Ferric iron partitioning between plagioclase and silicate liquid: thermodynamics and petrological applications

A series of Fe and Mg partition experiments between plagioclase and silicate liquid were performed in the system SiO₂-Al₂O₃-Fe₂O₃-FeO-MgO-CaO-Na₂O under oxygen fugacities from below the IW buffer up to that of air. A thermodynamic model of plagioclase solid solution for the (CaAl,NaSi,KSi)(Fe³⁺,Al³⁺)Si₂O₈-Ca(Fe²⁺,Mg)Si₃O₈ system is proposed and is calibrated by regression analysis based on new and previously reported experimental data of Fe and Mg partitioning between plagioclase and silicate liquid, and reported thermodynamic properties of end members, ternary feldspar and silicate liquid. Using the derived thermodynamic model, FeO^t, MgO content and Mg/(Fe^t+Mg) in plagioclase can be predicted from liquid composition with standard deviations of ǂ.34 wt% (relative error =9%) and ǂ.08 wt% (14%) and ǂ.7 (8%) respectively. Calculated Fe³⁺-Al exchange chemical potentials of plagioclase, m_{Fe^{3 +} ( Al )- 1} ^Pl{\rm \mu }_{{\rm Fe}^{{\rm 3 + }} \left( {{\rm Al}} \right)_{{\rm - 1}} }^{{\rm Pl}} agree with those calculated using reported thermodynamic models for multicomponent spinel, m_{Fe^{3 +} ( Al )- 1} ^Sp{\rm \mu }_{{\rm Fe}^{{\rm 3 + }} \left( {{\rm Al}} \right)_{{\rm - 1}} }^{{\rm Sp}} and clinopyroxene, m_{Fe^{3 +} ( Al )- 1} ^Cpx{\rm \mu }_{{\rm Fe}^{{\rm 3 + }} \left( {{\rm Al}} \right)_{{\rm - 1}} }^{{\rm Cpx}} . The FeO^t content of plagioclase coexisting with spinel or clinopyroxene is affected by Fe³⁺/(Fe³⁺+Al) and Mg/(Fe+Mg) of spinel or clinopyroxene and temperature, while it is independent of the anorthite content of plagioclase. Three oxygen barometers based on the proposed model are investigated. Although the oxygen fugacities predicted by the plagioclase-liquid oxygen barometer are scattered, this study found that plagioclase-spinel-clinopyroxene-oxygen and plagioclase-olivine-oxygen equilibria can be used as practical oxygen barometers. As a petrological application, prediction of plagioclase composition and f_O2 are carried out for the Upper Zone of the Skaergaard intrusion. The estimated oxygen fugacities are well below QFM buffer and consistent with the estimation of oxidization states in previous studies.     

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.     

