Opening and resetting temperatures in heating geochronological systems

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

Weathering Processes in the Min Jiang: Major Elements, {}^{87}{\text{Sr/}}{}^{86}{\text{Sr}},\;\delta {}^{34}{\text{S}}_{{\text{SO}}_{\text{4}} } ,\;{\text{and}}\;\delta {}^{18}{\text{O}}_{{\text{SO}}_{\text{4}} }

We investigated the dissolved major elements, $ {}^{87}{\text{Sr/}}{}^{86}{\text{Sr}},\;\delta {}^{34}{\text{S}}_{{\text{SO}}_{\text{4}} } ,\;{\text{and}}\;\delta {}^{18}{\text{O}}_{{\text{SO}}_{\text{4}} } $ composition of the Min Jiang, a headwater tributary of the Chang Jiang (Yangtze River). A forward calculation method was applied to quantify the relative contribution to the dissolved load from rain, evaporite, carbonate, and silicate reservoirs. Input from carbonate weathering dominated the major element composition (58–93%) and that from silicate weathering ranged from 2 to 18% in unperturbed Min Jiang watersheds. Most samples were supersaturated with respect to calcite, and the CO₂ partial pressures were similar to or up to ～5 times higher than atmospheric levels. The Sr concentrations in our samples were low (1.3–2.5 μM) with isotopic composition ranging from 0.7108 to 0.7127, suggesting some contribution from felsic silicates. The Si/(Na^* + K) ratios ranged from 0.5 to 2.5, which indicate low to moderate silicate weathering intensity. The $ \delta {}^{34}{\text{S}}_{{\text{SO}}_{\text{4}} } \;{\text{and}}\;\delta {}^{18}{\text{O}}_{{\text{SO}}_{\text{4}} } $ for five select samples showed that the source of dissolved sulfate was combustion of locally consumed coal. The silicate weathering rates were 23–181 × 10³ mol/km²/year, and the CO₂ consumption rates were 31–246 × 10³ mol/km²/year, which are moderate on a global basis. Upon testing various climatic and geomorphic factors for correlation with the CO₂ consumption rate, the best correlation coefficients found were with water temperature (r ² = 0.284, p = 0.009), water discharge (r ² = 0.253, p = 0.014), and relief (r ² = 0.230, p = 0.019).     

WASP-121b Secondary Eclipses Revisited Using TESS Observation

Astronomy Reports - We present the detection and characterization of the ultrahot Jupiter WASP-121b ( $${{R}_{p}} \simeq 1.865{\kern 1pt} {{R}_{J}}$$ , $${{M}_{p}} \simeq 1.184{\kern 1pt}...     

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.     

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.

     

Instability in the System of the Distant Post-AGB Star LS III +52°24 (IRAS 22023+5249)

Astronomy Reports - The optical spectra of the B-supergiant LS III +52°24 (IRAS 22023+5249) obtained at the 6-m BTA telescope with a resolution $${\text{R}} \geqslant 60{\kern 1pt} {\kern 1pt}...     

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.

     

Heat capacity of ferrosilite, Fe2Si2O6

The heat capacity of synthetic ferrosilite, Fe₂Si₂O₆, was measured between 2 and 820 K. The physical properties measurement system (PPMS, Quantum Design^®) was used in the low-temperature region between 2 and 303 K. In the temperature region between 340 and 820 K measurements were performed using differential scanning calorimetry (DSC). The C _p data show two transitions, a sharp λ-type at 38.7 K and a small shoulder near 9 K. The λ-type transition can be related to collinear antiferromagnetic ordering of the Fe²⁺ spin moments and the shoulder at 10 K to a change from a collinear to a canted-spin structure or to a Schottky anomaly related to an electronic transition. The C _p data in the temperature region between 145 and 830 K are described by the polynomial $C_{p} {\left[ {\hbox{J\,mol}^{{ - 1}}\,{\hbox{K}}^{{ - 1}} } \right]} = 371.75 - 3219.2T^{{ - 1/2}} - 15.199 \times 10^{5} T^{{ - 2}} + 2.070 \times 10^{7} T^{{ - 3}} $ The heat content [H ₂₉₈ – H ₀] and the standard molar entropy [S ₂₉₈ – S ₀] are 28.6 ± 0.1 kJ mol^?1 and 186.5 ± 0.5 J mol^?1 K^?1, respectively. The vibrational part of the heat capacitiy was calculated using an elastic Debye temperature of 541 K. The results of the calculations are in good agreement with the maximum theoretical magnetic entropy of 26.8 J mol^?1 K^?1 as calculated from the relationship 2*Rln5.     

