H-bonding scheme and cation partitioning in axinite: a single-crystal neutron diffraction and Mössbauer spectroscopic study

The crystal chemistry of a ferroaxinite from Colebrook Hill, Rosebery district, Tasmania, Australia, was investigated by electron microprobe analysis in wavelength-dispersive mode, inductively coupled plasma–atomic emission spectroscopy (ICP–AES), ⁵⁷Fe Mössbauer spectroscopy and single-crystal neutron diffraction at 293 K. The chemical formula obtained on the basis of the ICP–AES data is the following: \( ^{X1,X2} {\text{Ca}}_{4.03} \,^{Y} \left( {{\text{Mn}}_{0.42} {\text{Mg}}_{0.23} {\text{Fe}}^{2 + }_{1.39} } \right)_{\varSigma 2.04} \,^{Z1,Z2} \left( {{\text{Fe}}^{3 + }_{0.15} {\text{Al}}_{3.55} {\text{Ti}}_{0.12} } \right)_{\varSigma 3.82} \,^{T1,T2,T3,T4} \left( {{\text{Ti}}_{0.03} {\text{Si}}_{7.97} } \right)_{\varSigma 8} \,^{T5} {\text{B}}_{1.96} {\text{O}}_{30} \left( {\text{OH}} \right)_{2.18} \). The ⁵⁷Fe Mössbauer spectrum shows unambiguously the occurrence of Fe²⁺ and Fe³⁺ in octahedral coordination only, with Fe²⁺/Fe³⁺ = 9:1. The neutron structure refinement provides a structure model in general agreement with the previous experimental findings: the tetrahedral T1, T2, T3 and T4 sites are fully occupied by Si, whereas the T5 site is fully occupied by B, with no evidence of Si at the T5, or Al or Fe³⁺ at the T1–T5 sites. The structural and chemical data of this study suggest that the amount of B in ferroaxinite is that expected from the ideal stoichiometry: 2 a.p.f.u. (for 32 O). The atomic distribution among the X1, X2, Y, Z1 and Z2 sites obtained by neutron structure refinement is in good agreement with that based on the ICP–AES data. For the first time, an unambiguous localization of the H site is obtained, which forms a hydroxyl group with the oxygen atom at the O16 site as donor. The H-bonding scheme in axinite structure is now fully described: the O16–H distance (corrected for riding motion effect) is 0.991(1) Å and an asymmetric bifurcated bonding configuration occurs, with O5 and O13 as acceptors [i.e. with O16···O5 = 3.096(1) Å, H···O5 = 2.450(1) Å and O16–H···O5 = 123.9(1)°; O16···O13 = 2.777(1) Å, H···O13 = 1.914(1) Å and O16–H···O13 = 146.9(1)°].     

Experimental calibration of Forsterite–Anorthite–Ca-Tschermak–Enstatite (FACE) geobarometer for mantle peridotites

The crystallization of plagioclase-bearing assemblages in mantle rocks is witness of mantle exhumation at shallow depth. Previous experimental works on peridotites have found systematic compositional variations in coexisting minerals at decreasing pressure within the plagioclase stability field. In this experimental study we present new constraints on the stability of plagioclase as a function of different Na₂O/CaO bulk ratios, and we present a new geobarometer for mantle rocks. Experiments have been performed in a single-stage piston cylinder at 5–10 kbar, 1050–1150?°C at nominally anhydrous conditions using seeded gels of peridotite compositions (Na₂O/CaO?=?0.08–0.13; X _Cr = Cr/(Cr?+?Al)?=?0.07–0.10) as starting materials. As expected, the increase of the bulk Na₂O/CaO ratio extends the plagioclase stability to higher pressure; in the studied high-Na fertile lherzolite (HNa-FLZ), the plagioclase-spinel transition occurs at 1100?°C between 9 and 10 kbar; in a fertile lherzolite (FLZ) with Na₂O/CaO?=?0.08, it occurs between 8 and 9 kbar at 1100?°C. This study provides, together with previous experimental results, a consistent database, covering a wide range of P–T conditions (3–9 kbar, 1000–1150?°C) and variable bulk compositions to be used to define and calibrate a geobarometer for plagioclase-bearing mantle rocks. The pressure sensitive equilibrium:

$$\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{4}}}^{{\text{Ol}}}}\limits_{{\text{Forsterite}}} +\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{8}}}^{{\text{Pl}}}}\limits_{{\text{Anorthite}}~} =\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{6}}}^{{\text{Cpx}}}}\limits_{{\text{Ca-Tschermak}}} +{\text{ }}\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{6}}}^{{\text{Opx}}}}\limits_{{\text{Enstatite}}} ,$$

has been empirically calibrated by least squares regression analysis of experimental data combined with Monte Carlo simulation. The result of the fit gives the following equation:

$$P=7.2( \pm 2.9)+0.0078( \pm 0.0021)T{\text{ }}+0.0022( \pm 0.0001)T{\text{ }}\ln K,$$

$${R^2}=0.93,$$

where P is expressed in kbar and T in kelvin. K is the equilibrium constant K?=?a _CaTs × a _en/a _an × a _fo, where a _CaTs, a _en, a _an and a _fo are the activities of Ca-Tschermak in clinopyroxene, enstatite in orthopyroxene, anorthite in plagioclase and forsterite in olivine. The proposed geobarometer for plagioclase peridotites, coupled to detailed microstructural and mineral chemistry investigations, represents a valuable tool to track the exhumation of the lithospheric mantle at extensional environments.