Rare earth element diffusion in a natural pyrope single crystal at 2.8 GPa

Volume diffusion rates of Ce, Sm, Dy, and Yb have been measured in a natural pyrope-rich garnet single crystal (Py₇₁Alm₁₆Gr₁₃) at a pressure of 2.8 GPa and temperatures of 1,200-1,450 °C. Pieces of a single gem-quality pyrope megacryst were polished, coated with a thin layer of polycrystalline REE oxide, then annealed in a piston cylinder device for times between 2.6 and 90 h. Diffusion profiles in the annealed samples were measured by SIMS depth profiling. The dependence of diffusion rates on temperature can be described by the following Arrhenius equations (diffusion coefficients in m²/s): % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbfv3ySLgzGueE0jxyaibaieYlf9irVeeu0d % Xdh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9 % pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca % qabeaadaabauaaaOqaauaabeqaeeaaaaqaaiGbcYgaSjabc+gaVjab % cEgaNnaaBaaaleaacqaIXaqmcqaIWaamaeqaaOGaemiraq0aaSbaaS % qaaiabbMfazjabbkgaIbqabaGccqGH9aqpcqGGOaakcqGHsislcqaI % 3aWncqGGUaGlcqaI3aWncqaIZaWmcqGHXcqScqaIWaamcqGGUaGlcq % aI5aqocqaI3aWncqGGPaqkcqGHsisldaqadaqaaiabiodaZiabisda % 0iabiodaZiabgglaXkabiodaZiabicdaWiaaysW7cqqGRbWAcqqGkb % GscaaMe8UaeeyBa0Maee4Ba8MaeeiBaW2aaWbaaSqabeaacqqGTaql % cqqGXaqmaaGccqGGVaWlcqaIYaGmcqGGUaGlcqaIZaWmcqaIWaamcq % aIZaWmcqWGsbGucqWGubavaiaawIcacaGLPaaaaeaacyGGSbaBcqGG % VbWBcqGGNbWzdaWgaaWcbaGaeGymaeJaeGimaadabeaakiabdseaen % aaBaaaleaacqqGebarcqqG5bqEaeqaaOGaeyypa0JaeiikaGIaeyOe % I0IaeGyoaKJaeiOla4IaeGimaaJaeGinaqJaeyySaeRaeGimaaJaei % Ola4IaeGyoaKJaeG4naCJaeiykaKIaeyOeI0YaaeWaaeaacqaIZaWm % cqaIWaamcqaIYaGmcqGHXcqScqaIZaWmcqaIWaamcaaMe8Uaee4AaS % MaeeOsaOKaaGjbVlabb2gaTjabb+gaVjabbYgaSnaaCaaaleqabaGa % eeyla0IaeeymaedaaOGaei4la8IaeGOmaiJaeiOla4IaeG4mamJaeG % imaaJaeG4mamJaemOuaiLaemivaqfacaGLOaGaayzkaaaabaGagiiB % aWMaei4Ba8Maei4zaC2aaSbaaSqaaiabigdaXiabicdaWaqabaGccq % WGebardaWgaaWcbaGaee4uamLaeeyBa0gabeaakiabg2da9iabcIca % OiabgkHiTiabiMda5iabc6caUiabikdaYiabigdaXiabgglaXkabic % daWiabc6caUiabiMda5iabiEda3iabcMcaPiabgkHiTmaabmaabaGa % eG4mamJaeGimaaJaeGimaaJaeyySaeRaeG4mamJaeGimaaJaaGjbVl % abbUgaRjabbQeakjaaysW7cqqGTbqBcqqGVbWBcqqGSbaBdaahaaWc % beqaaiabb2caTiabbgdaXaaakiabc+caViabikdaYiabc6caUiabio % daZiabicdaWiabiodaZiabdkfasjabdsfaubGaayjkaiaawMcaaaqa % aiGbcYgaSjabc+gaVjabcEgaNnaaBaaaleaacqaIXaqmcqaIWaamae % qaaOGaemiraq0aaSbaaSqaaiabboeadjabbwgaLbqabaGccqGH9aqp % cqGGOaakcqGHsislcqaI5aqocqGGUaGlcqaI3aWncqaI0aancqGHXc % qScqaIYaGmcqGGUaGlcqaI4aaocqaI0aancqGGPaqkcqGHsisldaqa % daqaaiabikdaYiabiIda4iabisda0iabgglaXkabiMda5iabigdaXi % aaysW7cqqGRbWAcqqGkbGscaaMe8UaeeyBa0Maee4Ba8MaeeiBaW2a % aWbaaSqabeaacqqGTaqlcqqGXaqmaaGccqGGVaWlcqaIYaGmcqGGUa % GlcqaIZaWmcqaIWaamcqaIZaWmcqWGsbGucqWGubavaiaawIcacaGL % Paaaaaaaaa!0C76!

The effect of H<Subscript>2</Subscript>O on the olivine liquidus of basaltic melts: experiments and thermodynamic models

We designed and carried out experiments to investigate the effect of H₂O on the liquidus temperature of olivine-saturated primitive melts. The effect of H₂O was isolated from other influences by experimentally determining the liquidus temperatures of the same melt composition with various amounts of H₂O added. Experimental data indicate that the effect of H₂O does not depend on pressure or melt composition in the basaltic compositional range. The influence of H₂O on melting point lowering can be described as a polynomial function This expression can be used to account for the effect of H₂O on olivine-melt thermometers, and can be incorporated into fractionation models for primitive basalts. The non-linear effect of H₂O indicates that incorporation of H₂O in silicate melts is non-ideal, and involves interaction between H₂O and other melt components. The simple speciation approach that seems to account for the influence of H₂O in simple systems (albite-H₂O, diopside-H₂O) fails to describe the mixing behavior of H₂O in multi-component silicate melts. However, a non-ideal solution model that treats the effect of H₂O addition as a positive excess free energy can be fitted to describe the effect of melting point lowering.     

Practical Estimates of Tensile Strength and Hoek–Brown Strength Parameter m i of Brittle Rocks

By applying the Griffith stress criterion of brittle failure, one can find that the uniaxial compressive strength (σ_c) of rocks is eight times the value of the uniaxial tensile strength (σ_t). The Griffith strength ratio is smaller than what is normally measured for rocks, even with the consideration of crack closure. The reason is that Griffith’s theories address only the initiation of failure. Under tensile conditions, the crack propagation is unstable so that the tensile crack propagation stress (σ_cd)_t and the peak tensile strength σ_t are almost identical to the tensile crack initiation stress (σ_ci)_t. On the other hand, the crack growth after crack initiation is stable under a predominantly compressive condition. Additional loading is required in compression to bring the stress from the crack initiation stress σ_ci to the peak strength σ_c. It is proposed to estimate the tensile strength of strong brittle rocks from the strength ratio of R = \fracs_\textc | s_\textt | = 8\fracs_\textc s_\textci . R = {\frac{{\sigma_{\text{c}} }}{{\left| {\sigma_{\text{t}} } \right|}}} = 8{\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}}. The term \fracs_\textc s_\textci {\frac{{\sigma_{\text{c}} }}{{\sigma_{\text{ci}} }}} accounts for the difference of crack growth or propagation in tension and compression in uniaxial compression tests. \fracs_c s_ci {\frac{{\sigma_{c} }}{{\sigma_{ci} }}} depends on rock heterogeneity and is larger for coarse grained rocks than for fine grained rocks. σ_ci can be obtained from volumetric strain measurement or acoustic emission (AE) monitoring. With the strength ratio R determined, the tensile strength can be indirectly obtained from | s_\textt | = \fracs_\textc R = \fracs_\textci 8. \left| {\sigma_{\text{t}} } \right| = {\frac{{\sigma_{\text{c}} }}{R}} = {\frac{{\sigma_{\text{ci}} }}{8}}. It is found that the predicted tensile strengths using this method are in good agreement with test data. Finally, a practical estimate of the Hoek–Brown strength parameter m _i is presented and a bi-segmental or multi-segmental representation of the Hoek–Brown strength envelope is suggested for some brittle rocks. In this fashion, the rock strength parameters like σ_t and m _i, which require specialty tests such as direct tensile (or Brazilian) and triaxial compression tests for their determination, can be reasonably estimated from uniaxial compression tests.     

