Young Stellar Complexes in the Giant Galaxy UGC 11973

We present results of the analysis of photometric and spectroscopic observations of the young stellar complexes in the late giant spiral galaxy UGC 11973. Photometric analysis in the $$UBVRI$$ bands have been carried out for the 13 largest complexes. For one of them, metallicity of the surrounding gas $$Z = 0.013 \pm 0.005$$ , the mass $$M = (4.6 \pm 1.6) \times {{10}^{6}}{\kern 1pt} {{M}_{ \odot }}$$ , and the age of the stellar complex $$t = (2.0 \pm 1.1) \times {{10}^{6}}$$ yr were evaluated, using spectroscopic data. It is shown that all complexes are massive ( $$M \geqslant 1.7 \times {{10}^{5}}{\kern 1pt} {{M}_{ \odot }}$$ ) stellar groups younger than $$3 \times {{10}^{8}}$$ yr.     

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,

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}...     

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.     

Genesis of secondary uranium minerals associated with jasperoid veins,El Erediya area,Eastern Desert,Egypt

Uranium mineralization in the El Erediya area, Egyptian Eastern Desert, has been affected by both high temperature and low temperature fluids. Mineralization is structurally controlled and is associated with jasperoid veins that are hosted by a granitic pluton. This granite exhibits extensive alteration, including silicification, argillization, sericitization, chloritization, carbonatization, and hematization. The primary uranium mineral is pitchblende, whereas uranpyrochlore, uranophane, kasolite, and an unidentified hydrated uranium niobate mineral are the most abundant secondary uranium minerals. Uranpyrochlore and the unidentified hydrated uranium niobate mineral are interpreted as alteration products of petscheckite. The chemical formula of the uranpyrochlore based upon the Electron Probe Micro Analyzer (EPMA) is . It is characterized by a relatively high Zr content (average ZrO₂ = 6.6 wt%). The average composition of the unidentified hydrated uranium niobate mineral is , where U and Nb represent the dominant cations in the U and Nb site, respectively. Uranophane is the dominant U⁶⁺ silicate phase in oxidized zones of the jasperoid veins. Kasolite is less abundant than uranophane and contains major U, Pb, and Si but only minor Ca, Fe, P, and Zr. A two-stage metallogenetic model is proposed for the alteration processes and uranium mineralization at El Erediya. The primary uranium minerals were formed during the first stage of the hydrothermal activity that formed jasperoid veins in El Eradiya granite (130–160 Ma). This stage is related to the Late Jurassic–Early Cretaceous phase of the final Pan-African tectono-thermal event in Egypt. After initial formation of El Erediya jasperoid veins, a late stage of hydrothermal alteration includes argillization, dissolution of iron-bearing sulfide minerals, formation of iron-oxy hydroxides, and corrosion of primary uranium minerals, resulting in enrichment of U, Ca, Pb, Zr, and Si. During this stage, petscheckite was altered to uranpyrochlore and oxy-petscheckite. Uranium was likely transported as uranyl carbonate and uranyl fluoride complexes. With change of temperature and pH, these complexes became unstable and combined with silica, calcium, and lead to form uranophane and kasolite. Finally, at a later stage of low-temperature supergene alteration, oxy-petscheckite was altered to an unidentified hydrated uranium niobate mineral by removal of Fe.     

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.     

Effects of site–city interaction and polarization of the incident S-wave on the transfer function and fundamental frequency of structures

Natural Hazards - The variation of 2D fundamental frequency of stand-alone structure on rock $$ ({F}_{{02{\text{D}}}}^{\text{S}} ) $$ and in a basin $$ ({F}_{{02{\text{D}}}}^{\text{BS}} ) $$ with...     

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.     

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.     

Central Field Motion with Perturbing Acceleration Varying According to the Inverse Square Law in the Reference Frame Associated with the Radius Vector

Astronomy Reports - The motion of a point with zero mass under the action of attraction to the central body $$\mathcal{S}$$ and perturbing acceleration $${\mathbf{P}}{\kern 1pt} ' =...     