     

Galena Non-oxidative Dissolution Kinetics in Seawater

The rate of non-oxidative galena dissolution in seawater compositions over the pH range of 2–4.5 was determined from batch reactor experiments. The derivative at zero time of a polynomial fit of the Pb concentration versus time data for the first 30 min was used to determine the rate. A plot of R_Gn (rate of galena dissolution) versus pH for data from six experiments is linear (R²?=?0.96), with a slope of 0.5. The rate equation describing the rate of galena dissolution as a function of hydrogen ion activity is

$$R_{\text{Gn}} = - \,10^{ - 10.72} \left( {a_{{{\text{H}}^{ + } }} } \right)^{0.50}$$

Varying the concentration of dissolved oxygen produced no significant effect on the measured rates. The activation energy, based on four experiments carried out over the temperature range of 7–30 °C, is 61.1 kJ/mol.

     

Theoretical calculation of equilibrium Mg isotope fractionation between silicate melt and its vapor

Isotope fractionation during the evaporation of silicate melt and condensation of vapor has been widely used to explain various isotope signals observed in lunar soils, cosmic spherules, calcium–aluminum-rich inclusions, and bulk compositions of planetary materials. During evaporation and condensation, the equilibrium isotope fractionation factor (α) between high-temperature silicate melt and vapor is a fundamental parameter that can constrain the melt’s isotopic compositions. However, equilibrium α is difficult to calibrate experimentally. Here we used Mg as an example and calculated equilibrium Mg isotope fractionation in MgSiO₃ and Mg₂SiO₄ melt–vapor systems based on first-principles molecular dynamics and the high-temperature approximation of the Bigeleisen–Mayer equation. We found that, at 2500 K, δ²⁵Mg values in the MgSiO₃ and Mg₂SiO₄ melts were 0.141?±?0.004 and 0.143?±?0.003‰ more positive than in their respective vapors. The corresponding δ²⁶Mg values were 0.270?±?0.008 and 0.274?±?0.006‰ more positive than in vapors, respectively. The general \(\alpha - T\) equations describing the equilibrium Mg α in MgSiO₃ and Mg₂SiO₄ melt–vapor systems were: \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.264 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\) and \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.340 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\), respectively, where m is the mass of light isotope ²⁴Mg and m′ is the mass of the heavier isotope, ²⁵Mg or ²⁶Mg. These results offer a necessary parameter for mechanistic understanding of Mg isotope fractionation during evaporation and condensation that commonly occurs during the early stages of planetary formation and evolution.     

The effect of silica activity on the diffusion of Ni and Co in olivine

The diffusion of Ni and Co was measured at atmospheric pressure in synthetic monocrystalline forsterite (Mg₂SiO₄) from 1,200 to 1,500 °C at the oxygen fugacity of air, along [100], with the activities of SiO₂ and MgO defined by either forsterite + periclase (fo + per buffer) or forsterite + protoenstatite (fo + en buffer). Diffusion profiles were measured by three methods: laser-ablation inductively-coupled-plasma mass-spectrometry, nano-scale secondary ion mass spectrometry and electron microprobe, with good agreement between the methods. For both Ni and Co, the diffusion rates in protoenstatite-buffered experiments are an order of magnitude faster than in the periclase-buffered experiments at a given temperature. The diffusion coefficients D _M (M = Ni or Co) for the combined data set can be fitted to the equation:

$$\log \,D_{\text{M}} \,\left( {{\text{in}}\,{\text{m}}^{2} \,{\text{s}}^{ - 1} } \right) = - 6.77( \pm 0.33) + \Delta E_{\text{a}} (M)/RT + 2/3\log a_{{SiO_{2} }}$$

with E_a(Ni) = ? 284.3 kJ mol^?1 and E_a(Co) = ? 275.9 kJ mol^?1, with an uncertainty of ±10.2 kJ mol^?1. This equation fits the data (24 experiments) to ±0.1 in log D _M. The dependence of diffusion on \(a_{{{\text{SiO}}_{2} }}\) is in agreement with a point-defect model in which Mg-site vacancies are charge-balanced by Si interstitials. Comparative experiments with San Carlos olivine of composition Mg_1.8Fe_0.2SiO₄ at 1,300 °C give a slightly small dependence on \(a_{{{\text{SiO}}_{2} }}\), with D \(\propto\) (\(a_{{{\text{SiO}}_{2} }}^{0.5}\)), presumably because the Mg-site vacancies increase with incorporation of Fe³⁺ in the Fe-bearing olivines. However, the dependence on fO₂ is small, with D \(\propto\) (fO₂)^0.12±0.12. These results show the necessity of constraining the chemical potentials of all the stoichiometric components of a phase when designing diffusion experiments. Similarly, the chemical potentials of the major-element components must be taken into account when applying experimental data to natural minerals to constrain the rates of geological processes. For example, the diffusion of divalent elements in olivine from low SiO₂ magmas, such as kimberlites or carbonatites, will be an order of magnitude slower than in olivine from high SiO₂ magmas, such as tholeiitic basalts, at equal temperatures and fO₂.

