Experimental and computational study of trace element distribution between orthopyroxene and anhydrous silicate melt: substitution mechanisms and the effect of iron

Although orthopyroxene (Opx) is present during a wide range of magmatic differentiation processes in the terrestrial and lunar mantle, its effect on melt trace element contents is not well quantified. We present results of a combined experimental and computational study of trace element partitioning between Opx and anhydrous silicate melts. Experiments were performed in air at atmospheric pressure and temperatures ranging from 1,326 to 1,420°C in the system CaO–MgO–Al₂O₃–SiO₂ and subsystem CaO–MgO–SiO₂. We provide experimental partition coefficients for a wide range of trace elements (large ion lithophile: Li, Be, B, K, Rb, Sr, Cs, Ba, Th, U; rare earth elements, REE: La, Ce, Nd, Sm, Y, Yb, Lu; high field strength: Zr, Nb, Hf, Ta, Ti; transition metals: Sc, V, Cr, Co) for use in petrogenetic modelling. REE partition coefficients increase from $ D_{\text{La}}^{{\text{Opx}} {\hbox{-}} {\text{melt}}} \sim 0.0005 Although orthopyroxene (Opx) is present during a wide range of magmatic differentiation processes in the terrestrial and lunar mantle, its effect on melt trace element contents is not well quantified. We present results of a combined experimental and computational study of trace element partitioning between Opx and anhydrous silicate melts. Experiments were performed in air at atmospheric pressure and temperatures ranging from 1,326 to 1,420°C in the system CaO–MgO–Al₂O₃–SiO₂ and subsystem CaO–MgO–SiO₂. We provide experimental partition coefficients for a wide range of trace elements (large ion lithophile: Li, Be, B, K, Rb, Sr, Cs, Ba, Th, U; rare earth elements, REE: La, Ce, Nd, Sm, Y, Yb, Lu; high field strength: Zr, Nb, Hf, Ta, Ti; transition metals: Sc, V, Cr, Co) for use in petrogenetic modelling. REE partition coefficients increase from $ D_{\text{La}}^{{\text{Opx}} {\hbox{-}} {\text{melt}}} \sim 0.0005 $ D_{\text{La}}^{{\text{Opx}} {\hbox{-}} {\text{melt}}} \sim 0.0005 to $ D_{\text{Lu}}^{{{\text{Opx}} {\hbox{-}} {\text{melt}}}} \sim 0.109 $ D_{\text{Lu}}^{{{\text{Opx}} {\hbox{-}} {\text{melt}}}} \sim 0.109 , D values for highly charged elements vary from $ D_{\text{Th}}^{{{\text{Opx}} {\hbox{-}} {\text{melt}}}} \sim 0.0026 $ D_{\text{Th}}^{{{\text{Opx}} {\hbox{-}} {\text{melt}}}} \sim 0.0026 through $ D_{\text{Nb}}^{{{\text{Opx}} {\hbox{-}} {\text{melt}}}} \sim 0.0033 $ D_{\text{Nb}}^{{{\text{Opx}} {\hbox{-}} {\text{melt}}}} \sim 0.0033 and $ D_{\text{U}}^{{{\text{Opx}} {\hbox{-}} {\text{melt}}}} \sim 0.0066 $ D_{\text{U}}^{{{\text{Opx}} {\hbox{-}} {\text{melt}}}} \sim 0.0066 to $ D_{\text{Ti}}^{{\text{Opx}} {\hbox{-}} {\text{melt}}} \sim 0.058 $ D_{\text{Ti}}^{{\text{Opx}} {\hbox{-}} {\text{melt}}} \sim 0.058 , and are all virtually independent of temperature. Cr and Co are the only compatible trace elements at the studied conditions. To elucidate charge-balancing mechanisms for incorporation of REE into Opx and to assess the possible influence of Fe on Opx-melt partitioning, we compare our experimental results with computer simulations. In these simulations, we examine major and minor trace element incorporation into the end-members enstatite (Mg₂Si₂O₆) and ferrosilite (Fe₂Si₂O₆). Calculated solution energies show that R²⁺ cations are more soluble in Opx than R³⁺ cations of similar size, consistent with experimental partitioning data. In addition, simulations show charge balancing of R³⁺ cations by coupled substitution with Li⁺ on the M1 site that is energetically favoured over coupled substitution involving Al–Si exchange on the tetrahedrally coordinated site. We derived best-fit values for ideal ionic radii r ₀, maximum partition coefficients D ₀, and apparent Young’s moduli E for substitutions onto the Opx M1 and M2 sites. Experimental r ₀ values for R³⁺ substitutions are 0.66–0.67 ? for M1 and 0.82–0.87 ? for M2. Simulations for enstatite result in r ₀ = 0.71–0.73 ? for M1 and ~0.79–0.87 ? for M2. Ferrosilite r ₀ values are systematically larger by ~0.05 ? for both M1 and M2. The latter is opposite to experimental literature data, which appear to show a slight decrease in $ r_{0}^{{{\text{M}}2}} $ r_{0}^{{{\text{M}}2}} in the presence of Fe. Additional systematic studies in Fe-bearing systems are required to resolve this inconsistency and to develop predictive Opx-melt partitioning models for use in terrestrial and lunar magmatic differentiation models.     

