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1.
 The empirical linear relation between volume and logarithm of bulk modulus of a material, discovered by Grover, Getting and Kennedy is taken as the basis for our equation of state. Using the latest experimental information on the adiabatic bulk modulus, the equation of state is applied to the three polymorphs of Mg2SiO4 to develop a consistent dataset of their thermodynamic properties in the temperature range of 200–2273 K and a pressure range of 0.1 MPa–30 GPa. The results imply that the bulk sound velocity contrast (v βv α)/v α increases with temperature along the α–β phase boundary and reaches the value 8.9% at 13.5 GPa, a pressure equivalent to 410 km depth in the Earth. The bulk sound velocity contrast (v γv β)/v β decreases with temperature along the β–γ phase boundary and becomes less than 0.7% at temperatures and pressures equivalent to those associated with the 520-km seismic discontinuity in the Earth. Received: 1 August 2000 / Accepted: 1 March 2001  相似文献   

2.
A technique for density measurement under high pressure and high temperature was developed using the X-ray absorption imaging method combined with an externally heated diamond anvil cell. The densities of solid and liquid In were measured in the pressure and temperature ranges of 3.2–18.6 GPa and 294–719 K. The densities obtained through the X-ray absorption imaging method were in good agreement (less than 2.0% difference) with those obtained through X-ray diffraction. Based on the measured density, the isothermal bulk modulus of solid In is determined as 48.0 ± 1.1?40.9 ± 0.8 GPa at 500 K, assuming K′ = 4 to 6. The compression curve of liquid In approaches that of solid In at higher pressures and does not cross over the solid compression curve in the measurement range. The present technique enables us to determine the densities of both solids and liquids precisely in a wide pressure and temperature range.  相似文献   

3.
The Raman frequencies of quartz are used to evaluate deviatoric stresses in rocksalt-structure media in diamond-anvil cell experiments to pressures up to 20 GPa. The piezospectroscopic effect in quartz is modeled by first-principles calculations. Non-hydrostatic stresses measured in halogen salts give yield strength estimates of 3 GPa in the B1 structure (NaCl), and 4.5 GPa for the B2 structure (KCl and KBr). Raman measurements in MgO show that the yield strength is reached at around 6 ± 1 GPa. Measurements on quartz alone indicate similar yield strength. The estimated yield strength in MgO is thus likely a lower bound, in consistency with former radial X-ray diffraction measurements that gave a yield strength of 8 ± 1 GPa, and lower-pressure large-volume press experiments indicating a yield strength of 6 GPa at 5 GPa. Former values of the yield strength below 2 GPa determined by pressure gradient measurements were underestimated due to unverified assumptions in boundary conditions. The yield strength increases with increasing coordination of ionic solids, likely contributing to increase viscosity at phase transitions near the upper–lower mantle boundary.  相似文献   

4.
A new experimental setup for simultaneous P-wave velocity (VP) and density (ρ) measurements for liquid alloys is developed using ultrasonic and X-ray absorption methods combined with X-ray tomography at high pressures and high temperatures. The new setup allows us to directly determine adiabatic bulk moduli (KS) and to discuss the correlation between the VP and ρ of the liquid sample. We measured VP and ρ of liquid Ni68S32 up to 5.6 GPa and 1045 K using this technique. The effect of pressure on the VP and ρ values of liquid Ni68S32 is similar to that of liquid Fe57S43. (Both compositions correspond to near-eutectic ones.) The obtained KS values are well fitted to the finite strain equation with a KS0 value (KS at ambient pressure) of 31.1 GPa and a dKS/dP value of 8.44. The measured VP was found to increase linearly with increasing ρ, as approximated by the relationship: VP [m/s] = 1.29 ρ [kg/m3] – 5726, suggesting that liquid Ni–S follows an empirical linear relationship, Birch's law. The dVP/dρ slope is similar between Ni68S32 and Fe57S43 liquids, while the VPρ plot of liquid Ni–S is markedly different from that of liquid Fe–S, which indicates that the effect of Ni on Birch's law is important for understanding the VPρ relation of planetary and Moon's molten cores.  相似文献   

