between textures, mineral compositions and the topologies of the calculated pseudosections suggests that the pseudosection approach is an appropriate tool for inferring the P–T evolution of high‐P anatectic quartzo‐feldspathic rocks.     

Thermal diffusivity of garnets at high temperature

Thermal diffusivity (D) of garnets with diverse chemical compositions was measured using the laser-flash technique, which is accurate (±2%) and isolates the lattice component from direct radiative transfer. Temperatures ranged from ~290 to ~1,600 K (unless limited by melting). Seven synthetic (e.g., YAG, GGG) and 15 natural garnets with two types of ionic substitution [Ca₃(Fe,Al)₂Si₃O₁₂ and (Mg,Fe,Ca)₃Al₂Si₃O₁₂] and varying amounts of OH^- were examined. Cation substitution or hydroxyl incorporation lowers D from end-member values. Thermal diffusivity is constant once the temperature (T) exceeds a critical value (T _sat) of ~1,100 to 1,500 K. From ~290 K to T _sat, the measurements are best represented by 1/D=A+BT+CT ² where A, B, and C are constants. These constants vary little among diverse chemical compositions, suggesting that the oxygen sublattice controls heat transport. Higher order terms are needed only when T _sat is low, such as Ant Hill garnet wherein 1/D=0.049403+0.0032299T−2.3992T ²×10⁻⁶+6.0168T ³×10⁻¹⁰(1/D in s/mm²; T in K). The mean free path (λ, computed from D and sound velocities) is slightly larger than the lattice parameter above T _sat, in accord with phonon–phonon interactions requiring non-localized modes. At most temperatures, λ is nm-sized. Large values of λ are obtained by extrapolation to a few Kelvins, suggesting that boundary scattering can only be important at extremely cold temperatures. The observed behavior with T and chemical composition is consistent with the damped harmonic oscillator model. Phonon transport is best represented by inverse thermal diffusivity wherein 1/D goes as T ⁿ where n is between 1 and 3 up to ~200 K, depends on a quadratic or cubic polynomial at moderate T, but is constant above T _sat. The predicted and observed temperature response of 1/D mimics the well-known form for heat capacity, in that acoustic modes control heat transport near cryogenic temperatures, optic phonons dominate above ambient temperature, and a limit analogous to that of Dulong and Petit is reached at very high temperature, due to full population of discrete phonon states.     

Inference of a detailed P–T path from P–T pseudosections using metapelitic rocks of variable composition from a single outcrop, Shackleton Range, Antarctica

Generally, P–T pseudosections for reduced compositional systems, such as K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O, Na₂O–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O and MnO–K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O, are well suited for inferring detailed P–T paths, comparing mineral assemblages observed in natural rocks with those calculated. Examples are provided by P–T paths inferred for four metapelitic samples from a 1 m² wide outcrop of the Herbert Mountains in the Shackleton Range, Antarctica. The method works well if the bulk composition used is reconstituted from average mineral modes and mineral compositions (AMC) or when X‐ray fluorescence (XRF) data are corrected for Al₂O₃ and FeO. A plagioclase correction is suitable for Al₂O₃. Correction for FeO is dependent on additional microscopic observations, e.g. the kind and amount of opaque minerals. In some cases, all iron can be treated as FeO^tot, whereas in others a magnetite or hematite correction yields much better results. Comparison between calculated and observed mineral modes and mineral compositions shows that the AMC bulk composition is best suited to the interpretation of rock textures using P–T pseudosections, whereas corrected XRF data yield good results only when the investigated sample has few opaque minerals. The results indicate that metapelitic rocks from the Herbert Mountains of the Northern Shackleton Range underwent a prograde P–T evolution from about 600 °C/5.5 kbar to 660 °C/7 kbar, followed by nearly adiabatic cooling to about 600 °C at 4.5 kbar.