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1.
 The P–V–T equation of state (EoS) models of Birch–Murnaghan, Vinet and Poirier–Tarantola have been compared with one another and discussed in the light of their ability to reproduce thermoelastic functions and parameters by means of fitting to pressure–volume–temperature data artificially generated for spinel, corundum and forsterite. Numerical simulations relying upon semi-empirical potentials, lattice dynamics and the quasiharmonic approximation have been used to generate P–V–T data. The results obtained indicate that all the P–V–T EoSs tested predict bulk modulus at ambient conditions with errors confined, at worst, within a few percent, and reproduce correctly its dependence on temperature. The derivatives of the bulk modulus versus P and PT are less satisfactorily modelled. The bulk thermal expansion is determined by EoSs within a few percent error, but the deviations increase significantly if the approximation of linear dependence of EoS on temperature is used (linearised thermal pressure model). Received: 30 January 2001 / Accepted: 16 June 2001  相似文献   

2.
The pressure-dependent elastic properties of the Fe–S system are important to understand the dynamic properties of the Earth’s interior. We have therefore undertaken a first-principles study of the structural and elastic properties of FeS2 polymorphs under high pressure using a method based on plane-wave pseudopotential density function theory. The lattice constants, elastic constants, zero-pressure bulk modulus, and its pressure derivative of pyrite are in good agreement with the previous experiments and theoretical approaches; the lattice constants of marcasite are also consistent with the available experimental data. Calculations of the elastic constants of pyrite and marcasite have been determined from 0 to 200 GPa. Based on the relationship between the calculated elastic constants and the pressure, which can provide the stability of mineral, it would appear that pyrite is stable, whereas marcasite is unstable when the pressure rises above 130 GPa. Static lattice energy calculations predict the marcasite-to-pyrite phase transition to occur at 5.4 GPa at 0 K.  相似文献   

3.
We report in this paper results of lattice dynamical calculations of the thermodynamic properties, namely, the equation of state and the melting point of forsterite. The root mean square displacements of atoms and thermal parameters are also evaluated. It is observed from our results, that, a modified Lindemann criterion for melting may be proposed for an ionic ‘molecular’ solid like forsterite. Agreement among various theoretical and experimental results is satisfactory indicating that lattice dynamical studies based on microscopic quasiharmonic formulations help in understanding the macroscopic properties of forsterite, over a wide range of temperature and pressure.  相似文献   

4.
Numerical simulations, using empirical interatomic potentials within the framework of lattice dynamics and quasi-harmonic approximation, have been carried out to model the behaviour of the structure and of some thermoelastic properties of pyrope at high pressure and high temperature conditions (0–50 GPa, 300–1500 K). Comparison with observed data, available as a function either of P or of T, suggests that the pressure effects are satisfactorily modelled, whilst the effect of T on the simulations is underestimated. The cell edge, bond lengths and polyhedral volumes have been studied as a function of P along five isotherms, spaced by 300 K steps. These isotherms tend to converge at high pressure, which demonstrates that the pressure effects become dominant compared to those of thermal origin in affecting the structural properties far from ambient conditions. The cell parameter, bond distances, and other structural and thermoelastic quantities determined through simulations have been parametrised as a function of P and T by polynomial expansions. Bulk modulus and thermal expansion have been discussed in the light of the high-temperature-Birch-Murnaghan and of the Vinet P – V – T equations of state. The predictions of the bulk modulus versus P and T from the present calculations and from the Vinet-EOS agree up to 10 GPa, but they differ at higher pressure. Received: 23 October, 1998 / Revised, accepted: 23 April, 1999  相似文献   