Primary fluids entrapped at blueschist to eclogite transition: evidence from the Tianshan meta-subduction complex in northwestern China

Orthopyroxene and olivine exposed along the rim of a harzburgite xenolith from La Palma (Canary Islands) show polycrystalline selvages and diffusion zones that result from contact with mafic, alkaline, silica-undersaturated melts during at least 10-100 years before eruption. The zoned selvages consist of a fine-grained reaction rim towards the xenolith and a coarser grained, cumulate-like layer towards the melt contact. The diffusion zones are characterized by decreasing magnesium number from about 89-91 in the xenolith interior to 79-85 at the rims, and clearly result from Fe-Mg exchange with surrounding mafic melt. The width of the diffusion zones is 80-200 µm in orthopyroxene and 1,020-1,730 µm in olivine. Orthopyroxene also shows decreasing Al₂O₃ and Cr₂O₃ and increasing MnO and TiO₂ towards the reaction rims. Textural relations and comparisons with dissolution experiments suggest that orthopyroxene dissolution by silica-undersaturated melt essentially ceased after days to weeks of melt contact, possibly because of decreasing temperature and formation of the reaction rims. The short dissolution phase was followed by prolonged growth of diffusion zones through cation exchange between xenolith minerals and melt across the reaction rims, and by the growth of cumulus crystals. The observations indicate that orthopyroxene xenocrysts and harzburgite xenoliths can survive in mafic, silica-undersaturated, subliquidus magmas at 1,050-1,200 °C and 200-800 MPa for tens of years. Modeling and comparison of the diffusion zones indicate that the average Fe-Mg interdiffusion coefficient D_FeMg in orthopyroxene is 2 log units lower than that in olivine; at 1,130 °C and QFM-buffered oxygen fugacity, D_FeMg^opx = 3 ×10 ^{- 19}  m²  s^{- 1}D_{FeMg}^{opx} = 3 \times 10^{ - 19} \,{\rm m}^2 \,{\rm s}^{{\rm - 1}} . The new data overlap well with recently published data for D_FeMg in diopside, and indicate that D_FeMg ^opxD_{FeMg\,}^{opx} (as predicted by previous authors) may be extrapolated to higher temperatures and oxygen fugacities. It is suggested that D_FeMg ^opx D_{FeMg\,}^{opx} and D_FeMg in Mn-poor ferromagnesian garnet are similar within 0.5 log units at temperatures between 1,050 and 1,200 °C.     

Thermodynamic properties and stability of AlF-bearing titanite CaTiOSiO4–CaAlFSiO4