A multi-isotope approach for understanding sources of water,carbon and sulfur in natural springs of the Central Appalachian region

Natural springs have been reliable sources of domestic water and have allowed for the development of recreational facilities and resorts in the Central Appalachians. The structural history of this area is complex and it is unknown whether these natural springs receive significant recharge from modern precipitation or whether they discharge old water recharged over geological times scales. The main objective of this study was to use stable isotopes of water ( $\delta^{18} {\text{O}}_{{{\text{H}}_{2} {\text{O}}}}$ and $\delta^{2} {\text{H}}_{{{\text{H}}_{2} {\text{O}}}}$ ), dissolved inorganic carbon ( $\delta^{13} {\text{C}}_{\text{DIC}}$ ) and dissolved sulfate ( $\delta^{34} {\text{S}}_{{{\text{SO}}_{4} }}$ and $\delta^{18} {\text{O}}_{{{\text{SO}}_{4} }}$ ) to delineate sources of water, carbon and sulfur in several natural springs of the region. Our preliminary isotope data indicate that all springs are being recharged by modern precipitation. The oxygen isotope composition indicates that waters in thermal springs did not encounter the high temperatures required for O isotope exchange between the water and silicate/carbonate minerals, and/or the residence time of water in the aquifers was short due to high flow rates. The carbon isotopic composition of dissolved inorganic carbon and sulfur/oxygen isotopic composition of dissolved sulfate provide evidence of low-temperature water–rock interactions and various biogeochemical transformations these waters have undergone along their flow path.     

Crystallographic preferred orientation in wüstite (FeO) through the cubic-to-rhombohedral phase transition

Magnesiowüstite, (Mg_0.08Fe_0.88)O, and wüstite, Fe_0.94O, were compressed to ~36?GPa at ambient temperature in the diamond anvil cell (DAC) at the Advanced Light Source. X-ray diffraction patterns were taken in situ in radial geometry in order to study the evolution of crystallographic preferred orientation through the cubic-to-rhombohedral phase transition. Under uniaxial stress in the DAC, {100}_c planes aligned perpendicular to the compression direction. The {100}_c in cubic became { $\left\{ {10\bar 14} \right\}$ }_r in rhombohedral and remained aligned perpendicular to the compression direction. However, the {101}_c and {111}_c planes in the cubic phase split into { ${10{\bar{1}}4}$ }_r and { ${11{\bar{2}}0}$ }_r, and (0001)_r and { ${10{\bar{1}}1}$ }_r, respectively, in the rhombohedral phase. The { ${11{\bar{2}}0}$ }_r planes preferentially aligned perpendicular to the compression direction while { ${10{\bar{1}}4}$ }_r oriented at a low angle to the compression direction. Similarly, { ${10{\bar{1}}1}$ }_r showed a slight preference to align more closely perpendicular to the compression direction than (0001)_r. This variant selection may occur because the 〈 ${10{\bar{1}}4}$ 〉_r and [0001]_r directions are the softer of the two sets of directions. The rhombohedral texture distortion may also be due to subsequent deformation. Indeed, polycrystal plasticity simulations indicate that for preferred { ${10{\bar{1}}4}$ }〈 ${1{\bar{2}}10}$ 〉_r and { ${11{\bar{2}}0}$ }〈 ${{\bar{1}}101}$ 〉_r slip and slightly less active { ${10{\bar{1}}1}$ }〈 ${{\bar{1}}2{\bar{1}}0}$ 〉_r slip, the observed texture pattern can be obtained.     

