Molecular Orbital Study on the Optimized Geometries and Spectroscopic Parameters of Borate Polyhedra

In this paper several methods including MNDO, multiple scattering Xα and ab initio self-consistent-field MO theories have been used to calculate the minimum energy geometries, force constants, vibrational frequencies ,and ^11B quadruple coupling constants of B-O polyhedra such as [BO3],[BO4],[OB2] and [OB3].The results are in good agreement with the experimental and calcu-lated values so far published by other authors.     

The oxygen isotope fractionation behaviour of kyanite in experiment and nature

The oxygen isotope fractionation between kyanite and calcium carbonate has been investigated experimentally at four temperatures in the range between 625 and 775 °C at 13 kbar. Because of low exchange rates, the isotopic reaction was enhanced by polymorphic transformation of andalusite to kyanite. With this experimental modification a close approach to equilibrium was reached in all runs. The temperature dependence of the equilibrium fractionation is described by the equation 1000 ln _ky-cc=−2.62×10⁶/T ². Application of the experimental results to natural quartz-kyanite-garnet assemblages indicates the preservation of the oxygen isotope composition of kyanite acquired during its formation, reflecting its extremely low oxygen diffusivity. This refractory behaviour restricts the use of kyanite for thermometry but opens the possibility to use its O-isotope composition as an indicator for recognition of polymetamorphic rock histories and reconstruction of the prograde evolution of a metamorphic sequence. Received: 8 June 1998 / Accepted: 24 August 1998     

HTP21/c–C2/c phase transition and kinetics of Fe2+–Mg order–disorder of an Fe-poor pigeonite: implications for the cooling history of ureilites

A natural Ca-poor pigeonite (Wo₆En₇₆Fs₁₈) from the ureilite meteorite sample PCA82506-3, free of exsolved augite, was studied by in situ high-temperature single-crystal X-ray diffraction. The sample, monoclinic P2₁/c, was annealed up to 1,093°C to induce a phase transition from P2₁/c to C2/c symmetry. The variation with increasing temperature of the lattice parameters and of the intensity of the b-type reflections (h + k = 2n + 1, present only in the P2₁/c phase) showed a displacive phase transition P2₁/c to C2/c at a transition temperature T _Tr = 944°C, first order in character. The Fe–Mg exchange kinetics was studied by ex situ single-crystal X-ray diffraction in a range of temperatures between the closure temperature of the Fe–Mg exchange reaction and the transition temperature. Isothermal disordering annealing experiments, using the IW buffer, were performed on three crystals at 790, 840 and 865°C. Linear regression of ln k _D versus 1/T yielded the following equation: ln k_\textD = - 3717( ±416)/T(K) + 1.290( ±0.378);    (R² = 0.988) \ln \,k_{\text{D}} = - 3717( \pm 416)/T(K) + 1.290( \pm 0.378);\quad (R^{2} = 0.988) . The closure temperature (T _c) calculated using this equation was ∼740(±30)°C. Analysis of the kinetic data carried out taking into account the e.s.d.'s of the atomic fractions used to define the Fe–Mg degree of order, performed according to Mueller’s model, allowed us to retrieve the disordering rate constants C ₀ K _dis⁺ for all three temperatures yielding the following Arrhenius relation: ln( C₀ K_\textdis ⁺ ) = ln K₀ - Q/(RT) = 20.99( ±3.74) - 26406( ±4165)/T(K);    (R² = 0.988) \ln \left( {C_{0} K_{\text{dis}}^{ + } } \right) = \ln \,K_{0} - Q/(RT) = 20.99( \pm 3.74) - 26406( \pm 4165)/T(K);\quad (R^{2} = 0.988) . An activation energy of 52.5(±4) kcal/mol for the Fe–Mg exchange process was obtained. The above relation was used to calculate the following Arrhenius relation modified as a function of X _Fe (in the range of X _Fe = 0.20–0.50): ln( C₀ K_\textdis ⁺ ) = (21.185 - 1.47X_\textFe ) - \frac(27267 - 4170X_\textFe )T(K) \ln \left( {C_{0} K_{\text{dis}}^{ + } } \right) = (21.185 - 1.47X_{\text{Fe}} ) - {\frac{{(27267 - 4170X_{\text{Fe}} )}}{T(K)}} . The cooling time constant, η = 6 × 10⁻¹ K⁻¹ year⁻¹ calculated on the PCA82506-3 sample, provided a cooling rate of the order of 1°C/min consistent with the extremely fast late cooling history of the ureilite parent body after impact excavation.     

Thermobarometry of mafic igneous rocks based on clinopyroxene-liquid equilibria, 0–30 kbar

 Models for estimating the pressure and temperature of igneous rocks from co-existing clino-pyroxene and liquid compositions are calibrated from existing data and from new data obtained from experiments performed on several mafic bulk compositions (from 8–30 kbar and 1100–1475° C). The resulting geothermobarometers involve thermodynamic expressions that relate temperature and pressure to equilibrium constants. Specifically, the jadeite (Jd; NaAlSi₂O₆)–diopside/hedenbergite (DiHd; Ca(Mg, Fe) Si₂O₆) exchange equilibrium between clinopyroxene and liquid is temperature sensitive. When compositional corrections are made to the calibrated equilibrium constant the resulting geothermometer is (i) 10⁴ T=6.73−0.26^* ln [Jd^px*Ca^liq*Fm^liqDiHd^px*Na^liq*Al^liq] −0.86^* ln [Mg^liqMg^liq+Fe^liq]+0.52^*ln [Ca^liq] an expression which estimates temperature to ±27 K. Compared to (i), the equilibrium constant for jadeite formation is more sensitive to pressure resulting in a thermobarometer (ii) P=−54.3+299^* T10⁴+36.4^* T10⁴ ln [Jd^px[Si^liq]^2*Na^liq*Al^liq] +367^*[Na^liq*Al^liq] which estimates pressure to ± 1.4 kbar. Pressure is in kbar, T is in Kelvin. Quantities such as Na^liq represent the cation fraction of the given oxide (NaO_0.5) in the liquid and Fm=MgO+FeO. The mole fractions of Jd and diopside+hedenbergite (DiHd) components are calculated from a normative scheme which assigns the lesser of Na or octahedral Al to form Jd; any excess Al^VI forms Calcium Tschermak’s component (CaTs; CaAlAlSiO₆); Ca remaining after forming CaTs and CaTiAl₂O₆ is taken as DiHd. Experimental data not included in the regressions were used to test models (i) and (ii). Error on predictions of T using model (i) is ±40 K. A pressure-dependent form of (i) reduces this error to ±30 K. Using model (ii) to predict pressures, the error on mean values of 10 isobaric data sets (0–25 kbar, 118 data) is ±0.3 kbar. Calculating thermodynamic properties from regression coefficients in (ii) gives V^Jd _f of 23.4 ±1.3 cm³/mol, close to the value anticipated from bar molar volume data (23.5 cm³/mol). Applied to clinopyroxene phenocrysts from Mauna Kea, Hawaii lavas, the expressions estimate equilibration depths as great as 40 km. This result indicates that transport was sufficiently rapid that at least some phenocrysts had insufficient time to re-equilibrate at lower pressures. Received: 16 May 1994/Accepted: 15 June 1995     

Calibration of the calcite-water oxygen-isotope geothermometer at Devils Hole, Nevada, a natural laboratory

The δ¹⁸O of ground water (−13.54 ± 0.05 ‰) and inorganically precipitated Holocene vein calcite (+14.56 ± 0.03 ‰) from Devils Hole cave #2 in southcentral Nevada yield an oxygen isotopic fractionation factor between calcite and water at 33.7 °C of 1.02849 ± 0.00013 (1000 ln α_{calcite-water} = 28.09 ± 0.13). Using the commonly accepted value of ∂(α_{calcite-water})/∂T of −0.00020 K⁻¹, this corresponds to a 1000 ln α_{calcite-water} value at 25 °C of 29.80, which differs substantially from the current accepted value of 28.3. Use of previously published oxygen isotopic fractionation factors would yield a calcite precipitation temperature in Devils Hole that is 8 °C lower than the measured ground water temperature. Alternatively, previously published fractionation factors would yield a δ¹⁸O of water, from which the calcite precipitated, that is too negative by 1.5 ‰ using a temperature of 33.7 °C. Several lines of evidence indicate that the geochemical environment of Devils Hole has been remarkably constant for at least 10 ka. Accordingly, a re-evaluation of calcite-water oxygen isotopic fractionation factor may be in order.Assuming the Devils Hole oxygen isotopic value of α_{calcite-water} represents thermodynamic equilibrium, many marine carbonates are precipitated with a δ¹⁸O value that is too low, apparently due to a kinetic isotopic fractionation that preferentially enriches ¹⁶O in the solid carbonate over ¹⁸O, feigning oxygen isotopic equilibrium.     

An empirical model for the calculation of spinel-melt equilibria in mafic igneous systems at atmospheric pressure: 1. Chromian spinels

 In order to develop a model for simulating naturally occurring chromian spinel compositions, we have processed published experimental data on chromian spinel-melt equilibrium. Out of 259 co-existing spinel-melt experiments reported in the literature, we have selected 118 compositions on the basis of run time, melt composition and experimental technique. These data cover a range of temperatures 1150–1500° C, oxygen fugacities of −13<log f _O2< −0.7, and bulk compositions ranging from basalt and norite, to komatiite. Six major spinel components with Cr³⁺, Al³⁺, Ti⁴⁺, Mg²⁺, Fe³⁺ and Fe²⁺-bearing end-members were considered for the purpose of describing chromite saturation as a function of melt composition, temperature and oxygen fugacity at 1 atmosphere pressure (0.101 MPa). The empirically calibrated mineral-melt expression based on multiple linear regressions is: K ^Sp _i =A/T(K)+B log f _O2+C ln (Fe³⁺/Fe²⁺)_L+D ln R _L +E, where K ^Sp _i is an equilibrium constant and R _L is a melt structure-chemical parameter (MSCP). Twenty-eight forms of equilibrium constants were considered, including single distribution coefficients, exchange equilibrium constants, formation constants for AB₂O₄ components, as well as simple “spinel cation ratios”. For each form of the equilibrium constants, a set of 16 combinations of the MSCPs have been investigated. The MSCP is present in the form of composite ratios [e.g., Si/O, NBO/T,(Al+Si)/Si, or (Na+K)/Al] or as simple cation ratios (e.g., Mg/Fe²⁺). For the calculation of Fe³⁺ and Fe²⁺ species in silicate melts, we used existing equations, whereas the Fe³⁺/Fe²⁺ ratio of spinels was calculated from the spinel stoichiometry. The regression parameters that best repoduce the experimental data were for the following constants: (Fe³⁺/Fe²⁺) _Sp , (Mg/Fe²⁺) _Sp /(Mg/Fe²⁺) _L , (Cr/Al) _Sp / (Cr/Al) _L , K _FeCr2O4, and Ti _Sp /Ti _L . These expressions have been combined into a single program called SPINMELT, which calculates chromite crystallization temperature and composition at a given f _O2 with an average accuracy of ∼10° C and 1–2 mol%. An example of the use of SPINMELT is presented for a magma parental to the Bushveld Complex. Received: 30 May 1995/Accepted: 1 November 1995     

Calculation of individual isotope equilibrium constants for geochemical reactions

Theory is derived from the work of Urey (Urey H. C. [1947] The thermodynamic properties of isotopic substances. J. Chem. Soc. 562-581) to calculate equilibrium constants commonly used in geochemical equilibrium and reaction-transport models for reactions of individual isotopic species. Urey showed that equilibrium constants of isotope exchange reactions for molecules that contain two or more atoms of the same element in equivalent positions are related to isotope fractionation factors by α = (K^ex)^1/n, where n is the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example ¹³C¹⁶O¹⁸O and ¹H²H¹⁸O. The equilibrium constants of the isotope exchange reactions can be expressed as ratios of individual isotope equilibrium constants for geochemical reactions. Knowledge of the equilibrium constant for the dominant isotopic species can then be used to calculate the individual isotope equilibrium constants.Individual isotope equilibrium constants are calculated for the reaction CO_2g = CO_2aq for all species that can be formed from ¹²C, ¹³C, ¹⁶O, and ¹⁸O; for the reaction between ¹²C¹⁸O_2aq and ¹H₂¹⁸O_l; and among the various ¹H, ²H, ¹⁶O, and ¹⁸O species of H₂O. This is a subset of a larger number of equilibrium constants calculated elsewhere (Thorstenson D. C. and Parkhurst D. L. [2002] Calculation of individual isotope equilibrium constants for implementation in geochemical models. Water-Resources Investigation Report 02-4172. U.S. Geological Survey). Activity coefficients, activity-concentration conventions for the isotopic variants of H₂O in the solvent ¹H₂¹⁶O_l, and salt effects on isotope fractionation have been included in the derivations. The effects of nonideality are small because of the chemical similarity of different isotopic species of the same molecule or ion. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation factors.The derivations can be extended to calculation of individual isotope equilibrium constants for ion pairs and equilibrium constants for isotopic species of other chemical elements. The individual isotope approach calculates the same phase isotopic compositions as existing methods, but also provides concentrations of individual species, which are needed in calculations of mass-dependent effects in transport processes. The equilibrium constants derived in this paper are used to calculate the example of gas-water equilibrium for CO₂ in an acidic aqueous solution.     

Thermal Expansion of Periclase (MgO) and Tungsten (W) to Melting Temperatures

 In situ x-ray data on molar volumes of periclase and tungsten have been collected over the temperature range from 300 K to melting. We determine the temperature by combining the technique of spectroradiometry and electrical resistance wire heating. The thermal expansion (α) of periclase between 300 and 3100 K is given by α=2.6025 10⁻⁵+1.3535 10⁻⁸ T+6.5687 10⁻³ T⁻¹−1.8281 T⁻². For tungsten, we have (300 to 3600 K) α=7.862 10⁻⁶+6.392 10⁻⁹ T. The data at 298 K for periclase is: molar volume 11.246 (0.031) cm³, α=3.15 (0.07) 10⁻⁵ K⁻¹, and for tungsten: molar volume 9.55 cm³, α=9.77 (10.08) 10⁻⁶ K⁻¹. Received: July 18, 1996 / Revised, accepted: February 14, 1997     

Temperature-dependent isotopic fractionation of lithium between clinopyroxene and high-pressure hydrous fluids

The fractionation of lithium isotopes between synthetic spodumene as representative of Li-bearing clinopyroxene and Cl- and OH-bearing aqueous fluids was experimentally determined between 500 and 900°C at 2.0 GPa. In all the experiments, ⁷Li was preferentially partitioned into the fluid. The fractionation is temperature dependent and approximated by the equation Δ⁷Li_{(clinopyroxene–fluid)}=−4.61×(1,000/T [K]) + 2.48; R ²=0.86. Significant Li isotopic fractionation of about 1.0‰ exists even at high temperatures of 900°C. Using neutral and weakly basic fluids revealed that the amount of fractionation is not different. The Li isotopic fractionation between altered basalt and hot spring water (350°C) in natural samples is in good agreement with our experimentally determined fractionation curve. The data confirm earlier speculations drawn from the Li isotopic record of dehydrated metamorphic rocks that fluids expelled from a dehydrating slab carry heavier Li into the mantle wedge, and that a light Li component is introduced into the deeper mantle. Li and Li isotopes are redistributed among wedge minerals as fluids travel across the wedge into hotter regions of arc magma production. This modifies the Li isotopic characteristics of slab-derived fluids erasing their source memory, and explains the absence of cross-arc variations of Li isotopes in arc basalts.     

Oxygen isotope fractionation between calcite and tremolite: an experimental study

Oxygen isotope partitioning between calcite and tremolite was experimentally calibrated in the presence of small amounts of a supercritical CO₂–H₂O fluid at temperatures from 520 to 680° C and pressures from 3 to 10 kbar. The experiments were carried out within the stability field of the calcite-tremolite assemblage based on phase equilibrium relationships in the system CaO–MgO–SiO₂–CO₂–H₂O, so that decomposition of calcite and tremolite was avoided under the experimental conditions. Appropriate proportions of carbon dioxide to water were used to meet this requirement. Large weight ratios of mineral to fluid were employed in order to make the isotopic exchange between calcite and tremolite in the presence of a fluid close to that without fluid. The data processing method for isotopic exchange in a three-phase system has been applied to extrapolate partial equilibrium data to equilibrium values. The determined fractionation factors between calcite (Cc) and tremolite (Tr) are expressed as:10³1n _Cc-Tr=3.80 × 10⁶/T ²-1.67By combining the present data with the experimental calibrations of Clayton et al. (1989) on the calcite-quartz system, we obtain the fractionation for the quartztremolite system: 10³1n _Qz-Tr=4.18 × 10⁶/T ²-1.67Our experimental calibrations are in good agreement with the theoretical calculations of Hoffbauer et al. (1994) and the empirical estimates of Bottinga and Javoy (1975) based on isotopic data from naturall assemblages. At 700 C good agreement also exists between our experimental data and theoretical values calculated by Zheng (1993b). With decreasing temperature, however, an increasing difference between these data appears.Retrograde isotopic reequilibration by oxygen diffusion may be common for amphibole relative to diopside in metamorphic rocks. However, isotopic equilibrium in amphibole can be preserved in cases of rapid cooling.     

平衡热液体系中硫同位素演化的几个图解

根据含硫矿物的同位素组成推断热液矿床成因是很有意义的。 1968年首先由H.Sakai指出热液的温度和pH值可以影响硫化物的同位素组成。接着,1972年H.Ohmoto以及1979年他和R.O.Rye系统讨论了平衡条件下热液的物理化学条件对硫同位素分馏的影响,建立了高温热液系统和低温热液系统的热液流体以及含硫矿物与热液成分和物理化学条件(温度、压力、氧逸度和酸碱度等)之间的数学表达式。     

H2O activity in concentrated NaCl solutions at high pressures and temperatures measured by the brucite-periclase equilibrium

 H₂O activities in concentrated NaCl solutions were measured in the ranges 600°–900° C and 2–15 kbar and at NaCl concentrations up to halite saturation by depression of the brucite (Mg(OH)₂) – periclase (MgO) dehydration equilibrium. Experiments were made in internally heated Ar pressure apparatus at 2 and 4.2 kbar and in 1.91-cm-diameter piston-cylinder apparatus with NaCl pressure medium at 4.2, 7, 10 and 15 kbar. Fluid compositions in equilibrium with brucite and periclase were reversed to closures of less than 2 mol% by measuring weight changes after drying of punctured Pt capsules. Brucite-periclase equilibrium in the binary system was redetermined using coarsely crystalline synthetic brucite and periclase to inhibit back-reaction in quenching. These data lead to a linear expression for the standard Gibbs free energy of the brucite dehydration reaction in the experimental temperature range: ΔG° (±120J)=73418–134.95T(K). Using this function as a baseline, the experimental dehydration points in the system MgO−H₂O−NaCl lead to a simple systematic relationship of high-temperature H₂O activity in NaCl solution. At low pressure and low fluid densities near 2 kbar the H₂O activity is closely approximated by its mole fraction. At pressures of 10 kbar and greater, with fluid densities approaching those of condensed H₂O, the H₂O activity becomes nearly equal to the square of its mole fraction. Isobaric halite saturation points terminating the univariant brucite-periclase curves were determined at each experimental pressure. The five temperature-composition points in the system NaCl−H₂O are in close agreement with the halite saturation curves (liquidus curves) given by existing data from differential thermal analysis to 6 kbar. Solubility of MgO in the vapor phase near halite saturation is much less than one mole percent and could not have influenced our determinations. Activity concentration relations in the experimental P-T range may be retrieved for the binary system H₂O-NaCl from our brucite-periclase data and from halite liquidus data with minor extrapolation. At two kbar, solutions closely approach an ideal gas mixture, whereas at 10 kbar and above the solutions closely approximate an ideal fused salt mixture, where the activities of H₂O and NaCl correspond to an ideal activity formulation. This profound pressure-induced change of state may be characterized by the activity (a) – concentration (X) expression: a _{H 2}O=X _{H 2}O/(1+αX _NaCl), and a _NaCl=(1+α)^(1+α)[X _NaCl/(1+αX _NaCl)]^(1+α). The parameter α is determined by regression of the brucite-periclase H₂O activity data: α=exp[A–B/ϱ_{H 2}O ]-CP/T, where A=4.226, B=2.9605, C=164.984, and P is in kbar, T is in Kelvins, and ϱ_{H 2}O is the density of H₂O at given P and T in g/cm³. These formulas reproduce both the H₂O activity data and the NaCl activity data with a standard deviation of ±0.010. The thermodynamic behavior of concentrated NaCl solutions at high temperature and pressure is thus much simpler than portrayed by extended Debye-Hückel theory. The low H₂O activity at high pressures in concentrated supercritical NaCl solutions (or hydrosaline melts) indicates that such solutions should be feasible as chemically active fluids capable of coexisting with solid rocks and silicate liquids (and a CO₂-rich vapor) in many processes of deep crustal and upper mantle metamorphism and metasomatism. Received: 1 September 1995 / Accepted: 24 March 1996     

Oxygen isotopic fractionation during inorganic calcite precipitation ― Effects of temperature, precipitation rate and pH

Stable oxygen isotopic fractionation during inorganic calcite precipitation was experimentally studied by spontaneous precipitation at various pH (8.3 < pH < 10.5), precipitation rates (1.8 < log R < 4.4 μmol m^− 2 h^− 1) and temperatures (5, 25, and 40 °C) using the CO₂ diffusion technique.The results show that the apparent stable oxygen isotopic fractionation factor between calcite and water (α_{calcite–water}) is affected by temperature, the pH of the solution, and the precipitation rate of calcite. Isotopic equilibrium is not maintained during spontaneous precipitation from the solution. Under isotopic non-equilibrium conditions, at a constant temperature and precipitation rate, apparent 1000lnα_{calcite–water} decreases with increasing pH of the solution. If the temperature and pH are held constant, apparent 1000lnα_{calcite–water} values decrease with elevated precipitation rates of calcite. At pH = 8.3, oxygen isotopic fractionation between inorganically precipitated calcite and water as a function of the precipitation rate (R) can be described by the expressions

at 5, 25, and 40 °C, respectively.The impact of precipitation rate on 1000lnα_{calcite–water} value in our experiments clearly indicates a kinetic effect on oxygen isotopic fractionation during calcite precipitation from aqueous solution, even if calcite precipitated slowly from aqueous solution at the given temperature range. Our results support Coplen's work [Coplen T. B. (2007) Calibration of the calcite–water oxygen isotope geothermometer at Devils Hole, Nevada, a natural laboratory. Geochim. Cosmochim. Acta 71, 3948–3957], which indicates that the equilibrium oxygen isotopic fractionation factor might be greater than the commonly accepted value.     

角闪石族矿物的氧同位素分馏

利用增量方法和同位素交换技术,对角闪石族矿物的氧同位素分馏进行了理论计算和实验测定。理论结果表明,不同化学成分的角闪石之间存在一定的氧同位素分馏,其13O富集顺序为:钠闪石>蓝闪石>铁闪石>阳起石=镁铁门石≥直闪石≥透闪石>普通角闪石>铝直闪石>韭闪石。高温条件下(>500℃),角闪石相对于水亏损¹⁸O达1‰至3‰。实验进行在有少量流体存在的条件下,温度为520℃至680℃。所确定的方解石-透闪石氧同位素分馏系数与理论计算值在误差范围内完全一致。理论和实验确定的石英-透闪石分馏曲线均显着低于已知的经验校准曲线,反映了变质岩中含角闪石矿物集合体内部的退化同位素再平衡。     

Oxygen stable isotope fractionation behavior of cerussite and hydrocerussite: New results and reconciliation of the recent literature

Recent empirical and theoretical calculations of the temperature-dependant oxygen stable isotope fractionation behavior of cerussite have highlighted potential problems with earlier work on this topic. The synthetic cerussite which was used earlier by the lead author to determine fractionation factors was re-examined using energy dispersive X-ray analysis, and found to be internally contaminated with inclusions of the phase hydrocerussite at levels of 5-10% by volume. The volume of hydrocerussite present within the samples is not sufficient to explain the entire discrepancy between this work and the empirical and theoretical calculations made earlier by the second author of this paper. Regardless of the exact causes of experimental failure or kinetic effects, the hydrocerussite contamination and the difficulty of demonstrating that these experiments reached isotopic equilibrium suggest that the use of cerussite oxygen isotope fractionation factors determined by slow precipitation experiments be discontinued in favor of the empirically calibrated fractionation factor 1000 ln α_{cerussite-water} = 2.29(10⁶/T²) − 3.56. In addition, we have determined that the oxygen isotope fractionation factor between hydrocerussite and water at 20 °C is 1.0232.     

Temperature variation of elastic constants of quartz across the α - β transition

The α − β transition of quartz was successfully observed with using a single sample by means of the rectangular parallelepiped resonance (RPR) method. An oriented rectangular parallelepiped of α-quartz single crystal was prepared and the resonant frequencies of 30–11 vibrational modes were measured from room temperature to 700°C. The softening of quartz crystal was observed as the significant reduction of resonant frequencies near the α–β transition. The present study is the first application of the RPR method to the study of phase transition. The complete set of elastic constants of α- and β-quartz were determined as a function of temperature by the least-squares inversion of the measured frequency data obtained by a single run. This is a merit yielded by the RPR method. It is shown near the α − β transition in both α- and β-quartz that the elastic parameters decrease proportionally to |T−T ₀|⁻ⁿ , where T is temperature and T ₀ is the transition temperature, 573.0°C for α-quartz and 574.3°C for β-quartz. It was also seen that linear incompressibilities K ₁ = (C ₁₁ +C ₁₂ +C ₁₃)/3 and K ₃ = (C ₃₃ +2C ₁₃)/3 decrease rapidly toward the transition, whereas, shear moduli C ₄₄, C _S1 = (C ₁₁ +C ₃₃ -2C ₁₃)/4 and C _S3 = (C ₁₁ -C ₁₂)/2 = C ₆₆ decrease only slightly. The shear modulus C _S3 = C ₆₆ increased slightly in α-quartz. The elastic properties of isotropic aggregate of quartz were calculated, and it is shown that the longitudinal wave velocity significantly decreases at the α − β transition, whereas, the shear wave velocity decreases only slightly.     

Thermal equations of state of dioctahedral micas on the join muscovite–paragonite

 Powder diffraction measurements at simultaneous high pressure and temperature on samples of 2M1 polytype of muscovite (Ms) and paragonite (Pg) were performed at the beamline ID30 of ESRF (Grenoble), using the Paris-Edinburgh cell. The bulk moduli of Ms, calculated from the least-squares fitting of V–P data on each isotherm using a second-order Birch–Murnaghan EoS, were: 57.0(6), 55.1(7), 51.1(7) and 48.9(5) GPa on the isotherms at 298, 573, 723 and 873 K, respectively. The value of (∂K _T /∂T) was −0.0146(2) GPa K⁻¹. The thermal expansion coefficient α varied from 35.7(3) × 10⁻⁶ K⁻¹ at P ambient to 20.1(3) × 10⁻⁶ K⁻¹ at P = 4 GPa [(∂α/∂P) _T = −3.9(1) × 10⁻⁶ GPa⁻¹ K⁻¹]. The corresponding values for Pg on the isotherms at 298, 723 and 823 K were: bulk moduli 59.9(5), 55.7(6) and 53.8(7) GPa, (∂K _T /∂T) −0.0109(1) GPa K⁻¹. The thermal expansion coefficient α varied from 44.1(2) × 10⁻⁶ K⁻¹ at P ambient to 32.5(2) × 10⁻⁶ K⁻¹ at P = 4 GPa [(∂α/∂P) _T = −2.9(1) × 10⁻⁶ GPa⁻¹ K⁻¹]. Thermoelastic coefficients showed that Pg is stiffer than Ms; Ms softens more rapidly than Pg upon heating; thermal expansion is greater and its variation with pressure is smaller in Pg than in Ms. Received: 28 January 2002 / Accepted: 5 April 2002     

An Experimental Study of Oxygen Isotope Fractionation in the Quartz—Wolframite—Water System

Oxygen isotope fractionation was experimentally studied in the quartz-wolframite-water system from 200 to 420 °C. The starting wolframite was synthesized in aqueous solutions of Na₂WO₄ · 2H₂O + FeCl₂ · 4H₂O or MnCl₂ · 4H₂O. The starting solutions range in salinity from 0 to 10 equivalent wt.% NaCl. Experiments were conducted in a gold-lined stainless steel autoclave, with filling degrees of about 50%. The results showed no significant difference in equilibrium isotope fractionation between water and wolframite, ferberite and huebnerite at the same temperature (310 °C ). The equilibrium oxygen isotope fractionation factors of wolframite and water tend to be equal with increasing temperature above 370 °C, but to increase significantly with decreasing temperature below 370 °C: 1000 ln α_wf-H₂o= 1.03×10⁶T−2-4.91 (370 °C ±200 °C ) 1000 ln α_wf-H₂o = 0.21×10⁶T −2-2.91 (420 °C -370 °C ±) This projects was financially supported by the National Natural Science Foundation of China.     

Theoretical Analyses of the Infrared Spectrum of Baiyuneboite—（Ce）

Baiyuneboite-(Ce) is a new fluor-carbonate mineral.Based on the fine data on the structure of the mineral,the factor group and normal coordinate analyses for its infrared spectrum have been carried out.The factor group analyses indicate that the site group and factor group splittings of the internal vibration bands of CO3^2- ions do not occur and that the double bands of normal modes result from two non-equal sets of CO3^2- ions in the crystal structure,The normal coordinate analyses give the stretching force constants.bend force constants and calculated frequencies of CO3^2- ions.The calculations of potential energy distribution allow us to assign v3 and v4 to the stretching vibration and the bend vibration of CO3^2- ions.respectively.     

Experimental study of silicon isotope dynamic fractionation and its application in geology

Silicon shows no variation in its chemical valence in nature and exists mainly in the form of silicon-oxygen tetrahedra, so very small silicon isotope thermodynamic fractionation occurs and the resultant silicon isotope variation is limited. Dynamic fractionation of Si isotopes during precipitation of SiO₂ from a solution is a main factor leading to substantial variations in silicon isotopes in nature. In this experimental study, we determined the dynamic fractionation factorα for silicon isotopes during precipitation of SiO₂ from the solution. And in combination of α, a theoretical explanation is presented of the considerably low δ³⁰Si values of black smokers on modern seafloor, Archean banded magnetite-quartzite and clay minerals of weathering origin, and of clearly high δ³⁰Si values of siliceous rocks in shallow-sea carbonate platforms. This paper won the Paper of Excellence in the Second National Young Scientist Symposium on Geochemistry of Minerals and Rocks.