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.     

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.     

Thermodynamic properties of glaucophane new data from calorimetric and spectroscopic measurements

New data concerning glaucophane are presented. New high temperature drop calorimetry data from 400 to 800 K are used to constrain the heat capacity at high temperature. Unpublished low temperature calorimetric data are used to estimate entropy up to 900 K. These data, corrected for composition, are fitted for C _p and S to the polynomial expressions (J · mol^?1 · K^?2) for T> 298.15 K: $$\begin{gathered} C_p = 11.4209 * 10^2 - 40.3212 * 10^2 /T^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - 41.00068 * 10^6 /T^2 \hfill \\ + 52.1113 * 10^8 /T^3 \hfill \\ \end{gathered} $$ $$\begin{gathered} S = 539 + 11.4209 * 10^2 * \left( {\ln T - \ln 298.15} \right) - 80.6424 * 10^2 \hfill \\ * \left( {T^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - 1/\left( {298.15} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right) + 20.50034 * 10^6 \hfill \\ * \left( {T^{ - 2} - 1/\left( {298.15} \right)^2 } \right) - 17.3704 * 10^8 * \left( {T^{ - 3} - \left( {1/298.15} \right)^3 } \right) \hfill \\ \end{gathered} $$ IR and Raman spectra from 50 to 3600 cm^?1 obtained on glaucophane crystals close to the end member composition are also presented. These spectroscopic data are used with other data (thermal expansion, acoustic velocities etc.) in vibrational modelling. This last method provides an independent way for the determination of the thermodynamic properties (C_p and entropy). The agreement between measured and calculated properties is excellent (less than 2% difference between 100 and 1000 K). It is therefore expected that vibrational modelling could be applied to other amphiboles for which spectroscopic data are available. Finally, the enthalpy of formation of glaucophane is calculated.     

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.     

Metasomatic coronas around hornblendite xenoliths in granulite facies marble, Ivrea zone, N Italy, I: constraints on component mobility

Centimeter- to decimeter-thick reaction bands occur at hornblendite/marble interfaces in Val Fiorina in the granulite facies metamorphic Ivrea zone. From hornblendite to marble the reaction bands show a consistent succession of sharply bounded mineral layers comprising a monomineralic clinopyroxene layer, a garnet-clinopyroxene layer and a scapolite-clinopyroxene layer. Reaction band formation occurred as a response to gradients in the chemical potentials of calcium and magnesium as defined by the hornblendite assemblage and the marble matrix. The metasomatic corona primarily replaced the hornblendite, and only minor amounts of marble were consumed. The reaction band behaved as an open system with net transfer of calcium from the marble into the reaction band, and a net transfer of iron and magnesium in the opposite direction. Mass balance considerations allow us to constrain a range of feasible mass balance scenarios for which major element fluxes across the boundaries of the reaction band may be quantified. Modeling of layer growth as a steady diffusion process yields ratios of the phenomenological diffusion coefficients for Si, Al, Mg, and Ca of ${{L_{SiSi} } \over {L_{CaCa} }}> 2.5,{\kern 1pt} {\rm }{{L_{AlAl} } \over {L_{CaCa} }}<10,{\rm }{{L_{MgMg} } \over {L_{CaCa} }}> 1.${{L_{SiSi} } \over {L_{CaCa} }}> 2.5,{\kern 1pt} {\rm }{{L_{AlAl} } \over {L_{CaCa} }}<10,{\rm }{{L_{MgMg} } \over {L_{CaCa} }}> 1. . The relative diffusivities are primarily constrained by the sequence of mineral layers of the reaction band and by the relative thickness of the layers. The results of steady-state diffusion modeling are relatively insensitive with respect to variations in the major element boundary fluxes.     

