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1.
2.
We have performed first-principles molecular dynamics simulations of CaAl2Si2O8 (anorthite) liquid at pressures up to 120 GPa and temperatures of 3000, 4000 and 6000 K. At the lowest degrees of compression the liquid is seen to accommodate changes in density through decreasing the abundance of 3- and 4-membered rings, while increases in coordination of network forming cations take effect at somewhat higher degrees of compression. Results are fit to a fundamental thermodynamic relation with 4th order finite strain and 1st order thermal variable expansions. Upon compression by a factor of two, the Grüneisen parameter (γ) is found to increase continuously from 0.35 to 1.10. Weak temperature dependence in γ is thermodynamically consistent with a slight decrease in isochoric heat capacity (CV), for which values of between 4.4 and 5.2 NkB are obtained, depending on the temperature. Pressure and temperature dependence of self-diffusivities is found to be well represented by an Arrhenius relation, except at 3000 K and pressures lower than 5 GPa, where self-diffusivities of Si, Al, and O increase with pressure. Analysis of the lifetimes of individual coordination species reveals that this phenomenon arises due to the disproportionately high stability of 4-fold coordinated Si, and to a lesser extent 4-fold coordinated Al. Our results represent a marked improvement in accuracy and reliability in describing the physics of CaAl2Si2O8 liquid at deep mantle pressures, pointing the way to a general thermodynamic model of melts at extreme pressures and temperatures relevant to planetary-scale magma oceans and deep mantle partial melting.  相似文献   

3.
The short range distribution of interatomic distances in three feldspar glasses has been determined by X-ray radial distribution analysis. The resulting radial distribution functions (RDF's) are interpreted by comparison with RDF's calculated for various quasi-crystalline models of the glass structure.The experimental RDF's of the alkali feldspar glasses were found to be inconsistent with the four-membered rings of tetrahedra associated with crystalline feldspars; the structures of these glasses are probably based on interconnected six-membered rings of the type found in tridymite, nepheline, or kalsilite. In contrast, the RDF of calcic feldspar glass is consistent with a four-membered ring structure of the type found in crystalline anorthite. T-O bond lengths (T = Si,Al) increase from 1.60 Å in SiO2 glass [J. H. Konnert and J. Karle (1973) Acta Cryst.A29, 702–710] to 1.63 Å in the alkali feldspar glasses to 1.66 Å in the calcic feldspar glass due to the substitution of Al for Si in the tetrahedra] sites. The T-O-T bond angles inferred from the RDF peak positions are 151° in SiO2 glass (see reference above), 146° in the alkali feldspar glasses, and 143° in the calcic feldspar glass. Detail in the RDF at distances greater than 5 Å suggests that the alkali feldspar glasses have a higher degree of long range order than the calcic feldspar glasses.Assuming that the structural details of our feldspar glasses are similar to those of the melts, the observed structural differences between the alkali feldspar and calcic feldspar glasses helps explain the differences in crystallization kinetics of anhydrous feldspar composition melts. Structural interpretations of some thermodynamic and rheologic phenomena associated with feldspar melts are also presented based on these results.  相似文献   

4.
Five hundred eighty-five viscosity measurements on 40 melt compositions from the ternary system CaMgSi2O6 (Di)-CaAl2Si2O8 (An)-NaAlSi3O8 (Ab) have been compiled to create an experimental database spanning a wide range of temperatures (660-2175°C). The melts within this ternary system show near-Arrhenian to strongly non-Arrhenian properties, and in this regard are comparable to natural melts. The database is used to produce a chemical model for the compositional and temperature dependence of melt viscosity in the Di-An-Ab system. We use the Vogel-Fulcher-Tammann equation (VFT: log η = A + B/(T − C)) to account for the temperature dependence of melt viscosity. We also assume that all silicate melts converge to a common viscosity at high temperature. Thus, A is independent of composition, and all compositional dependence resides in the parameters B and C. The best estimate for A is −5.06, which implies a high-temperature limit to viscosity of 10-5.06 Pa s. The compositional dependence of B and C is expressed by 12 coefficients (bi=1,2.6, cj=1,2..6) representing linear (e.g., bi=1:3) and higher order, nonlinear (e.g., bi=4:6) contributions. Our results suggest a near-linear compositional dependence for B (<10% nonlinear) and C (<7% nonlinear). We use the model to predict model VFT functions and to demonstrate the systematic variations in viscosity due to changes in melt composition. Despite the near linear compositional dependence of B and C, the model reproduces the pronounced nonlinearities shown by the original data, including the crossing of VFT functions for different melt compositions. We also calculate values of Tg for melts across the Di-An-Ab ternary system and show that intermediate melt compositions have Tg values that are depressed by up to 100°C relative to the end-members Di-An-Ab. Our non-Arrhenian viscosity model accurately reproduces the original database, allows for continuous variations in rheological properties, and has a demonstrated capacity for extrapolation beyond the original data.  相似文献   