     

The effect of liquid composition on the partitioning of Ni between olivine and silicate melt

We report the results of experiments designed to separate the effects of temperature and pressure from liquid composition on the partitioning of Ni between olivine and liquid, \(D_{\text{Ni}}^{\text{ol/liq}}\). Experiments were performed from 1300 to 1600 °C and 1 atm to 3.0 GPa, using mid-ocean ridge basalt (MORB) glass surrounded by powdered olivine in graphite–Pt double capsules at high pressure and powdered MORB in crucibles fabricated from single crystals of San Carlos olivine at one atmosphere. In these experiments, pressure and temperature were varied in such a way that we produced a series of liquids, each with an approximately constant composition (~12, ~15, and ~21 wt% MgO). Previously, we used a similar approach to show that \(D_{\text{Ni}}^{\text{ol/liq}}\) for a liquid with ~18 wt% MgO is a strong function of temperature. Combining the new data presented here with our previous results allows us to separate the effects of temperature from composition. We fit our data based on a Ni–Mg exchange reaction, which yields \(\ln \left( {D_{\text{Ni}}^{\text{molar}} } \right) = \frac{{ -\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } }}{RT} + \frac{{\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } }}{R} - \ln \left( {\frac{{X_{\text{MgO}}^{\text{liq}} }}{{X_{{{\text{MgSi}}_{ 0. 5} {\text{O}}_{ 2} }}^{\text{ol}} }}} \right).\) Each subset of constant composition experiments displays roughly the same temperature dependence of \(D_{\text{Ni}}^{\text{ol/liq}}\) (i.e.,\(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\)) as previously reported for liquids with ~18 wt% MgO. Fitting new data presented here (15 experiments) in conjunction with our 13 previously published experiments (those with ~18 wt% MgO in the silicate liquid) to the above expression gives \(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = 3641 ± 396 (K) and \(\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = ? 1.597 ± 0.229. Adding data from the literature yields \(-\Delta _{r(1)} H_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = 4505 ± 196 (K) and \(\Delta _{r(1)} S_{{T_{\text{ref}} ,P_{\text{ref}} }}^{ \circ } /R\) = ? 2.075 ± 0.120, a set of coefficients that leads to a predictive equation for \(D_{\text{Ni}}^{\text{ol/liq}}\) applicable to a wide range of melt compositions. We use the results of our work to model the melting of peridotite beneath lithosphere of varying thickness and show that: (1) a positive correlation between NiO in magnesian olivine phenocrysts and lithospheric thickness is expected given a temperature-dependent \(D_{\text{Ni}}^{\text{ol/liq}} ,\) and (2) the magnitude of the slope for natural samples is consistent with our experimentally determined temperature dependence. Alternative processes to generate the positive correlation between NiO in magnesian olivines and lithospheric thickness, such as the melting of olivine-free pyroxenite, are possible, but they are not required to explain the observed correlation of NiO concentration in initially crystallizing olivine with lithospheric thickness.     

The thermal expansion and crystal structure of mirabilite (Na<Subscript>2</Subscript>SO<Subscript>4</Subscript>·10D<Subscript>2</Subscript>O) from 4.2 to 300 K,determined by time-of-flight neutron powder diffraction

We have collected high resolution neutron powder diffraction patterns from Na₂SO₄·10D₂O over the temperature range 4.2–300 K following rapid quenching in liquid nitrogen, and over a series of slow warming and cooling cycles. The crystal is monoclinic, space-group P2₁/c (Z = 4) with a = 11.44214(4) Å, b = 10.34276(4) Å, c = 12.75486(6) Å, β = 107.847(1)°, and V = 1436.794(8) Å³ at 4.2 K (slowly cooled), and a = 11.51472(6) Å, b = 10.36495(6) Å, c = 12.84651(7) Å, β = 107.7543(1)°, V = 1460.20(1) Å³ at 300 K. Structures were refined to R _P (Rietveld powder residual, \( R_{P} = {{\sum {\left| {I_{\text{obs}} - I_{\text{calc}} } \right|} } \mathord{\left/ {\vphantom {{\sum {\left| {I_{\text{obs}} - I_{\text{calc}} } \right|} } {\sum {I_{\text{obs}} } }}} \right. \kern-\nulldelimiterspace} {\sum {I_{\text{obs}} } }} \)) better than 2.5% at 4.2 K (quenched and slow cooled), 150 and 300 K. The sulfate disorder observed previously by Levy and Lisensky (Acta Cryst B34:3502–3510, 1978) was not present in our specimen, but we did observe changes with temperature in deuteron occupancies of the orientationally disordered water molecules coordinated to Na. The temperature dependence of the unit-cell volume from 4.2 to 300 K is well represented by a simple polynomial of the form V = ? 4.143(1) × 10^?7 T ³ + 0.00047(2) T² ? 0.027(2) T + 1437.0(1) Å³ (R ² = 99.98%). The coefficient of volume thermal expansion, α _V , is positive above 40 K, and displays a similar magnitude and temperature dependence to α _V in deuterated epsomite and meridianiite. The relationship between the magnitude and orientation of the principal axes of the thermal expansion tensor and the main structural elements are discussed; freezing in of deuteron disorder in the quenched specimen affects the thermal expansion, manifested most obviously as a change in the behaviour of the unit-cell parameter β.     