5.
Magnesium-rich olivine (Mg0.9Fe0.1)2SiO4 is considered to be a major constituent of the Earth's upper mantle. Because of its major geophysical importance, the temperature and pressure dependence of its crystal structure, elastic and dielectric constants, long-wavelength phonon modes and specific heat have been measured using a variety of experimental techniques. Theoretical study of lattice dynamics provides a means of analyzing and understanding a host of such experimental data in a unified manner. A detailed study of the lattice dynamics of forsterite, Mg2SiO4, has been made using a crystal potential function consisting of Coulombic and short-range terms. Quasiharmonic lattice dynamical calculations based on a rigid molecular-ion model have provided theoretical estimates of elastic constants, long-wavelength modes, phonon dispersion relation for external modes along the three high symmetry directions in the Brillouin zone, total and partial density of states and inelastic neutron scattering cross-sections. The neutron cross-sections were used as guides for the coherent inelastic neutron scattering experiment on a large single crystal using a triple axis spectrometer in the constant Q mode. The observed and predicted phonon dispersion relation show excellent agreement. The inelastically scattered neutron spectra from a powder sample have been analyzed on the basis of a phonon density of states calculated from a rigid-ion model, which includes both external and internal modes. The experimental data from a powder sample show good agreement with the calculated spectra, which include a multiphonon contribution in the incoherent approximation. The computed phonon densities of states are used to calculate the specific heat as a function of temperature using both the rigid molecular-ion and rigid ion models. These results are in very good agreement with the calorimetric measurement of the specific heat. The interatomic potential developed here can be used with some confidence to study physical properties of forsterite as a function of pressure and temperature.  相似文献   

6.
High pressure and temperature reactions of a mixture of forsterite and hydrogen molecules have been carried out using a laser heated diamond anvil cell at 9.8–13.2 GPa and ~1,000 K. In situ X-ray diffraction measurements showed no sign of decomposition or phase transitions of the forsterite under these experimental conditions, indicating that the olivine structure was maintained throughout all runs. However, a substantial expansion of the unit cell volume of the forsterite was observed for samples down to ~3 GPa upon quenching to ambient pressure at room temperature. The Raman spectroscopy measurements under pressure showed significant shifts of the Raman peaks of the Si–O vibration modes for forsterite and of the intramolecular vibration mode for H2 molecules toward a lower frequency after heating. Additionally, no OH vibration modes were observed by Raman and FT-IR spectroscopic measurements. These lines of evidence show that the observed volume expansion in forsterite is not explained by the incorporation of hydrogen atoms as hydroxyl, but suggest the presence of hydrogen as molecules in the forsterite structure under these high pressure and temperature conditions.  相似文献   

7.
 A thermoelastic model for calculating the high-pressure and high-temperature properties of isotropic solids is presented by extending the formalism by Thomsen and combining the resulting one with the Vinet model for static lattice and the Debye model for lattice vibration. Applying it to polycrystalline corundum, we have shown that the calculated values of entropy and heat capacity at constant pressure are in agreement with literature values to 2325 K at zero pressure and that the calculated values of thermal expansivity agree reasonably with experimental data to 1100 K at zero pressure. The model reproduces experimental data of sound velocities v p and v s of compressional and shear waves to 1825 K at zero pressure and those to 62 GPa at room temperature, and it reproduces also experimental shock-wave equation of state to 150 GPa. The velocity correlation (∂ln v s /∂ln v p ) S was found to have weak pressure and temperature dependences and the results under lower mantle conditions are compared with those of magnesian and calcium silicate perovskites and magnesiowüstite, and the PREM values of the Earth's lower mantle. Received: 12 February 2000 / Accepted: 15 July 2000  相似文献   

8.
Geological sequestration is one of the most effective ways to reduce greenhouse gases, such as carbon dioxide (CO2). The deep oceanic crust dominated by ultrabasic rock could store CO2 permanently. However, the storage mechanism has not been thoroughly understood because of the limited amount of research and experiments conducted. This study explored the reactive mechanisms of water–rock–gas in an ultrabasic system under different conditions. Forsterite, the most dominant mineral found in ultrabasic reservoirs, was used to conduct laboratory physical simulation experiments. Two experimental systems were designed including an scCO2–forsterite–water system and an N2–forsterite–water system. All experiments were performed for 1000 h at an experimental temperature of 150°C and a pressure of 150 bar, respectively, to mimic the geological conditions. The liquid products from the experiments were analysed by inductively coupled plasma-optical emission spectrometry, whereas the solid samples were analysed by scanning electron microscopy with energy disperse spectroscopy. Results showed that: (1) in the early stage during scCO2/N2–forsterite–water interaction, forsterite was dissolved with a reactive transitional zone forming on the surface, which caused H+ to enter into the silicate framework and accelerated the reaction; (2) in the N2 system, the dissolution of forsterite was inhibited by the Mg2+ concentration after reaching its saturation in the late stage; and (3) in the scCO2 system, magnesite was precipitated as a secondary mineral during the late stage, which promoted the dissolution of forsterite. As a result, the degree of dissolution of forsterite in the scCO2 system was far higher than in the N2 system. The experimental results are consistent with the numerical simulation using TOUGHREACT, a geochemical simulation procedure, which showed that CO2 promotes the dissolution of forsterite greatly at high temperature and pressure.  相似文献   