5.
Enthalpies of solution in 2PbO· B2O3 at 712°C have been measured for glasses in the systems albite anorthite diopside, NaAlO2-SiO2, Ca0.5AlO2-SiO2 and albite-anorthite-quartz. The systems albite-anorthite and diopside-anorthite show substantial negative enthalpies of mixing, albite-diopside shows significant positive heats of mixing. For compositions up to NaAlO2 = 0.42 (which includes the subsystem albite-silica) the system NaAlO2-SiO2 shows essentially zero heats of mixing. A negative ternary excess heat of mixing is found in the plagioclase-rich portion of the albite-anorthite-diopside system. The join Si4O8-CaAl2Si2O8 shows small but significant heats of mixing. In albite-anorthite-quartz. ternary glasses, the ternary excess enthalpy of mixing is positive.Based on available heat capacity data and appropriate consideration of the glass transition, the enthalpy of the crystal-glass transition (vitrification) is a serious underestimate of the enthalpy of the crystal-liquid transition (fusion) especially when the melting point, Tf, is many hundreds of degrees higher than the glass transition temperature, Tg. On the other hand, the same heat capacity data suggest that the enthalpies of mixing in albite-anorthite-diopside liquids are calculated to be quite similar to those in the glasses. The enthalpies of mixing observed in general support the structural models proposed by Taylor and Brown (1979a, b) and others for the structure of aluminosilicate glasses.  相似文献   

6.
Enthalpies of solution in 2PbO · B2O3 at 981 K have been measured for glasses in the system albite-orthoclase-silica and along the join Na1.6Al1.6Si2.4O8-K1.6Al1.6Si2.4O8. The join KAlSi3O8-Si4O8 shows zero heat of mixing similar to that found previously for NaAlSi3O8-Si4O8 glasses. Albite-orthoclase glasses show negative heats of mixing symmetric about Ab50Or50 (Wn = ? 2.4 ± 0.8 kcal). Negative heats of (Na, K) mixing are also found at Si(Si + Al) = 0.6. Ternary excess enthalpies of mixing in the glassy system Ab-Or-4Q are positive but rarely exceed 1 kcal mol?1.Using earlier studies of the thermodynamic properties of the crystals, the present calorimetric data and the “two-lattice” entropy model, the albite-orthoclase phase diagram is calculated in good agreement with experimental data. Attempts to calculate albite-silica and orthoclase-silica phase diagrams reveal complexities probably related to significant (but unknown) mutual solid solubility between cristobalite and alkali feldspar and to the very small heat and entropy of fusion of SiO2.  相似文献   

7.
Enthalpies of solution in 2PbO · B2O3 at 974 K have been measured for glasses along the joins Ca2Si2O6 (Wo)-Mg2Si2O6 (En) and Mg2Si2O6-MgAl2SiO6 (MgTs). Heats of mixing are symmetric and negative for Wo-En with WH = ?31.0 ± 3.6 kJ mol?. Negative heats of mixing were also found for the En-MgTs glasses (WH = ?33.4 ± 3.7 kJ mol?).Enthalpies of vitrification of pyroxenes and pyroxenoids generally increase with decreasing alumina content and with decreasing basicity of the divalent cation.Heats of mixing along several glassy joins show systematic trends. When only non-tetrahedral cations mix (outside the aluminosilicate framework), small exothermic heats of mixing are seen. When both nontetrahedral and framework cations mix (on separate sublattices, presumably), the enthalpies of mixing are substantially more negative. Maximum enthalpy stabilization near compositions with Al/Si ≈ 1 is suggested.  相似文献   

