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)°].     

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.     

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.

     

Water diffusion in Mount Changbai peralkaline rhyolitic melt

Diffusion couple experiments with wet half (up to 4.6 wt%) and dry half were carried out at 789–1,516 K and 0.47–1.42 GPa to investigate water diffusion in a peralkaline rhyolitic melt with major oxide concentrations matching Mount Changbai rhyolite. Combining data from this work and a related study, total water diffusivity in peralkaline rhyolitic melt can be expressed as:

$ D_{{{\text{H}}_{ 2} {\text{O}}_{\text{t}} }} = D_{{{\text{H}}_{ 2} {\text{O}}_{\text{m}} }} \left( {1 - \frac{0.5 - X}{{\sqrt {[4\exp (3110/T - 1.876) - 1](X - X^{2} ) + 0.25} }}} \right), $

$ {\text{with}}\;D_{{{\text{H}}_{ 2} {\text{O}}_{\text{m}} }} = \exp \left[ { - 1 2. 7 8 9- \frac{13939}{T} - 1229.6\frac{P}{T} + ( - 27.867 + \frac{60559}{T})X} \right], $

where D is in m² s^?1, T is the temperature in K, P is the pressure in GPa, and X is the mole fraction of water and calculated as X = (C/18.015)/(C/18.015 + (100 ? C)/33.14), where C is water content in wt%. We recommend this equation in modeling bubble growth and volcanic eruption dynamics in peralkaline rhyolitic eruptions, such as the ~1,000-ad eruption of Mount Changbai in North East China. Water diffusivities in peralkaline and metaluminous rhyolitic melts are comparable within a factor of 2, in contrast with the 1.0–2.6 orders of magnitude difference in viscosities. The decoupling of diffusivity of neutral molecular species from melt viscosity, i.e., the deviation from the inversely proportional relationship predicted by the Stokes–Einstein equation, might be attributed to the small size of H₂O molecules. With distinct viscosities but similar diffusivity, bubble growth controlled by diffusion in peralkaline and metaluminous rhyolitic melts follows similar parabolic curves. However, at low confining pressure or low water content, viscosity plays a larger role and bubble growth rate in peralkaline rhyolitic melt is much faster than that in metaluminous rhyolite.

     

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.     

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.

     

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 dilatant behaviour of sand–pile interface subjected to loading and stress relief

Property and behaviour of sand–pile interface are crucial to shaft resistance of piles. Dilation or contraction of the interface soil induces change in normal stress, which in turn influences the shear stress mobilised at the interface. Although previous studies have demonstrated this mechanism by laboratory tests and numerical simulations, the interface responses are not analysed systematically in terms of soil state (i.e. density and stress level). The objective of this study is to understand and quantify any increase in normal stress of different pile–soil interfaces when they are subjected to loading and stress relief. Distinct element modelling was carried out. Input parameters and modelling procedure were verified by experimental data from laboratory element tests. Parametric simulations of shearbox tests were conducted under the constant normal stiffness, constant normal load and constant volume boundary conditions. Key parameters including initial normal stress ( $ \sigma_{{{\text{n}}0}}^{\prime } $ ), initial void ratio (e ₀), normal stiffness constraining the interface and loading–unloading stress history were investigated. It is shown that mobilised stress ratio ( $ \tau /\sigma_{\text{n}}^{\prime } $ ) and normal stress increment ( $ \Updelta \sigma_{\text{n}}^{\prime } $ ) on a given interface are governed by $ \sigma_{{{\text{n}}0}}^{\prime } $ and e ₀. An increase in $ \sigma_{{{\text{n}}0}}^{\prime } $ from 100 to 400 kPa leads to a 30 % reduction in $ \Updelta \sigma_{\text{n}}^{\prime } $ . An increase in e ₀ from 0.18 to 0.30 reduces $ \Updelta \sigma_{\text{n}}^{\prime } $ by more than 90 %, and therefore, shaft resistance is much lower for piles in loose sands. A unique relationship between $ \Updelta \sigma_{\text{n}}^{\prime } $ and normal stiffness is established for different soil states. It can be applied to assess the shaft resistance of piles in soils with different densities and subjected to loading and stress relief. Fairly good agreement is obtained between the calculated shaft resistance based on the proposed relationship and the measured results in centrifuge model tests.     