9.
High-temperature infrared properties of forsterite   总被引：1，自引：0，他引：1  
Polarized emittance measurements were acquired for synthetic forsterite, the pure magnesium end member of the olivines group, on the whole infrared spectral range and up to the melting point by using CO2 laser heating. The experimental data, fitted with a semi-quantum dielectric function model, allowed the retrieval of the temperature dependence of the absorption coefficient of forsterite both in the opaque and semi-transparent regions. The analysis of the phonon parameters indicates that the lattice dynamics evolve drastically with increasing temperature. The normal modes involving motions of the magnesium cations located in site 1 are the more impacted, and some of them vanish around 1,200 K. The results confirm that the enhancement of the lattice anharmonicity and the increasing mobility of the magnesium cations are closely linked and are at the origin of the anomalies observed in the evolution of the thermophysical properties. This complete set of spectroscopic data may be a step toward a more precise evaluation of the impact of thermal radiation heat transfer inside systems involving forsterite and quantification of their heat budget.  相似文献   

10.
We calculated the forsterite Mg K-edge and the fayalite Fe K-edge X-ray absorption spectra both for the M 1 and M 2 sites and for the overall edge by using the one-electron multiple-scattering theory. The validity of the theoretical model is well illustrated by comparison of calculations with experimental data at the Mg K-edge of MgO (periclase) and at the Mg and Fe K-edges spectra of forsterite and fayalite. Starting from these results at room conditions, we calculated the Mg and Fe K-edges X-ray absorption spectra of forsterite and fayalite at low and high temperatures and at high pressures as well. Variations of fine structures occur mostly in the intermediate multiple scattering (IMS) regions and as a result of the applied pressure. In order to demonstrate the capability of XAS to lead to deeper knowledge of structure relevant to Earth's upper mantle we also attempted calcuating the high-P edge for Fe 2+ in low-spin using a different occupation of valence electrons. If a change in spin state really occurs in fayalite, our simple model shows that XAS would evidence it easily even with low resolution.  相似文献   

11.
In the system CaO-MgO-Al2O3-SiO2, the tetrahedron CaMgSi2O6(di)-Mg2SiO4(fo)-SiO2-CaAl2 SiO6(CaTs) forms a simplified basalt tetrahedron, and within this tetrahedron, the plane di-fo-CaAl2Si2O8(an) separates simplified tholeiitic from alkalic basalts. Liquidus phase relations on this join have been studied at 1 atm and at 7, 10, 15, and 20 kbar. The temperature maximum on the 1 atm isobaric quaternary univariant line along which forsterite, diopside, anorthite, and liquid are in equilibrium lies to the SiO2-rich side of the join di-fo-an. The isobaric quaternary invariant point at which forsterite, diopside, anorthite, spinel, and liquid are in equilibrium passes, with increasing pressure, from the silica-poor to the silica-rich side of the join di-fo-an, which causes the piercing points on this join to change from forsterite+diopside+anorthite+liquid and forsterite +spinel+anorthite+liquid below 5 kbar to forsterite +diopside+spinel+liquid and diopside +spinel+anorthite+liquid above 5 kbar. As pressure increases, the forsterite and anorthite fields contract and the diopside and corundum fields expand. The anorthite primary phase field disappears entirely from the join di-fo-an between 15 and 20 kbar. Below about 4 kbar, the join di-fo-an represents, in simplified form, a thermal divide between alkalic and tholeiitic basalts. From about 4 to at least 12 kbar, alkalic basalts can produce tholeiitic basalts by fractional crystallization, and at pressures above about 12 kbar, it is possible for alkalic basalt to be produced from oceanite by crystallization of both olivine and orthopyroxene. If alkalic basalts are primary melts from a lherzolite mantle, they must be produced at high pressures, probably greater than about 12 kbar.Department of Geosciences, University of Texas at Dallas Contribution No. 327. Hawaii Institute of Geophysics Contribution No. 814.  相似文献   

