Thermodynamics of plagioclase II: Temperature evolution of the spontaneous strain at the I\bar 1 \leftrightarrow P\bar 1 phase transition in anorthite

The temperature dependence of the lattice parameters of pure anorthite with high Al/Si order reveals the predicted tricritical behaviour of the \(I\bar 1 \leftrightarrow P\bar 1\) phase transition at T _c ^* =510 K. The spontaneous strain couples to the order parameter Q° as x _i∝S _xQ ⁱ Q°² with S _xQ ¹ =4.166×10^?3, S _xQ ² =0.771×10^?3, S _xQ ³ =?7.223×10^?3 for the diagonal elements. The temperature dependence of Q° is $$Q^{\text{o}} = \left( {1 - \frac{T}{{510}}} \right)^\beta ,{\text{ }}\beta = \tfrac{{\text{1}}}{{\text{4}}}$$ A strong dependence of T _c ^* , S _xQ ⁱ and β is predicted for Al/Si disordered anorthite.     

Phase equilibria in the granite-H2O-HF system and effect of fluorine on granitic melt structure

Experiments carried out in the system granite-H₂O-HF at 0.1 GPa show that the crystal-liquid equilibrium temperature of quartz rises and that of alkali-feldspar goes down with increasing F content. The calculated results of quartz and alkali feldspar crystal-liquid equilibrium show that the activity of SiO₂ in melt increases and the activities of NaAlSi₃O₈(Ab) and KAlSi₃O₈(Or) decrease, with a greater decreasing extent for a _Ab ^L than a _Or ^L . These systematic changes are believed to be caused by F complexing with Al, Na, K, but not Si in the melt, and are consistent with F decomposing AlO ₂ ^? tetrahedra and more preferentially forming complexes with Na than K. The comparison between effects of F and H₂O on phase equilibrium suggests that the maximum difference affecting melt structure between F and OH is F complexing without Si and OH complexing with Si in granitic melt.     

Bayes estimation: A novel approach to derivation of internally consistent thermodynamic data for minerals,their uncertainties,and correlations. Part II: Application

Internally consistent thermodynamic data, including their uncertainties and correlations, are reported for 22 phases of the quaternary system CaO-Al₂O₃-SiO₂-H₂O. These data have been derived by simultaneous evaluation of the appropriate phase properties (PP) and reaction properties (RP) by the novel technique of Bayes estimation (BE). The thermodynamic model used and the theory of BE was expounded in Part I of this paper. Part II is the follow-up study illustrating an application of BE. The input for BE comprised, among others, the a priori values for standard enthalpy of formation of the i-th phase, Δ_f H _i ⁰ , and its standard entropy, S _i ⁰ , in addition to the reaction reversal constraints for 33 equilibria involving the relevant phases. A total of 269 RP restrictions have been processed, of which 107 turned out to be non-redundant. The refined values for Δ_f H _i ⁰ and S _i ⁰ obtained by BE, including their 2σ-uncertainties, appear in Table 4; the Appendix reproduces the corresponding correlation matrix. These data permit generation of computed phase diagrams with 2σ-uncertainty envelopes based on conventional error propagation; Fig. 3 depicts such a phase diagram for the system CaO-Al₂O₃-SiO₂. It shows that the refined dataset is capable of yielding phase diagrams with uncertainty envelopes narrow enough to be geologically useful. The results in Table 4 demonstrate that the uncertainties of the prior values for Δ_f H _i ^Emphasis>0 , given in Table 1, have decreased by up to an order of magnitude, while those for S _i ⁰ improved by a factor of up to two. For comparison, Table 4 also lists the refined Δ_f H _i ⁰ and S _i ⁰ data obtained by mathematical programming (MAP), minimizing a quadratic objective function used earlier by Berman (1988). Examples of calculated phase diagrams are given to demonstrate the advantages of BE for deriving internally consistent thermodynamic data. Although P-T curves generated from both MAP and BE databases will pass through the reversal restrictions, BE datasets appear to be better suited for extrapolations beyond the P-T range explored experimentally and for predicting equilibria not constrained by reversals.     