5.
The structure of deuterated portlandite, Ca(OD)2, has been investigated using time-of-flight neutron diffraction at pressures up to ∼4.5 GPa and temperatures up to ∼823 K. Rietveld analysis of the data reveals that with increasing pressure, unit-cell parameter c decreases at a rate about 4.5 times larger than that for a, which is largely due to rapid contraction of the interlayer spacing in this pressure range. Fitting of the determined cell volumes to the third-order Birch–Murnaghan equation of state yields a bulk modulus (K 0) of 32.2 ± 1.0 GPa and its first derivative (K 0′) of 4.4 ± 0.6. Moreover, on compression, hydrogen-mediated interatomic interactions within the interlayer become strengthened, as reflected by decreases in interlayer D···O and D···D distances with increasing pressure. Correspondingly, D–D, the distance between the three equivalent sites over which D is disordered, increases, suggesting a pressure-induced hydrogen disorder. This behavior is similar to that reported in brucite at elevated pressure. On heating at ∼2.1 GPa, cell parameter c increases more rapidly than a, as expected. However, because of the pressure effect, the thermal expansion coefficients, particularly along c, are much smaller than those at ambient pressure. With increasing temperature, the three partially occupied D sites become further apart, and the D-mediated interactions, mainly the interlayer D···D repulsion, become weakened.  相似文献   

6.
High-precision unit-cell volume data of stibnite, collected in the pressure range of 0–10 GPa, was used for fitting a third-order Birch–Murnaghan equation of state. The zero-pressure volume, bulk modulus and its pressure derivative were found to be 487.73(6) Å3, 26.91(14) GPa and 7.9(1), respectively. A series of X-ray intensity data was collected in the same pressure range using a CCD-equipped Bruker diffractometer. The high-pressure structures were all refined to R1(|F0|>4) values of approximately 0.03. Crystal-chemical parameters as polyhedron volume, centroid and eccentricity were calculated for the seven coordinated cation positions using the software IVTON. The cation eccentricity appears to be a very useful tool for quantification of the lone electron pair activity. U2S3, Dy2S3 and Nd2Te3 are all isostructural with stibnite, but the cations in these materials have no lone electron pair. Their eccentricity is much smaller than that of Sb, and close to zero. This confirms that the stibnite structure type alone does not force eccentricity upon the cations involved and it is the lone electron pairs of Sb that generate the eccentricity of cation positions in the structures of stibnite. At increasing pressure the eccentricity of Sb is decreasing. It is therefore reasonable to conclude that the lone electron pair activity is decreasing with increasing pressure.  相似文献   

7.
Crystal structure of Bi2S3 was refined at eight distinct hydrostatic pressures in the range 0–10 GPa using a CCD equipped 4-circle diffractometer and a diamond-anvil cell. Coefficients of the BM3 equation of state are as follows: zero-pressure volume 498.4(7) Å3, bulk modulus K 0 36.6(15) GPa and its pressure derivative 6.4(5). The bulk of compression takes place in the structural space between Bi4S6 ribbons, where lone-electron pairs are accommodated. Eccentricity of Bi in its coordination polyhedra decreases in the process, with long Bi–S distances decreasing, whereas the opposing short Bi–S distances stay constant or even increase in length. All these phenomena are compatible with the movement of lone-electron pairs of Bi closer to the parent atom at increasing pressure.  相似文献   