12.
We perform first principles molecular dynamics simulations of Mg2SiO4 liquid and crystalline forsterite. On compression by a factor of two, we find that the Grüneisen parameter of the liquid increases linearly from 0.6 to 1.2. Comparison of liquid and forsterite equations of state reveals a temperature-dependent density crossover at pressures of ∼12-17 GPa. Along the melting curve, which we calculate by integration of the Clapeyron equation, the density crossover occurs within the forsterite stability field at P = 13 GPa and T = 2550 K. The melting curve obtained from the root mean-square atomic displacement in forsterite using the Lindemann law fails to match experimental or calculated melting curves. We attribute this failure to the liquid structure that differs significantly from that of forsterite, and which changes markedly upon compression, with increases in the degree of polymerization and coordination. The mean Si coordination increases from 4 in the uncompressed system to 6 upon twofold compression. The self-diffusion coefficients increase with temperature and decrease monotonically with pressure, and are well described by the Arrhenian relation. We compare our equation of state to the available highpressure shock wave data for forsterite and wadsleyite. Our theoretical liquid Hugoniot is consistent with partial melting along the forsterite Hugoniot at pressures 150-170 GPa, and complete melting at 170 GPa. The wadsleyite Hugoniot is likely sub-liquidus at the highest experimental pressure to date (200 GPa).  相似文献   

13.
Water incorporation in forsterite samples synthesized under low to medium silica-activity conditions mostly occurs via a substitutional mechanism in which a Si vacancy is compensated by four protons. Corresponding IR absorption spectra display a cluster of narrow and weakly anharmonic OH-stretching bands at wavenumbers above 3,500 cm?1. However, this diagnostic spectrum is often superimposed to one broader absorption band, rarely two, displaying pronounced temperature-dependent properties and tentatively assigned to H atoms in interstitial position (Ingrin et al. in Phys Chem Miner 40:499–510, 2013). Here, we investigate the structural and vibrational properties of selected interstitial H-bearing defects in forsterite using a first-principles modeling approach. We show that the broad bands discussed by Ingrin et al. (Phys Chem Miner 40:499–510, 2013) are most likely related to interstitial OH groups in the vacant octahedral sites alternating with the M2 sites along the c axis of the forsterite structure. The corresponding OH defects lead to the formation of fivefold coordinated Si species. Their peculiar thermal properties stem from the vibrational phase relaxation due to the anharmonic coupling of the high-energy local OH-stretching mode with a low-energy vibrational mode. This “exchange mode” corresponds to the hindered longitudinal translation of the OH group. These results suggest that at high pressure, hydrogen incorporation in forsterite is dominated by coexisting interstitial OH groups and (4H)Si defects.  相似文献   

14.
The nine adiabatic elastic stiffness constants of synthetic single-crystal fayalite, Fe2SiO4, were measured as functions of pressure (range, 0 to 1.0 GPa) and temperature (range, 0 to 40° C) using the pulse superposition ultrasonic method. Summary calculated results for a dense fayalite polycrystalline aggregate, based on the HS average of our single-crystal data, are as follows: Vp = 6.67 km/s; Vs = 3.39km/s; K= 127.9 GPa; μ = 50.3 GPa; (?K/?P)T = 5.2; (?μ/?P)T=1.5;(?K/?T)P= ?0.030 GPa/K;and,(?/?T)P =-0.013 GPa/K (the pressure and temperature data are referred to 25° C and 1 atm, respectively). Accuracy of the single-crystal results was maintained by numerous cross and redundancy checks. Compared to the single-crystal elastic properties of forsterite, Mg2SiO4, the fayalite stiffness constants, as well as their pressure derivatives, are lower for each of the on-diagonal (C ij for which i=j) values, and generally higher for the off-diagonal (C ij for which i≠j) data. As a result, the bulk moduli (K) and dK/dP for forsterite and fayalite are very similar, but the rigidity modulus (μ) and dμ/dP for polycrystalline fayalite are much lower than their forsterite counterparts. The bulk compression properties derived from this study are very consistent with the static-compression x-ray results of Yagi et al. (1975). The temperature dependence of the bulk modulus of fayalite is somewhat greater (in a negative sense) than that of forsterite. The rigidity dependencies are almost equivalent. Over the temperature range relevant to this study, the elastic property results are generally consistent with the data of Sumino (1978), which were obtained using the RPR technique. However, some of the compressional modes are clearly discrepant. The elastic constants of fayalite appear to be less consistent with a theoretical HCP model (Leibfried 1955) than forsterite, reflecting the more covalent character of the Fe-O bonding in the former.  相似文献   

15.
The pressure dependence of the Raman spectrum of forsterite was measured over its entire frequency range to over 200 kbar. The shifts of the Raman modes were used to calculate the pressure dependence of the heat capacity, C v, and entropy, S, by using statistical thermodynamics of the lattice vibrations. Using the pressure dependence of C v and other previously measured thermodynamic parameters, the thermal expansion coefficient, α, at room temperature was calculated from α = K S (?T/?P) S C V/TVK T, which yields a constant value of (? ln α/? ln V)T= 6.1(5) for forsterite to 10% compression. This value is in agreement with (? ln α/? ln V)T for a large variety of materials. At 91 kbar, the compression mechanism of the forsterite lattice abruptly changes causing a strong decrease of the pressure derivative of 6 Raman modes accompanied by large reductions in the intensities of all of the modes. This observation is in agreement with single crystal x-ray diffraction studies to 150 kbar and is interpreted as a second order phase transition.  相似文献   

16.
The high-pressure and temperature equation of state of majorite solid solution, Mj0.8Py0.2, was determined up to 23 GPa and 773 K with energy-dispersive synchrotron X-ray diffraction at high pressure and high temperature using the single- and double-stage configurations of the multianvil apparatuses, MAX80 and 90. The X-ray diffraction data of the majorite sample were analyzed using the WPPD (whole-powder-pattern decomposition) method to obtain the lattice parameters. A least-squares fitting using the third-order Birch-Murnaghan equation of state yields the isothermal bulk modulus, K T0  = 156 GPa, its pressure derivative, K′ = 4.4(±0.3), and temperature derivative (∂K T /∂T) P = −1.9(±0.3)× 10−2 GPa/K, assuming that the thermal expansion coefficient is similar to that of pyrope-almandine solid solution. Received: 5 October 1998 / Revised, accepted: 24 June 1999  相似文献   

17.
The temperature-X CO 2-equilibrium data for the reaction 1 tremolite + 11 dolomite 8 forsterite + 13 calcite + 9 CO2 +1H2O have been determined at total pressures (P CO 2 + P H2O) of 3,000 and 5,000 bars. The results are shown in Figure 2 along with the data for the total pressure of 1,000 bars (Metz, 1967).The MgCO3 contents of the magnesian-calcites formed during the experiments agree very well with the calcite-dolomite-solvus which can be recalculated from Equation (1) and the activity coefficients for MgCO3 in magnesiancalcite as given by Gordon and Greenwood (1970).If the T-X CO 2-equilibrium data are calculated from the equilibrium constant as given by Skippen (1974), assuming ideal mixing of CO2 and H2O, good agreement is achieved for the total pressure of 1,000 bars (see Figs. 4 and 5). At a total pressure of 3,000 bars, however, the calculated equilibrium temperatures are about 40 ° C below the experimentally determined values (see Fig. 6). This difference increases up to 70 ° C for a total pressure of 5,000 bars (see Fig. 7).From the experimentally determined equilibrium conditions of the assemblage: tremolite + dolomite + forsterite + magnesian calcite (see Fig. 8) the pressure of metamorphism can be estimated if the temperature is determined by the MgCO3-content of the magnesian-calcite from the calcite-dolomite solvus. However, when using the data of Figure 8, attention has to be drawn to the limiting condition of X CO 20.2.Simplified reaction equation not considering solid solution in the carbonates  相似文献   

18.
A structural, petrological and geochronological (U‐Th‐Pb of zircon and monazite) study reveals that the lower crust sequences of the Variscan high‐grade basement cropping out between Solenzara and Porto Vecchio, south‐east Corsica (France) have been tectonically juxtaposed along with middle crustal rocks during the extrusion of the orogenic root of the Variscan chain. We propose that a system of high‐temperature, orogen‐parallel shear zones that developed under a transpressive dextral tectonic regime caused the exhumation of the entire sequence. This tectonic complex is thus made up of rocks having undergone different P–T conditions (eclogite‐?, high‐pressure granulite facies and amphibolite facies) at different times, reflecting the progressive foreland migration of the orogenic front. The Solenzara granulites were derived from burial of continental crust to high‐pressure (1.8–1.4 GPa) and high‐ to ultrahigh‐temperature conditions (900–1000 °C) during the Variscan convergence: U–Pb ELA‐ICPMS zircon dating constrained the timing of this metamorphism at c. 360 Ma. The gneisses cropping out at Porto Vecchio are middle crustal‐level rocks that reached their peak temperature conditions (700–750 °C at <1.0 GPa) at c. 340 Ma. The diachronism of the metamorphic events, the foliation patterns and their geometry suggest that the granulites were exhumed to middle crustal levels through channel flow tectonics under continuous compression. The amphibolite facies gneisses of Porto Vecchio and the granulites of Solenzara were accreted through the development of a major dextral mylonitic zone forming under amphibolite facies conditions: in situ monazite isotope dating (ELA‐ICPMS) revealed that this deformation occurred at c. 320 Ma and was accompanied by the emplacement of syntectonic high‐K melts. A final HTLP static overprint, constrained at 312–308 Ma by monazite U‐Th‐Pb isotope dating, is related to the emplacement of the igneous products of the Sardinia‐Corsica batholith and marks the transition from the Variscan orogenic event to the Permian extension.  相似文献   

19.
The pressure dependence of the Raman spectrum of forsterite was measured over its entire frequency range to over 200 kbar. The shifts of the Raman modes were used to calculate the pressure dependence of the heat capacity, C v, and entropy, S, by using statistical thermodynamics of the lattice vibrations. Using the pressure dependence of C v and other previously measured thermodynamic parameters, the thermal expansion coefficient, , at room temperature was calculated from = K S (T/P) S C V/TVK T, which yields a constant value of ( ln / ln V)T= 6.1(5) for forsterite to 10% compression. This value is in agreement with ( ln / ln V)T for a large variety of materials.At 91 kbar, the compression mechanism of the forsterite lattice abruptly changes causing a strong decrease of the pressure derivative of 6 Raman modes accompanied by large reductions in the intensities of all of the modes. This observation is in agreement with single crystal x-ray diffraction studies to 150 kbar and is interpreted as a second order phase transition.  相似文献   

20.
Experiments on water solubility in forsterite in the systems Mg2SiO4–K2Mg(CO3)2–H2O and Mg2SiO4–H2O–C were conducted at 7.5–14.0 GPa and 1200–1600 °C. The resulting crystals contain 448 to 1480 ppm water, which is 40–70% less than in the forsterite–water system under the same conditions. This can be attributed to lower water activity in the carbonate-bearing melt. The water content of forsterite was found to vary systematically with temperature and pressure. For instance, at 14 GPa in the system forsterite–carbonate–H2O the H2O content of forsterite drops from 1140 ppm at 1200 °C to 450 ppm at 1600 °C, and at 8 GPa it remains constant or increases from 550 to 870 ppm at 1300–1600 °C. Preliminary data for D-H-bearing forsterite are reported. Considerable differences were found between IR spectra of D-H- and H-bearing forsterite. The results suggest that CO2 can significantly affect the width of the olivine-wadsleyite transition, i.e., the 410-km seismic discontinuity, which is a function of the water content of olivine and wadsleyite.  相似文献   

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