8.
Enthalpies of solution of synthetic clinopyroxenes on the join CaMgSi2O6-Mg2Si2O6 have been measured in a melt of composition Pb2B2O5 at 970 K. Most of the measurements were made on samples crystallized at 1600°–1700°C and 30 kbar pressure, which covered the range 0–78 mole per cent Mg2Si2O6, and whose X-ray patterns could be satisfactorily indexed on the diopside (C2/c) structure. For the reaction: Mg2Si2O6→-Mg2Si2O6 enstatite diopside the present data, in conjunction with previous and new measurements on Mg2Si2O6 enstatite, determine ΔH° ~ 2 kcal and WH (regular solution parameter) ~ 7 kcal. These values are in good agreement with those deduced by Saxena and Nehru (1975) from a study of high temperature, high pressure phase equilibrium data under the assumption that the excess entropy of mixing is small, but, in light of the recent theoretical treatment of Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), the meanings of these parameters may be ambiguous.Heat of solution measurements on Ca-rich binary diopsides made by annealing glasses at 1358°C in air gave slighter higher values than the higher temperature high pressure samples. This may be evidence for some (Ca, Mg) disorder of the sort postulated by Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), although no differences in heat of solution dependent on synthesis temperature in the range 1350°–1700°C could be found in stoichiometric CaMgSi2O6.  相似文献   

9.
The and (1984) excess free energy model (B&B) is extremely convenient to use in modelling multicomponent solutions. However, spinodal calculations reveal that their calibration of this model for CaO-Al2O3-SiO2 produces liquation tielines that do not appear to be in agreement with experimental work. In addition, their calibration contains some strongly negative excess entropy parameters and these permit a most unusual inverted liquation field to start at approximately >2115°C, wt% (SiO2, Al2O3, CaO) = (70, 16, 14). This inverted field expands rapidly to cover most of the ternary for T> 2300°C and continues to expand at all higher temperatures. The Berman and Brown calibration for this system carries these negative excess entropies of mixing because the solution model is very strongly asymmetric as a result of the use of normal oxide mole weights in modelling the configurational entropy of mixing. A suggestion is made for a fairly natural restriction on the relative sizes of empirical models for excess versus configurational entropy.

Expressions are presented for the general consolute condition (all solution models) and for the second and third partials of the B&B Gx model.  相似文献   


10.
The system CaMgSi2O6CaAl2SiO6CaFeAlSiO6 has been studied in air at 1 atm. The phase assemblage at subsolidus temperatures in the CaMgSi2O6-rich portion is Cpx + An + Mel and that in the CaMgSi2O6-poor portion Cpx + An + Mel + Sp. At subsolidus temperatures the sigle-phase field of clinopyroxene increases with an increase in the CaFeAlSiO6 component of the system. The Al2O3 content of clinopyroxene, however, continues to increase beyond the single-phase field and attains at least 16.04 wt.% Al2O3 with 3.9 wt.% Fe2O3. The stability field of fassaite in the system over a range of pressures and oxygen fugacities has been estimated from data in the literature as well as the present data. The CaFeAlSiO6 content of fassaite is dependent on oxygen fugacity, but is not influenced by pressure. The stability field is strongly influenced by oxygen fugacity at low and high pressure, and decreases with decreasing oxygen fugacity. Clinopyroxenes in both volcanic and metamorphic rocks from various localities, when plotted on the CaMgSi2O6CaAl2SiO6CaFeAlSiO6 triangle, show that there is no compositional gap between diopside and fassaitic pyroxene in metamorphic rocks, and that the fassaitic pyroxene in alkalic rocks becomes richer in both CaAl2SiO6 and CaFeAlSiO5 components as crystallization proceeds. These results agree with those obtained in the experimental study.  相似文献   

11.
12.
Glasses in the systems NaAlSi3O8-KAlSi3O8 and NaAlSi3O8-Si4O8 have been studied by means of hydrofluoric acid solution calorimetry at 50°C. Results indicate small negative enthalpies of mixing in the former system and small positive departures from ideality in the latter.  相似文献   

13.
A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al2O3-SiO2 at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO2 binary liquid immiscibility gap, solid-solid P-T reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties.  相似文献   

14.
Based on our previous development of the molecular interaction potential for pure H2O and CO2 [Zhang, Z.G., Duan, Z.H. 2005a. Isothermal-isobaric molecular dynamics simulations of the PVT properties of water over wide range of temperatures and pressures. Phys. Earth Planet Interiors149, 335-354; Zhang, Z.G., Duan, Z.H. 2005b. An optimized molecular potential for carbon dioxide. J. Chem. Phys.122, 214507] and the ab initio potential surface across CO2-H2O molecules constructed in this study, we carried out more than one thousand molecular dynamics simulations of the PVTx properties of the CO2-H2O mixtures in the temperature-pressure range from 673.15 to 2573.15 K up to 10.0 GPa. Comparison with extensive experimental PVTx data indicates that the simulated results generally agree with experimental data within 2% in density, equivalent to experimental uncertainty. Even the data under the highest experimental temperature-pressure conditions (up to 1673 K and 1.94 GPa) are well predicted with the agreement within 1.0% in density, indicating that the high accuracy of the simulation is well retained as the temperature and pressure increase. The consistent and stable predictability of the simulation from low to high temperature-pressure and the fact that the molecular dynamics simulation resort to no experimental data but to ab initio molecular potential makes us convinced that the simulation results should be reliable up to at least 2573 K and 10 GPa with errors less than 2% in density. In order to integrate all the simulation results of this study and previous studies [Zhang and Duan, 2005a, 2005b] and the experimental data for the calculation of volumetric properties (volume, density, and excess volume), heat properties, and chemical properties (fugacity, activity, and possibly supercritical phase separation), an equation of state (EOS) is laboriously developed for the CO2, H2O, and CO2-H2O systems. This EOS reproduces all the experimental and simulated data covering a wide temperature and pressure range from 673.15 to 2573.15 K and from 0 to 10.0 GPa within experimental or simulation uncertainty.  相似文献   

15.
We use first principles molecular dynamics simulations based on density functional theory in the local density approximation to investigate CaMgSi2O6 liquid over the entire mantle pressure regime. We find that the liquid structure becomes much more densely packed with increasing pressure, with the mean Si-O coordination number increasing nearly linearly with volume from fourfold near ambient pressure to sixfold at the base of the mantle. Fivefold Si-O coordination environments are most abundant at intermediate compression. The properties of Mg and Si coordination environments are nearly identical to those in MgSiO3 liquid, whereas Ca is more highly coordinated with larger mean Ca-O bond length as compared with Mg. The density increases smoothly with increasing pressure over the entire range studied. The Grüneisen parameter increases by a factor of three on twofold compression. The density contrast between diopside composition liquid and the isochemical crystalline assemblage is less than 2% at the core mantle boundary, less than that in the case of MgSiO3. Thermodynamic properties are described in terms of a liquid-state fundamental thermodynamic relation.  相似文献   

16.
17.
Armenite, ideal formula BaCa2Al6Si9O30·2H2O, and its dehydrated analog BaCa2Al6Si9O30 and epididymite, ideal formula Na2Be2Si6O15·H2O, and its dehydrated analog Na2Be2Si6O15 were studied by low-temperature relaxation calorimetry between 5 and 300 K to determine the heat capacity, Cp, behavior of their confined H2O. Differential thermal analysis and thermogravimetry measurements, FTIR spectroscopy, electron microprobe analysis and powder Rietveld refinements were undertaken to characterize the phases and the local environment around the H2O molecule.The determined structural formula for armenite is Ba0.88(0.01)Ca1.99(0.02)Na0.04(0.01)Al5.89(0.03)Si9.12(0.02)O30·2H2O and for epididymite Na1.88(0.03)K0.05(0.004)Na0.01(0.004)Be2.02(0.008)Si6.00(0.01)O15·H2O. The infrared (IR) spectra give information on the nature of the H2O molecules in the natural phases via their H2O stretching and bending vibrations, which in the case of epididymite only could be assigned. The powder X-ray diffraction data show that armenite and its dehydrated analog have similar structures, whereas in the case of epididymite there are structural differences between the natural and dehydrated phases. This is also reflected in the lattice IR mode behavior, as observed for the natural phases and the H2O-free phases. The standard entropy at 298 K for armenite is S° = 795.7 ± 6.2 J/mol K and its dehydrated analog is S° = 737.0 ± 6.2 J/mol K. For epididymite S° = 425.7 ± 4.1 J/mol K was obtained and its dehydrated analog has S° = 372.5 ± 5.0 J/mol K. The heat capacity and entropy of dehydration at 298 K are Δ = 3.4 J/mol K and ΔSrxn = 319.1 J/mol K and Δ = −14.3 J/mol K and ΔSrxn = 135.7 J/mol K for armenite and epididymite, respectively. The H2O molecules in both phases appear to be ordered. They are held in place via an ion-dipole interaction between the H2O molecule and a Ca cation in the case of armenite and a Na cation in epididymite and through hydrogen-bonding between the H2O molecule and oxygen atoms of the respective silicate frameworks. Of the three different H2O phases ice, liquid water and steam, the Cp behavior of confined H2O in both armenite and epididymite is most similar to that of ice, but there are differences between the two silicates and from the Cp behavior of ice. Hydrogen-bonding behavior and its relation to the entropy of confined H2O at 298 K is analyzed for various microporous silicates.The entropy of confined H2O at 298 K in various silicates increases approximately linearly with increasing average wavenumber of the OH-stretching vibrations. The interpretation is that decreased hydrogen-bonding strength between a H2O molecule and the silicate framework, as well as weak ion-dipole interactions, results in increased entropy of H2O. This results in increased amplitudes of external H2O vibrations, especially translations of the molecule, and they contribute strongly to the entropy of confined H2O at T < 298 K.  相似文献   

18.
Using the model of fictive ideal components, Gibbs free energies of formation of pyrope and Al2O3-enstatite have been determined from the experimental data on coexisting garnet and orthopyroxene and orthopyroxene and spinel in the temperature range of 1200–1600 K. The negative free energies in kJ/mol are:
  相似文献   

19.
The oxidation of Fe(II) with H2O2 at nanomolar levels in seawater have been studied using an UV-Vis spectrophotometric system equipped with a long liquid waveguide capillary flow cell. The effect of pH (6.5 to 8.2), H2O2 (7.2 × 10−8 M to 5.2 × 10−7 M), HCO3 (2.05 mM to 4.05 mM) and Fe(II) (5 nM to 500 nM) as a function of temperature (3 to 35 °C) on the oxidation of Fe(II) are presented. The oxidation rate is linearly related to the pH with a slope of 0.89 ± 0.01 independent of the concentration of HCO3. A kinetic model for the reaction has been developed to consider the interactions of Fe(II) with the major ions in seawater. The model has been used to examine the effect of pH, concentrations of Fe(II), H2O2 and HCO3 as a function of temperature. FeOH+ is the most important contributing species to the overall rate of oxidation from pH 6 to pH 8. At a pH higher than 8, the Fe(OH)2 and Fe(CO3)22− species contribute over 20% to the rates. Model results show that when the concentration of O2 is two orders of magnitude higher than the concentration of H2O2, the oxidation with O2 also needs to be considered. The rate constants for the five most kinetically active species (Fe2+, FeOH+, Fe(OH)2, FeCO3, Fe(CO3)22−) in seawater as a function of temperature have been determined. The kinetic model is also valid in pure water with different concentrations of HCO3 and the conditions found in fresh waters.  相似文献   

20.
TK12001300140015001600
Pyrope4869.924747.054614.264462.634311.00
Al2O3-enstatite1257.251244.281191.931158.671125.64
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