Norm of the Position Shift of a Celestial Body in a Dynamical Astronomy Problem

The averaging method is widely used in celestial mechanics, in which a mean orbit is introduced and slightly deviates from an osculating one, as long as disturbing forces are small. The difference $$\delta {\mathbf{r}}$$ in the celestial body positions in the mean and osculating orbits is a quasi-periodic function of time. Estimating the norm $$\left\| {\delta {\mathbf{r}}} \right\|$$ for deviation is interesting to note. Earlier, the exact expression of the mean-square norm for one problem of celestial mechanics was obtained: a zero-mass point moves under the gravitation of a central body and a small perturbing acceleration $${\mathbf{F}}$$. The vector $${\mathbf{F}}$$ is taken to be constant in a co-moving coordinate system with axes directed along the radius vector, the transversal, and the angular momentum vector. Here, we solved a similar problem, assuming the vector $${\mathbf{F}}$$ to be constant in the reference frame with axes directed along the tangent, the principal normal, and the angular momentum vector. It turned out that $${{\left\| {\delta {\mathbf{r}}} \right\|}^{2}}$$ is proportional to $${{a}^{6}}$$, where $$a$$ is the semi-major axis. The value $${{\left\| {\delta {\mathbf{r}}} \right\|}^{2}}{{a}^{{ - 6}}}$$ is the weighted sum of the component squares of $${\mathbf{F}}$$. The quadratic form coefficients depend only on the eccentricity and are represented by the Maclaurin series in even powers of $$e$$ that converge, at least for $$e < 1$$. The series coefficients are calculated up to $${{e}^{4}}$$ inclusive, so that the correction terms are of order $${{e}^{6}}$$.     

A thermodynamic formulation of hydrous cordierite

A thermodynamic formulation of hydrous Mg-cordierite (Mg₂Al₄Si₅O₁₈·nH₂O) has been obtained by application of calorimetric and X-ray diffraction data for hydrous cordierite to the results of hydrothermal syntheses. The data include measurements of the molar heat capacity and enthalpy of hydration and the molar volume. The synthesis data are consistent with a thermodynamic formulation in which H₂O mixes ideally on a single crystallographic site in hydrous cordierite. The standard molar Gibbs free energy of hydration is-9.5±1.0 kJ/mol (an average of 61 syntheses). The standard molar entropy of hydration derived from this value is-108±3 J/mol-K. An equation providing the H₂O content of cordierite as a function of temperature and fugacity of H₂O is as follows (n moles of H₂O per formula unit, n<1): $$\begin{gathered}n = {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } \mathord{\left/{\vphantom {{f_{{\text{ H}}_{\text{2}} O}^{\text{V}} } {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}}} \right.\kern-\nulldelimiterspace} {\left( {f_{{\text{ H}}_{\text{2}} O}^{\text{V}} + {\text{exp}}\left[ { - {\text{3}}{\text{.8389}} - 5025.2\left( {\frac{1}{T} - \frac{1}{{298.15}}} \right)} \right.} \right.}} \hfill \\{\text{ }}\left. {\left. { - {\text{ln}}\left( {\frac{T}{{{\text{298}}{\text{.15}}}}} \right) - \left( {\frac{{298.15}}{T} - 1} \right)} \right]} \right) \hfill \\\end{gathered}$$ Application of this formulation to the breakdown reaction of Mg-cordierite to an assemblage of pyrope-sillimanite-quartz±H₂O shows that cordierite is stabilized by 3 to 3.5 kbar under H₂O-saturated conditions. The thermodynamic properties of H₂O in cordierite are similar to those of liquid water, with a standard molar enthalpy and Gibbs free energy of hydration that are the same (within experimental uncertainty) as the enthalpy and Gibbs free energy of vaporization. By contrast, most zeolites have Gibbs free energies of hydration two to four times more negative than the corresponding value for the vaporization of water.     