Statistical mechanics of coupled solid solutions in the dilute limit

A statistical mechanical analysis of the limiting laws for coupled solid solutions shows that the random model, in which the configurational entropy is calculated as if atoms mix randomly on each crystallographic site, is correct as a first approximation. In coupled solid solutions, since atoms of different valence substitute on the same sites, significant short-range order which reduces the entropy can be expected. A first-order correction is rigorously obtained for the entropy in dilute binary short-range ordered coupled solid solutions: $$\bar S^{{\text{XS}}} {\text{/R = }}Q\left( {{\text{e}}^{--H_{\text{A}} /{\text{R}}T} \left( {\frac{{H_{\text{A}} }}{{{\text{R}}T}} + 1} \right) - 1} \right)N_2^a N_4^b ,$$ where Q is the number of positions an associated cation pair can assume per formula unit, H _A is the association energy per formula unit, and N ₂ ^a and N ₄ ^b are the site occupancy fractions for atoms 2 and 4 that are dilute on sites a and b. S ^XS is the configurational entropy minus the random model entropy. Aluminous pyroxenes on the joints diopside-jadeite and diopside-CaTs are examined as examples. A generalization for dilute multiple component solutions, including possible long-range ordering variations is given by: $$\frac{{\bar S^{{\text{XS}}} }}{{\text{R}}}{\text{ = }}\sum\limits_i {\sum\limits_j {\sum\limits_k {Q_i } } \left( {{\text{e}}^{--H_{\text{A}}^{j{\text{ }}k{\text{, }}i} /{\text{R}}T} \left( {\frac{{H_{\text{A}}^{j{\text{ }}k{\text{, }}i} }}{{{\text{R}}T}} + 1} \right) - 1} \right)N_j^l N_k^m ,} $$ where i labels each crystallographically distinct pair, j and k label atomic species, l and m label crystallographic sites, and the N's are site occupancy fractions for the solute atoms. A total association model is examined as well as the partial association and random models. Real solution behavior must lie between the total association model and the random model. Molecular models in which the ideal activity is proportional to a mole fraction, which in itself is not always unambiguously defined, do not lie in this range and furthermore have no physical justification.     

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.     

The combined effect of F and H2O on interdiffusion between peralkaline dacitic and rhyolitic melts