H<Subscript>2</Subscript>O diffusion in peralkaline to peraluminous rhyolitic melts

The diffusion of water in a peralkaline and a peraluminous rhyolitic melt was investigated at temperatures of 714–1,493 K and pressures of 100 and 500 MPa. At temperatures below 923 K dehydration experiments were performed on glasses containing about 2 wt% H₂O _t in cold seal pressure vessels. At high temperatures diffusion couples of water-poor (<0.5 wt% H₂O _t ) and water-rich (~2 wt% H₂O _t ) melts were run in an internally heated gas pressure vessel. Argon was the pressure medium in both cases. Concentration profiles of hydrous species (OH groups and H₂O molecules) were measured along the diffusion direction using near-infrared (NIR) microspectroscopy. The bulk water diffusivity () was derived from profiles of total water () using a modified Boltzmann-Matano method as well as using fittings assuming a functional relationship between and Both methods consistently indicate that is proportional to in this range of water contents for both bulk compositions, in agreement with previous work on metaluminous rhyolite. The water diffusivity in the peraluminous melts agrees very well with data for metaluminous rhyolites implying that an excess of Al₂O₃ with respect to alkalis does not affect water diffusion. On the other hand, water diffusion is faster by roughly a factor of two in the peralkaline melt compared to the metaluminous melt. The following expression for the water diffusivity in the peralkaline rhyolite as a function of temperature and pressure was obtained by least-squares fitting:

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.     

An experimental study of amphibole stability in low-pressure granitic magmas and a revised Al-in-hornblende geobarometer

We report new experimental data on the composition of magmatic amphiboles synthesised from a variety of granite (sensu lato) bulk compositions at near-solidus temperatures and pressures of 0.8–10 kbar. The total aluminium content (Al^tot) of the synthetic calcic amphiboles varies systematically with pressure (P), although the relationship is nonlinear at low pressures (<2.5 kbar). At higher pressures, the relationship resembles that of other experimental studies, which suggests of a general relationship between Al^tot and P that is relatively insensitive to bulk composition. We have developed a new Al-in-hornblende geobarometer that is applicable to granitic rocks with the low-variance mineral assemblage: amphibole + plagioclase (An_15–80) + biotite + quartz + alkali feldspar + ilmenite/titanite + magnetite + apatite. Amphibole analyses should be taken from the rims of grains, in contact with plagioclase and in apparent textural equilibrium with the rest of the mineral assemblage at temperatures close to the haplogranite solidus (725 ± 75 °C), as determined from amphibole–plagioclase thermometry. Mean amphibole rim compositions that meet these criteria can then be used to calculate P (in kbar) from Al^tot (in atoms per formula unit, apfu) according to the expression:

$${\textit{P }}\left( {\text{kbar}} \right) = 0.5 + 0.331\left( 8 \right) \times {\text{Al}}^{\text{tot}} + 0.995\left( 4 \right) \times \left( {{\text{Al}}^{\text{tot}} } \right)^{2}$$

This expression recovers equilibration pressures of our calibrant dataset, comprising both new and published experimental and natural data, to within ±16 % relative uncertainty. An uncertainty of 10 % relative for a typical Al^tot value of 1.5 apfu translates to an uncertainty in pressure estimate of 0.5 kbar, or 15 % relative. Thus the accuracy of the barometer expression is comparable to the precision with which near-solidus amphibole rim composition can be characterised.

     

An experimental study of Ti and Zr partitioning among zircon, rutile, and granitic melt

In order to evaluate the effect of trace and minor elements (e.g., P, Y, and the REEs) on the high-temperature solubility of Ti in zircon (zrc), we conducted 31 experiments on a series of synthetic and natural granitic compositions [enriched in TiO₂ and ZrO₂; Al/(Na + K) molar ~1.2] at a pressure of 10 kbar and temperatures of ~1,400 to 1,200 °C. Thirty of the experiments produced zircon-saturated glasses, of which 22 are also saturated in rutile (rt). In seven experiments, quenched glasses coexist with quartz (qtz). SiO₂ contents of the quenched liquids range from 68.5 to 82.3 wt% (volatile free), and water concentrations are 0.4–7.0 wt%. TiO₂ contents of the rutile-saturated quenched melts are positively correlated with run temperature. Glass ZrO₂ concentrations (0.2–1.2 wt%; volatile free) also show a broad positive correlation with run temperature and, at a given T, are strongly correlated with the parameter (Na + K + 2Ca)/(Si·Al) (all in cation fractions). Mole fraction of ZrO₂ in rutile $ \left( {\mathop X\nolimits_{{{\text{ZrO}}_{ 2} }}^{\text{rt}} } \right) $ in the quartz-saturated runs coupled with other 10-kbar qtz-saturated experimental data from the literature (total temperature range of ~1,400 to 675 °C) yields the following temperature-dependent expression: $ {\text{ln}}\left( {\mathop X\nolimits_{{{\text{ZrO}}_{ 2} }}^{\text{rt}} } \right) + {\text{ln}}\left( {a_{{{\text{SiO}}_{2} }} } \right) = 2.638(149) - 9969(190)/T({\text{K}}) $ , where silica activity $ a_{{{\text{SiO}}_{2} }} $ in either the coexisting silica polymorph or a silica-undersaturated melt is referenced to α-quartz at the P and T of each experiment and the best-fit coefficients and their uncertainties (values in parentheses) reflect uncertainties in T and $ \mathop X\nolimits_{{{\text{ZrO}}_{2} }}^{\text{rt}} $ . NanoSIMS measurements of Ti in zircon overgrowths in the experiments yield values of ~100 to 800 ppm; Ti concentrations in zircon are positively correlated with temperature. Coupled with values for $ a_{{{\text{SiO}}_{2} }} $ and $ a_{{{\text{TiO}}_{2} }} $ for each experiment, zircon Ti concentrations (ppm) can be related to temperature over the range of ~1,400 to 1,200 °C by the expression: $ \ln \left( {\text{Ti ppm}} \right)^{\text{zrc}} + \ln \left( {a_{{{\text{SiO}}_{2} }} } \right) - \ln \left( {a_{{{\text{TiO}}_{2} }} } \right) = 13.84\left( {71} \right) - 12590\left( {1124} \right)/T\left( {\text{K}} \right) $ . After accounting for differences in $ a_{{{\text{SiO}}_{2} }} $ and $ a_{{{\text{TiO}}_{2} }} $ , Ti contents of zircon from experiments run with bulk compositions based on the natural granite overlap with the concentrations measured on zircon from experiments using the synthetic bulk compositions. Coupled with data from the literature, this suggests that at T ≥ 1,100 °C, natural levels of minor and trace elements in “granitic” melts do not appear to influence the solubility of Ti in zircon. Whether this is true at magmatic temperatures of crustal hydrous silica-rich liquids (e.g., 800–700 °C) remains to be demonstrated. Finally, measured $ D_{\text{Ti}}^{{{\text{zrc}}/{\text{melt}}}} $ values (calculated on a weight basis) from the experiments presented here are 0.007–0.01, relatively independent of temperature, and broadly consistent with values determined from natural zircon and silica-rich glass pairs.     