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.     

Chemistry, Raman and infrared spectroscopic characterization of the phosphate mineral reddingite: (MnFe)3(PO4)2(H2O,OH)3, a mineral found in lithium-bearing pegmatite

Detailed investigation of an intermediate member of the reddingite–phosphoferrite series, using infrared and Raman spectroscopy, scanning electron microcopy and electron microprobe analysis, has been carried out on a homogeneous sample from a lithium-bearing pegmatite named Cigana mine, near Conselheiro Pena, Minas Gerais, Brazil. The determined formula is $ ({\text{Mn}}_{1.60} {\text{Fe}}_{1.21} {\text{Ca}}_{0.01} {\text{Mg}}_{0.01} )_{\sum 2.83} ({\text{PO}}_{4} )_{2.12} \cdot ({\text{H}}_{2} {\text{O}}_{2.85} {\text{F}}_{0.01} )_{\sum 2.86} $ , indicating predominance in the reddingite member. Raman spectroscopy coupled with infrared spectroscopy supports the concept of phosphate, hydrogen phosphate and dihydrogen phosphate units in the structure of reddingite-phosphoferrite. Infrared and Raman bands attributed to water and hydroxyl stretching modes are identified. Vibrational spectroscopy adds useful information to the molecular structure of reddingite–phosphoferrite.     

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.     

The crystal structure of waylandite from Wheal Remfry, Cornwall, United Kingdom

Sr- and Ca-rich waylandite, $ {\left( {{\hbox{B}}{{\hbox{i}}_{0.{54}}}{\hbox{S}}{{\hbox{r}}_{0.{31}}}{\hbox{C}}{{\hbox{a}}_{0.{25}}}{{\hbox{K}}_{0.0{1}}}{\hbox{B}}{{\hbox{a}}_{0.0{1}}}} \right)_{\Sigma 1.12}}{{\hbox{H}}_{0.{18}}}{\left( {{\hbox{A}}{{\hbox{l}}_{{2}.{96}}}{\hbox{C}}{{\hbox{u}}_{0.0{2}}}} \right)_{\Sigma 2.98}}{\left[ {{{\left( {{{\hbox{P}}_{0.{97}}}{{\hbox{S}}_{0.0{3}}}{\hbox{S}}{{\hbox{i}}_{0.0{1}}}} \right)}_{\Sigma 1.00}}{{\hbox{O}}_4}} \right]_2}{\left( {\hbox{OH}} \right)_6} $ , from Wheal Remfry, Cornwall, United Kingdom has been investigated by single-crystal X-ray diffraction and electron microprobe analyses. Waylandite crystallises in space group R $ \overline 3 $ ? m, with the cell parameters: a?=?7.0059(7) Å, c?=?16.3431(12) Å and V?=?694.69(11) ų. The crystal structure has been refined to R ₁?=?3.76%. Waylandite has an alunite-type structure comprised of a rhombohedral stacking of (001) composite layers of corner-shared AlO₆ octahedra and PO₄ tetrahedra, with (Bi,Sr,Ca) atoms occupying icosahedrally coordinated sites between the layers.     

