On the nonstoichiometry and point defects of olivine

This paper presents the point-defect thermodynamics for fayalite and olivine solid solutions (Fe _x Mg_1?x )₂SiO₄. By means of thermogravimetry, the metal-to-oxygen ratio of these silicates has been determined as a function of oxygen potential, compositionx and temperature. Experiments were performed in the range of 1,000° C≦T≦1,280° C and 0.2≦x≦1.0. It is found that V _Me ^″ , Fe _Me ^· and the associate {Fe′ _Si ^′ Fe _Me ^· } are the majority defects. With this knowledge it is possible to calculate the nonstoichiometry at given temperature as a function of \(p_{O_2 } \) and \(a_{SiO_2 } \) . The cation vacancy concentration shows a \(p_{O_2 }^{1/5} \) -dependence (forx≧0.2) and increases at givenT and \(p_{O_2 } \) almost exponentially with compositionx. In the composition range studied here, the silicates show an oxygen excess, and FeO is more soluble in the olivine than SiO₂.     

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.     

Dislocation-assisted diffusion of oxygen in albite

Oxygen diffusion in albite has been determined by the integrating (bulk ¹⁸O) method between 750° and 450° C, for a P _H2O of 2 kb. The original material has a low dislocation density (<10⁶ cm^?2), and its lattice diffusion coefficient (D ₁), given below, agrees well with previous determinations. A sample was deformed at high temperature and pressure to produce a uniform dislocation density of 5 × 10⁹ cm^?2. The diffusion coefficient (D _a) for this deformed material, given below, is about 0.5 and 0.7 orders of magnitude larger than D ₁ at 700° and 450° C, respectively. This enhancement is believed due to faster diffusion along the cores of dislocations. Assuming a dislocation core radius of 4 Å, the calculated pipe diffusion coefficient (D _p), given below, is about 5 orders of magnitude larger than D ₁. These results suggest that volume diffusion at metamorphic conditions may be only slightly enhanced by the presence of dislocations. $$\begin{gathered} D_1 = 9.8 \pm 6.9 \times 10^{ - 6} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 33.4 \pm 0.6(kcal/mole)/RT] \hfill \\ \end{gathered} $$ $$\begin{gathered} D_a = 7.6 \pm 4.0 \times 10^{ - 6} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 30.9 \pm 1.1(kcal/mole)/RT] \hfill \\ \end{gathered} $$ $$\begin{gathered} D_p \approx 1.2 \times 10^{ - 1} (cm^2 /\sec ) \hfill \\ {\text{ }} \cdot \exp [ - 29.8(kcal/mole)/RT]. \hfill \\ \end{gathered} $$      

Concentration dependence of water diffusion in obsidian and dacitic melts at high-pressures

The diffusion of water in natural obsidian and model dacitic melts (Ab90Di8Wo2, mol %) has been studied at water vapor pressure up to 170 MPa, temperatures of 1200°C, H₂O contents in melts up to ～6 wt % using a high gas pressure apparatus equipped with a unique internal device. The experiments were carried out by a new low-gradient technique with application of diffusion hydration of a melt from fluid phase. The water solubility in the melts and its concentration along $C_{H_2 O} $ diffusion profiles were determined using IR microspectrometry by application of the modified Bouguer-Beer-Lambert equation. A structural-chemical model was proposed to calculate and predict the concentration dependence of molar absorption coefficients of the hydroxyl groups (OH^?) and water molecules (H₂O) in acid polymerized glasses (quenched melts) in the obsidian-dacite series. The water diffusion coefficients $D_{H_2 O} $ were obtained by the mathematical analysis of concentration profiles and the analytical solution of the second Fick diffusion law using the Boltzman-Matano method. It was shown experimentally that $D_{H_2 O} $ exponentially increases with a growth of water concentration in the obsidian and dacitic melts within the entire range of diffusion profiles. Based on the established quantitative correlation between $D_{H_2 O} $ and viscosity of such melts, a new method was developed to predict and calculate the concentration, temperature, and pressure dependences of $D_{H_2 O} $ in acid magmatic melts (obsidian, rhyolite, albite, granite, dacite) at crustal T, P parameters and water concentrations up to 6 wt %.     