Calorimetric and experimental data on AlF-bearing titanite are presented that yield thermodynamic properties of CaAlFSiO₄, as well as activity-composition relations of binary titanite CaTiOSiO₄-CaAlFSiO₄. The heat capacity of synthetic CaAlFSiO₄ was measured with differential scanning calorimetry between 170 and 850 K: C_P=689.96-0.38647T+2911300T^-2-8356.1T^-0.5+0.00016179T² Based on low-temperature heat capacity calculations with lattice vibrational theory (Debye model), the calorimetric entropy of CaAlFSiO₄ can be expected to lie between 104.7 and 118.1 J mol^-1 K^-1. The temperature of the P2₁/a to A2/a phase change was determined calorimetrically for a titanite with X_Al=0.09 (T_transition=390 K). The decrease of the transition temperature at a rate of about 11 K per mol% CaAlFSiO₄ is in good agreement with previous TEM investigations. The displacement of the reaction anorthite + fluorite = CaAlFSiO₄ in the presence of CaTiOSiO₄ was studied with high P-T experiments. Titanite behaves as a non-ideal, symmetrical solid-solution. The thermodynamic properties of CaAlFSiO₄ consistent with a multi-site mixing model are: % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2Daebbnrfi % fHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk % 0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9 % Fve9Ff0dmeaabaqaciaacaGaaeqabaWaaeaaeaaakeaafaqaaiWaca % aabaGaeeyrauKaeeOBa4MaeeiDaqNaeeiAaGMaeeyyaeMaeeiBaWMa % eeiCaaNaeeyEaKNaeeiiaaIaee4Ba8MaeeOzayMaeeiiaaIaeeOzay % Maee4Ba8MaeeOCaiNaeeyBa0MaeeyyaeMaeeiDaqNaeeyAaKMaee4B % a8MaeeOBa4MaeeiiaaIaeeikaGIaeeyzauMaeeiBaWMaeeyzauMaee % yBa0MaeeyzauMaeeOBa4MaeeiDaqNaee4CamNaeeykaKIaeeiiaaIa % emizaq2aaSbaaSqaaiabdAgaMbqabaGccqWGibasdaahaaWcbeqaai % abicdaWaaaaOqaaiabg2da9iabgkHiTiabikdaYiabiEda3iabisda % 0iabicdaWiabc6caUiabiIda4iabgglaXkabiodaZiabc6caUiabic % daWiabbccaGiabbUgaRjabbQeakjabb2gaTjabb+gaVjabbYgaSnaa % CaaaleqabaGaeyOeI0IaeGymaedaaaGcbaGaee4uamLaeeiDaqNaee % yyaeMaeeOBa4MaeeizaqMaeeyyaeMaeeOCaiNaeeizaqMaeeiiaaIa % ee4CamNaeeiDaqNaeeyyaeMaeeiDaqNaeeyzauMaeeiiaaIaeeyzau % MaeeOBa4MaeeiDaqNaeeOCaiNaee4Ba8MaeeiCaaNaeeyEaKNaeeii % aaIaee4uam1aaWbaaSqabeaacqqGWaamaaaakeaacqqG9aqpcqqGXa % qmcqqGWaamcqqG0aancqqGUaGlcqqG5aqocqGHXcqScqqGXaqmcqqG % UaGlcqqGXaqmcqqGGaaicqqGkbGscqqGTbqBcqqGVbWBcqqGSbaBda % ahaaWcbeqaaiabgkHiTiabigdaXaaakiabbUealnaaCaaaleqabaGa % eyOeI0IaeGymaedaaaGcbaGaeeyta0KaeeyyaeMaeeOCaiNaee4zaC % MaeeyDauNaeeiBaWMaeeyzauMaee4CamNaeeiiaaIaeeiCaaNaeeyy % aeMaeeOCaiNaeeyyaeMaeeyBa0MaeeyzauMaeeiDaqNaeeyzauMaee % OCaiNaeeiiaaYaamWaaeaacqWGxbWvdaWgaaWcbaGaemisaG0aaWba % aWqabeaacqGHsislaaaaleqaaOGaeeivaqLaem4vaC1aaSbaaSqaai % abdohaZbqabaaakiaawUfacaGLDbaaaeaacqGH9aqpcqaIXaqmcqaI % ZaWmcqGGUaGlcqaI2aGncqGHXcqScqaIWaamcqGGUaGlcqaI0aanca % aMe8UaeeOsaOKaeeyBa0Maee4Ba8MaeeiBaW2aaWbaaSqabeaacqGH % sislcqaIXaqmaaaaaaaa!E403!

The behaviour of boron in a peraluminous granite-pegmatite system and associated hydrothermal solutions: a melt and fluid-inclusion study

Detailed analyses of melt and fluid inclusions combined with an electron-microprobe survey of boron-bearing minerals reveal the evolution of boron in a highly evolved peraluminous granite-pegmatite complex and the associated high- and medium-temperature ore-forming hydrothermal fluids (Ehrenfriedersdorf, Erzgebirge, Germany). Melt inclusions in granite represent embryonic pegmatite-forming melts containing about 10 wt% H₂O and 1.8 wt% B₂O₃. These melts are also enriched in F, P, and other incompatible elements such as Be, Sn, Rb, and Cs. Ongoing differentiation and volatile enrichment drove the system into a solvus, where two pegmatite-forming melts coexisted. The critical point is at about 712 °C, 100 MPa, 20 wt% H₂O and 4.1 wt% B₂O₃. Cooling and concomitant fractional crystallisation from 700 to 500 °C induced development of two conjugate melts, an H₂O-poor (A-melt) and an H₂O-rich melt (B-melt) along the opening solvus. Boron is a major element in both melts and is preferentially partitioned into the H₂O-rich melt. Temperature-dependent distribution coefficients D_boron^{B - melt/A - melt} D_{{\rm{boron}}}^{{\rm{B - melt/A - melt}}} are 1.3 at 650 °C, 1.5 at 600 °C, and 1.8 at 500 °C. In both melts, boron concentrations decreased during cooling because of exsolution of a boron-rich hypersaline brine throughout the pegmatitic stage. Boromuscovite containing up to 8.5 wt% was another sink for boron at this stage. The end of the melt-dominated pegmatitic stage was attained at a solidus temperature of around 490 °C. Fluid inclusions of the hydrothermal stage reveal trapping temperatures of 480 to 370 °C, along with varying densities and highly variable B₂O₃ contents ranging from 0.20 to 2.94 wt%. A boiling system evolved, indicating a complex interplay between closed- and open-system behaviour. Pressure switched from lithostatic to hydrostatic and back, generating hydrothermal convection cells where meteoric waters were introduced and mixed with magmatic fluids. Boron-rich solutions originated from magmatic fluids, whereas boron-depleted fluids were mainly of meteoric origin. This highlights the potential of boron for discriminating fluids of different origin. Tin is continuously enriched during the evolution because tin and boron are cross-linked by formation of boron-, fluorine- and tin-fluorine-bearing complexes and is finally deposited within quartz-cassiterite veins during the transition from closed- to open-system behaviour. Boron does not only trace the complex evolution of the Ehrenfriedersdorf complex but exerts, together with H₂O, F and P, an important control on the physical and chemical properties of pegmatite-forming melts, and particularly on the formation of a two-melt solvus at low pressure. We discuss this with respect to experimental results on H₂O solubility and the critical behaviour of the haplogranite-water system which contained variable concentrations of volatiles.     