8.
High-pressure in situ X-ray diffraction experiment of Fe- and Al-bearing phase D (Mg0.89Fe0.14Al0.25Si1.56H2.93O6) has been carried out to 30.5 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields values of V 0 = 86.10 ± 0.05 Å3; K 0 = 136.5 ± 3.3 GPa and K′ = 6.32 ± 0.30. If K′ is fixed at 4.0 K 0 = 157.0 ± 0.7 GPa, which is 6% smaller than Fe–Al free phase D reported previously. Analysis of axial compressibilities reveals that the c-axis is almost twice as compressible (K c  = 93.6 ± 1.1 GPa) as the a-axis (K a  = 173.8 ± 2.2 GPa). Above 25 GPa the c/a ratio becomes pressure independent. No compressibility anomalies related to the structural transitions of H-atoms were observed in the pressure range to 30 GPa. The density reduction of hydrated subducting slab would be significant if the modal amount of phase D exceeds 10%.  相似文献   

9.
In-situ synchrotron X-ray diffraction experiments were conducted using the SPEED-1500 multi-anvil press of SPring-8 on stishovite SiO2 and pressure-volume-temperature data were collected at up to 22.5 GPa and 1,073 K, which corresponds to the pressure conditions of the base of the mantle transition zone. The analysis of room-temperature data yielded V0=46.56(1) Å3, KT 0=296(5) GPa and K T =4.2(4), and these properties were consistent with the subsequent thermal equation of state (EOS) analyses. A fit of the present data to high-temperature Birch-Murnaghan EOS yielded (KT /T) P =–0.046(5) GPa K–1 and = a + bT with values of a =1.26(11)×10–5 K–1 and b =1.29(17)×10–8 K–2. A fit to the thermal pressure EOS gives 0=1.62(9)×10–5 K–1, ( K T / T) V =–0.027(4) GPa K–1 and (2P /T 2) V =27(5)×10–7 GPa K–2. The lattice dynamical approach by Mie-Grüneisen-Debye EOS yielded 0=1.33(6), q =6.1(8) and 0=1160(120) K. The strong volume dependence of the thermal pressure of stishovite was revealed by the analysis of present data, which was not detectable by the previous high-temperature data at lower pressures, and this yields ( K T / T) V 0 and q 1. The analyses for the fictive volume for a and c axes show that relative stiffness of c axis to a axis is similar both on compression and thermal expansion. Present EOS enables the accurate estimate of density of SiO2 in the deep mantle conditions.  相似文献   

10.
In situ X-ray diffraction measurements of KAlSi3O8-hollandite (K-hollandite) were performed at pressures of 15–27 GPa and temperatures of 300–1,800 K using a Kawai-type apparatus. Unit-cell volumes obtained at various pressure and temperature conditions in a series of measurements were fitted to the high-temperature Birch-Murnaghan equation of state and a complete set of thermoelastic parameters was obtained with an assumed K300,0=4. The determined parameters are V 300,0=237.6(2) Å3, K 300,0=183(3) GPa, (?K T,0/?T) P =?0.033(2) GPa K?1, a 0=3.32(5)×10?5 K?1, and b 0=1.09(1)×10?8 K?2, where a 0 and b 0 are coefficients describing the zero-pressure thermal expansion: α T,0 = a 0 + b 0 T. We observed broadening and splitting of diffraction peaks of K-hollandite at pressures of 20–23 GPa and temperatures of 300–1,000 K. We attribute this to the phase transitions from hollandite to hollandite II that is an unquenchable high-pressure phase recently found. We determined the phase boundary to be P (GPa)=16.6 + 0.007 T (K). Using the equation of state parameters of K-hollandite determined in the present study, we calculated a density profile of a hypothetical continental crust (HCC), which consists only of K-hollandite, majorite garnet, and stishovite with 1:1:1 ratio in volume. Density of HCC is higher than the surrounding mantle by about 0.2 g cm?3 in the mantle transition zone while this relation is reversed below 660-km depth and HCC becomes less dense than the surrounding mantle by about 0.15 g cm?3 in the uppermost lower mantle. Thus the 660-km seismic discontinuity can be a barrier to prevent the transportation of subducted continental crust materials to the lower mantle and the subducted continental crust may reside at the bottom of the mantle transition zone.  相似文献   

