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.     

Reaction textures and P–T conditions of Opx-Crd gneisses from Karimnagar, Andhra Pradesh, India

Summary The Karimnagar granulite terrain is an integral part of the Eastern Dharwar Craton (EDC). It has received much interest because of the only reported granulite facies rocks in the EDC. These granulites contain quartz-free sapphirine-spinel-bearing granulites, kornerupine – bearing granulites, mafic granulites, orthopyroxene-cordierite gneisses, charnockites, amphibolites, dolerite dykes, granite gneisses, quartzites and banded magnetite quartzite. The orthopyroxene-cordierite gneisses occur as enclaves within granite-gneiss in association with banded magnetite quartzites, charnockites and amphibolites. The observed reaction textures, spectacular as they are, have an extraordinary information content within a tiny domain. Coronas, symplectites and resorption textures are of particular interest as they reflect discontinuous or continuous reactions under changing physical conditions. The main mineral assemblages encountered in these gneisses are orthopyroxene – cordierite – biotite – plagioclase – perthite – quartz and garnet – orthopyroxene – cordierite – biotite – quartz – plagioclase – perthite ± sillimanite. Multiphase reaction textures in conjunction with mineral chemical data in the KFMASH system indicate the following reactions: Based on chemographic relationships and petrogenetic grids in the K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O (KFMASH) system, a sequence of prograde (early stage), isothermal decompression (middle stage) and retrograde (late stage) reactions (‘back reactions’ and hydration reactions) are inferred. Relatively lower P–T estimates (0.35 GPa/550–750 °C) obtained from the different geothermobarometers are attributed to late Fe–Mg re-equilibration during cooling. Therefore, the convergence method has been applied to retrieve simultaneously the P–T conditions of the thermal peak of metamorphism. The near thermal peak condition of metamorphism estimated by the convergence method are 850 °C/0.62 GPa. The P–T estimates define a retrograde trajectory with substantial decompression.     

Dissolution Kinetics of Dolomite in Water at Elevated Temperatures

Kinetic experiments of dolomite dissolution in water over a temperature range from 25 to 250°C were performed using a flow through packed bed reactor. Authors chose three different size fractions of dolomite samples: 18–35 mesh, 35–60 mesh, and 60–80 mesh. The dissolution rates of the three particle size samples of dolomite were measured. The dissolution rate values are changed with the variation of grain size of the sample. For the sample through 20–40 mesh, both the release rate of Ca and the release rate of Mg increase with increasing temperature until 200°C, then decrease with continued increasing temperature. Its maximum dissolution rate occurs at 200°C. The maximum dissolution rates for the sample through 40–60 mesh and 60–80 mesh happen at 100°C. Experimental results indicate that the dissolution of dolomite is incongruent in most cases. Dissolution of fresh dolomite was non-stoichiometric, the Ca/Mg ratio released to solution was greater than in the bulk solid, and the ratio increases with rising temperatures from 25 to 250°C. Observations on dolomite dissolution in water are presented as three parallel reactions, and each reaction occurs in consecutive steps as

Thermodynamic Properties of Brucite Determined by Solubility Studies and Their Significance to Nuclear Waste Isolation

Solubility experiments were conducted for the dissolution reaction of brucite, Mg(OH)₂ (cr): Experiments were conducted from undersaturation in deionized (DI) water and 0.010–4.4 m NaCl solutions at 22.5°C. In addition, brucite solubility was measured from supersaturation in an experiment in which brucite was precipitated via dropwise addition of 0.10 m NaOH into a 0.10 m MgCl₂ solution also at 22.5°C. The attainment of the reversal in equilibrium was demonstrated in this study. The solubility constant at 22.5°C at infinite dilution calculated from the experimental results from the direction of supersaturation by using the specific interaction theory (SIT) is: with a corresponding value of 17.0 ± 0.2 (2σ) when extrapolated to 25°C. The dimensionless standard chemical potential (μ°/RT) of brucite derived from the solubility data in 0.010 m to 4.4 m NaCl solutions from undersaturation extrapolated to 25°C is −335.76 ± 0.45 (2σ), with the corresponding Gibbs free energy of formation of brucite, , being −832.3 ± 1.1 (2σ) kJ mol⁻¹. In combination with the auxiliary thermodynamic data, the is calculated to be 17.1 ± 0.2 (2σ), based on the above Gibbs free energy of formation for brucite. This study recommends an average value of 17.05 ± 0.2 in logarithmic unit as solubility constant of brucite at 25°C, according to the values from both supersaturation and undersaturation. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.     