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.     

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 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.     

Crystal chemistry of Fe3+-bearing (Mg,Fe)SiO3 perovskite: a single-crystal X-ray diffraction study

Magnesium silicate perovskite is the predominant phase in the Earth’s lower mantle, and it is well known that incorporation of iron has a strong effect on its crystal structure and physical properties. To constrain the crystal chemistry of (Mg, Fe)SiO₃ perovskite more accurately, we synthesized single crystals of Mg_0.946(17)Fe_0.056(12)Si_0.997(16)O₃ perovskite at 26 GPa and 2,073 K using a multianvil press and investigated its crystal structure, oxidation state and iron-site occupancy using single-crystal X-ray diffraction and energy-domain Synchrotron Mössbauer Source spectroscopy. Single-crystal refinements indicate that all iron (Fe²⁺ and Fe³⁺) substitutes on the A-site only, where \( {\text{Fe}}^{ 3+ } /\Upsigma {\text{Fe}}\sim 20\,\% \) based on Mössbauer spectroscopy. Charge balance likely occurs through a small number of cation vacancies on either the A- or the B-site. The octahedral tilt angle (Φ) calculated for our sample from the refined atomic coordinates is 20.3°, which is 2° higher than the value calculated from the unit-cell parameters (a = 4.7877 Å, b = 4.9480 Å, c = 6.915 Å) which assumes undistorted octahedra. A compilation of all available single-crystal data (atomic coordinates) for (Mg, Fe)(Si, Al)O₃ perovskite from the literature shows a smooth increase of Φ with composition that is independent of the nature of cation substitution (e.g., \( {\text{Mg}}^{ 2+ } - {\text{Fe}}^{ 2+ } \) or \( {\text{Mg}}^{ 2+ } {\text{Si}}^{ 4+ } - {\text{Fe}}^{ 3+ } {\text{Al}}^{ 3+ } \) substitution mechanism), contrary to previous observations based on unit-cell parameter calculations.     

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.     

The high-pressure stability of chlorite and other hydrates in subduction mélanges: experiments in the system Cr<Subscript>2</Subscript>O<Subscript>3</Subscript>–MgO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–SiO<Subscript>2</Subscript>–H<Subscript>2</Subscript>O