Redox-controlled iron isotope fractionation during magmatic differentiation: an example from the Red Hill intrusion, S. Tasmania

This study presents accurate and precise iron isotopic data for 16 co-magmatic rocks and 6 pyroxene–magnetite pairs from the classic, tholeiitic Red Hill sill in southern Tasmania. The intrusion exhibits a vertical continuum of compositions created by in situ fractional crystallisation of a single injection of magma in a closed igneous system and, as such, constitutes a natural laboratory amenable to determining the causes of Fe isotope fractionation in magmatic rocks. Early fractionation of pyroxenes and plagioclase, under conditions closed to oxygen exchange, gives rise to an iron enrichment trend and an increase in $ f_{{{\text{O}}_{2} }} $ of the melt relative to the Fayalite–Magnetite–Quartz (FMQ) buffer. Enrichment in Fe³⁺/ΣFe_melt is mirrored by δ⁵⁷Fe, where ^VIFe²⁺-bearing pyroxenes partition ⁵⁷Fe-depleted iron, defining an equilibrium pyroxene-melt fractionation factor of $ \Updelta^{57} {\text{Fe}}_{{{\text{px}} - {\text{melt}}}} \le - 0.25\,\permille \times 10^{6} /T^{2} $ . Upon magnetite saturation, the $ f_{{{\text{O}}_{2} }} $ and δ⁵⁷Fe of the melt fall, commensurate with the sequestration of the oxidised, ⁵⁷Fe-enriched iron into magnetite, quantified as $ \Updelta^{57} {\text{Fe}}_{{{\text{mtn}} - {\text{melt}}}} = + 0.20\,\permille \times 10^{6} /T^{2} $ . Pyroxene–magnetite pairs reveal an equilibrium fractionation factor of $ \Updelta^{57} {\text{Fe}}_{{{\text{mtn}} - {\text{px}}}} \approx + 0.30\,\permille $ at 900–1,000?°C. Iron isotopes in differentiated magmas suggest that they may act as an indicator of their oxidation state and tectonic setting.     

Light scattering in jadeite melt: Strain relaxation measurements by photon correlation spectroscopy

Photon correlation spectroscopy has been applied to the study of longitudinal strain relaxation of vitreous Jadeite (NaAlSi₂O₆) in the temperature range 811–1014° C. The correlation function $\left| {g^{\left( 1 \right)} \left. {\left( t \right)} \right|^2 \propto \exp \left( {\left( { - 2t/\tau _\beta } \right)^\beta } \right)} \right.$ obeys a Kohlrausch type function with β=0.64±0.01. Individual correlation functions fit altogether a master relaxation curve, thus demonstrating thermorheological simplicity (TRS). The temperature dependence of the measured relaxation times shows Arrhenian behaviour with $\log \left( \tau \right) = - 21.4 \pm 0.3{\text{s}} {\text{ + }} {\text{471}}{\text{.6}} \pm {\text{22}} {\text{kJmol}}^{{\text{ - 1}}} /RT$ . The time scale of longitudinal strain relaxation is consistent with the existing data on shear relaxation derived from shear viscosity and structural relaxation calculated from calorimetric C _pmeasurements. Comparison with oxygen diffusion indicates that network forming elements relax at about the same time scale as viscoelastic properties. On the other hand, Na⁺ relaxation times derived from impedance spectroscopy are short compared to viscoelastic relaxation times at low temperatures. This difference is decreasing with increasing temperature and possibly disappearing at approximately 1100° C.     

The role of the minor substitutions in the crystal structure of natural challacolloite, KPb2Cl5, and hephaistosite, TlPb2Cl5, from Vulcano (Aeolian Archipelago, Italy)

Crystals of challacolloite, KPb₂Cl₅, and hephaistosite, TlPb₂Cl₅, from volcanic sublimates formed on the crater rim of the “La Fossa Crater” at Vulcano, Aeolian Archipelago, Italy, were investigated. Chemical compositions were ${\left( {{\text{K}}_{{0.93}} {\text{Tl}}_{{0.02}} } \right)}_{{\Sigma = 0.95}} {\text{Pb}}_{{2.04}} {\left( {{\text{Cl}}_{{4.90}} {\text{Br}}_{{0.11}} } \right)}_{{\Sigma = 5.01}} $ and ${\text{Tl}}_{{0.94}} {\text{Pb}}_{{2.01}} {\left( {{\text{Cl}}_{{4.91}} {\text{Br}}_{{0.14}} } \right)}_{{\Sigma = 5.05}} $ , respectively. Single crystal X-ray measurements showed monoclinic symmetry for both phases, space group P2₁/c, with the following unit-cell parameters: a = 8.8989(4), b = 7.9717(5), c = 12.5624(8) Å, β = 90.022(4)°, V = 891.2(1) ų, Z = 4 (challacolloite) and a = 9.0026(6), b = 7.9723(6), c = 12.5693(9) Å, β = 90.046(4)°, V = 902.1(1) ų, Z = 4 (hephaistosite). The structure refinements converge to R = 3.99% and R = 3.86%, respectively. The effects of Br?Cl and K?Tl substitutions on the structure of these natural compounds have been discussed.     