On the least-squares fit of small and great circles to spherically projected orientation data

Given the direction cosines a _i ^′ = (a ₁ ⁱ , a ₂ ⁱ , a ₃ ⁱ )corresponding to a set of pspherically projected fabric poles, an initial estimate x′ = (x₁, x₂, x₃, x₄)for the angular radius x₄,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking x_j+1 = x_j + Δxwhere x_j is the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ where As an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. Generalization of this approach to fitting variously constrained great and small circles is easily made. The relative merits of differently constrained fits to the same data can be tested approximately if it is assumed that the errors in the location of the poles are isotropic and normally distributed. It is thus possible to statistically assess the relative significance of conflicting structural models which predict different geometrical patterns of fabric elements.     

High temperature calorimetry of sulfide systems

The standard enthalpies of formation of FeS (troilite), FeS₂ (pyrite), Co_0.9342S, Co₃S₄ (linnaeite), Co₉S₈ (cobalt pentlandite), CoS₂ (cattierite), CuS (covellite), and Cu₂S (chalcocite) have been determined by high temperature direct reaction calorimetry at temperatures between 700 K and 1021 K. The following results are reported: $$\Delta {\rm H}_{f,FeS}^{tr} = - 102.59 \pm 0.20kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,FeS}^{py} = - 171.64 \pm 0.93kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_{0.934} S} = - 99.42 \pm 1.52kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_9 S_8 }^{ptl} = - 885.66 \pm 16.83kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Co_3 S_4 }^{In} = - 347.47 \pm 7.27kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,CoS_2 }^{ct} = - 150.94 \pm 4.85kJ mol^{ - 1} ,$$ $$\Delta {\rm H}_{f,Cu_2 S}^{cc} = - 80.21 \pm 1.51kJ mol^{ - 1} ,$$ and $$\Delta {\rm H}_{f,CuS}^{cv} = - 53.14 \pm 2.28kJ mol^{ - 1} ,$$ The enthalpy of formation of CuFeS₂ (chalcopyrite) from (CuS+FeS) and from (Cu+FeS₂) was determined by solution calorimetry in a liquid Ni_0.60S_0.40 melt at 1100 K. The results of these measurements were combined with the standard enthalpies of formation of CuS, FeS, and FeS₂, to calculate the standard enthalpy of formation of CuFeS₂. We found \(\Delta {\rm H}_{f,CuFeS_2 }^{ccp} = - 194.93 \pm 4.84kJ mol^{ - 1}\) . Our results are compared with earlier data given in the literature; generally the agreement is good and our values agree with previous estimates within the uncertainties present in both.     

Ephesite,Na(LiAl2) [Al2Si2O10] (OH)2: I. thermal stability and standard state thermodynamic properties

Ephesite, Na(LiAl₂) [Al₂Si₂O₁₀] (OH)₂, has been synthesized for the first time by hydrothermal treatment of a gel of requisite composition at 300≦T(° C)≦700 and \(P_{H_2 O}\) upto 35 kbar. At \(P_{H_2 O}\) between 7 and 35 kbar and above 500° C, only the 2M₁ polytype is obtained. At lower temperatures and pressures, the 1M polytype crystallizes first, which then inverts to the 2M₁ polytype with increasing run duration. The X-ray diffraction patterns of the 1M and 2M₁ poly types can be indexed unambiguously on the basis of the space groups C2 and Cc, respectively. At its upper thermal stability limit, 2M₁ ephesite decomposes according to the reaction (1) $$\begin{gathered} {\text{Na(LiAl}}_{\text{2}} {\text{) [Al}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{{\text{10}}} {\text{] (OH)}}_{\text{2}} \hfill \\ {\text{ephesite}} \hfill \\ {\text{ = Na[AlSiO}}_{\text{4}} {\text{] + LiAl[SiO}}_{\text{4}} {\text{] + }}\alpha {\text{ - Al}}_{\text{2}} {\text{O}}_{\text{3}} {\text{ + H}}_{\text{2}} {\text{O}} \hfill \\ {\text{nepheline }}\alpha {\text{ - eucryptite corundum}} \hfill \\ \end{gathered}$$ Five reversal brackets for (1) have been established experimentally in the temperature range 590–750° C, at \(P_{H_2 O}\) between 400 and 2500 bars. The equilibrium constant, K, for this reaction may be expressed as (2) $$log K{\text{ = }}log f_{{\text{H}}_{\text{2}} O}^* = 7.5217 - 4388/T + 0.0234 (P - 1)T$$ where \(f_{H_2 O}^* = f_{H_2 O} (P,T)/f_{H_2 O}^0\) (1,T), with T given in degrees K, and P in bars. Combining these experimental data with known thermodynamic properties of the decomposition products in (1), the following standard state (1 bar, 298.15 K) thermodynamic data for ephesite were calculated: H _f,298.15 ⁰ =-6237372 J/mol, S _298.15 ⁰ =300.455 J/K·mol, G _298.15 ⁰ =-5851994 J/mol, and V _298.15 ⁰ =13.1468 J/bar·mol.     