The solubility of chromium in chlorite as a function of pressure, temperature, and bulk composition was investigated in the system Cr₂O₃–MgO–Al₂O₃–SiO₂–H₂O, and its effect on phase relations evaluated. Three different compositions with X _Cr = Cr/(Cr + Al) = 0.075, 0.25, and 0.5 respectively, were investigated at 1.5–6.5 GPa, 650–900 °C. Cr-chlorite only occurs in the bulk composition with X _Cr = 0.075; otherwise, spinel and garnet are the major aluminous phases. In the experiments, Cr-chlorite coexists with enstatite up to 3.5 GPa, 800–850 °C, and with forsterite, pyrope, and spinel at higher pressure. At P > 5 GPa other hydrates occur: a Cr-bearing phase-HAPY (Mg_2.2Al_1.5Cr_0.1Si_1.1O₆(OH)₂) is stable in assemblage with pyrope, forsterite, and spinel; Mg-sursassite coexists at 6.0 GPa, 650 °C with forsterite and spinel and a new Cr-bearing phase, named 11.5 Å phase (Mg:Al:Si = 6.3:1.2:2.4) after the first diffraction peak observed in high-resolution X-ray diffraction pattern. Cr affects the stability of chlorite by shifting its breakdown reactions toward higher temperature, but Cr solubility at high pressure is reduced compared with the solubility observed in low-pressure occurrences in hydrothermal environments. Chromium partitions generally according to \(X_{\text{Cr}}^{\text{spinel}}\) ? \(X_{\text{Cr}}^{\text{opx}}\) > \(X_{\text{Cr}}^{\text{chlorite}}\) ≥ \(X_{\text{Cr}}^{\text{HAPY}}\) > \(X_{\text{Cr}}^{\text{garnet}}\). At 5 GPa, 750 °C (bulk with X _Cr = 0.075) equilibrium values are \(X_{\text{Cr}}^{\text{spinel}}\) = 0.27, \(X_{\text{Cr}}^{\text{chlorite}}\) = 0.08, \(X_{\text{Cr}}^{\text{garnet}}\) = 0.05; at 5.4 GPa, 720 °C \(X_{\text{Cr}}^{\text{spinel}}\) = 0.33, \(X_{\text{Cr}}^{\text{HAPY}}\) = 0.06, and \(X_{\text{Cr}}^{\text{garnet}}\) = 0.04; and at 3.5 GPa, 850 °C \(X_{\text{Cr}}^{\text{opx}}\) = 0.12 and \(X_{\text{Cr}}^{\text{chlorite}}\) = 0.07. Results on Cr–Al partitioning between spinel and garnet suggest that at low temperature the spinel- to garnet-peridotite transition has a negative slope of 0.5 GPa/100 °C. The formation of phase-HAPY, in assemblage with garnet and spinel, at pressures above chlorite breakdown, provides a viable mechanism to promote H₂O transport in metasomatized ultramafic mélanges of subduction channels.     

Majoritic garnet grains within shock-induced melt veins in amphibolites from the Ries impact crater suggest ultrahigh crystallization pressures between 18 and 9 GPa

Shock-induced melt veins in amphibolites from the Nördlinger Ries often have chemical compositions that are similar to bulk rock (i.e., basaltic), but there are other veins that are confined to chlorite-rich cracks that formed before the impact and these are poor in Ca and Na. Majoritic garnets within the shock veins show a broad chemical variation between three endmembers: (1) \({}^{\text{VIII}}{{\text{M}^{2+}}_3} {}^{\text{VI}}{\text{Al}}_{2} ({}^{\text{IV}}{\text{SiO}}_{4} )_{3}\) (normal garnet, Grt), (2) \({}^{\text{VIII}}{{\text{M}^{2+}}_3} {}^{\text{VI}}[{\text{M}}^{2 + } ({\text{Si,Ti}})]({}^{\text{IV}}{\text{SiO}}_{4} )_{3}\)  (majorite, Maj), and (3) \({}^{\text{VIII}}({{\text {Na} {\text M}^{2+}}_2}) {}^{\text{VI}}[ ({\text{Si,Ti}}){\text {Al}}]({}^{\text{IV}}{\text{SiO}}_{4} )_{3}\) (Na-majorite₅₀Grt₅₀), whereby M²⁺ = Mg²⁺, Fe²⁺, Mn²⁺, Ca²⁺. In particular, we observed a broad variation in ^VI(Si,Ti) which ranges from 0.12 to 0.58 cations per formula unit (cpfu). All these majoritic garnets crystallized during shock pressure release at different ultrahigh pressures. Those with high ^VI(Si,Ti) (0.36–0.58 cpfu) formed at high pressures and temperatures from amphibole-rich melts, while majoritic garnets with lower ^VI(Si,Ti) of 0.12–0.27 cpfu formed at lower pressures and temperatures from chlorite-rich melts. Furthermore, majoritic garnets with intermediate values of ^VI(Si,Ti) (0.24–0.39) crystallized from melts with intermediate contents of Ca and Na. To the best of our knowledge the ‘MORB-type’ Ca–Na-rich majoritic garnets with maximum contents of 2.99 wt% Na₂O and calculated crystallisation pressures of 16–18 GPa are the most extreme representatives ever found in terrestrial shocked materials. At the Ries, the duration of the initial contact and compression stage at the central location of impact is estimated to only ~ 0.1 s. We used a ~ 200-µm-thick shock-induced vein in a moderately shocked amphibolite to model its pressure–temperature–time (P–T–t) path. The graphic model manifests a peak temperature of ~ 2600 °C for the vein, continuum pressure lasting for ~ 0.02 s, a quench duration of ~ 0.02 s and a shock pulse of ~ 0.038 s. The small difference between the continuum pressure and the pressure of majoritic garnet crystallization underlines the usefulness of applying crystallisation pressures of majoritic garnets from metabasites for calculation of dynamic shock pressures of host rocks. Majoritic garnets of chlorite provenance, however, are not suitable for the determination of continuum pressure since they crystallized relatively late during shock release. An extraordinary glass- and majorite-bearing amphibole fragment in a shock-vein of one amphibolite documents the whole unloading path.     