Interaction of Freshly Precipitated Silica Gel with Aqueous Silicic Acid Solutions under Ambient and Near Neutral pH-conditions: A Detailed Analysis of Linear Rate Law

Interaction of freshly precipitated silica gel with aqueous solutions was studied at laboratory batch experiments under ambient and near neutral pH-conditions. The overall process showed excellent reversibility: gel growth could be considered as an opposite process to dissolution and a linear rate law could be applied to experimental data. Depending on the used rate law form, the resulting rate constants were sensitive to errors in parameters/variables such as gel surface area, equilibrium constants, Si-fluxes, and reaction quotients. The application of an Integrated Exponential Model appeared to be the best approach for dissolution data evaluation. It yielded the rate constants k _dissol ∼ (4.50 ± 0.68) × 10⁻¹² and k _growth ∼ (2.58 ± 0.39) × 10⁻⁹ mol m⁻² s⁻¹ for zero ionic strength. In contrast, a Differential Model gave best results for growth data modeling. It yielded the rate constants k _dissol ∼ (1.14 ± 0.44) × 10⁻¹¹ and k _growth ∼ (6.08 ± 2.37) × 10⁻⁹ mol m⁻² s⁻¹ for higher ionic strength (I ∼ 0.04 to 0.11 mol L⁻¹). The found silica gel solubility at zero ionic strength was somewhat lower than the generally accepted value. Based on the and standard Gibbs free energy of silica gel formation was calculated as and −850,318 ± 20 J mol⁻¹, respectively. Activation energies for silica gel dissolution and growth were determined as and respectively. An universal value for growth of any silica polymorph, is not consistent with the value for silica gel growth, which questions the hypothesis about one unique activated complex controlling the silica polymorph growth.     

Use of Pitzer Equations to Examine the Formation of Mercury(II) Hydroxide and Chloride Complexes in NaClO<Subscript>4</Subscript> Media

The thermodynamic stability constants for the hydrolysis and formation of mercury (Hg²⁺) chloride complexes

Experimental investigation of the reaction forsterite + H2O ⇌ serpentine + brucite

A new determination of the equilibrium reaction: $$\begin{gathered} 2{\text{ Mg}}_{\text{2}} [{\text{SiO}}_{\text{4}} ] + 3{\text{ H}}_{\text{2}} {\text{O}} \rightleftharpoons {\text{1 Mg}}_{\text{3}} [({\text{OH)}}_{\text{4}} |{\text{Si}}_{\text{2}} {\text{O}}_{\text{5}} ] + 1{\text{ Mg(OH)}}_{\text{2}} \hfill \\ \hfill \\ {\text{ forsterite serpentine brucite}} \hfill \\ \end{gathered} $$ yielded equilibrium temperatures which lie (at identical H₂O-pressures) about 60° C lower than all previously published data (Bowen and Tuttle, 1949; Yoder, 1952; Kitahara et al., 1966; Kitahara and Kennedy, 1967). It has been shown that the above authors have determined not the stable equilibrium curve but instead a metastable “synthesis boundary”. The actual (stable) equilibrium curve is located at 0,5 kb and 350° C 2,0 kb and 380° C 3,5 kb and 400° C 5,0 kb and 420° C 6,5 kb and 430° C.     

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.     