Some geobarometers involving cordierite in the FeO-Al2O3-SiO2(±H2O) system: refinements,thermodynamic calibration,and applicability in granulite facies rocks

Five geobarometers involving cordierite have been formulated for quantitative pressure sensing in high grade metapelites. The relevant reactions in the FeO-Al₂O₃-SiO₂ (±H₂O) system are based on the assemblages (A) cordierite-garnet-sillimanite-quartz, (B) cordierite-spinel-quartz, (C) cordierite-garnet-spinel-sillimanite, (D) cordierite-garnet-orthopyroxene-quartz and (E) cordierite-orthopyroxene-sillimanite-quartz. Application of the barometric formulations to a large number of granulite grade rocks indicates that the cordierite-garnet-sillimanite-quartz equilibrium is widely applicable and registers pressures which are in good agreement with the “consensus” pressure estimates. The dispersion in the computed P values, expressed as one standard deviation, is within ±1.2 kbar. The geobarometers (B) and (C) also yield pressures which are reasonable and compare well with those computed from equilibrium (A). The estimated pressures from (D) and (E), both involving orthopyroxene, are at variance with these estimates. It has been argued that the discrepancy in pressures obtained from these geobarometers stems from an inadequate knowledge of activity-composition relations and/or errors in input thermodynamic data of aluminous orthopyroxene. The convergence of pressure values estimated from the barometric formulations, especially (A), (B) and (C), implies that the present formulations are more dependable than the existing formulations and are also capable of setting limits on P values in response to varying $$\begin{gathered} {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} \hfill \\ {\text{ = 1/3Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 2/3Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + 5/6SiO}}_{\text{2}} {\text{. (A)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ = FeAl}}_{\text{2}} {\text{O}}_{\text{4}} {\text{ + 5/2SiO}}_{\text{2}} {\text{. (B)}} \hfill \\ {\text{Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ + FeAl}}_{\text{2}} {\text{O}}_{\text{4}} \hfill \\ = {\text{Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 2Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{. (C)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}_{\text{4}} {\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} {\text{ + Fe}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} \hfill \\ = {\text{Fe}}_{\text{3}} {\text{Al}}_{\text{2}} {\text{Si}}_{\text{3}} {\text{O}}_{{\text{12}}} {\text{ + 3/2SiO}}_{\text{2}} .{\text{ (D)}} \hfill \\ {\text{1/2Fe}}_{\text{2}} {\text{Al}}{}_{\text{4}}{\text{Si}}_{\text{5}} {\text{O}}_{{\text{18}}} \hfill \\ = 1/2{\text{Fe}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{\text{6}} {\text{ + Al}}_{\text{2}} {\text{SiO}}_{\text{5}} {\text{ + 1/2SiO}}_{\text{2}} .{\text{ (E)}} \hfill \\ \end{gathered}$$ . The present communication addresses the calibration, applicability and reliability of these barometers with reference to granulite facies metapelites.     