11.
The stability and pressure–volume equation of state of iron–silicon alloys, Fe-8.7 wt% Si and Fe-17.8 wt% Si, have been investigated using diamond-anvil cell techniques up to 196 and 124 GPa, respectively. Angular–dispersive X-ray diffractions of iron–silicon alloys were measured at room temperature using monochromatic synchrotron radiation and an imaging plate (IP). A bcc–Fe-8.7 wt% Si transformed to hcp structure at around 1636 GPa. The high-pressure phase of Fe-8.7 wt% Si with hexagonal close-packed (hcp) structure was found to be stable up to 196 GPa and no phase transition of bcc–Fe-17.8 wt% Si was observed up to 124 GPa. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state (BM EOS) with zero–pressure parameters: V0=22.2(8) Å3, K0=198(9) GPa, and K0=4.7(3) for hcp–Fe-8.7 wt% Si and V0=179.41(45) Å3, K0=207(15) GPa and K0=5.1(6) for Fe-17.8 wt% Si. The density and bulk sound velocity of hcp–Fe-8.7 wt% Si indicate that the inner core could contain 3–5 wt% Si.  相似文献   

12.
Fiber-based laser heating systems offer high flexibility and are increasingly used in high-pressure/high-temperature research. Previous fiber-based laser heating systems were based on lasers delivering radiation with 1-μm wavelength that show unfavorable heating characteristics for many sample materials. We report on the development and first experiments of a waveguide (fiber)-based CO2-laser heating system that can be used in a flexible manner for high-temperature research and for high-pressure/temperature experiments when combined with diamond-anvil cells. The waveguide-based CO2-laser heating system allows convenient heating of optically transparent samples without the need for adding an additional laser absorber. In a pilot experiment, the flexible heating system has been installed on a Brillouin scattering system to measure high-temperature sound-wave velocities in single-crystal MgO. The waveguide-based CO2-laser heating system offers perspectives for a variety of scientific applications, most importantly those that require the use of synchrotron facilities where space is limited and flexible solutions are required.  相似文献   

13.
Polycrystalline samples of natural edingtonite (New Brunswick, Canada) and thomsonite (Oregon, USA) were studied up to 6 GPa using monochromatic synchrotron X-ray powder diffraction and a diamond-anvil cell with a methanol:ethanol:water mixture as a penetrating pressure-transmitting fluid. Unlike natrolite, previously studied under the same conditions, edingtonite and thomsonite do not show any apparent pressure-induced hydration (PIH) or phase transitions. All these fibrous zeolites are characterized by their anisotropic compressibilities, with the linear compressibilities of the fibrous chains (c-axis) being as small as one third of those perpendicular to the chains (a-, b-axes); for edingtonite, 0 a =0.0050(3) GPa–1, 0 b =0.0054(2) GPa–1, 0 c =0.0034(1) GPa–1; for thomsonite, 0 a = 0.0080(2) GPa–1, 0 b =0.0084(2) GPa–1, 0 c =0.0032(1) GPa–1. The pressure–volume data were fitted to a second-order Birch–Murnaghan equation of state using a fixed pressure derivative of 4. As a result of the 0000-type connectivity of the chains, the bulk modulus of edingtonite is found to be about 40% larger than that of thomsonite; KEDI 0=73(3) GPa, KTHO 0=52(1) GPa. Distance least-squares refinements were used to model the expected framework, following the observed linear compression behaviors. The chain-bridging T–O–T angle is proposed to be correlated with the different compressibilities across the chains in each framework type.  相似文献   