Quantifying the tectono-metamorphic evolution of pelitic rocks from a wide range of tectonic settings: mineral compositions in equilibrium

Commonly used thermometer and barometer calibrations are sensitive to mineral assemblage and, thus, bulk-rock composition. Calculated mineral stabilities for an average pelitic rock over a pressure–temperature (PT) range appropriate for normal, thickened, heated and shallowly subducted continental crust (400–900°C at 0.1–3.0 GPa) reveal more than one hundred possible assemblages. Individual phase compositions are dependent on the assemblage in which they belong and combining isopleth sets to represent and reveals several PT-ranges where commonly used mineral thermobarometers are less effective. For example, the garnet-biotite thermometer becomes increasingly P dependent in the absence of muscovite in high T melt-bearing assemblages, and biotite and plagioclase are not stable at pressures appropriate for lower thickened continental crust. Compositional thermobarometers involving equilibration between alternative phases (namely garnet, phengite and omphacite) are presented. Although the equilibrium compositions of phases at any P and T may change significantly as a function of bulk-rock composition, compositional-ratio thermobarometers are typically insensitive to this, unless a pseudo-univariant reaction is crossed and the buffering assemblage is altered. Quantification of the limits of efficacy of various thermobarometers allows the mineralogy of metapelites to be used to precisely determine segments of PT paths and infer their likely tectonic controls. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

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High temperature calorimetry of sulfide systems

The standard enthalpies of formation of FeS (troilite), FeS₂ (pyrite), Co_0.9342S, Co₃S₄ (linnaeite), Co₉S₈ (cobalt pentlandite), CoS₂ (cattierite), CuS (covellite), and Cu₂S (chalcocite) have been determined by high temperature direct reaction calorimetry at temperatures between 700 K and 1021 K. The following results are reported: $$\Delta {\rm H}_{f,FeS}^{tr} = - 102.59 \pm 0.20kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,FeS}^{py} = - 171.64 \pm 0.93kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_{0.934} S} = - 99.42 \pm 1.52kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_9 S_8 }^{ptl} = - 885.66 \pm 16.83kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_3 S_4 }^{In} = - 347.47 \pm 7.27kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,CoS_2 }^{ct} = - 150.94 \pm 4.85kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Cu_2 S}^{cc} = - 80.21 \pm 1.51kJ mol^{ - 1} ,$$ and $$\Delta {\rm H}_{f,CuS}^{cv} = - 53.14 \pm 2.28kJ mol^{ - 1} ,$$ The enthalpy of formation of CuFeS₂ (chalcopyrite) from (CuS+FeS) and from (Cu+FeS₂) was determined by solution calorimetry in a liquid Ni_0.60S_0.40 melt at 1100 K. The results of these measurements were combined with the standard enthalpies of formation of CuS, FeS, and FeS₂, to calculate the standard enthalpy of formation of CuFeS₂. We found \(\Delta {\rm H}_{f,CuFeS_2 }^{ccp} = - 194.93 \pm 4.84kJ mol^{ - 1}\) . Our results are compared with earlier data given in the literature; generally the agreement is good and our values agree with previous estimates within the uncertainties present in both.     

New thermodynamic models and revised calibrations for the Ti-in-zircon and Zr-in-rutile thermometers

The models recognize that ZrSiO₄, ZrTiO₄, and TiSiO₄, but not ZrO₂ or TiO₂, are independently variable phase components in zircon. Accordingly, the equilibrium controlling the Zr content of rutile coexisting with zircon is ZrSiO₄ = ZrO₂ (in rutile) + SiO₂. The equilibrium controlling the Ti content of zircon is either ZrSiO₄ + TiO₂ = ZrTiO₄ + SiO₂ or TiO₂ + SiO₂ = TiSiO₄, depending whether Ti substitutes for Si or Zr. The Zr content of rutile thus depends on the activity of SiO₂ as well as T, and the Ti content of zircon depends on and as well as T. New and published experimental data confirm the predicted increase in the Zr content of rutile with decreasing and unequivocally demonstrate that the Ti content of zircon increases with decreasing . The substitution of Ti in zircon therefore is primarily for Si. Assuming a constant effect of P, unit and that and are proportional to ppm Zr in rutile and ppm Ti in zircon, [log(ppm Zr-in-rutile) + log] = A₁ + B₁/T(K) and [log(ppm Ti-in-zircon) + log − log] = A₂ + B₂/T, where the A and B are constants. The constants were derived from published and new data from experiments with buffered by either quartz or zircon + zirconia, from experiments with defined by the Zr content of rutile, and from well-characterized natural samples. Results are A₁ = 7.420 ± 0.105; B₁ = −4,530 ± 111; A₂ = 5.711 ± 0.072; B₂ = −4,800 ± 86 with activity referenced to α-quartz and rutile at P and T of interest. The zircon thermometer may now be applied to rocks without quartz and/or rutile, and the rutile thermometer applied to rocks without quartz, provided that and are estimated. Maximum uncertainties introduced to zircon and rutile thermometry by unconstrained and can be quantitatively assessed and are ≈60 to 70°C at 750°C. A preliminary assessment of the dependence of the two thermometers on P predicts that an uncertainty of ±1 GPa introduces an additional uncertainty at 750°C of ≈50°C for the Ti-in-zircon thermometer and of ≈70 to 80°C for the Zr-in-rutile thermometer.     