Adsorption kinetics of chromium(III) removal from aqueous solutions using natural red earth

Laboratory-scale-simulated experiments were carried out using Cr(III) solutions to identify the Cr(III) retention behavior of natural red earth (NRE), a natural soil available in the northwestern coastal belt of Sri Lanka. The effects of solution pH, initial Cr(III) concentration and the contact time were examined. The NRE showed almost 100 % Cr(III) adsorption within the first 90 min. [initial [Cr(III)] = 0.0092–0.192 mM; initial pH 4.0–9.0]. At pH 2 (298 K), when particle size ranged from 125 to 180 μm the Cr(III) adsorption data were modeled according to Langmuir convention assuming site homogeneity. The pH-dependent Cr(III) adsorption data were quantified by diffused layer model assuming following reaction stoichiometries: $$ \begin{aligned} 2\, {>}{\text{AlOH}}_{{({\text{s}})}} + {\text{ Cr }}\left( {\text{OH}} \right)_{{ 2\,({\text{aq}})}}^{ + } \, \to \, \left( { {>}{\text{AlO}}} \right)_{ 2} {\text{Cr}}_{{({\text{s}})}}^{ + } + {\text{ 2H}}_{ 2} {\text{O}} \quad {\text{log K 15}}. 5 6\\ 2\, {>}{\text{FeOH}}_{{({\text{s}})}} + {\text{ Cr}}\left( {\text{OH}} \right)_{{ 2\,({\text{aq}})}}^{ + } \, \to \, \left( { {>}{\text{FeO}}} \right)_{ 2} {\text{Cr}}_{{({\text{s}})}}^{ + } + {\text{ 2H}}_{ 2} {\text{O}}\quad {\text{log K 5}}.0 8.\\ \end{aligned} $$ The present data showed that NRE can effectively be used to mitigate Cr(III) from aqueous solutions and this method is found to be simple, effective, economical and environmentally benign.     

The Reaction Titanite+Kyanite=Anorthite+Rutile and Titanite-Rutile Barometry in Eclogites

Titanite and rutile are a common mineral pair in eclogites, and many equilibria involving these phases are potentially useful in estimating pressures of metamorphism. We have reversed one such reaction,

Eclipsing System PS UMa: Evolutionary Status and Physical Parameters of the Components

We present the first high accuracy UBVRI(RI)c CCD light curves of the newly discovered eclipsing system PS UMa = GSC 4375 1733 ($$P = 9_{·}^{d}27$$, $$V = 12_{·}^{m}42$$). The photometric solutions are found, the physical parameters of the components are derived. The eccentricity of the orbit was found to be negligible e = 0.074, which made it difficult to measure the rate of the apsidal rotation. High accuracy of our observations allowed us to find the reliable parameters of the system. Components (Sp = F7 + G1) have advanced significantly in their evolution, the age of the system is 2.4 billion years. The mass and the radius of G1 component is larger and it is ahead of the F7 component in its evolution. The model of the system best suits the theory in the absence of the overshooting in the core. Obtained from our observations photometrical parallax π = 0$$_{.}^{\prime\prime }$$00102(2) coincides with GAIA DR2 value $$\pi =0_{·}^{\prime\prime }00106(3)$$ within their errors. The new EW type variable with period $$ \approx {\kern 1pt} 0_{·}^{d}40$$ was found in the field of PS UMa.     

Central Field Motion with Variation of Perturbing Acceleration According to the Inverse Square Law in a Reference Frame Associated with the Velocity Vector

Astronomy Reports - A problem is considered in which a zero-mass point moves under the attraction of the central body&nbsp; $$\mathcal{S}$$ and perturbing acceleration $${\mathbf{P}}{\kern 1pt}...     

(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.     

Reversed experimental calibration of the garnet-clinopyroxene Fe — Mg exchange thermometer

The temperature-sensitive Fe,Mg exchange equilibrium,

Basal slip and texture development in calcite: new results from torsion experiments

The deformation behavior of calcite has been of longstanding interest. Through experiments on single crystals, deformation mechanisms were established such as mechanical twinning on in the positive sense and slip on and both in the negative sense. More recently it was observed that at higher temperatures slip in both senses becomes active and, based on slip line analysis, it was suggested that slip may occur. So far there had been no direct evidence for basal slip, which is the dominant system in dolomite. With new torsion experiments on calcite single crystals at 900 K and transmission electron microscopy, this study identifies slip unambiguously by direct imaging of dislocations and diffraction contrast analysis. Including this slip system in polycrystal plasticity simulations, enigmatic texture patterns observed in compression and torsion of calcite rocks at high temperature can now be explained, resolving a long-standing puzzle.     

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.