The effective binary diffusion coefficient (EBDC) of silicon has been measured during the interdiffusion of peralkaline, fluorine-bearing (1.3 wt% F), hydrous (3.3 and 6 wt% H₂O), dacitic and rhyolitic melts at 1.0 GPa and temperatures between 1100°C and 1400°C. From Boltzmann-Matano analysis of diffusion profiles the diffusivity of silicon at 68 wt% SiO₂ can be described by the following Arrhenius equations (with standard errors): $$\begin{gathered} {\text{with 1}}{\text{.3 wt\% F and 3}}{\text{.3\% H}}_{\text{2}} {\text{O:}} \hfill \\ {\text{D}}_{{\text{Si}}} = \begin{array}{*{20}c} { + {\text{3}}{\text{.59}}} \\ {{\text{3}}{\text{.66}} \times {\text{10}}^{ - {\text{9}}} } \\ { - {\text{1}}{\text{.86}}} \\ \end{array} {\text{exp}}\left( {{{ - {\text{86}}{\text{.1}} \pm {\text{8}}{\text{.9}}} \mathord{\left/ {\vphantom {{ - {\text{86}}{\text{.1}} \pm {\text{8}}{\text{.9}}} {{\text{RT}}}}} \right. \kern-\nulldelimiterspace} {{\text{RT}}}}} \right) \hfill \\ {\text{with 1}}{\text{.3 wt\% F and 6}}{\text{.0\% H}}_{\text{2}} {\text{O:}} \hfill \\ {\text{D}}_{{\text{Si}}} = \begin{array}{*{20}c} { + {\text{3}}{\text{.59}}} \\ {{\text{3}}{\text{.51}} \times {\text{10}}^{ - {\text{8}}} } \\ { - {\text{1}}{\text{.77}}} \\ \end{array} {\text{exp}}\left( {{{ - {\text{109}}{\text{.5}} \pm {\text{8}}{\text{.9}}} \mathord{\left/ {\vphantom {{ - {\text{109}}{\text{.5}} \pm {\text{8}}{\text{.9}}} {{\text{RT}}}}} \right. \kern-\nulldelimiterspace} {{\text{RT}}}}} \right) \hfill \\ \end{gathered} $$ where D is in m²s^?1 and activation energies are in kJ/mol. Diffusivities measured at 64 and 72 wt% SiO₂ are only slightly different from those at 68 wt% SiO₂ and frequently all measurements are within error of each other. Silicon, aluminum, iron, magnesium, and calcium EBDCs were also calculated from diffusion profiles by error function inversion techniques assuming constant diffusivity. With one exception, silicon EBDCs calculated by error function techniques are within error of Boltzmann-Matano EBDCs. Average diffusivities of Fe, Mg, and Ca were within a factor of 2.5 of silicon diffusivities whereas Al diffusivities were approximately half those of silicon. Alkalies diffused much more rapidly than silicon and non-alkalies, however their diffusivities were not quantitatively determined. Low activation energies for silicon EBDCs result in rapid diffusion at magmatic temperatures. Assuming that water and fluorine exert similar effects on melt viscosity at high temperatures, the viscosity can be calculated and used in the Eyring equation used to determine diffusivities, typically to within a factor of three of those measured in this study. This correlation between viscosity and diffusivity can be inverted to calculate viscosities of fluorine- and water-bearing granitic melts at magmatic temperatures; these viscosities are orders of magnitude below those of hydrous granitic melts and result in more rapid and effective separation of granitic magmas from partially molten source rocks. Comparison of Arrhenius parameters for diffusion measured in this study with Arrhenius parameters determined for diffusion in similar compositions at the same pressure demonstrates simple relationships between Arrhenius parameters, activation energy-E_a, kJ/mol, pre-exponential factor-D_o, m²s^?1, and the volatile, X=F or OH^?, to oxygen, O, ratio of the melt {(X/X+O)}: $$\begin{gathered} {\text{E}}a = - {\text{1533\{ }}{{\text{X}} \mathord{\left/ {\vphantom {{\text{X}} {\left( {{\text{X}} + {\text{O}}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{\text{X}} + {\text{O}}} \right)}}{\text{\} }} + {\text{213}}{\text{.3}} \hfill \\ {\text{D}}_{\text{O}} = {\text{2}}{\text{.13}} \times {\text{10}}^{ - {\text{6}}} {\text{exp}}\left[ { - {\text{6}}{\text{.5\{ }}{{\text{X}} \mathord{\left/ {\vphantom {{\text{X}} {\left( {{\text{X}} + {\text{O}}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{\text{X}} + {\text{O}}} \right)}}{\text{\} }}} \right] \hfill \\ \end{gathered} $$ These relationships can be used to estimate diffusion in various melts of dacitic to rhyolitic composition containing both fluorine and water. Calculations for the contamination of rhyolitic melts by dacitic enclaves at 800°C and 700°C provide evidence for the virtual inevitability of diffusive contamination in hydrous and fluorine-bearing magmas if they undergo magma mixing of any form.     