The reversed alumina contents of orthopyroxene in equilibrium with spinel and forsterite in the system MgO-Al2O3-SiO2

Equilibrium alumina contents of orthopyroxene coexisting with spinel and forsterite in the system MgO-Al₂O₃-SiO₂ have been reversed at 15 different P-T conditions, in the range 1,030–1,600° C and 10–28 kbar. The present data and three reversals of Danckwerth and Newton (1978) have been modeled assuming an ideal pyroxene solid solution with components Mg₂Si₂O₆ (En) and MgAl₂SiO₆ (MgTs), to yield the following equilibrium condition (J, bar, K): $$\begin{gathered} RT{\text{ln(}}X_{{\text{MgTs}}} {\text{/}}X_{{\text{En}}} {\text{) + 29,190}} - {\text{13}}{\text{.42 }}T + 0.18{\text{ }}T + 0.18{\text{ }}T^{1.5} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [0.013 + 3.34 \times 10^{ - 5} (T - 298) - 6.6 \times 10^{ - 7} P]P. \hfill \\ \end{gathered} $$ The data of Perkins et al. (1981) for the equilibrium of orthopyroxene with pyrope have been similarly fitted with the result: $$\begin{gathered} - RT{\text{ln(}}X_{{\text{MgTs}}} \cdot X_{{\text{En}}} {\text{) + 5,510}} - 88.91{\text{ }}T + 19{\text{ }}T^{1.2} \hfill \\ + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP = 0,} \hfill \\ \end{gathered} $$ where $$\begin{gathered} + \int\limits_1^P {\Delta V_{T,P}^{\text{0}} dP} \hfill \\ = [ - 0.832 - 8.78{\text{ }} \times {\text{ 10}}^{ - {\text{5}}} (T - 298) + 16.6{\text{ }} \times {\text{ 10}}^{ - 7} P]{\text{ }}P. \hfill \\ \end{gathered} $$ The new parameters are in excellent agreement with measured thermochemical data and give the following properties of the Mg-Tschermak endmember: $$H_{f,970}^0 = - 4.77{\text{ kJ/mol, }}S_{298}^0 = 129.44{\text{ J/mol}} \cdot {\text{K,}}$$ and $$V_{298,1}^0 = 58.88{\text{ cm}}^{\text{3}} .$$ The assemblage orthopyroxene+spinel+olivine can be used as a geothermometer for spinel lherzolites, subject to a choice of thermodynamic mixing models for multicomponent orthopyroxene and spinel. An ideal two-site mixing model for pyroxene and Sack's (1982) expressions for spinel activities provide, with the present experimental calibration, a geothermometer which yields temperatures of 800° C to 1,350° C for various alpine peridotites and 850° C to 1,130° C for various volcanic inclusions of upper mantle origin.     

The H<Subscript>2</Subscript>O solubility of alkali basaltic melts: an experimental study