TiO2 exsolution from garnet by open-system precipitation: evidence from crystallographic and shape preferred orientation of rutile inclusions

We investigated rutile needles with a clear shape preferred orientation in garnet from (ultra) high-pressure metapelites from the Kimi Complex of the Greek Rhodope by electron microprobe, electron backscatter diffraction and TEM techniques. A definite though complex crystallographic orientation relationship between the garnet host and rutile was identified in that Rt[001] is either parallel to Grt<111> or describes cones with opening angle 27.6° around Grt<111>. Each Rt[001] small circle representing a cone on the pole figure displays six maxima in the density plots. This evidence together with microchemical observations in TEM, when compared to various possible mechanisms of formation, corroborates a precipitate origin. A review of exchange vectors for Ti substitution in garnet indicates that rutile formation from garnet cannot occur in a closed system. It requires that components are exchanged between the garnet interior and the rock matrix by solid-state diffusion, a process we refer to as “open-system precipitation” (OSP). The kinetically most feasible reaction of this type will dominate the overall process. The perhaps most efficient reaction involves internal oxidation of Fe²⁺ to Fe³⁺ and transfer from the dodecahedral to the octahedral site just vacated by $ {\text{Ti}}^{ 4+ }: 6\,{\text{M}}^{ 2+ }_{ 3} {\text{TiAl}}\left[ {{\text{AlSi}}_{ 2} } \right]{\text{O}}_{ 1 2} + 6\,{\text{M}}^{ 2+ }_{ 2, 5} {\text{TiAlSi}}_{ 3} {\text{O}}_{ 1 2} = 10\,{\text{M}}^{ 2+ }_{ 3.0} {\text{Al}}_{ 1. 8} {\text{Fe}}_{0. 2} {\text{Si}}_{ 3} {\text{O}}_{ 1 2} + {\text{M}}^{2+} + 2 {\text{e}}^{-} + 1 2\,{\text{TiO}}_{ 2} . $ OSP is likely to occur at conditions where the transition of natural systems to open-system behaviour becomes apparent, as in the granulite and high-temperature eclogite facies.     

基于摩擦与变形耗能的滚石切向恢复系数影响因素

切向恢复系数是滚石碰撞回弹的重要控制参数,目前的理论公式不能完全反映其作用机制,这是滚石动力学研究的一个难点问题.为此,根据滚石不同的回弹状态,提出基于入射角度变化的切向力模型;进一步,以切向接触理论和动能定理为基础,考虑碰撞过程中切向的摩擦耗能与变形耗能,推导了切向恢复系数的理论公式;最后研究入射速度、入射角、被撞击物体的变形模量对切向恢复系数的影响.结果表明:滚动回弹的切向恢复系数主要受切向变形量的影响;滑动回弹时,入射速度对切向恢复系数的影响参数为\begin{document}$ {v}^{\frac{1}{20}} $\end{document},切向恢复系数随着其增加而缓慢减少;入射角度对切向恢复系数的影响参数为$ \frac{\mathrm{c}\mathrm{o}{\mathrm{s}}^{\frac{1}{20}}{\beta }_{i}}{\mathrm{t}\mathrm{a}\mathrm{n}{\beta }_{i}} $,切向恢复系数随其增加而增大;被撞击物体的变形模量对切向恢复系数的影响参数为$ {E}_{2}^{-\frac{5}{8}} $,切向恢复系数随其增加而增加.基于摩擦与变形耗能的切向恢复系数计算公式为滚石的碰撞回弹过程提供了新的计算模型.      

Multiple-pumped-well aquifer test to determine the anisotropic properties of a karst limestone aquifer in Pasco County, Florida, USA

Groundwater-level data from an aquifer test utilizing four pumped wells conducted in the South Pasco wellfield in Pasco County, Florida, USA, were analyzed to determine the anisotropic transmissivity tensor, storativity, and leakance in the vicinity of the wellfield. A weighted least-squares procedure was used to analyze drawdowns measured at eight observation wells, and it was determined that the major axis of transmissivity extends approximately from north to south and the minor axis extends approximately from west to east with an angle of anisotropy equal to N4.54°W. The transmissivity along the major axis ${\left( {T_{{\xi \xi }} } \right)}$ is 14,019 m² day^–1, and the transmissivity along the minor axis ${\left( {T_{{\eta \eta }} } \right)}$ is 4,303 m² day^–1. The equivalent transmissivity $T_{e} = {\left( {T_{{\xi \xi }} T_{{\eta \eta }} } \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} = 7,767{{\text{m}}^{2} } \mathord{\left/ {\vphantom {{{\text{m}}^{2} } {{\text{day}}^{{ - {\text{1}}}} }}} \right. \kern-0em} {{\text{day}}^{{ - {\text{1}}}} }$ , and the ratio of anisotropy is 3.26. The storativity of the aquifer is 7.52?×?10^?4, and the leakance of the overlying confining unit is 1.37?×?10^?4 day^?1. The anisotropic properties determined for the South Pasco wellfield in this investigation confirm the results of previous aquifer tests conducted in the wellfield and help to quantify the NW–SE to NE–SW trends for regional fracture patterns and inferred solution-enhanced flow zones in west-central Florida.     