Experimental determination of liquidus H<Subscript>2</Subscript>O contents of haplogranite at deep-crustal conditions

The liquidus water content of a haplogranite melt at high pressure (P) and temperature (T) is important, because it is a key parameter for constraining the volume of granite that could be produced by melting of the deep crust. Previous estimates based on melting experiments at low P (≤0.5 GPa) show substantial scatter when extrapolated to deep crustal P and T (700–1000 °C, 0.6–1.5 GPa). To improve the high-P constraints on H₂O concentration at the granite liquidus, we performed experiments in a piston–cylinder apparatus at 1.0 GPa using a range of haplogranite compositions in the albite (Ab: NaAlSi₃O₈)—orthoclase (Or: KAlSi₃O₈)—quartz (Qz: SiO₂)—H₂O system. We used equal weight fractions of the feldspar components and varied the Qz between 20 and 30 wt%. In each experiment, synthetic granitic composition glass + H₂O was homogenized well above the liquidus T, and T was lowered by increments until quartz and alkali feldspar crystalized from the liquid. To establish reversed equilibrium, we crystallized the homogenized melt at the lower T and then raised T until we found that the crystalline phases were completely resorbed into the liquid. The reversed liquidus minimum temperatures at 3.0, 4.1, 5.8, 8.0, and 12.0 wt% H₂O are 935–985, 875–900, 775–800, 725–775, and 650–675 °C, respectively. Quenched charges were analyzed by petrographic microscope, scanning electron microscope (SEM), X-ray diffraction (XRD), and electron microprobe analysis (EMPA). The equation for the reversed haplogranite liquidus minimum curve for Ab_36.25Or_36.25Qz_27.5 (wt% basis) at 1.0 GPa is \(T = - 0.0995 w_{{{\text{H}}_{ 2} {\text{O}}}}^{ 3} + 5.0242w_{{{\text{H}}_{ 2} {\text{O}}}}^{ 2} - 88.183 w_{{{\text{H}}_{ 2} {\text{O}}}} + 1171.0\) for \(0 \le w_{{{\text{H}}_{ 2} {\text{O}}}} \le 17\) wt% and \(T\) is in °C. We present a revised \(P - T\) diagram of liquidus minimum H₂O isopleths which integrates data from previous determinations of vapor-saturated melting and the lower pressure vapor-undersaturated melting studies conducted by other workers on the haplogranite system. For lower H₂O (<5.8 wt%) and higher temperature, our results plot on the high end of the extrapolated water contents at liquidus minima when compared to the previous estimates. As a consequence, amounts of metaluminous granites that can be produced from lower crustal biotite–amphibole gneisses by dehydration melting are more restricted than previously thought.     

Energetics of hydration of cordierite and water barometry in cordierite-granulites

The Gibbs free energy and volume changes attendant upon hydration of cordierites in the system magnesian cordierite-water have been extracted from the published high pressure experimental data at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P _total, assuming an ideal one site model for H₂O in cordierite. Incorporating the dependence of ΔG and ΔV on temperature, which was found to be linear within the experimental conditions of 500°–1,000°C and 1–10,000 bars, the relation between the water content of cordierite and P, T and \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) has been formulated as $$\begin{gathered} X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} = \hfill \\ \frac{{f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }}{{\left[ {{\text{exp}}\frac{1}{{RT}}\left\{ {64,775 - 32.26T + G_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{1, }}T} - P\left( {9 \times 10^{ - 4} T - 0.5142} \right)} \right\}} \right] + f_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{P, T}}} }} \hfill \\ \end{gathered} $$ The equation can be used to compute H₂O in cordierites at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) <1. Our results at different P, T and partial pressure of water, assuming ideal mixing of H₂O and CO₂ in the vapour phase, are in very good agreement with the experimental data of Johannes and Schreyer (1977, 1981). Applying the formulation to determine \(X_{{\text{H}}_{\text{2}} {\text{O}}}^{{\text{crd}}} \) in the garnet-cordierite-sillimanite-plagioclase-quartz granulites of Finnish Lapland as a test case, good agreement with the gravimetrically determined water contents of cordierite was obtained. Pressure estimates, from a thermodynamic modelling of the Fe-cordierite — almandine — sillimanite — quartz equilibrium at \(P_{{\text{H}}_{\text{2}} {\text{O}}} = 0\) and \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =P_total, for assemblages from South India, Scottish Caledonides, Daly Bay and Hara Lake areas are compatible with those derived from the garnetplagioclase-sillimanite-quartz geobarometer.     

Heat capacity of hydrous trachybasalt from Mt Etna: comparison with CaAl<Subscript>2</Subscript>Si<Subscript>2</Subscript>O<Subscript>8</Subscript> (An)–CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript> (Di) as basaltic proxy compositions

The specific heat capacity (C _p) of six variably hydrated (~3.5 wt% H₂O) iron-bearing Etna trachybasaltic glasses and liquids has been measured using differential scanning calorimetry from room temperature across the glass transition region. These data are compared to heat capacity measurements on thirteen melt compositions in the iron-free anorthite (An)–diopside (Di) system over a similar range of H₂O contents. These data extend considerably the published C _p measurements for hydrous melts and glasses. The results for the Etna trachybasalts show nonlinear variations in, both, the heat capacity of the glass at the onset of the glass transition (i.e., C _p ^g ) and the fully relaxed liquid (i.e., C _p ^l ) with increasing H₂O content. Similarly, the “configurational heat capacity” (i.e., C _p ^c  = C _p ^l  ? C _p ^g ) varies nonlinearly with H₂O content. The An–Di hydrous compositions investigated show similar trends, with C _p values varying as a function of melt composition and H₂O content. The results show that values in hydrous C _p ^g , C _p ^l and C _p ^c in the depolymerized glasses and liquids are substantially different from those observed for more polymerized hydrous albitic, leucogranitic, trachytic and phonolitic multicomponent compositions previously investigated. Polymerized melts have lower C _p ^l and C _p ^c and higher C _p ^g with respect to more depolymerized compositions. The covariation between C _p values and the degree of polymerization in glasses and melts is well described in terms of SM_hydrous and NBO/T _hydrous. Values of C _p ^c increase sharply with increasing depolymerization up to SM_hydrous ~ 30–35 mol% (NBO/T _hydrous ~ 0.5) and then stabilize to an almost constant value. The partial molar heat capacity of H₂O for both glasses (\( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{g}} \)) and liquids (\( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{l}} \)) appears to be independent of composition and, assuming ideal mixing, we obtain a value for \( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{l}} \) of 79 J mol^?1 K^?1. However, we note that a range of values for \( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{l}} \) (i.e., ~78–87 J mol^?1 K^?1) proposed by previous workers will reproduce the extended data to within experimental uncertainty. Our analysis suggests that more data are required in order to ascribe a compositional dependence (i.e., nonideal mixing) to \( C_{{{\text{p}}\;{\text{H}}_{2} {\text{O}}}}^{\text{l}} \).     

The effect of alkalis and polymerization on the solubility of H<Subscript>2</Subscript>O and CO<Subscript>2</Subscript> in alkali-rich silicate melts

The effect of alkalis on the solubility of H₂O and CO₂ in alkali-rich silicate melts was investigated at 500 MPa and 1,250 °C in the systems with H₂O/(H₂O + CO₂) ratio varying from 0 to 1. Using a synthetic analog of phonotephritic magma from Alban Hills (AH1) as a base composition, the Na/(Na + K) ratio was varied from 0.28 (AH1) to 0.60 (AH2) and 0.85 (AH3) at roughly constant total alkali content. The obtained results were compared with the data for shoshonitic and latitic melts having similar total alkali content but different structural characteristics, e.g., NBO/T parameter (the ratio of non-bridging oxygens over tetrahedrally coordinated cations), as those of the AH compositions. Little variation was observed in H₂O solubility (melt equilibrated with pure H₂O fluid) for the whole compositional range in this study with values ranging between 9.7 and 10.2 wt. As previously shown, the maximum CO₂ content in melts equilibrated with CO₂-rich fluids increases strongly with the NBO/T from 0.29 wt % for latite (NBO/T = 0.17) to 0.45 wt % for shoshonite (NBO/T = 0.38) to 0.90 wt % for AH2 (NBO/T = 0.55). The highest CO₂ contents determined for AH3 and AH1 are 1.18 ± 0.05 wt % and 0.86 ± 0.12 wt %, respectively, indicating that Na is promoting carbonate incorporation stronger than potassium. At near constant NBO/T, CO₂ solubility increases from 0.86 ± 0.12 wt % in AH1 [Na/(Na + K)] = 0.28, to 1.18 ± 0.05 wt % in AH3 [Na/(Na + K)] = 0.85, suggesting that Na favors CO₂ solubility on an equimolar basis. An empirical equation is proposed to predict the maximum CO₂ solubility at 500 MPa and 1,100–1,300 °C in various silicate melts as a function of the NBO/T, (Na + K)/∑cations and Na/(Na + K) parameters: \({\text{wt}}\% \;{\text{CO}}_{2} = - 0.246 + 0.014\exp \left( {6.995 \cdot \frac{\text{NBO}}{T}} \right) + 3.150 \cdot \frac{{{\text{Na}} + {\text{K}}}}{{\varSigma {\text{cations}}}} + 0.222 \cdot \frac{\text{Na}}{{{\text{Na}} + {\text{K}}}}.\) This model is valid for melt compositions with NBO/T between 0.0 and 0.6, (Na + K)/∑cation between 0.08 and 0.36 and Na/(Na + K) ratio from 0.25 to 0.95 at oxygen fugacities around the quartz–fayalite–magnetite buffer and above.     

The system Fe-Si-O: Oxygen buffer calibrations to 1,500K

The five solid-phase oxygen buffers of the system Fe-Si-O, iron-wuestite (IW), wuestite-magnetite (WM), magnetite-hematite (MH), quartz-iron-fayalite (QIF) and fayalite-magnetite-quartz (FMQ) have been recalibrated at 1 atm pressure and temperatures from 800°–1,300° C, using a thermogravimetric gas mixing furnace. The oxygen fugacity, \(f_{{\text{O}}_{\text{2}} }\) was measured with a CaO-doped ZrO₂ electrode. Measurements were made also for wuestite solid solutions in order to determine the redox behavior of wuestites with O/Fe ratios varying from 1.05 to 1.17. For FMQ, additional determinations were carried out at 1 kb over a temperature range of 600° to 800° C, using a modified Shaw membrane. Results agree reasonably well with published data and extrapolations. The reaction parameters K, ΔG _r ^o , ΔH _r ^o , and ΔS _r ^o were calculated from the following log \(f_{{\text{O}}_{\text{2}} }\) /T relations (T in K): $$\begin{gathered} {\text{IW }}\log f_{{\text{O}}_{\text{2}} } = - 26,834.7/T + 6.471\left( { \pm 0.058} \right) \hfill \\ {\text{ }}\left( {{\text{800}} - 1,260{\text{ C}}} \right), \hfill \\ {\text{WM }}\log f_{{\text{O}}_{\text{2}} } = - 36,951.3/T + 16.092\left( { \pm 0.045} \right) \hfill \\ {\text{ }}\left( {{\text{1,000}} - 1,300{\text{ C}}} \right), \hfill \\ {\text{MH }}\log f_{{\text{O}}_{\text{2}} } = - 23,847.6/T + 13.480\left( { \pm 0.055} \right) \hfill \\ {\text{ }}\left( {{\text{1,040}} - 1,270{\text{ C}}} \right), \hfill \\ {\text{QIF }}\log f_{{\text{O}}_{\text{2}} } = - 27,517.5/T + 6.396\left( { \pm 0.049} \right) \hfill \\ {\text{ }}\left( {{\text{960}} - 1,140{\text{ C}}} \right), \hfill \\ {\text{FMQ }}\log f_{{\text{O}}_{\text{2}} } = - 24,441.9/T + 8.290\left( { \pm 0.167} \right) \hfill \\ {\text{ }}\left( {{\text{600}} - 1,140{\text{ C}}} \right). \hfill \\ \end{gathered}$$ These experimentally determined reaction parameters were combined with published 298 K data to determine the parameters G_f, H_f, and S_f for the phases wuestite, magnetite, hematite, and fayalite from 298 K to the temperatures of the experiments. The T? \(f_{{\text{O}}_{\text{2}} }\) data for wuestite solid solutions were used to obtain activities, excess free energies and Margules mixing parameters. The new data provide a more reliable, consistent and complete reference set for the interpretation of redox reactions at elevated temperatures in experiments and field settings encompassing the crust, mantle and core as well as extraterrestrial environments.     

Assemblages among tephroite,pyroxmangite, rhodochrosite,quartz: Experimental data and occurrences in the Rhetic Alps

Reactions involving the phases quartz-rhodochrosite-tephroite-pyroxmangite-fluid have been studied experimentally in the system MnO-SiO₂-CO₂-H₂O at a pressure of 2 000 bars and resulted in the following expressions 1 $$\begin{gathered} {\text{Rhodochrosite + Quartz = Pyroxmangite + CO}}_2 \hfill \\ {\text{ log}}_{{\text{10}}} K^{{\text{2000 bars}}} = - \frac{{11.765}}{T} + 18.618. \hfill \\ {\text{Rhodochrosite + Pyroxmangite = Tephroite + CO}}_2 \hfill \\ {\text{ log}}_{{\text{10}}} K^{{\text{2000 bars}}} = - \frac{{7.083}}{T} + 11.870. \hfill \\ \end{gathered}$$ which can be used to derive data for the remaining two reactions among the phases under consideration. Field data from the Alps are in agreement with the metamorphic sequence resulting from the experiments.     

(Ca,Mg)2Si2O6 clinopyroxenes: A solution model based on nonconvergent site-disorder

Experiments at high pressure and temperature indicate that excess Ca may be dissolved in diopside. If the (Ca, Mg)₂Si₂O₆ clinopyroxene solution extends to more Ca-rich compositions than CaMgSi₂O₆, macroscopic regular solution models cannot strictly be applied to this system. A nonconvergent site-disorder model, such as that proposed by Thompson (1969, 1970), may be more appropriate. We have modified Thompson's model to include asymmetric excess parameters and have used a linear least-squares technique to fit the available experimental data for Ca-Mg orthopyroxene-clinopyroxene equilibria and Fe-free pigeonite stability to this model. The model expressions for equilibrium conditions \(\mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Mg}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction A) and \(\mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{opx}}} = \mu _{{\text{Ca}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} }^{{\text{cpx}}} \) (reaction B) are given by: 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Mg}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ W_{21} [2(X_{{\text{Ca}}}^{{\text{M2}}} )^3 - (X_{{\text{Ca}}}^{{\text{M2}}} ] \hfill \\ {\text{ + 2W}}_{{\text{22}}} [X_{{\text{Ca}}}^{{\text{M2}}} )^2 - (X_{{\text{Ca}}}^{{\text{M2}}} )^3 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{Wo}}}^{{\text{opx}}} )^2 \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = {\text{RT 1n}}\left[ {\frac{{(X_{{\text{Ca}}}^{{\text{opx}}} )^2 }}{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Ca}}}^{{\text{M2}}} }}} \right] - \frac{1}{2}\{ 2W_{21} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^2 - (X_{{\text{Mg}}}^{{\text{M2}}} )^3 ] \hfill \\ {\text{ + W}}_{{\text{22}}} [2(X_{{\text{Mg}}}^{{\text{M2}}} )^3 - (X_{{\text{Mg}}}^{{\text{M2}}} )^2 + \Delta {\text{G}}_{\text{*}}^{\text{0}} (X_{{\text{Mg}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} )\} \hfill \\ {\text{ + W}}^{{\text{opx}}} (X_{{\text{En}}}^{{\text{opx}}} )^2 \hfill \\ \hfill \\ \end{gathered} $$ where 1 $$\begin{gathered} \Delta \mu _{\text{A}}^{\text{O}} = 2.953 + 0.0602{\text{P}} - 0.00179{\text{T}} \hfill \\ \Delta \mu _{\text{B}}^{\text{O}} = 24.64 + 0.958{\text{P}} - (0.0286){\text{T}} \hfill \\ {\text{W}}_{{\text{21}}} = 47.12 + 0.273{\text{P}} \hfill \\ {\text{W}}_{{\text{22}}} = 66.11 + ( - 0.249){\text{P}} \hfill \\ {\text{W}}^{{\text{opx}}} = 40 \hfill \\ \Delta {\text{G}}_*^0 = 155{\text{ (all values are in kJ/gfw)}}{\text{.}} \hfill \\ \end{gathered} $$ . Site occupancies in clinopyroxene were determined from the internal equilibrium condition 1 $$\begin{gathered} \Delta G_{\text{E}}^{\text{O}} = - {\text{RT 1n}}\left[ {\frac{{X_{{\text{Ca}}}^{{\text{M1}}} \cdot X_{{\text{Mg}}}^{{\text{M2}}} }}{{X_{{\text{Ca}}}^{{\text{M2}}} \cdot X_{{\text{Mg}}}^{{\text{M1}}} }}} \right] + \tfrac{1}{2}[(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} )(2{\text{X}}_{{\text{Ca}}}^{{\text{M2}}} - 1) \hfill \\ {\text{ + }}\Delta G_*^0 (X_{{\text{Ca}}}^{{\text{M1}}} - X_{{\text{Ca}}}^{{\text{M2}}} ) + \tfrac{3}{2}(2{\text{W}}_{{\text{21}}} - {\text{W}}_{{\text{22}}} ) \hfill \\ {\text{ (1}} - 2X_{{\text{Ca}}}^{{\text{M1}}} )(X_{{\text{Ca}}}^{{\text{M1}}} + \tfrac{1}{2})] \hfill \\ \end{gathered} $$ where δG _E ⁰ =153+0.023T+1.2P. The predicted concentrations of Ca on the clinopyroxene Ml site are low enough to be compatible with crystallographic studies. Temperatures calculated from the model for coexisting ortho- and clinopyroxene pairs fit the experimental data to within 10° in most cases; the worst discrepancy is 30°. Phase relations for clinopyroxene, orthopyroxene and pigeonite are successfully described by this model at temperatures up to 1,600° C and pressures from 0.001 to 40 kbar. Predicted enthalpies of solution agree well with the calorimetric measurements of Newton et al. (1979). The nonconvergent site disorder model affords good approximations to both the free energy and enthalpy of clinopyroxenes, and, therefore, the configurational entropy as well. This approach may provide an example for Febearing pyroxenes in which cation site exchange has an even more profound effect on the thermodynamic properties.     

Oxygen isotope fractionation between rutile and water

Synthetic rutile-water fractionations (1000 ln α) at 775, 675, and 575° C were found to be ?2.8, ?3.5, and ?4.8, respectively. Partial exchange experiments with natural rutile at 575° C and with synthetic rutile at 475° C failed to yield reliable fractionations. Isotopic fractionation within the range 575–775° C may be expressed as follows: 1 $$1000\ln \alpha ({\rm T}i{\rm O}_{2 } - H_2 O) = - 4.1 \frac{{10^6 }}{{T_{k^2 } }} + 0.96$$ . Combined with previously determined quartz-water fractionations, the above data permit calibration of the quartz-rutile geothermometer: 1 $$1000\ln \alpha ({\text{S}}i{\rm O}_{2 } - Ti{\rm O}_{2 } ) = 6.6 \frac{{10^6 }}{{T_{k^2 } }} - 2.9$$ . When applied to B-type eclogites from Europe, as an example, the latter equation yields a mean equilibration temperature of 565° C.