Experiments were conducted to determine the water solubility of alkali basalts from Etna, Stromboli and Vesuvius volcanoes, Italy. The basaltic melts were equilibrated at 1,200°C with pure water, under oxidized conditions, and at pressures ranging from 163 to 3,842 bars. Our results show that at pressures above 1 kbar, alkali basalts dissolve more water than typical mid-ocean ridge basalts (MORB). Combination of our data with those from previous studies allows the following simple empirical model for the water solubility of basalts of varying alkalinity and fO₂ to be derived: \textH ₂ \textO( \textwt% ) = \text H ₂ \textO_\textMORB ( \textwt% ) + ( 5.84 ×10 ^{- 5} *\textP - 2.29 ×10 ^{- 2} ) ×( \textNa₂ \textO + \textK₂ \textO )( \textwt% ) + 4.67 ×10 ^{- 2} ×\Updelta \textNNO - 2.29 ×10 ^{- 1} {\text{H}}_{ 2} {\text{O}}\left( {{\text{wt}}\% } \right) = {\text{ H}}_{ 2} {\text{O}}_{\text{MORB}} \left( {{\text{wt}}\% } \right) + \left( {5.84 \times 10^{ - 5} *{\text{P}} - 2.29 \times 10^{ - 2} } \right) \times \left( {{\text{Na}}_{2} {\text{O}} + {\text{K}}_{2} {\text{O}}} \right)\left( {{\text{wt}}\% } \right) + 4.67 \times 10^{ - 2} \times \Updelta {\text{NNO}} - 2.29 \times 10^{ - 1} where H₂O_MORB is the water solubility at the calculated P, using the model of Dixon et al. (1995). This equation reproduces the existing database on water solubilities in basaltic melts to within 5%. Interpretation of the speciation data in the context of the glass transition theory shows that water speciation in basalt melts is severely modified during quench. At magmatic temperatures, more than 90% of dissolved water forms hydroxyl groups at all water contents, whilst in natural or synthetic glasses, the amount of molecular water is much larger. A regular solution model with an explicit temperature dependence reproduces well-observed water species. Derivation of the partial molar volume of molecular water using standard thermodynamic considerations yields values close to previous findings if room temperature water species are used. When high temperature species proportions are used, a negative partial molar volume is obtained for molecular water. Calculation of the partial molar volume of total water using H₂O solubility data on basaltic melts at pressures above 1 kbar yields a value of 19 cm³/mol in reasonable agreement with estimates obtained from density measurements.     

The magnesiowüstite: iron equilibrium and its implications for the activity-composition relations of (Mg,Fe)<Subscript>2</Subscript>SiO<Subscript>4</Subscript> olivine solid solutions

The chemical potential of oxygen (µO₂) in equilibrium with magnesiowüstite solid solution (Mg, Fe)O and metallic Fe has been determined by gas-mixing experiments at 1,473 K supplemented by solid-cell EMF experiments at lower temperatures. The results give:

Multiple-pumped-well aquifer test to determine the anisotropic properties of a karst limestone aquifer in Pasco County, Florida, USA

Groundwater-level data from an aquifer test utilizing four pumped wells conducted in the South Pasco wellfield in Pasco County, Florida, USA, were analyzed to determine the anisotropic transmissivity tensor, storativity, and leakance in the vicinity of the wellfield. A weighted least-squares procedure was used to analyze drawdowns measured at eight observation wells, and it was determined that the major axis of transmissivity extends approximately from north to south and the minor axis extends approximately from west to east with an angle of anisotropy equal to N4.54°W. The transmissivity along the major axis ${\left( {T_{{\xi \xi }} } \right)}$ is 14,019 m² day^–1, and the transmissivity along the minor axis ${\left( {T_{{\eta \eta }} } \right)}$ is 4,303 m² day^–1. The equivalent transmissivity $T_{e} = {\left( {T_{{\xi \xi }} T_{{\eta \eta }} } \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} = 7,767{{\text{m}}^{2} } \mathord{\left/ {\vphantom {{{\text{m}}^{2} } {{\text{day}}^{{ - {\text{1}}}} }}} \right. \kern-0em} {{\text{day}}^{{ - {\text{1}}}} }$ , and the ratio of anisotropy is 3.26. The storativity of the aquifer is 7.52?×?10^?4, and the leakance of the overlying confining unit is 1.37?×?10^?4 day^?1. The anisotropic properties determined for the South Pasco wellfield in this investigation confirm the results of previous aquifer tests conducted in the wellfield and help to quantify the NW–SE to NE–SW trends for regional fracture patterns and inferred solution-enhanced flow zones in west-central Florida.     

Cu diffusivity in granitic melts with application to the formation of porphyry Cu deposits

We report new experimental data of Cu diffusivity in granite porphyry melts with 0.01 and 3.9 wt% H₂O at 0.15–1.0 GPa and 973–1523 K. A diffusion couple method was used for the nominally anhydrous granitic melt, whereas a Cu diffusion-in method using Pt₉₅Cu₅ as the source of Cu was applied to the hydrous granitic melt. The diffusion couple experiments also generate Cu diffusion-out profiles due to Cu loss to Pt capsule walls. Cu diffusivities were extracted from error function fits of the Cu concentration profiles measured by LA-ICP-MS. At 1 GPa, we obtain \({D_{{\text{Cu, dry, 1 GPa}}}}=\exp \left[ {( - {\text{13.89}} \pm {\text{0.42}}) - \frac{{{\text{12878}} \pm {\text{540}}}}{T}} \right],\) and \({D_{{\text{Cu, 3}}{\text{.9 wt\% }}{{\text{H}}_{\text{2}}}{\text{O}},{\text{ 1 GPa}}}}=\exp \left[ {( - 16.31 \pm 1.30) - \frac{{{\text{8148}} \pm {\text{1670}}}}{T}} \right],\) where D is Cu diffusivity in m²/s and T is temperature in K. The above expressions are in good agreement with a recent study on Cu diffusion in rhyolitic melt using the approach of Cu₂S dissolution. The observed pressure effect over 0.15–1.0 GPa can be described by an activation volume of 5.9 cm³/mol for Cu diffusion. Comparison of Cu diffusivity to alkali diffusivity and its variation with melt composition implies fourfold-coordinated Cu⁺ in silicate melts. Our experimental results indicate that in the formation of porphyry Cu deposits, the diffusive transport of magmatic Cu to sulfide liquids or fluid bubbles is highly efficient. The obtained Cu diffusivity data can also be used to assess whether equilibrium Cu partitioning can be reached within certain experimental durations.     