Burial metamorphism of a Cretaceous volcanic sequence west from Santiago,Chile

This report is a petrographic study of alteration phenomena in an area of 100 km² in the Coastal Range west of Santiago. The stratified sequence of the area is of Cretaceous age and belongs to the western monoclinal limb of the Andean Geosyncline. Two structural units are present, separated by an angular unconformity. The older is about 9,000 m thick, and the younger 300 m thick. The rock types are mostly altered andesitic flows and flow breccias, and keratophyric ignimbrites and lavas, with alternating marine, brackish-water and terrestrial interbeds. Stratified rocks are cut locally by acid and basic apophyses and dikes, probably feeders of their volcanic host rocks. Discordant Cretaceous granitic plutons intrude the older unit. Throughout the whole stratigraphic section there are alteration minerals, which selectively replace the primary minerals, or fill amygdules and open fractures, or form a cement in flows, dikes and sedimentary interbeds. Patterns of alteration are regular and persistent; they correlate on a large scale with stratigraphic level and on a smaller scale with position within each individual flow and situation within amygdules. The stratigraphically controlled pattern is as follows: $$\begin{gathered} 1.{\text{ Younger unit}}{\text{.}} \hfill \\ {\text{ }}\left. \begin{gathered} {\text{Lower portion: 30m: albite}}---{\text{pistacite}}---{\text{actinolite}}---{\text{chlorite}}---{\text{ }} \hfill \\ {\text{calcite}}---{\text{sphene}}---{\text{quartz}} \hfill \\ \end{gathered} \right\}{\text{greenschist facies}} \hfill \\ {\text{2}}{\text{. Older unit}}{\text{.}} \hfill \\ {\text{ }}\left. \begin{gathered} {\text{a) 0}}---{\text{1,280 m : albite}}---{\text{pumpellyite}}---{\text{prehnite}}---{\text{calcite}}---{\text{chlorite}}---{\text{ }} \hfill \\ {\text{ laumontite}} \hfill \\ {\text{b) 1,280}}---{\text{4,850 m: albite}}---{\text{adularia}}---{\text{calcite}}---{\text{prehnite}}---{\text{pumpellyite}}--- \hfill \\ {\text{pistacite}}---{\text{white mica}}---{\text{quartz}} \hfill \\ {\text{c) 4,850}}---{\text{8,110 m: albite}}---{\text{pistacite}}---{\text{quartz}}---{\text{chlorite}}---{\text{calcite}}--- \hfill \\ {\text{white mica}}---{\text{sphene}}---{\text{adularia prehnite}}---{\text{pumpellyite}} \hfill \\ \end{gathered} \right\}{\text{prehnite}}---{\text{pumpellyite facies}} \hfill \\ {\text{ d) 8,110}}---{\text{9,060 m: albite}}---{\text{pistacite}}---{\text{actinolite}}---{\text{sphene}}---{\text{calcite \} greenschist facies}} \hfill \\ \end{gathered} $$ The pattern of alteration in the older unit is comparable to that described for burial metamorphosed sequences in New Zealand and Australia. Reappearence of the greenschist facies at a higher level in the younger unit poses a problem for which several explanations are possible. The smaller scale pattern of alteration shows a persistent tendency —not without exception — for the “grade” of the alteration assemblage (as correlated with depth on the large scale) to increase: from the base of the flow (non-amygdaloidal part) upward (amygdaloidal part), and from the rim of each amygdule inward. Also recognizable on the scale of a single flow is a tendency for upward increase in: a) extent of alteration (the basal zone may be fresh andesite), and b) weight percent of Na₂O, K₂O (with complementary depletion in CaO), and of Fe₂O₃/FeO. Preliminary observations indicate that this alteration pattern persists for at least 400 km north of the area here described in rocks of similar lithology and age. It is unrelated to local granitic plutons.     

Temperature coefficients of elastic constants of single crystal MgO between 80 and 1,300 K

Elastic constants of single crystal MgO have been measured by the rectangular parallelepiped resonance (RPR) method at temperatures between 80 and 1,300 K. Elastic constants C _ij (Mbar=10³ kbar) and their temperature coefficients (kbar/K) are: $$\begin{gathered} {\text{ }}C_{{\text{11}}} {\text{ }}C_{{\text{12}}} {\text{ }}C_{{\text{44}}} {\text{ }}K_s {\text{ }}C_s \hfill \\ C_{ij} {\text{ 300 K 2}}{\text{.966 0}}{\text{.959 1}}{\text{.562 1}}{\text{.628 1}}{\text{.004}} \hfill \\ \partial C_{ij} {\text{/}}\partial T{\text{100 K }} - {\text{0}}{\text{.259 0}}{\text{.013 }} - {\text{0}}{\text{.072 }} - {\text{0}}{\text{.078 }} - {\text{0}}{\text{.136}} \hfill \\ {\text{ 300K }} - {\text{0}}{\text{.596 0}}{\text{.068 }} - {\text{0}}{\text{.122 }} - {\text{0}}{\text{.153 }} - {\text{0}}{\text{.332}} \hfill \\ {\text{ 800 K }} - {\text{0}}{\text{.619 0}}{\text{.009 }} - {\text{0}}{\text{.152 }} - {\text{0}}{\text{.200 }} - {\text{0}}{\text{.314}} \hfill \\ {\text{ 1,300 K }} - {\text{0}}{\text{.598 0}}{\text{.036 }} - {\text{0}}{\text{.130 }} - {\text{0}}{\text{.223 }} - {\text{0}}{\text{.218}} \hfill \\ \end{gathered} $$ By combining the present results with the previous data on the thermal expansivity and specific heat, the thermodynamic properties of magnesium oxide are presented and discussed. The elastic parameters of MgO at very high temperatures in the earth's lower mantle are also clarified.     

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

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

Low dispersive modeling of Rayleigh waves on partly staggered grids

In elastic media, finite-difference (FD) implementations of free-surface (FS) boundary conditions on partly staggered grid (PSG) use the highly dispersive vacuum formulation (VPSG). The FS boundary is embedded into a “vacuum” grid layer (null Lame’s constants and negligible density values) where the discretized equations of motion allow computing surface displacements. We place a new set of compound (stress-displacement) nodes along a planar FS and use unilateral mimetic FD discretization of the zero-traction conditions for displacement computation (MPSG). At interior nodes, MPSG reduces to standard VPSG methods and applies fourth-order centered FD along cell diagonals for staggered differentiation combined with nodal second-order FD in time. We perform a dispersion analysis of these methods on a Lamb’s problem and estimate dispersion curves from the phase difference of windowed numerical Rayleigh pulses at two FS receivers. For a given grid sampling criterion (e.g., six or ten nodes per reference S wavelength λ ^S), MPSG dispersion errors are only a quarter of the VPSG method. We also quantify root-mean-square (RMS) misfits of numerical time series relative to analytical waveforms. MPSG RMS misfits barely exceed 10 % when nine nodes sample the minimum S wavelength $\lambda _{\text {MIN}}^{\mathrm {S}}$ in transit (along distances $\sim $ 145 $\lambda _{\text {MIN}}^{\mathrm {S}}$ ). In same tests, VPSG RMS misfits exceed 70 %. We additionally compare MPSG to a consistently fourth-order mimetic method designed on a standard staggered grid. The latter equates the former’s dispersion errors on grids twice denser and shows higher RMS precision only on grids with six or less nodes per $\lambda _{\text {MIN}}^{\mathrm {S}}$ .     

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,

(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.