Aluminum partitioning between olivine and ultrabasic silicate liquid to 6 GPa

Trace element analyses of 1-atm and high-pressure experiments show that in komatiite and peridotite, the olivine (OL)/liquid (L) distribution coefficient for Al₂O₃ ( ) increases with pressure and temperature. Olivine in equilibrium with liquid accepts as much as 0.2 wt% Al₂O₃ in solution at 6 GPa. Convergence to equilibrium compositions at this high level is shown by cation diffusion of Al into synthetic forsterite crystals of low-Al contents in the presence of melt. Convergence to low-Al equilibrium compositions at lower P and T is shown by diffusion of Al out of synthetic forsterite with high initial Al content. Isobaric and isothermal experimental data subsets reveal that temperature and pressure variations both have real effects on . Variation in silicate melt composition has no detectable effect on within the limited range of experimentally investigated mixtures. Least-squares regression for 24 experiments, using komatiite and peridotite, performed at 1 atm to 6 GPa and 1300 to 1960°C, gives the best fit equation: Increase in with increasingly higher-pressure melting is consistent with incorporation of a spinel-like component of low molar volume into olivine, although other substitutions possibly involving more complex coupling cannot be ruled out. High P-T ultrabasic melting residues, if pristine, may be recognized by the high calculated from microprobe analyses of Al₂O₃ concentrations in residual olivines and estimated Al₂O₃ concentration in the last liquid removed. In general the low levels of Al in natural olivine from mantle xenoliths suggest that pristine residues are rarely recovered.     

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

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

Microtextural constraints on the interplay between fluid–rock reactions and deformation

Schists from two mylonitic localities in the footwall of a low-angle normal fault in the eastern Alps record different degrees of embrittlement during exhumation, depending on the extent to which fluid–rock reactions proceeded. At one site, graphitic schists preserve textural evidence for two metamorphic reactions that modified and/or fluid volume: (1) reaction between graphite and aqueous fluid that increased without changing the molar amount of fluid, and (2) replacement of titanite by rutile, calcite, and quartz. The latter reaction involved net consumption of increasingly CO₂-rich fluid. Areas where the first reaction proceeded are associated with abundant Mode I microcracks. Fluid inclusion arrays within the microcracks show that increased from ∼0.1 to 0.6 during decompression from 4.75 to 2 kbar at a reference temperature of 500°C. Titanite consumption is most pronounced within transgranular Mode I microcracks, but microcracks do not crosscut products of this reaction; fluid consumption during reaction was coeval with the end of microcracking, at least on a local scale. At the other site, graphitic schists lack small-scale Mode I cracks as well as evidence for graphite consumption during decompression. SEM imaging shows that graphite is anhedral and pitted at the first site, but occurs in clusters of euhedral grains at the second site. Mass balance calculations demonstrate that rocks with partially consumed graphite were infiltrated by an externally derived, H₂O-rich fluid that drove subsequent graphite-fluid reaction. Evidence for similar fluid infiltration is absent at the second site. Variations in the degree of reaction progress indicate that fluid pathways and deformation style were heterogeneous on the scale of millimeters to kilometers during exhumation from mid-crustal depths.     