Iron in monticellite as an oxygen barometer for kimberlite magmas

Monticellite is a common magmatic mineral in the groundmass of kimberlites. A new oxygen barometer for kimberlite magmas is calibrated based on the Fe content of monticellite, CaMgSiO₄, in equilibrium with kimberlite liquids in experiments at 100 kPa from 1,230 to 1,350°C and at logfO₂ from NNO-4.1 to NNO+5.3 (where NNO is the nickel–nickel oxide buffer). The XFe_Mtc/XFe_liq was found to decrease with increasing fO₂, consistent with only Fe²⁺ entering the monticellite structure. Although the XFe-in-monticellite varies with temperature and composition, these dependencies are small compared to that with fO₂. The experimental data were fitted by weighted least square regression to the following relationship: \Updelta \textNNO = \frac{ log[ 0.858( ±0.021)\fracX_\textFe^\textLiq X_\textFe^\textMtc ] - 0.139( ±0.022) }0.193( ±0.004) \Updelta {\text{NNO}} = \frac{{\left\{ {\log \left[ {0.858( \pm 0.021)\frac{{X_{\text{Fe}}^{\text{Liq}} }}{{X_{\text{Fe}}^{\text{Mtc}} }}} \right] - 0.139( \pm 0.022)} \right\}}}{0.193( \pm 0.004)} where ΔNNO is the fO₂ relative to that of the Nickel-bunsenite (NNO) buffer and XFe_liq/XFe_Mtc is the ratio of mole fraction of Fe in liquid and Fe-in-monticellite (uncertainties at 2σ). The application of this oxygen barometer to natural kimberlites from both the literature and our own investigations, assuming the bulk rock FeO is that of their liquid FeO, revealed a range in fO₂ from NNO-3.5 to NNO+1.7. A range of Mg/(Mg + Fe²⁺) (Mg#) for kimberlite melts of 0.46–0.88 was derived from the application of the experimentally determined monticellite-liquid Kd Fe²⁺–Mg to natural monticellites. The range in Mg# is broader and less ultramafic than previous estimates of kimberlites, suggesting an evolution under a wide range of petrologic conditions.     

Activity-composition relations of the magnesiowüstite solid solution series in equilibrium with metallic iron in the temperature range 1050–1400 K

The equilibrium $${\text{(1}} - y{\text{)Fe}}_{(s)} + \tfrac{{\text{1}}}{{\text{2}}}{\text{O}}_{{\text{2(g)}}} \rightleftarrows {\text{Fe}}_{{\text{1}} - y} {\text{O}}_{{\text{(}}s,{\text{ in MW)}}} $$ was studied by measuring oxygen potentials for a range of different magnesiowüstite compositions relative to those of the iron-wüstite system in an oxygen concentration cell involving yttria stabilized zirconia as the solid electrolyte. The temperature range covered was 1050 to 1400 K. Separate measurements of the mole fraction of trivalent iron in magnesiowüstite (x(Fe³⁺)) were made and the composition dependence ofx(Fe³⁺) was taken into account in calculations of the activity-composition relations of FeO, Fe_2/3O and MgO.     

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.     

Light scattering in jadeite melt: Strain relaxation measurements by photon correlation spectroscopy

Photon correlation spectroscopy has been applied to the study of longitudinal strain relaxation of vitreous Jadeite (NaAlSi₂O₆) in the temperature range 811–1014° C. The correlation function $\left| {g^{\left( 1 \right)} \left. {\left( t \right)} \right|^2 \propto \exp \left( {\left( { - 2t/\tau _\beta } \right)^\beta } \right)} \right.$ obeys a Kohlrausch type function with β=0.64±0.01. Individual correlation functions fit altogether a master relaxation curve, thus demonstrating thermorheological simplicity (TRS). The temperature dependence of the measured relaxation times shows Arrhenian behaviour with $\log \left( \tau \right) = - 21.4 \pm 0.3{\text{s}} {\text{ + }} {\text{471}}{\text{.6}} \pm {\text{22}} {\text{kJmol}}^{{\text{ - 1}}} /RT$ . The time scale of longitudinal strain relaxation is consistent with the existing data on shear relaxation derived from shear viscosity and structural relaxation calculated from calorimetric C _pmeasurements. Comparison with oxygen diffusion indicates that network forming elements relax at about the same time scale as viscoelastic properties. On the other hand, Na⁺ relaxation times derived from impedance spectroscopy are short compared to viscoelastic relaxation times at low temperatures. This difference is decreasing with increasing temperature and possibly disappearing at approximately 1100° C.     