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.     

Pyroxene-melt equilibria: an updated model

An updated model for pyroxene-melt equilibria at 1 atm has been developed and calibrated using new and existing experimental data in order to refine calculations of liquid lines of descent, which simulate the effect of igneous differentiation processes. We combine the Davidson and Lindsley (1985) model for activities of components in clinopyroxene and orthopyroxene solid solutions, a _i ^p , where i represents a quadrilateral endmember, with the Nielsen and Drake (1979) expressions for component activities in the melt, a _i ^L (two-lattice melt model). The chemical potential differences for pyroxene-melt equilibria are expressed in the form: $$\Delta \mu _{\iota } = 0 = In \left( {{{a_i^p } \mathord{\left/{\vphantom {{a_i^p } {a_i^L }}} \right.\kern-\nulldelimiterspace} {a_i^L }}} \right) + A_i + {{B_i } \mathord{\left/{\vphantom {{B_i } T}} \right.\kern-\nulldelimiterspace} T}$$ Pyroxene compositions were projected to quadrilateral compositions with the method of Lindsley and Anderson (1983). The regression constants A _i and B _i were calculated from experimental data that consists of 282 pyroxene-melt pairs, including 83 orthopyroxene-melt pairs. These experiments were all performed at 1 atm and represent compositions ranging from basalts (alkali to lunar) to dacites (42–66 wt% SiO₂). The model is calibrated for 1000相似文献   

Distribution of REE,LILE, and HFSE between biotite,feldspar, and the melt in the granulite facies migmatite,nimnyr block,Aldan shield

The behavior of trace elements under conditions of partial melting of granitoid rocks has been studied. The element’s partition coefficients between minerals and the melt D_i^min/melt depends, in the first place, on the composition of the primary melt. In biotite the HREE D_i are a little below 1, while those of LREE, especially D_i for Ce, are 1–3 orders of magnitude less. This leads to an efficient differentiation of REEs in anatexic melts especially when biotite is the main mineral phase of restite. On the contrary, there are feldspars, the D_i of which cannot provide such a magnitude of differentiation. Unlike garnets and pyroxenes, whose stability in restite permits enrichment of anatexic melts produced in migmatization zones with Nb, Ti, and Cr, the presence of biotite in restite causes depletion of melts with those elements as well as with Rb. Feldspars, under conditions of their fractional crystallization or during differentiation of an anatexic melt, deplete the latter with Sr, Ba, and Rb, but enrich it with Nb, Ti, Cr, Y, Zr, and V.     

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.     

Zn and Pb solubility and speciation in aqueous chloride fluids at T-P parameters corresponding to granitoid magma degassing and crystallization

The solubility of all possible Zn and Pb species in aqueous chloride fluids was evaluated by means of thermodynamic simulations in systems ZnO(PbO)-aqueous solution of NaCl (KCl, NaCl + HCl) within broad ranges of temperature (600–900°C), pressure (0.7–5 kbar), and chloride concentrations, under parameters corresponding to the crystallization and degassing of granitoid magmas in the Earth’s crust. Our simulation results demonstrate that the addition of Cl to the fluid phase in the form of Na(K)Cl and HCl significantly increases the concentrations of Cl-bearing Zn and Pb complexes and the total concentration of the metals in the solutions in equilibrium with the solid oxides. In Zn-bearing fluids, the Zn(OH) ₂ ⁰ , ZnOH⁺, and Zn(OH) ₃ ^? —hydroxyl complexes and the ZnCl ₂ ⁰ , and ZnCl⁺ chlorocomplexes, which are predominant at low Cl concentrations (C_Cl < 0.05–0.1 m) give way to ZnCl ₄ ^2? with increasing C_Cl, which becomes the predominant Zn species of the fluid at C_Cl > 0.1–0.5 m throughout the whole temperature range in question and pressures higher than 1 kbar. For Pb-bearing fluids, the T-P-X region dominated by the Pb(OH) ₂ ⁰ , and Pb(OH) ₃ ^? hydroxyl complexes is remarkably wider than the analogous region for Zn, particularly at elevated temperatures (≥700°C) in alkaline solutions. An increase in C_Cl is associated with an increase in the concentration and changes in the speciation of Pb chlorocomplexes: PbCl ₂ ⁰ → PbCl ₃ ^? → PbCl ₄ ^2? . The concentrations of Zn and Pb chlorocomplexes increase with increasing pressure, decreasing temperature, and decrease pH with the addition of HCl to the system. It is demonstrated that the solubility of ZnO at any given T-P-X in alkaline solutions with low chloride concentrations are lower than the solubility of PbO. The Zn concentration increases more significantly than with the Pb concentration with increasing C_Cl and decreasing pH, so that the Zn concentration in acidic solutions is higher than the Pb concentration over broad ranges of temperature, pressure, and Cl concentration. Chloride complexes of Zn (ZnCl ₂ ⁰ , and ZnCl ₄ ^2? ) and Pb (PbCl ₂ ⁰ , and PbCl ₃ ^? are proved to be predominant within broad T-P-X-pH ranges corresponding to the parameters under which magmatic fluid are generated. Our simulation results confirm the hypothesis that chlorocomplexes play a leading role in Zn and Pb distribution between aqueous chloride fluids and granitic melts. These simulation results are consistent with experimental data on the Zn and Pb distribution coefficients (D(Zn)^f/m and D(Pb)^f/m, respectively) between aqueous chloride fluids and granitic melts that demonstrated that (1) D(Zn)^f/m and D(Pb)^f/m increase with increasing Na and K chloride concentrations in the aqueous fluid, (2) both D(Zn)^f/m and D(Pb)^f/m drastically increase when HCl is added to the fluid, and (3) (D(Zn)^f/m is higher than D(Pb)^f/m at any given T-P-X parameters. The experimentally established decrease in D(Zn)^f/m and D(Pb)^f/m with increasing pressure (at unchanging temperature and Cl concentration) is likely explained by an increase in the alkalinity of the aqueous chloride fluid in equilibrium with granite melt and, correspondingly, a decrease in the Zn and Pb solubility in this fluid.     

Carbon Dioxide in igneous petrogenesis: I

A number of experimental CO₂ solubility data for silicate and aluminosilicate melts at a variety of P- T conditions are consistent with solution of CO₂ in the melt by polymer condensation reactions such as SiO _4(m ^4? +CO_2(v)+Si _n O _3n+1(m) ⁽²ⁿ⁺¹⁾ ?Si _n+1O _3n+4(m) ^(2n+4)? +CO _3(m ^)2? . For various metalsilicate systems the relative solubility of CO₂ should depend markedly on the relative Gibbs free change of reaction. Experimental solubility data for the systems Li₂O-SiO₂, Na₂O-SiO₂, K₂O-SiO₂, CaO-SiO₂, MgO-SiO₂ and other aluminosilicate melts are in complete accord with predictions based on Gibbs Free energies of model polycondesation reactions. A rigorous thermodynamic treatment of published P- T-wt.% CO₂ solubility data for a number of mineral and natural melts suggests that for the reaction CO_2(m) ? CO_2(v)

1. CO₂-melt mixing may be considered ideal (i.e., { \(a_{{\text{CO}}_{\text{2}} }^m = X_{{\text{CO}}_{\text{2}} }^m \) );
2. \(\bar V_{{\text{CO}}_{\text{2}} }^m \) , the partial molal volume of CO₂ in the melt, is approximately equal to 30 cm³ mole^?1 and independent of P and T;
3. Δ C _p ⁰ is approximately equal to zero in the T range 1,400° to 1,650 °C and
4. enthalpies and entropies of the dissolution reaction depend on the ratio of network modifiers to network builders in the melt. Analytic expressions which relate the CO₂ content of a melt to P, T, and \(f_{{\text{CO}}_{\text{2}} } \) for andesite, tholeiite and olivine melilite melts of the form

$$\ln X_{{\text{CO}}_{\text{2}} }^m = \ln f_{{\text{CO}}_{\text{2}} } - \frac{A}{T} - B - \frac{C}{T}(P - 1)$$ have been determined. Regression parameters are (A, B, C): andesite (3.419, 11.164, 0.408), tholeiite (14.040, 5.440,0.393), melilite (9.226, 7.860, 0.352). The solubility equations are believed to be accurate in the range 3<P<30 kbar and 1,100°<T<1,650 °C. A series of CO₂ isopleth diagrams for a wide range of T and P are drawn for andesitic, tholeiitic and alkalic melts.     

The competing models for the origin and internal evolution of granitic pegmatites in the light of melt and fluid inclusion research

In this paper we discuss the main petrogenetic models for granitic pegmatites and how these models have evolved over time. We suggest that the present state of knowledge requires that some aspects of these models to be modified, or absorbed into newer ones. Pegmatite formation and internal evolution have long supposed the need for highly water- and flux-enriched magmas to explain the differences between pegmatites and other intrusives of similar major element composition. Compositions and textural characteristics of fluid and melt inclusions in pegmatite minerals provide strong evidence for such magmas. Furthermore, we show that melt inclusion research has increased the number of potential flux components, which may include H₂O, OH^?, CO₂, HCO ₃ ^? , CO ₃ ^2? , SO ₄ ^2? , PO ₄ ^3? , H₃BO₃, F , and Cl, as well as the elements Li, Na, K, Rb, Cs, and Be, herein described as melt structure modifiers. In this paper we emphasize that the combined effect which these components have on the properties of pegmatite melts is difficult to deduce from experimental studies using only a limited number of these components. The combination and the amount of the different magmatic species, together with differences in the source region, and variations in pressure and temperature cause the great diversity of the pegmatites observed. Some volatile species, such as CO ₃ ^2? and alkalis, have the capacity to increase the solubility of H₂O in silicate melt to an extraordinary degree, to the extent that melt-melt-fluid immiscibility becomes inevitable. It is our view that the formation of pegmatites is connected with the complex interplay of many factors.     

Experimental partitioning of halogens and other trace elements between olivine, pyroxenes, amphibole and aqueous fluid at 2 GPa and 900–1,300 °C

We present new partition coefficients for various trace elements including Cl between olivine, pyroxenes, amphibole and coexisting chlorine-bearing aqueous fluid in a series of high-pressure experiments at 2 GPa between 900 and 1,300 °C in natural and synthetic systems. Diamond aggregates were added to the experimental capsule set-up in order to separate the fluid from the solid residue and enable in situ analysis of the quenched solute by LA–ICP–MS. The chlorine and fluorine contents in mantle minerals were measured by electron microprobe, and the nature of OH defects was investigated by infrared spectroscopy. Furthermore, a fluorine-rich olivine from one selected sample was investigated by TEM. Results reveal average Cl concentrations in olivine and pyroxenes around 20 ppm and up to 900 ppm F in olivine, making olivine an important repository of halogens in the mantle. Chlorine is always incompatible with Cl partition coefficients D _Cl ^{olivine/fluid} varying between 10^?5 and 10^?3, whereas D _Cl ^{orthopyroxene/fluid} and D _Cl ^{clinopyroxene/fluid} are ~10^?4 and D _Cl ^{amphibole/fluid} is ~5 × 10^?3. Furthermore, partitioning results for incompatible trace element show that compatibilities of trace elements are generally ordered as D ^amph/fluid ≈ D ^cpx/fluid > D ^opx/fluid > D ^ol/fluid but that D ^{mineral/fluid} for Li and P is very similar for all observed silicate phases. Infrared spectra of olivine synthesized in a F-free Ti-bearing system show absorption bands at 3,525 and ~3,570 cm^?1. In F ± TiO₂-bearing systems, additional absorption bands appear at ~3,535, ~3,595, 3,640 and 3,670 cm^?1. Absorption bands at ~3,530 and ~3,570 cm^?1, previously assigned to humite-like point defects, profit from low synthesis temperatures and the presence of F. The presence of planar defects could not be proved by TEM investigations, but dislocations in the olivine lattice were observed and are suggested to be an important site for halogen incorporation in olivine.     

First principles quantum mechanical calculation of the electric dipole polarizabilities of the borate,carbonate, nitrate and related ions

Electric dipole polarizabilities have been calculated from first principles of quantum mechanics for the BO ₃ ^3? , CO ₃ ^2? , NO ₃ ^? series and for NO ₂ ^? and LiNO₃(g). Calculated trends in average polarizability and polarizability anisotropy in the BO ₃ ^3? -NO ₃ ^? series are in agreement with experiment and can be qualitatively interpreted in terms of the varying energies of the a₁′, a₂″ and e′ symmetry unoccupied MO's of the oxyanions. Embedding a CO ₃ ^2? ion in a D_3h symmetry array of divalent cations reduces both the average polarizability and its anisotropy, particularly when diffuse s and p functions are included in the calculation. Calculations on the gas phase LiNO₃ molecule and on the free NO ₃ ^? ion in the distorted geometry found in LiNO₃(g) allow us to separate polarizability contributions internal to the NO ₃ ^? and Li⁺ ions from those which arise from the Li⁺-NO ₃ ^? interaction. The Li⁺-NO ₃ ^? interaction term so obtained is much smaller than the NO ₃ ^? contribution but is in turn larger than the Li⁺ contribution, suggesting that the inclusion of this interaction term is essential for obtaining accurate results for ion pairs. Although static polarizabilities are in reasonable agreement with experiment for NO ₃ ^? the wavelength dispersion of the polarizability is underestimated by about a factor of two, apparently as a result of inadequacies in the quantum mechanical method. Calculated values are also presented for ¹⁴N NMR shieldings in the nitrogen oxyanions but these are in only qualitative agreement with the experimental values. Similarly, calculated values of magnetic susceptibility are in only qualitative agreement with experiment although trends along the BO ₃ ^3? -NO ₃ ^? series are properly reproduced.     

A new method of material balance evaluation in metamorphic differentiated systems

The methods used by earlier workers for evaluating material balance in core-mantle-matrix type differentiated systems are examined in detail. It is demonstrated that these methods can be successfully employed only when the true core-mantle volume ratio is known. On geometric grounds, it is rarely possible to have a reliable estimate of this ratio from natural specimen. Consequently, the scope of balance evaluation by these methods is severely restricted. From theoretical consideration of mass transfer relations in differentiated systems, a new computational method is proposed that can be effectively employed for quantitative balance evaluation without any prior knowledge of the core-mantle volume ratio provided the chemical analyses of the core, mantle and matrix are available. This method involves the application of the following mass balance equation: $$m_1 x_1^i + m_2 x_2^i = m_0 x_0^i {\text{ (}}i = {\text{1,2}}...{\text{,}}n{\text{)}}$$ where m ₁ and m ₂ are the mass of the core and mantle respectively, m ₀ is the mass of the matrix involved in differentiation, and x ₁ ⁱ , x ₂ ⁱ , x ₀ ⁱ are the weight fractions of the component i in the core, mantle and matrix respectively. This method would also permit a quantitative estimation of the materials added to or removed from the system. Three differentiated systems previously investigated by Mehnert (1951, 1968), Loberg (1963) and Kretz (1966) are selected for balance evaluation by the proposed method and the results are compared with the published balance analyses.     

Uranium-lead isotopic evidence from zircons for lower Palaeozoic tectonic activity in the Austroalpine Nappe,the Eastern Alps

U/Pb isotopic data for two zircon suites are presented:

1. a pre D ₁ tonalite gneiss gives an age of 443 ± ₁₆ ¹³ m.y.
2. a post D ₁ leucogranite gneiss gives 427 ± ₁₁ ¹⁰ m.y.

Both zircon suites contain a minor inherited pre-Cambrian component. The data confirm a lower Palaeozoic age for the major, fabric-forming D ₁ event. Hercynian metamorphism which was sufficient to reset muscovite K/Ar ages to ca. 290 m.y. had little effect on the zircons. The possible importance of lower Palaeozoic orogeny in southern Europe and the uncertainties in regional palaeogeography are emphasised.     

Optical absorption spectra of iron ions in vivianite

Absorption bands are determined in polarized optical spectra of vivianite Fe₃(PO₄)₂·8H₂O, recorded at room and low temperatures. These bands are caused by spin-allowed d-d transitions in structurally nonequivalent Fe _A ²⁺ (～11000 cm^-1 (γ-polarization) (and) ～12000 cm^-1 (β-polarization)) (and) Fe _B ²⁺ (～8400 cm^-1 (γ, α-polarization) and ～11200 cm^-1 (α-polarization)) ions. A charge transfer band (CTB) Fe _B ²⁺ +Fe _B ³⁺ →Fe _B ²⁺ +Fe _B ²⁺ (～15000 cm^-1) also determined, has polarizing features giving evidence of a change in the Fe _B ²⁺ -Fe _B ³⁺ bond direction, when compared with Fe _B ²⁺ -Fe _B ²⁺ . Bands of exchange-coupled Fe³⁺-Fe³⁺ pairs (～19400, ～20400, ～21300 and ～21700 cm^-1) which appear on oxidation of Fe²⁺ in paired Fe _B octahedra are also characterized.     

A theoretical study of bond distances,X-ray spectra and electron density distributions in borate polyhedra

The borate polyhedra BO ₃ ^3? , B(OH)₃, BO ₄ ^5? , and B(OH) ₄ ^? are studied using the ab initio and multiple scattering Xα quantum mechanical methods. The ab initio self-consistent-field (SCF) molecular orbital (MO) method, at the minimum basis set level, predicts equilibrium B-O distances within 0.04 Å of their average values in solids so long as the polyhedron charge is small. Orbital energies from double zeta basis set ab initio calculations and analogies with isoelectric compounds are used to assign the X-ray spectra of BO ₃ ^3? and to predict the valence region spectra of BO ₄ ^5? . Contour maps of the difference between molecular and superimposed free atom electron densities show charge buildup along the B-O bond which is only slightly smaller than that observed in CO ₃ ^2? .     

Thermodynamic calculation of peridotite phase relations in the system MgO-Al2O3-SiO2-Cr2O3, with some geological applications

The system MgO-Al₂O₃-SiO₂(MAS) comprises 88–90% of the bulk composition of an average peridotite. The MAS ternary is thus a suitable starting point for exploring peridotite phase relations in multicomponent natural systems. The basic MAS phase relations may be treated in terms of the reactions (see list of symbols etc).

1. py (in Gt)=en (in Opx)+mats (in Opx),
2. en (in Opx)+sp (in Sp)=mats (in Opx)+fo (in Ol), and
3. py (in Gt)+fo (in Ol)=en (in Opx)+sp (in Sp).

Extensive reversed phase equilibria data on these three reactions by Danckwerth and Newton (1978), Perkins et al. (1981), and Gasparik and Newton (1984) employing identical experimental methods in the same laboratory have been used by us to deduce the following internally consistent thermodynamic data applying the technique of linear programming:ΔH ₂₉₈₍₁₎ ⁰ = 2536 J, ΔS ₂₉₈₍₁₎ ⁰ =? 6.064 J/K;ΔH ₂₉₈₍₂₎ ⁰ = 29435 J, ΔS ₂₉₈₍₂₎ ⁰ = 8.323 J/K; andΔH ₂₉₈₍₃₎ ⁰ =?26899 J, ΔS ₂₉₈₍₃₎ ⁰ =?14.388 J/K.These data are also found to be consistent with results of calorimetry. Figure 2 shows the calculated phase relations based on our thermodynamic data; they are consistent with the phase equilibria experiments. Successful extension of the MAS phase relations to multicomponent peridotites pivots on the extent to which the effects of the “non-ternary” (i.e. other than MAS) components can be quantitatively handled. Particularly hazardous in this context is Cr₂O₃, although it barely makes up 0.2 to 0.5 wt% of such rocks. This is because Cr⁺³ fractionates extremely strongly into Sp. This study focuses on the peridotite phase relations in the MgO-Al₂O₃-SiO₂-Cr₂O₃ (MASCr) quaternary. Thermodynamic calculations of the MASCr phase relations have been accomplished by using ΔH ₂₉₈ ⁰ and ΔS ₂₉₈ ⁰ values for the reactions (1) through (3) indicated above, in conjunction with data on thermodynamic mixing properties of

1. binary Sp (sp-pc) crystalline solution (Oka et al. 1984),
2. ternary Opx (en-mats-mcts) crystalline solution (this study), and
3. binary Gt (py-kn) crystalline solution (this study).

The results are shown in P-T projections (Figs. 3a and b) and isobaric-isothermal sections of MASCr in a projection through the component fo onto the SiO₂-Al₂O₃-Cr₂O₃ ternary (Figs. 4a and b). The most important results of this work may be summarized as follows:

1. With increasing incorporation of Cr⁺³ into Sp and Gt, the X _mats isopleths of the reactions (1) and (2) are shifted to higher temperatures (Fig. 3a); simultaneously, the spinel-peridotite to garnet-peridotite phase transition is moved to higher pressures (Fig. 3b).
2. At identical P and T, the X _mats values of Opx coexisting in equilibrium with Ol and Sp is strongly dependent upon the X _pc value in the latter phase (Figs. 4a and b). Accurate correction for the composition of Sp is, therefore, a necessary precondition for geothermometry of the spinelperidotites.
3. The discrepant temperatures reported by Sachtleben und Seck (1981, Fig. 5) from the spinel-peridotites of the Eifel area (systematically too high temperatures as a function of X _pc in Sp) are demonstrated to be the result of ignoring the nonideality in the chromian spinels.

     

Molecular orbitals of Si2O 7 6− , Si3O 10 8− , etc., and mixed (B,Al,P,Si) m applied to clusters and X-ray spectroscopy data of silicates

The Si, Al L_{II, III} and OK_α emission and quantum yield spectra were obtained for 24 silicates. It was found that in minerals of a homogeneous anion composition the Si L_{II, III} line has double-humped structure, and when in addition to SiO ₄ ^4? ions of other composition (BeO ₄ ^6? , AlO ₄ ^5? etc.) are present it has triple-humped structure. The process of crystal-glass transition was studied by X-ray spectroscopy. The result is that in spite of the original form of the Si L_{II, III} line of the mineral this line changes its structure in glass and exhibits a typical double-humped structure. The CNDO/2 approach was used to calculate the electronic structure of basic structural groups of silicates from SiO ₄ ^4? to Si₅O ₁₆ ^12? by replacing one or two of the Si atoms by Be, B, Al and P. A qualitative interpretation of the X-ray spectra is presented.     

Electron paramagnetic resonance of PO 3 2− and SO 3 − radicals in anhydrite,celestite and barite: the hyperfine structure and dynamics

Electron paramagnetic resonance (EPR) measurements of natural anhydrite CaSO₄, celestite SrSO₄ and barite BaSO₄ have revealed the presence of PO ₃ ^2? and SO ₃ ^? radicals. Hyperfine structure from³³S has been detected and measured for the first time. Low-symmetry effects, which are manifested in noncoincidence of g and hyperfine axes, were observed for SO ₃ ^? . The dynamics of one of the two SO ₃ ^? types in anhydrite has been investigated. Variations of spin Hamiltonian parameters with temperature have been attributed to thermally induced jumps between the two magnetically inequivalent sites of this center.