14.
The compression of synthetic pyrope Mg3Al2 (SiO4)3, almandine Fe3Al2(SiO4)3, spessartine Mn3Al2 (SiO4)3 grossular Ca3Al2(SiO4)3 and andradite Ca3Fe2 (SiO4)3 was studied by loading the crystals together in a diamond anvil cell. The unit-cell parameters were determined as a function of pressure by X-ray diffraction up to 15 GPa using neon as a pressure transmitting medium. The unit-cell parameters of pyrope and almandine were measured up to 33 and 21 GPa, respectively, using helium as a pressure medium. The bulk moduli, K T 0, and their first pressure derivatives, K T 0 , were simultaneously determined for all five garnets by fitting the volume data to a third order Birch-Murnaghan equation of state. Both parameters can be further constrained through a comparison of volume compressions between pairs of garnets, giving for K T 0 and K T 0 171(2) GPa and 4.4(2) for pyrope, 185(3) GPa and 4.2(3) for almandine, 189(1) GPa and 4.2 for spessartine, 175(1) GPa and 4.4 for grossular and 157(1) GPa and 5.1 for andradite, where the K T 0 are fixed in the case of spessartine, grossular and andradite. Direct comparisons of the unit-cell volumes determined at high pressures between pairs of garnets reveal anomalous compression behavior for Mg2+ in the 8-fold coordinated triangular dodecahedron in pyrope. This agrees with previous studies concerning the compression behaviors of Mg2+ in 6-fold coordinated polyhedra at high pressures. The results show that simple bulk modulus–volume systematics are not obeyed by garnets. Received: 29 July 1998 / Revised, accepted: 7 April 1999  相似文献   

15.
A single-crystal sample of galenobismutite was subjected to hydrostatic pressures in the range of 0.0001 and 9 GPa at room temperature using the diamond-anvil cell technique. A series of X-ray diffraction intensities were collected at ten distinct pressures using a CCD equipped 4-circle diffractometer. The crystal structure was refined to R1(|F0| > 4σ) values of approximately 0.05 at all pressures. By fitting a third-order Birch-Murnaghan equation of state to the unit-cell volumes V 0 = 700.6(2) Å3, K 0 = 43.9(7) GPa and dK/dP = 6.9(3) could be determined for the lattice compression. Both types of cations in galenobismutite have stereochemically active lone electron pairs, which distort the cation polyhedra at room pressure. The cation eccentricities decrease at higher pressure but are still pronounced at 9 GPa. Galenobismutite is isotypic with CaFe2O4 (CF) but moves away from the idealised CF-type structure during compression. Instead of the two octahedral cation sites and one bi-capped trigonal-prismatic site, PbBi2S4 attains a new high-pressure structure characterised by one octahedral site and two mono-capped trigonal-prismatic sites. Analyses of the crystal structure at high pressure confirm the preference of Bi for the octahedral site and the smaller one of the two trigonal-prismatic sites.  相似文献   

16.
Polynomial expressions for the elastic tensor coefficients, the bulk, the shear and Young’s moduli, the speed of sound for longitudinal and transverse waves, the equation of state and the x coordinate of the sulfur atom in pyrite are reported based on ab initio calculations in the range of 0–135 GPa. Comparison with published experimental data indicates good agreement for the equation of state and for values at 0 GPa as well as reasonable agreement for first derivatives. All modeling and interpretation was performed with Materials Toolkit v.2.0 and all ab initio computations with VASP.  相似文献   

17.
Fe-bearing dense hydrous magnesium silicate Phase A, Mg6.85Fe0.14Si2.00O8(OH)6 has been studied by single-crystal X-ray diffraction at ambient conditions and by high-pressure powder diffraction using synchrotron radiation to 33 GPa. Unit cell parameters at room temperature and pressure from single crystal diffraction are a=7.8678 (4) Å, c=9.5771 (5) Å, and V=513.43 (4) Å3. Fitting of the P–V data to a third-order Birch-Murnaghan isothermal equation of state yields V 0=512.3 (3) Å3, K T,0=102.9 (28) GPa and K′=6.4 (3). Compression is strongly anisotropic with the a-axes, which lie in the plane of the distorted close-packed layers, approximately 26% more compressible than the c-axis, which is normal to the plane. Structure refinement from single-crystal X-ray intensity data reveals expansion of the structure with Fe substitution, mainly by expansion of M-site octahedra. The short Si2–O6 distance becomes nearly 1% shorter with ~2% Fe substitution for Mg, possibly providing additional rigidity in the c-direction over the Mg end member. K T obtained for the Fe-bearing sample is ~5.5% greater than reported previously for Fe-free Phase A, despite the larger unit cell volume. This study represents a direct comparison of structure and K T–ρ relations between two compositions of a F-free dense hydrous magnesium silicate (DHMS) phase, and may help to characterize the effect of Fe substitution on the properties of other DHMS phases from studies of the Fe-free end-members.  相似文献   

18.
Phase D is a dense hydrous magnesium silicate (ideal formula MgSi2H2O6) which contains silicon cations exclusively in octahedral coordination. Measurements of the unit cell parameters of phase D were made to pressures of 30 GPa using a diamond anvil cell and employing synchrotron X-ray diffraction. A neon pressure medium was used. Using a third order Birch-Murnaghan equation of state the isothermal bulk modulus of phase D was determined as 166(±3) GPa with K′ equal to 4.1(±0.3). The compression of phase D is anisotropic with the c-axis twice as compressible as the a-axis. Above 20 GPa, however, the c/a ratio becomes pressure independent. Received: 29 July 1998/ Revised, accepted: 5 August 1998  相似文献   

19.
Barium carbonate (BaCO3) was examined in a diamond anvil cell up to a pressure of 73 GPa using an in situ angle-dispersive X-ray diffraction technique. Three new phases of BaCO3 were observed at pressures >10 GPa. From 10 to 24 GPa, BaCO3-IV had a post-aragonite structure with space group Pmmn. There are two molecules in a single unit cell (Z = 2) of the orthorhombic phase, which is same as the high-pressure phases of CaCO3 and SrCO3. The isothermal bulk modulus of BaCO3-IV is K 0 = 84(4) GPa, with V 0 = 129.0(7) Å3 when K 0′ = 4. The c axis of the unit cell parameter is less compressible than the a and b axes. The relative change in volume that accompanies the transformation between BaCO3-III and BaCO3-IV is ~6%. BaCO3-V, which has an orthorhombic symmetry, was synthesized at 50 GPa. As the pressure increases, BaCO3-V is transformed into tetragonal BaCO3-VI. This transformation is likely to be second order, because the diffraction pattern of BaCO3-V is similar to that of BaCO3-VI, and some single peaks in BaCO3-VI become doublets in BaCO3-V. After decompression, the new high-pressure phases transform into BaCO3-II. Our findings resolve a dispute regarding the stable high-pressure phases of BaCO3.  相似文献   

20.
We have determined the P-V equation of state of Al-rich H-bearing SiO2 stishovite by X-ray powder diffraction at pressures up to 58 GPa using synchrotron radiation. The sample contained 1.8 wt% Al2O3 and up to 500 ppm H2O, and had a composition that would coexist with Mg-silicate perovskite in a subducted slab. By fitting a third-order Birch-Murnaghan equation of state to our compression data, we obtained a bulk modulus K T0=298(7) GPa with K′=4.3(5). With K′ fixed to a value of 4, the bulk modulus K T0=304(3) GPa. Our results indicate that Al3+ and H+ have a small effect on the elastic properties of stishovite. Compared with data obtained up to 43.8 GPa, peak intensities changed and we observed a decreased quality of fit to a tetragonal unit cell at pressures of 49 GPa and higher. These changes may be an indication that the rutile↔CaCl2 transition occurs between these pressures. After laser annealing of the sample at 58.3(10) GPa and subsequent decompression to room conditions, the cell volume is the same as before compression, giving strong evidence that the composition of the recovered sample is also unchanged. This suggests that Al and H are retained in the sample under extreme P-T conditions and that stishovite can be an agent for transporting water to the deepest lower mantle.  相似文献   

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