Doppler SODAR observations of the temperature structure parameter during monsoon season over a tropical rural station,Gadanki

Doppler SODAR (Sound Detection and Ranging) measurements over a tropical Indian station at National Atmospheric Research Laboratory (NARL), Gadanki (13.5°N, 79.2°E) during two consecutive monsoon seasons, 2007 and 2008, are investigated to study the influence of mechanically generated turbulence on temperature structure parameter (C_T²)_{\rm T}^{2}) in the convective boundary layer. Increase in the C_T²_{\rm T}^{2} is observed after the arrival of monsoon for both seasons. Contribution of vertical wind shear in horizontal wind component to C_T²_{\rm T}^{2} due to zonal winds is responsible for the increase observed in the temperature structure parameter which is inferred from the results obtained. C_T²_{\rm T}^{2} is found to be increased by an order of 2 in both the lower and upper altitudes, respectively. Magnitude of wind speed is reported to be doubled with the arrival of monsoon. It is also observed that, southwest monsoon wind modulates the day-to-day variations of wind pattern over this station during the onset phase of monsoon season. The lower variability observed at lower height is attributed to the complex topography surrounding this region.     

Opening and resetting temperatures in heating geochronological systems

We present a theoretical model for diffusive daughter isotope loss in radiochronological systems with increasing temperature. It complements previous thermochronological models, which focused on cooling, and allows for testing opening and resetting of radiochronometers during heating. The opening and resetting temperatures are, respectively,

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:

Amphibole stability in primitive arc magmas: effects of temperature,H<Subscript>2</Subscript>O content,and oxygen fugacity

The water-saturated phase relations have been determined for a primitive magnesian andesite (57 wt% SiO₂, 9 wt% MgO) from the Mt. Shasta, CA region over the pressure range 200–800 MPa, temperature range of 915–1,070 °C, and oxygen fugacities varying from the nickel–nickel oxide (NNO) buffer to three log units above NNO (NNO+3). The phase diagram of a primitive basaltic andesite (52 wt% SiO₂, 10.5 wt% MgO) also from the Mt. Shasta region (Grove et al. in Contrib Miner Petrol 145:515–533; 2003) has been supplemented with additional experimental data at 500 MPa. Hydrous phase relations for these compositions allow a comparison of the dramatic effects of dissolved H₂O on the crystallization sequence. Liquidus mineral phase stability and appearance temperatures vary sensitively in response to variation in pressure and H₂O content, and this information is used to calibrate magmatic barometers-hygrometers for primitive arc magmas. H₂O-saturated experiments on both compositions reveal the strong dependence of amphibole stability on the partial pressure of H₂O. A narrow stability field is identified where olivine and amphibole are coexisting phases in the primitive andesite composition above 500 MPa and at least until 800 MPa, between 975–1,025 °C. With increasing H₂O pressure (\({P}_{\text {H}_2{\rm O}}\)), the temperature difference between the liquidus and amphibole appearance decreases, causing a change in chemical composition of the first amphibole to crystallize. An empirical calibration is proposed for an amphibole first appearance barometer-hygrometer that uses Mg# of the amphibole and \(f_{\text {O}_2}\):

$$ P_{\text{H}_{2}{\rm O}}({\rm MPa})=\left[{\frac{{\rm Mg\#}}{52.7}}-0.014 * \Updelta {\rm NNO}\right]^{15.12} $$

This barometer gives a minimum \({P}_{\text{H}_{2}{\rm O}}\) recorded by the first appearance of amphibole in primitive arc basaltic andesite and andesite. We apply this barometer to amphibole antecrysts erupted in mixed andesite and dacite lavas from the Mt. Shasta, CA stratocone. Both high H₂O pressures (500–900 MPa) and high pre-eruptive magmatic H₂O contents (10–14 wt% H₂O) are indicated for the primitive end members of magma mixing that are preserved in the Shasta lavas. We also use these new experimental data to explore and evaluate the empirical hornblende barometer of Larocque and Canil (2010).

     

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!

Estimation of covariance matrix from geochemical data with observations below detection limits

Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances, , , , and forY andZ: (ii) defining new variables by and and lettingA=C+D andB=C–D, and obtaining MLE for variances, and forA andB; (iii) estimating the correlation coefficient _YZ by and the covariance _YZ by . The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada.