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1.
 The second-order elastic constants of CaF2 (fluorite) have been determined by Brillouin scattering to 9.3 GPa at 300 K. Acoustic velocities have been measured in the (111) plane and inverted to simultaneously obtain the elastic constants and the orientation of the crystal. A notable feature of the present inversion is that only the density at ambient condition was used in the inversion. We obtain high-pressure densities directly from Brillouin data by conversion to isothermal conditions and iterative integration of the compression curve. The pressure derivative of the isentropic bulk modulus and of the shear modulus determined in this study are 4.78 ± 0.13 and 1.08 ± 0.07, which differ from previous low-pressure ultrasonic elasticity measurements. The pressure derivative of the isothermal bulk modulus is 4.83 ± 0.13, 8% lower than the value from static compression, and its uncertainty is lower by a factor of 3. The elastic constants of fluorite increase almost linearly with pressure over the whole investigated pressure range. However, at P ≥ 9 GPa, C 11 and C 12 show a subtle structure in their pressure dependence while C 44 does not. The behavior of the elastic constants of fluorite in the 9–9.3 GPa pressure range is probably affected by the onset of a high-pressure structural transition to a lower symmetry phase (α-PbCl2 type). A single-crystal Raman scattering experiment performed in parallel to the Brillouin measurements shows the appearance of new features at 8.7 GPa. The new features are continuously observed to 49.2 GPa, confirming that the orthorhombic high-pressure phase is stable along the whole investigated pressure range, in agreement with a previous X-ray diffraction study of CaF2 to 45 GPa. The high-pressure elasticity data in combination with room-pressure values from previous studies allowed us to determine an independent room-temperature compression curve of fluorite. The new compression curve yields a maximum discrepancy of 0.05 GPa at 9.5 GPa with respect to that derived from static compression by Angel (1993). This comparison suggests that the accuracy of the fluorite pressure scale is better than 1% over the 0–9 GPa pressure range. Received: 10 July 2001 / Accepted: 7 March 2002  相似文献   

2.
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   

3.
In order to examine pressure–volume–temperature (P–V–T) relations for CaSiO3 perovskite (Ca-perovskite), high-temperature compression experiments with in situ X-ray diffraction were performed in a laser-heated diamond anvil cell (DAC) to 127 GPa and 2,300 K. We also employed an external heating system in the DAC in order to obtain P–V data at a moderate temperature of 700 K up to 113 GPa, which is the reference temperature for constructing an equation of state. The P–V data at 700 K were fitted to the second-order Birch–Murnaghan equation of state, yielding K 700,1bar = 207 ± 4 GPa and V 700,1bar = 46.5 ± 0.1 Å3. Thermal pressure terms were evaluated in the framework of the Mie–Grüneisen–Debye model, yielding γ 700,1bar = 2.7 ± 0.3, q 700,1bar = 1.2 ± 0.8, and θ 700,1bar = 1,300 ± 500 K. A thermodynamic thermal pressure model was also employed, yielding α700,1bar = 5.7 ± 0.5 × 10?5/K and (?K/?T) V  = ?0.010 ± 0.004 GPa/K. Computed densities along a lower mantle geotherm demonstrate that Ca-perovskite is denser than the surrounding lower mantle, suggesting that Ca-perovskite-rich rocks do not rise up through the lower mantle. One of such rocks might be a residue of partial melting of subducted mid-oceanic ridge basalt (MORB) at the base of the mantle. Since the partial melt is FeO-rich and therefore denser than the mantle, all the components of subducted MORB may not return to shallow levels.  相似文献   

4.
We used an in situ measurement method to investigate the phase transition of Fe2SiO4 polymorphs under high pressures and temperatures. A multi-anvil high-pressure apparatus combined with synchrotron X-ray radiation was used. The stability of each polymorph was identified by observing the X-ray diffraction data from the sample. In most experiments, the diffraction patterns were collected 10–30 min after reaching the desired pressure and temperature conditions. The transition boundary between the olivine and spinel phase at T = 1,000–1,500 K and P = 2–8 GPa was determined to occur at P (GPa) = 0.5 + 0.0034 × T (K). The transition pressure determined in this study was in general agreement with that observed in previous high-pressure experiments. However, the slope of the transition, dP/dT, determined in our study was significantly higher than that estimated by the previous study combined with the in situ X-ray method.  相似文献   

5.
The density of liquid Fe–S was measured at 4 GPa and 1,923 K using a sink/float method with a composite density marker. The density marker consisted of a Pt rod core and an Al2O3 tube surrounding. The uncertainty in the density of the composite marker is much smaller than that of the composite sphere, which had been used in previous density measurements. The density of liquid Fe–S decreases nonlinearly with increasing sulfur content at 4 GPa and 1,923 K. This tendency is consistent with the results measured at ambient pressure. The molar volume of FeS calculated from the measured density gradually increases with sulfur content. The excess molar volume from ideal mixing of Fe and S at 4 GPa was negative value. The new method proposed here is applicable to the density measurement of other Fe alloys at high pressure. The tendency of the molar volume and the excess molar volume with sulfur content at ambient pressure is consistent with these at high pressure at least up to 4 GPa. The excess molar volume at high pressure is essential for estimating the amount of light elements in the outer core.  相似文献   

6.
In situ X-ray viscometry of the silicate melts was carried out at high pressure and at high temperature. The viscosity of the silicate melts in the diopside(Di)–jadeite(Jd) system was determined in the pressure range from 1.88 GPa to 7.9 GPa and in the temperature range from 2,003 K to 2,173 K. The viscosity of the Di 25%–Jd 75% melt decreases continuously to 5.0 GPa, whereas the viscosity of the Di 50%–Jd 50% melt increases over 3.5 GPa. The viscosity of the Di50%–Jd 50% melt reaches a minimum around 3.5 GPa. Since the amounts of silicon in the two melts are the same, the difference in the pressure dependence of the viscosity may be controlled by another network-forming element, i.e., aluminum. The difference in the pressure dependence of the viscosities in the melts with two intermediate compositions in the Di–Jd system is estimated to be due to the difference in the melt structures at high pressures and high temperatures.  相似文献   

7.
Polycrystalline Fe3C (cementite) was compressed in a neon pressure medium to 30.5 GPa at 300 K using diamond-anvil cell techniques. Angular dispersive X-ray diffraction of Fe3C was measured using monochromatic synchrotron radiation and imaging plates. No phase transition was observed up to the highest pressure studied. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state. With V 0 constrained to a measured value of 155.28 Å3, the best fit yielded a 300-K isothermal bulk modulus K 0 = 174 ± 6 GPa, and its pressure derivative at constant temperature K 0 ′ =(K 0 /P) T = 4.8±0.8.  相似文献   

8.
We investigate two key transport properties, self-diffusion and viscosity, of Mg2SiO4 liquid as a function of temperature and pressure using density functional theory-based molecular dynamics method. Liquid dynamics in a 224-atom supercell was captured in equilibrium simulations of relatively long durations (50-300 ps) to obtain an acceptable convergence. Our results show that Mg and Si are, respectively, the most and least mobile species at most conditions studied and all diffusivities become similar at high pressure. With increasing temperature from 2200 to 6000 K at ambient pressure, the self-diffusivities increase by factors of 25 (Mg), 80 (Si) and 65 (O), and the viscosity decreases by a factor of 30. The predicted temperature variations of all transport coefficients closely follow the Arrhenian law. However, their pressure variations show a significant non-Arrhenian behavior and also are sensitive to temperature. At 3000 K, the diffusivity (viscosity) decreases (increases) by more than one order of magnitude between 0 and 50 GPa with their activation volumes increasing on compression. Over the entire mantle pressure range, the variations at 4000 K are of two orders of magnitude with nearly constant activation volumes whereas the variations at 6000 K are within one order of magnitude with decreasing activation volumes. The predicted complex dynamical behavior of Mg2SiO4 liquid can be associated with the structural changes occurring on compression. We also estimate the diffusivity and viscosity profiles along a magma ocean isentrope, which suggest that the melt transport properties vary modestly over the relevant magma ocean depth ranges.  相似文献   

9.
The electrical conductivities of alkali feldspar solid solutions ranging in chemical composition from albite (NaAlSi3O8) to K-feldspar (KAlSi3O8) were measured at 1.0 GPa and temperatures of 873–1,173 K in a multi-anvil apparatus. The complex impedance was determined by the AC impedance spectroscopy technique in the frequency range of 0.1–106 Hz. Our experimental results revealed that the electrical conductivities of alkali feldspar solid solutions increase with increasing temperature, and the linear relationship between electrical conductivity and temperature fits the Arrhenius formula. The electrical conductivities of solid solutions increase with the increasing Na content at constant temperature. At 1.0 GPa, the activation enthalpy of solid solution series shows strong dependency on the composition, and there is an abrupt increase from the composition of Or40Ab60 to Or60Ab40, where it reaches a value of 0.96 eV. According to these results in this study, it is proposed that the dominant conduction mechanism in alkali feldspar solid solutions under high temperature and high pressure is ionic conduction. Furthermore, since the activation enthalpy is less than 1.0 eV for the alkali feldspar solid solutions, it is suggested to be a model where Na+ and K+ transport involves an interstitial mechanism for electrical conduction. The change of main charge carriers can be responsible for the abrupt increase in the activation energy for Or60Ab40. All electrical conductivity data were fitted by a general formula in order to show the dependence of activation enthalpy and pre-exponential factor on chemical composition. Combining our experimental results with the effective medium theory, we theoretically calculated the electrical conductivity of alkali feldspar granite, alkali feldspar quartz syenite, and alkali feldspar syenite with different mineral content and variable chemical composition of alkali feldspar at high temperatures at 1.0 GPa, and the calculated results are almost in agreement with previous experimental studies on silicate rocks.  相似文献   

10.
Calcium sulfate (CaSO4), one of the major sulfate minerals in the Earth’s crust, is expected to play a major role in sulfur recycling into the deep mantle. Here, we investigated the crystal structure and phase relation of CaSO4 up to ~90 GPa and 2300 K through a series of high-pressure experiments combined with in situ X-ray diffraction. CaSO4 forms three thermodynamically stable polymorphs: anhydrite (stable below 3 GPa), monazite-type phase (stable between 3 and ~13 GPa) and barite-type phase (stable up to at least 93 GPa). Anhydrite to monazite-type phase transition is induced by pressure even at room temperature, while monazite- to barite-type transition requires heating at least to 1500 K at ~20 GPa. The barite-type phase cannot always be quenched from high temperature and is distorted to metastable AgMnO4-type structure or another modified barite structure depending on pressure. We obtained the pressure–volume data and density of anhydrite, monazite- and barite-type phases and found that their densities are lower than those calculated from the PREM model in the studied P–T conditions. This suggests that CaSO4 is gravitationally unstable in the mantle and fluid/melt phase into which sulfur dissolves and/or sulfate–sulfide speciation may play a major role in the sulfur recycling into the deep Earth.  相似文献   

11.
The effects of pressure on the dehydration of gypsum materials were investigated up to 633 K and 25 GPa by using Raman spectroscopy and synchrotron X-ray diffraction with an externally heated diamond anvil cell. At 2.5 GPa, gypsum starts to dehydrate around 428 K, by forming bassanite, CaSO4 hemihydrate, which completely dehydrates to γ-anhydrite at 488 K. All the sulphate modes decrease linearly between 293 and 427 K with temperature coefficients ranging from −0.119 to −0.021 cm−1 K−1, where an abrupt change in the ν3 mode and in the OH-stretching region indicates the beginning of dehydration. Increasing the temperature to 488 K, the OH-stretching modes completely disappear, marking the complete dehydration and formation of γ-anhydrite. Moreover, the sample changes from transparent to opaque to transparent again during the dehydration sequence gypsum-bassanite-γ-anhydrite, which irreversibly transforms to β-anhydrite form at 593 K. These data compared with the dehydration temperature at room pressure indicate that the dehydration temperature increases with pressure with a ΔP/ΔT slope equal to 230 bar/K. Synchrotron X-ray diffraction experiments show similar values of temperature and pressure for the first appearance of bassanite. Evidence of phase transition from β-anhydrite structure to the monazite type was observed at about 2 GPa under cold compression. On the other hand at the same pressure (2 GPa and 633 K), β-anhydrite was found, indicating a positive Clausis-Clayperon slope of the transition. This transformation is completely reversible as showed by the Raman spectra on the sample recovered after phase transition.  相似文献   

12.
The hydroxyl stretching frequencies of four phyllosilicates have been measured at high pressures and temperatures using an externally heated diamond-anvil cell and synchrotron infrared spectroscopy. Spectra were measured up to 26, 31, 21 and 8 GPa at room temperature for samples of talc, pyrophyllite, muscovite and 10-Å phase, respectively. Spectra were also measured in the range 273–500 K at ambient pressure for all samples and at 8–9 GPa for talc and pyrophyllite. The frequency of the Mg3OH band in talc increases with pressure due to the absence of hydrogen bonding. The different orientation of the hydroxyl group in pyrophyllite and muscovite leads to hydrogen bonding and a decrease in the frequency of the Al2OH band with pressure. 10-Å phase is approximately equivalent to talc with the addition of interlayer H2O. In a spectrum of a sample synthesised for 143 h, two hydroxyl stretching bands are clearly resolved on compression. One is the same as the Mg3OH band in talc, indicating the presence of intra-layer hydroxyl in a talc-like environment with no hydrogen bonding. The other, which separates from the talc-like band at 1 GPa, is associated with intra-layer hydroxyl that is hydrogen bonded to interlayer H2O. There are equivalent bands in high-pressure spectra of a sample of deuterated 10-Å phase, synthesised for 400 h. This sample shows a greater extent of hydrogen bonding at ambient pressure than the 143 h sample. For all of the phases studied, increasing temperature leads to a decrease in frequency for every hydroxyl stretching vibration, both at low and high pressures. The shifts in frequency with temperature are an order of magnitude greater than the shifts with pressure when normalised to previously measured structural parameters.  相似文献   

13.
Shock-recovery experiments for obsidian and its fused glass have been carried out with pressure up to 35 GPa. Structural evolution accompanying the shock compression was investigated using X-ray diffraction technique, Raman and infrared spectroscopy. The densities of obsidian and its fused glass increased with applied shock pressure up to 25 GPa. Densification reached a maximum of 4.7 and 3.6% for obsidian and its fused glass, respectively. The densification mechanism is attributed to reduction of the T–O–T angle, and changes in ring statistics in the structure. Density reduction observed at greater than 25 GPa of applied shock pressure is due to partial annealing of the high-density glass structures brought by high post-shock residual temperature. The density of fused glass is almost equal to its original value at 35 GPa while the shocked obsidian has a slightly lower value than its original value. Amorphization of crystallites present in the obsidian due to shock compression is probably the cause of the density decrease. The structural evolution observed in shock-compressed obsidian and its fused glass can be explained by densification resulting from average T–O–T angle reduction and increase of small rings, and subsequent structural relaxation by high post-shock temperature at applied shock compression above 25 GPa.  相似文献   

14.
 The charge density and bond character of the rutile-type structure of SiO2 (stishovite) under compression to 30 GPa were investigated by X-ray diffraction study using synchrotron radiation and AgKα rotating anode X-ray generator through a newly devised diamond-anvil cell. The valence electron density was determined by least-squares refinement including the κ parameter and the electron population in the X-ray atomic scattering parameters. The oxygen κ-parameter of SiO2 is 0.94 under ambient conditions and 1.11 at 29.1 GPa and the silicon valence changes from +2.12(8) at ambient pressure to +2.26(15) at 29.1 GPa. These values indicate that the electron distributions are more localized with increasing pressure. The difference Fourier map shows the deformation of the valence electron distribution and the bonding electron population in residual electron densities. The bonding electron observed from the X-ray diffraction study is interpreted by molecular orbital calculations. The deformation of SiO6octahedra and the bonding electron density of stishovite structures are elucidated from the overlapping electron orbits. The O–O distances of shared and unshared edge of SiO6 octahedra change with the cation ionicity. The repulsive force between the two cations in the adjacent octahedron makes its shared edge shorter. The pressure changes of the apical and equatorial Si–O interatomic distances are explained by the electron density of state (DOS) of Si and electron configuration. Received: 7 January 2002 / Accepted: 6 May 2002  相似文献   

15.
Iron-rich orthopyroxene plays an important role in models of the thermal and magmatic evolution of the Moon, but its density at high pressure and high temperature is not well-constrained. We present in situ measurements of the unit-cell volume of a synthetic polycrystalline end-member orthoferrosilite (FeSiO3, fs) at simultaneous high pressures (3.4–4.8 GPa) and high temperatures (1,148–1,448 K), to improve constraints on the density of orthopyroxene in the lunar interior. Unit-cell volumes were determined through in situ energy-dispersive synchrotron X-ray diffraction in a multi-anvil press, using MgO as a pressure marker. Our volume data were fitted to a high-temperature Birch–Murnaghan equation of state (EoS). Experimental data are reproduced accurately, with a  $\varDelta P$ Δ P  standard deviation of 0.20 GPa. The resulting thermoelastic parameters of fs are: V 0 = 875.8 ± 1.4 Å3, K 0 = 74.4 ± 5.3 GPa, and $\frac{{\text d}K}{{\text d}T} = -0.032 \pm 0.005\,\hbox{GPa K}^{-1}$ d K d T = - 0.032 ± 0.005 GPa K - 1 , assuming ${K}^{\prime}_{0} = 10 $ K 0 ′ = 10 . We also determined the thermal equation of state of a natural Fe-rich orthopyroxene from Hidra (Norway) to assess the effect of magnesium on the EoS of iron-rich orthopyroxene. Comparison between our two data sets and literature studies shows good agreement for room-temperature, room-pressure unit-cell volumes. Preliminary thermodynamic analyses of orthoferrosilite, FeSiO3, and orthopyroxene solid solutions, (Mg1?x Fe x ) SiO3, using vibrational models show that our volume measurements in pressure–temperature space are consistent with previous heat capacity and one-bar volume–temperature measurements. The isothermal bulk modulus at ambient conditions derived from our measurements is smaller than values presented in the literature. This new simultaneous high-pressure, high-temperature data are specifically useful for calculations of the orthopyroxene density in the Moon.  相似文献   

16.
《Chemical Geology》2006,225(3-4):336-346
We present results of high temperature, high pressure atomistic simulations aimed at determining the thermodynamic mixing properties of key binary garnet solid solutions. Computations cover the pressure range 0–15 GPa and the temperature range 0–2000 K. Through a combination of Monte-Carlo and lattice-dynamics calculations, we derive thermodynamic mixing properties for garnets with compositions along the pyrope–almandine and pyrope–grossular joins, and compare these with existing experimental data. Across the pressure–temperature range considered, simulations show virtually ideal mixing behaviour in garnet on the pyrope–almandine join, while large excess volumes and enthalpies of mixing are predicted for garnet along the pyrope–grossular join. Excess heat capacities and entropies are also examined. These simulations shed additional light on the link between the behaviour at the atomic level and macroscopic thermodynamic properties: we illustrate the importance of certain atomistic Ca–Mg contacts in the pyrope–grossular solid solutions. For simulation techniques of this type to become sufficiently accurate for direct use in geological applications such as geothermobarometry, there is an urgent need for improved experimental determinations of several key quantities, such as the enthalpies of mixing along both joins.  相似文献   

17.
High pressure melting behavior of three Fe-alloys containing 5 wt% Ni and (1) 10 wt% Si, (2) 15 wt% Si or (3) 12 wt% S was investigated up to megabar pressures by in situ X-ray diffraction and laser-heated diamond anvil cell techniques. We observe a decrease in melting temperature with increasing Si content over the entire investigated pressure range. This trend is used to discuss the melting curve of pure Fe. Moreover, our measurements of eutectic melting in the Fe–Fe3S system show a change in slope around 50 GPa concomitant with the fcc–hcp phase transition in pure solid iron. Extrapolations of our melting curve up to the core–mantle boundary pressure yield values of 3,600–3,750 K for the freezing temperature of plausible outer core compositions.  相似文献   

18.
Brackets on the melting temperature of K2CO3 were experimentally determined at 1.86 ± 0.02 GPa (1,163–1,167°C), 2.79 ± 0.03 GPa (1,187–1,195°C), and 3.16 ± 0.04 GPa (1,183–1,189°C) in a piston-cylinder apparatus. These new data, in combination with published experiments at low pressure (<0.5 GPa), establish the K2CO3 fusion curve to 3.2 GPa. On the basis of these experiments and published thermodynamic data for crystalline and liquid K2CO3, the high-pressure density and compressibility of K2CO3 liquid were derived from the fusion curve. The pressure dependence of the liquid compressibility (K′0 = dK 0/dP, where K 0 = 1/β0) is between 16.2 and 11.6, with a best estimate of 13.7, in a third-order Birch–Murnaghan equation of state (EOS). This liquid K′0 leads to a density of 2,175 ± 36 kg/m3 at 4 GPa and 1,500°C, which is ∼30% lower than that reported in the literature on the basis of the falling-sphere method at the same conditions. The uncertainty in the liquid K′0 leads to an error in melt density of ± 2% at 4 GPa; the error decreases with decreasing pressure. With a K′0 of 13.7, the compressibility of K2CO3 at 1,500°C and 1 bar (K 0 = 3.8 GPa) drops rapidly with increasing pressure ( ), which prevents a density crossover with silicate melts, such as CaAlSi2O8 and CaMgSi2O6, at upper mantle depths.  相似文献   

19.
Unpolarized absorption spectra of single crystals of Cr3+ doped Al2O3 (synthetic ruby) have measured using a new, time-resolving, dispersive, streak photographic system over the range ～350 to ～700 nm during a series of shock loading experiments. The crystal field absorptions assigned to the transition 4 A 2g→4 T 2g were observed to shift in a series of experiments from 555±1 nm at atmospheric pressure to 503±5 nm at 46 GPa. In a single experiment at 32 GPa the 4 A 2g→4 T 1g transition was observed to shift from 405±1 to 386±5 nm. The present data extrapolate downwards in compression toward the 10 GPa data of Stephens and Drickamer (1961) although both crystal field absorption energies increase considerably less with compression than predicted by the simple ionic point charge model. The single datum observed for the Racah parameter B, 588±38 cm?1 at 32 GPa, is consistant with previous results to 10 GPa and the trend of decreasing B, with compression expected from the divergence of the data from the point charge model due to increasing covalancy.  相似文献   

20.
 Using the high-pressure differential thermal analysis (HP-DTA) system in a cubic multianvil high-pressure apparatus, we measured the melting points of portlandite, Ca(OH)2, up to 6 GPa and 1000 °C. We detected endothermic behavior at the temperature and pressure conditions of 800 °C and 2.5 GPa, 769 °C and 3.5 GPa, 752 °C and 4.0 GPa, 686 °C and 5.0 GPa, and 596 °C and 6.0 GPa, respectively, due to melting of portlandite. By in situ X-ray studies under pressure, the melting of portlandite was observed at 730 °C and 4.32 GPa and at 640 °C and 5.81 GPa, respectively. Results of both HP-DTA and X-ray studies were consistent within experimental error. The melting is congruent and has a negative Clapeyron slope, indicating that liquid Ca(OH)2 has higher densities than crystalline portlandite in this pressure range. Received: 19 June 1999 / Revised, accepted: 11 September 1999  相似文献   

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