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.     

Kinetic rate laws as derived from order parameter theory II: Interpretation of experimental data by laplace-transformation,the relaxation spectrum,and kinetic gradient coupling between two order parameters

A unifying theory of kinetic rate laws, based on order parameter theory, is presented. The time evolution of the average order parameter is described by $$\langle Q\rangle \propto \smallint P(x)e^{^{^{^{^{^{^{ - xt} } } } } } } dx = L(P)$$ where t is the time, x is the effective inverse susceptibility, and L indicates the Laplace transformation. The probability function P(x) can be determined from experimental data by inverse Laplace transformation. Five models are presented:

1. Polynomial distributions of P(x) lead to Taylor expansions of 〈Q〉 as $$\langle Q\rangle = \frac{{\rho _1 }}{t} + \frac{{\rho _2 }}{{t^2 }} + ...$$
2. Gaussian distributions (e.g. due to defects) lead to a rate law $$\langle Q\rangle = e^{ - x_0 t} e^{^{^{^{^{\frac{1}{2}\Gamma t^2 } } } } } erfc\left( {\sqrt {\frac{\Gamma }{2}} t} \right)$$ where x ₀ is the most probable inverse time constant, Γ is the Gaussian line width and erfc is the complement error integral.
3. Maxwell distributions of P are equivalent to the rate law 〈Q〉∝e^?k√t .
4. Pseudo spin glasses possess a logarithmic rate law 〈Q〉∝lnt.
5. Power laws with P(x)=x ^a lead to a rate law: ln〈Q〉=-(α + 1) ln t.

The power spectra of Q are shown for Gaussian distributions and pseudo spin glasses. The mechanism of kinetic gradient coupling between two order parameters is evaluated.     

The concept of geochemical potential field exemplified by ore formation field

Geochemical potential field is defined as the scope within the earth’s space where a given component in a certain phase of a certain material system is acted upon by a diffusion force, depending on its spatial coordinatesX, Y andZ. The three coordinates follow the relations: $$NF_{ix} = - \frac{{\partial \mu }}{{\partial x}}, NF_{iy} = - \frac{{\partial \mu }}{{\partial y}}, NF_{iz} = - \frac{{\partial \mu }}{{\partial z}}$$ The characteristics of such a field can be summarized as: (1) The summation of geochemical potentials related to the coordinatesX, Y, Z, or pseudo-velocity head, pseudo-pressure head and pseudo-potential head of a certain component in the earth is a constant as given by $$\mu _x + \mu _y + \mu _z = c$$ or $$\mu _{x2} + \mu _{y2} + \mu _{z2} = \mu _{x1} + \mu _{y1} + \mu _{z1} $$ Derived from these relations is the principle of geochemical potential conservation. The following relations have the same physical significance: $$\mu _k + \mu _u + \mu _p = c$$ or $$\mu _{k2} + \mu _{u2} + \mu _{p2} = \mu _{k1} + \mu _{u1} + \mu _{p1} $$ (2) Geochemical potential field is a vector field quantified by geochemical field intensity which is defined as the diffusion force applied to one molecular volume (or one atomic volume) of a certain component moving from its higher concentration phase to lower concentration phase. The geochemical potential field intensity is given by $$\begin{gathered} E = - grad\mu \hfill \\ E = \frac{{RT}}{x}i + \frac{{RT}}{y}j + \frac{{RT}}{z}K \hfill \\ \end{gathered} $$ The present theory has been inferred to interpret the mechanism of formation of some tungsten ore deposits in China.     

Bimetasomatic zoning in the CaO-MgO-SiO2-H2O-CO2 system: Experiments with the use of natural rock samples

Experiments reproducing the development of bimetasomatic zoning in the CaO-MgO-SiO₂-H₂O-CO₂ system were conducted at elevated P-T parameters with the use of samples of naturally occurring quartzdolomite and calcite-serpentinite rocks. In order to maintain mass transfer exclusively via the diffusion-controlled mechanism, we used the method of the ensured compaction of the cylindrical sample surface with a thin-walled gold tube. In the course of the experiments, a single diopside zone ～2.5 × 10^?5 m thick was obtained at the quartz-dolomite interface at T = 600°C, $P_{H_2 O + CO_2 } $ = 200 MPa, and $X_{CO_2 } $ = 0.5 for 25–40 days and a succession of metasomatic zones at T = 750°C, $P_{H_2 O + CO_2 } $ = 300 MPa, and $X_{CO_2 } $ = 0.4 for 48 days. The metasomatic zones were as follows (listed in order from quartz to dolomite): wollastonite ‖ diopside ‖ tremolite ‖ calcite + forsterite; with the average width of the diopside zone equal to ～1.3 × 10^?5 m and the analogous part of the wollastonite zone equal to ～2.6 × 10^?5 m. Two zones (listed in order from calcite to serpentine) diopside and diopside-forsterite (the average widths of these zones were ～6 × 10^?4 and ～8 × 10^?4 m, respectively) were determined to develop at contact between serpentine and calcite during experiments that lasted 124 days at T = 500°C, $P_{H_2 O + CO_2 } $ = 200 MPa, and $X_{CO_2 } $ = 0.2–0.4. In the former and latter situations, the growth rate of the zoning ranged between 3.1 × 10^?12 and 1.2 × 10^?11 m/s and between 5.6 × 10^?11 and 7.5 × 10^?11 m/s, respectively. The higher growth rate in the latter case can be explained by the higher water mole fraction in the fluid, with this water released during serpentinite decomposition in the experiments. The development of the only diopside zone in the experiments modeling the interaction of quartz and dolomite at T = 600–650°C and $P_{H_2 O + CO_2 } $ = 200 MPa is in conflict with theoretical considerations underlain by the Korzhinskii-Fisher-Joesten model. The interaction of quartz and dolomite in the CaO-MgO-SiO₂-CO₂-H₂O system at the P-T- $X_{CO_2 } $ parameters specified above should be attended by the origin of a number of reaction zones consisting of various proportions of talc, forsterite, tremolite, diopside, and calcite. The saturation of the fluid with respect to these minerals was likely not reached, and this resulted in the degeneration of the respective stability fields in the succession of zones. Conceivably, this was related to the insufficient rates of quartz and dolomite dissolution and the relatively low diffusion rates of the dissolved species in the low-permeable medium. In the experiments with interacting calcite and serpentine, the zoning calcite ‖ diopside ‖ diopside + forsterite ‖ serpentine developed in its complete form, in agreement with the theory. Equilibrium was likely achieved in these experiments due to the higher diffusion coefficients.     

Physical conditions in faint gigahertz-peaked spectrum radio sources

Weak, compact radio sources (～100 mJy peak flux, L～1–10 pc) with their spectral peaks at about a gigahertz are studied, based on the complete sample of 46 radio sources of Snellen, drawn from high-sensitivity surveys, including the low-frequency Westerbork catalog. The physical parameters have been estimated for 14 sources: the magnetic field (H _⊥), the number density of relativistic particles (n _e), the energy of the magnetic field $(E_{H_ \bot } )$ , and the energy of relativistic particles (E _e). Ten sources have $E_{H_ \bot } \ll E_e $ , three have approximate equipartition of the energies $(E_{H_ \bot } \sim E_e )$ , and only one has $E_{H_ \bot } \gg E_e $ . The mean magnetic fields in quasars (10^?3 G) and galaxies (10^?2 G) have been estimated. The magnetic field appears to be related to the sizes of compact features as $H \sim 1/\sqrt L $ .     

Thermochemical and pressure-volume-temperature systematics of data on solids,examples: Tungsten and MgO

Data systematization using the constraints from the equation $$Cp = Cv + \alpha _P {}^2V_T K_T T$$ where C _p, C _v, α _p, K _T and V are respectively heat capacity at constant pressure, heat capacity at constant volume, isobaric thermal expansion, isothermal bulk modulus and molar volume, has been performed for tungsten and MgO. The data are $$K_T (W) = 1E - 5/(3.1575E - 12 + 1.6E - 16T + 3.1E - 20T^2 )$$ $$\alpha _P (W) = 9.386E - 6 + 5.51E - 9T$$ $$C_P (W) = 24.1 + 3.872E - 3T - 12.42E - 7T^2 + 63.96E - 11T^3 - 89000T^{ - 2} $$ $$K_T (MgO) = 1/(0.59506E - 6 + 0.82334E - 10T + 0.32639E - 13T^2 + 0.10179E - 17T^3 $$ $$\alpha _P (MgO) = 0.3754E - 4 + 0.7907E - 8T - 0.7836/T^2 + 0.9148/T^3 $$ $$C_P (MgO) = 43.65 + 0.54303E - 2T - 0.16692E7T^{ - 2} + 0.32903E4T^{ - 1} - 5.34791E - 8T^2 $$ For the calculation of pressure-volume-temperature relation, a high temperature form of the Birch-Murnaghan equation is proposed $$P = 3K_T (1 + 2f)^{5/2} (1 + 2\xi f)$$ Where $$K_T = 1/(b_0 + b_1 T + b_2 T^2 + b_3 T^3 )$$ $$f = (1/2)\{ [V(1,T)/V(P,T)]^{2/3} - 1\} $$ $$\xi = ({3 \mathord{\left/ {\vphantom {3 4}} \right. \kern-\nulldelimiterspace} 4})[K'_0 + K'_1 \ln ({T \mathord{\left/ {\vphantom {T {300}}} \right. \kern-\nulldelimiterspace} {300}}) - 4]$$ where in turn $$V(1,T) = V_0 [\exp (\int\limits_{300}^T {\alpha dT)]} $$ . The temperature dependence of the pressure derivative of the bulk modulus (K′₁) is estimated by using the shock-wave data. For tungsten the data are K′₀ = 3.5434, K′₁ = 0.032; for MgO K′₀ = 4.17 and K′₁ = 0.1667. For calculating the Gibbs free energy of a solid at high pressure and at temperatures beyond that of melting at 1 atmosphere, it is necessary to define a high-temperature reference state for the fictive solid.     

Biradical states of oxygen-vacancy defects in ��-quartz: centers E_{2}^{\prime \prime } and E_{4}^{\prime \prime }

Several new radiation defects with total electron spin S?=?1 occurring in electron-irradiated, synthetic ??-quartz have been observed by using electron paramagnetic resonance spectroscopy. These defects are considered to be biradicals, i.e., pairs of S?=?1/2 species. The concentration of these centers depends on the condition of the fast-electron irradiation. They have different decay behaviors that allow measurements of any individual species especially when it predominates over the others. The primary spin Hamiltonian parameter matrices g ₁, g ₂, D have now been determined for two similar defects, which herein are labeled $ E_{2}^{\prime \prime } $ and $ E_{4}^{\prime \prime } $ . Inter-electron distances estimated by using the magnetic dipole model, suggest that the structures of centers $ E_{2}^{\prime \prime } $ and $ E_{4}^{\prime \prime } $ both involve the unpaired electrons each located in orbitals of two silicon atoms next to a common oxygen vacancy but which have slightly different Si?CSi distances at 0.90 and 0.79?nm, respectively. This model is consistent with previous DFT calculations of the triplet configurations with local energetic minima. Observed decay behaviors suggest a transformation of centers $ E_{2,4}^{\prime \prime } $ to the analogous $ E_{1}^{\prime \prime } $ center. These triplet centers in quartz provide new insights into the structures of analogous defects in amorphous silica.     

The ferric-ferrous ratio of natural silicate liquids equilibrated in air

Results of chemical analyses of glasses produced in 46 melting experiments in air at 1,350° C and 1,450° C on rocks ranging in composition from nephelinite to rhyolite have been combined with other published data to obtain an empirical equation relating in \((X_{{\text{Fe}}_{\text{2}} {\text{O}}_{\text{3}} }^{{\text{liq}}} /X_{{\text{FeO}}}^{{\text{liq}}} )\) to T, \(\ln f_{{\text{O}}_{\text{2}} } \) and bulk composition. The whole set of experimental data range over 1,200–1,450° C and oxygen fugacities of 10^?9.00 to 10^?0.69 bars, respectively. The standard errors of temperature and \(\log _{10} f_{{\text{O}}_{\text{2}} } \) predictions from this equation are 52° C and 0.5 units, respectively, for 186 experiments.     

Interaction of B(OH)_3^0 and HCO_3^ - in Seawater: Formation of B(OH)_2 CO_3^ -

Boron is known to interact with a wide variety of protonated ligands(HL) creating complexes of the form B(OH)₂L^-.Investigation of the interaction of boric acid and bicarbonate in aqueoussolution can be interpreted in terms of the equilibrium $B(OH)_3^0 + HCO_3^ - \rightleftharpoons B(OH)_2 CO_3^ - + H_2 O$ The formation constant for this reaction at 25 °C and 0.7 molkg^-1 ionic strength is $K_{BC} = \left[ {B(OH)_2 CO_3^ - } \right]\left[ {B(OH)_3^0 } \right]^{ - 1} \left[ {HCO_3^ - } \right]^{ - 1} = 2.6 \pm 1.7$ where brackets represent the total concentration of each indicatedspecies. This formation constant indicates that theB(OH)₂ $CO_3^ - $ concentration inseawater at 25 °C is on the order of 2 μmol kg^-1. Dueto the presence of B(OH)₂ $CO_3^ - $ , theboric acid dissociation constant ( $K\prime _B $ ) in natural seawaterdiffers from $K\prime _B $ determined in the absence of bicarbonate byapproximately 0.5%. Similarly, the dissociation constants of carbonicacid and bicarbonate in natural seawater differ from dissociation constantsdetermined in the absence of boric acid by about 0.1%. Thesedifferences, although small, are systematic and exert observable influenceson equilibrium predictions relating CO₂ fugacity, pH, totalcarbon and alkalinity in seawater.     

Thermodynamic properties of andradite and application to skarn with coexisting andradite and hedenbergite

The enthalpy of formation of andradite (Ca₃Fe₂Si₃O₁₂) has been estimated as-5,769.700 (±5) kJ/mol from a consideration of the calorimetric data on entropy (316.4 J/mol K) and of the experimental phaseequilibrium data on the reactions: 1 $$\begin{gathered} 9/2 CaFeSi_2 O_6 + O_2 = 3/2 Ca_3 Fe_2 Si_3 O_{12} + 1/2 Fe_3 O_4 + 9/2 SiO_2 (a) \hfill \\ Hedenbergite andradite magnetite quartz \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} 4 CaFeSi_2 O_6 + 2 CaSiO_3 + O_2 = 2 Ca_3 Fe_2 Si_3 O_{12} + 4 SiO_2 (b) \hfill \\ Hedenbergite wollastonite andradite quartz \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} 18 CaSiO_3 + 4 Fe_3 O_4 + O_2 = 6Ca_3 Fe_2 Si_3 O_{12} (c) \hfill \\ Wollastonite magnetite andradite \hfill \\ \end{gathered} $$ 1 $$\begin{gathered} Ca_3 Fe_2 Si_3 O_{12} = 3 CaSiO_3 + Fe_2 O_3 . (d) \hfill \\ Andradite pseudowollastonite hematite \hfill \\ \end{gathered} $$ and $$log f_{O_2 } = E + A + B/T + D(P - 1)/T + C log f_{O_2 } .$$ Oxygen-barometric scales are presented as follows: $$\begin{gathered} E = 12.51; D = 0.078; \hfill \\ A = 3 log X_{Ad} - 4.5 log X_{Hd} ; C = 0; \hfill \\ B = - 27,576 - 1,007(1 - X_{Ad} )^2 - 1,476(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite (Ad)-hedenbergite (Hd)-magnetite-quartz: $$\begin{gathered} E = 13.98; D = 0.0081; \hfill \\ A = 4 log(X_{Ad} / X_{Hd} ); C = 0; \hfill \\ B = - 29,161 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-wollastonite-quartz: 1 $$\begin{gathered} E = 13.98;{\text{ }}D = 0.0081; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 0;}} \hfill \\ B = - 29,161 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-calcitequartz: 1 $$\begin{gathered} E = - 1.69;{\text{ }}D = - 0.199; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 2;}} \hfill \\ B = - 20,441 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 . \hfill \\ \end{gathered} $$ For the assemblage andradite-hedenbergite-wollastonite-calcite: 1 $$\begin{gathered} E = - 17.36;{\text{ }}D = - 0.403; \hfill \\ A = 4\log (X_{Ad} /X_{Hd} );{\text{ C = 4;}} \hfill \\ B = - 11,720 - 1,342.8(1 - X_{Ad} )^2 - 1,312(1 - X_{Hd} )^2 \hfill \\ \end{gathered} $$ The oxygen fugacity of formation of those skarns where andradite and hedenbergite assemblage is typical can be calculated by using the above equations. The oxygen fugacity of formation of this kind of skarn ranges between carbon dioxide/graphite and hematite/magnetite buffers. It increases from the inside zones to the outside zones, and appears to decrease with the ore-types in the order Cu, Pb?Zn, Fe, Mo, W(Sn) ore deposits.     

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.     

Experimental study of subsolidus phase relations and mixing properties of pyroxene and plagioclase in the system Na2O-CaO-Al2O3-SiO2

In the system Na₂O-CaO-Al₂O₃-SiO₂ (NCAS), the equilibrium compositions of pyroxene coexisting with grossular and corundum were experimentally determined at 40 different P-T conditions (1,100–1,400° C and 20.5–38 kbar). Mixing properties of the Ca-Tschermak — Jadeite pyroxene inferred from the data are (J, K): $$\begin{gathered} G_{Px}^{xs} = X_{{\text{CaTs}}} X_{{\text{Jd}}} [14,810 - 7.15T - 5,070(X_{{\text{CaTs}}} - X_{{\text{Jd}}} ) \hfill \\ {\text{ }} - 3,350(X_{{\text{CaTs}}} - X_{{\text{Jd}}} )^2 ] \hfill \\ \end{gathered} $$ The excess entropy is consistent with a complete disorder of cations in the M2 and the T site. Compositions of coexisting pyroxene and plagioclase were obtained in 11 experiments at 1,190–1,300° C/25 kbar. The data were used to infer an entropy difference between low and high anorthite at 1,200° C, corresponding to the enthalpy difference of 9.6 kJ/mol associated with the C \(\bar 1\) =I \(\bar 1\) transition in anorthite as given by Carpenter and McConnell (1984). The resulting entropy difference of 5.0 J/ mol · K places the transition at 1,647° C. Plagioclase is modeled as ideal solutions, C \(\bar 1\) and I \(\bar 1\) , with a non-first order transition between them approximated by an empirical expression (J, bar, K): $$\Delta G_T = \Delta G_{1,473} \left[ {1 - 3X_{Ab} \tfrac{{T^4 - 1,473^4 }}{{\left( {1,920 - 0.004P} \right)^4 - 1,473^4 }}} \right],$$ where $$\Delta G_{1,473} = 9,600 - 5.0T - 0.02P$$ The derived mixing properties of the pyroxene and plagioclase solutions, combined with the thermodynamic properties of other phases, were used to calculate phase relations in the NCAS system. Equilibria involving pyroxene+plagioclase +grossular+corundum and pyroxene+plagioclase +grossular+kyani te are suitable for thermobarometry. Albite is the most stable plagioclase.     

Atmospheric pressure changes due to volcanic eruptions and possible water level fluctuations

The data of Reed (1983) are analysed to produce the following empirical equations for the amplitude p ₀ (overall fluctuation) in Pascals of the air pressure wave associated with a volcanic eruption of volume V km³ or a nuclear explosion of strength M Mt: Here s is the distance from the source in km. $$\begin{gathered} \log _{10} p_0 = 4.44 + \log _{10} V - 0.84\log _{10} s \hfill \\ {\text{ }} = 3.44 + \log _{10} M - 0.84\log _{10} s. \hfill \\ \end{gathered} $$ Garrett's (1970) theory is examined on the generation of water level fluctuations by an air pressure wave crossing a water depth discontinuity such as a continental shelf. The total amplitude of the ocean wave is determined to be where c ₂ ¹ = gh ₁, c ₂ ² = gh ₂, g is acceleration of gravity, h ₁ and h ₂ are the water depths on the ocean and shore side of the depth discontinuity, c is the speed of propagation of the air pressure wave, and ? is the water density. $$B = \left[ {\frac{{c_2^2 }}{{c^2 - c_2^2 }} + \frac{{c^2 (c_1 - c_2 )}}{{(c - c_1 )(c^2 - c_2^2 )}}} \right]\frac{{p_0 }}{{g\varrho }}$$ It is calculated that a 10 km³ eruption at Mount St. Augustine would cause a 460 Pa air pressure wave and a discernible water level fluctuation at Vancouver Island of several cm amplitude.