Total Dynamics of Quartz–Water System at Ambient Conditions

New data on the dissolution and growth of quartz in acid, nearly neutral and slightly alkaline solutions at ambient conditions are presented. During batch dissolutions, aqueous Si-concentrations increased nonlinearly towards limit values. During parallel growth experiments, however, the high Si-concentrations corresponding to 13-fold supersaturation with respect to quartz did not decreased. To interpret these results, two dynamic models (1) a reaction model and (2) a surface-complexation model, were derived. Both models were focused on (a) reversible dissolution/growth of ${{dn_{{\rm Si(aq)}}}\over{dt}}=\left(p+{{r}\over {a_{{\rm H}^+}}}\right)+\left(u-p- {{r}\over {a_{{\rm H}^+}}}\right){{n_{{\rm Q_D}}}\over {\sum\limits_i{n_{{\rm Qi}}}}}-{{1}\over {V}}\left(q+ {{s}\over {a_{{\rm H}^+}}}\right)n_{{\rm Si(aq)}},${{dn_{{\rm Si(aq)}}}\over{dt}}=\left(p+{{r}\over {a_{{\rm H}^+}}}\right)+\left(u-p- {{r}\over {a_{{\rm H}^+}}}\right){{n_{{\rm Q_D}}}\over {\sum\limits_i{n_{{\rm Qi}}}}}-{{1}\over {V}}\left(q+ {{s}\over {a_{{\rm H}^+}}}\right)n_{{\rm Si(aq)}},     

Solubility of Ca and Al in orthopyroxene from spinel peridotite: an improved version of an empirical geothermometer

Geothermometric equations for spinel peridotites by Fujii (1976), Gasparik and Newton (1984), and Chatterjee, and Terhart (1985) based on the reaction enstatite (en)+spinel (sp)Mg–Tschermaks (mats)+forsterite (fo) were tested using a nearly isothermal suite of mantle xenoliths from the Eifel, West Germany. In spite of using activities of MgAl₂O₄, en, and mats to allow for the non-ideal solution behaviour of the constituent phases, temperatures calculated from these equations systematically change as a function of Cr/(Cr+AL+Fe³⁺) in spinel. We propose an improved version of the empirical geothermometer for spinel peridotites of Sachtleben and Seck (1981) derived from the evaluation of the solubilities of Ca and Al in orthopyroxene from more than 100 spinel peridotites from the Rhenish Volcanic Province. A least squares regression yielded a smooth correlation between

Garnet-clinopyroxene geothermometer

A garnet-clinopyroxene geothermometer based on the available experimental data on compositions of coexisting phases in the system MgO-FeO-MnO-Al₂O₃-Na₂O-SiO₂ is as follows: $$T({\text{}}K) = \frac{{8288 + 0.0276 P {\text{(bar)}} + Q1 - Q2}}{{1.987 \ln K_{\text{D}} + 2.4083}}$$ where P is pressure, and Q1, Q2, and K _D are given by the following equations $$Q1 = 2,710{\text{(}}X_{{\text{Fe}}} - X_{{\text{Mg}}} {\text{)}} + 3,150{\text{ }}X_{{\text{Ca}}} + 2,600{\text{ }}X_{{\text{Mn}}} $$ (mole fractions in garnet) $$\begin{gathered}Q2 = - 6,594[X_{{\text{Fe}}} {\text{(}}X_{{\text{Fe}}} - 2X_{{\text{Mg}}} {\text{)]}} \hfill \\{\text{ }} - 12762{\text{ [}}X_{{\text{Fe}}} - X_{{\text{Mg}}} (1 - X_{{\text{Fe}}} {\text{)]}} \hfill \\{\text{ }} - 11,281[X_{{\text{Ca}}} (1 - X_{{\text{Al}}} ) - 2X_{{\text{Mg}}} 2X_{{\text{Ca}}} ] \hfill \\{\text{ + 6137[}}X_{{\text{Ca}}} (2X_{{\text{Mg}}} + X_{{\text{Al}}} )] \hfill \\{\text{ + 35,791[}}X_{{\text{Al}}} (1 - 2X_{{\text{Mg}}} )] \hfill \\{\text{ + 25,409[(}}X_{{\text{Ca}}} )^2 ] - 55,137[X_{{\text{Ca}}} (X_{{\text{Mg}}} - X_{{\text{Fe}}} )] \hfill \\{\text{ }} - 11,338[X_{{\text{Al}}} (X_{{\text{Fe}}} - X_{{\text{Mg}}} )] \hfill \\\end{gathered} $$ [mole fractions in clinopyroxene Mg = MgSiO₃, Fe = FeSiO₃, Ca = CaSiO₃, Al = (Al₂O₃-Na₂O)] K _D = (Fe/Mg) in garnet/(Fe/Mg) in clinopyroxene. Mn and Cr in clinopyroxene, when present in small concentrations are added to Fe and Al respectively. Fe is total Fe²⁺+Fe³⁺.