Intrinsic oxygen Fugacity measurements on chromites from the Bushveld Complex and their petrogenetic significance

Oxygen Fugacity measurements were carried out on chromites from the Eastern Bushveld Complex (Maandagshoek) and are compared with former measurements on chromites from the western Bushveld Complex (Zwartkop Chrome Mine). These results together with those of Hill and Roeder (1974) yield the following conditions of formation for the massive chromitite layers: Western Bushveld Complex (Zwartkop Chrome Mine) $$\begin{gathered} Layer{\text{ }}T(^\circ C) p_{O_2 } (atm) \hfill \\ LG3{\text{ 1160}} - {\text{1234 10}}^{ - {\text{5}}} - 10^{ - 7.6} \hfill \\ LG4{\text{ 1175}} - {\text{1200 10}}^{ - 6.35} - 10^{ - 7.20} \hfill \\ LG6{\text{ 1162}} - {\text{1207 10}}^{ - 6.20} - 10^{ - 7.50} \hfill \\ \hfill \\ \end{gathered} $$ Eastern Bushveld Complex (Farm Maandagshoek) $$\begin{gathered} {\text{LXI 1115}} - {\text{1150 10}}^{ - 7.80} - 10^{ - 8.80} \hfill \\ ( = {\text{Steelpoort Seam)}} \hfill \\ {\text{LX 1125 10}}^{ - 8.25} \hfill \\ {\text{V 1120 10}}^{ - 8.55} \hfill \\ {\text{LII 1120 10}}^{ - 8.0} - 10^{ - 8.60} \hfill \\ \end{gathered} $$ The comparison of the data shows, that the chronitite layers within each particular sequence were formed under approximately identicalp _{o 2}- andT-conditions. The chromites from the western Bushveld Complex, however, were formed at higher temperatures and higher oxygen fugacities than the chromites from the eastern Bushveld Complex. Fromp _{o 2}-T-curves of disseminated chromites and the temperatures derived above, the following conditions of formation for the host rocks were obtained: Western Bushveld Complex $$T = 1200^\circ {\text{C; }}p_{{\text{o}}_{\text{2}} } = 10^{ - 7.25} - 10^{ - 7.50} $$ Eastern Bushveld Complex $$T = 1125^\circ {\text{C; }}p_{{\text{o}}_{\text{2}} } = 10^{ - 8.50} - 10^{ - 9.25} $$ Consequently, the host rocks in the Zwartkop-Chrome-Mine, were formed under higher temperatures and higher oxygen fugacities than the host rocks at Maandagshoek. The rock sequence in the Zwartkop-Chrome-Mine therefore originated in an earlier stage of the differentiation of the Bushveld magma. Comparison of the chromites from the host rocks with the chromites from massive layers supports Ulmer's (1969) thesis that an increase of the oxygen fugacity is responsible for the formation of massive chromitite layers. The values in this investigation show that increases of only about 0.5–1.0 log units are necessary to enhance chromitite layer formation.     

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.     

(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.     

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.