Estimating the Density and Compressibility of Seawater to High Temperatures Using the Pitzer Equations

The density and compressibility of seawater solutions from 0 to 95 °C have been examined using the Pitzer equations. The apparent molal volumes (X = V) and compressibilities (X = κ) are in the form $$ X_{\phi } = \bar{X}^{0} + A_{X} I/(1.2 \, m)\ln (1 + 1.2 \, I^{0.5} ) + \, 2{\text{RT }}m \, (\beta^{(0)X} + \beta^{(1)X} g(y) + C^{X} m) $$ where $ \bar{X}^{0} $ is the partial molal volume or compressibility, I is the ionic strength, m is the molality of sea salt, A_X is the Debye–Hückel slope for volume (X = V) or adiabatic compressibility (X = κ _s), and g(y) = (2/y ²)[1 ? (1 + y) exp(?y)] where y = 2I ^0.5. The values of the partial molal volume and compressibility ( $ \bar{X}^{0} $ ) and Pitzer parameters (β ^(0)X , β ^(1)X and C ^X ) are functions of temperature in the form $$ Y^{X} = \sum_{i} a_{i} (T-T_{\text{R}} )^{i} $$ where a _i are adjustable parameters, T is the absolute temperature in Kelvin, and T _R = 298.15 K is the reference temperature. The standard errors of the seawater fits for the specific volumes and adiabatic compressibilities are 5.35E?06 cm³ g^?1 and 1.0E?09 bar^?1, respectively. These equations can be combined with similar equations for the osmotic coefficient, enthalpy and heat capacity to define the thermodynamic properties of sea salt to high temperatures at one atm. The Pitzer equations for the major components of seawater have been used to estimate the density and compressibility of seawater to 95 °C. The results are in reasonable agreement with the measured values (0.010E?03 g cm^?3 for density and 0.050E?06 bar^?1 for compressibility) from 0 to 80 °C and salinities from 0 to 45 g kg^?1. The results make it possible to estimate the density and compressibility of all natural waters of known composition over a wide range of temperature and salinity.     

The P–V–T equation of state of CaPtO3 post-perovskite

Orthorhombic post-perovskite CaPtO₃ is isostructural with post-perovskite MgSiO₃, a deep-Earth phase stable only above 100 GPa. Energy-dispersive X-ray diffraction data (to 9.4 GPa and 1,024 K) for CaPtO₃ have been combined with published isothermal and isobaric measurements to determine its P–V–T equation of state (EoS). A third-order Birch–Murnaghan EoS was used, with the volumetric thermal expansion coefficient (at atmospheric pressure) represented by α(T) = α₀ + α₁(T). The fitted parameters had values: isothermal incompressibility, $ K_{{T_{0} }} $  = 168.4(3) GPa; $ K_{{T_{0} }}^{\prime } $  = 4.48(3) (both at 298 K); $ \partial K_{{T_{0} }} /\partial T $  = ?0.032(3) GPa K^?1; α₀ = 2.32(2) × 10^?5 K^?1; α₁ = 5.7(4) × 10^?9 K^?2. The volumetric isothermal Anderson–Grüneisen parameter, δ _T , is 7.6(7) at 298 K. $ \partial K_{{T_{0} }} /\partial T $ for CaPtO₃ is similar to that recently reported for CaIrO₃, differing significantly from values found at high pressure for MgSiO₃ post-perovskite (?0.0085(11) to ?0.024 GPa K^?1). We also report axial P–V–T EoS of similar form, the first for any post-perovskite. Fitted to the cubes of the axes, these gave $ \partial K_{{aT_{0} }} /\partial T $  = ?0.038(4) GPa K^?1; $ \partial K_{{bT_{0} }} /\partial T $  = ?0.021(2) GPa K^?1; $ \partial K_{{cT_{0} }} /\partial T $  = ?0.026(5) GPa K^?1, with δ _T  = 8.9(9), 7.4(7) and 4.6(9) for a, b and c, respectively. Although $ K_{{T_{0} }} $ is lowest for the b-axis, its incompressibility is the least temperature dependent.