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1.
The elastic properties of CaSnO3 perovskite have been measured by both ultrasonic interferometry and single-crystal X-ray diffraction at high pressures. The single-crystal diffraction data collected using a diamond-anvil cell show that CaSnO3 perovskite does not undergo any phase transitions at pressures below 8.5?GPa at room temperature. Ultrasonic measurements in the multianvil press to a maximum pressure of ～8?GPa at room temperature yielded S- and P-wave velocity data as a function of pressure. For a third-order Birch-Murnaghan EoS the adiabatic elastic moduli and their pressure derivatives determined from these velocity data are K S0=167.2±3.1?GPa, K ′ S0=4.89±0.17, G 0=89.3±1.0?GPa, G ′ 0=0.90±0.02. The quoted uncertainties include contributions from uncertainties in both the room pressure length and density of the specimen, as well as uncertainties in the pressure calibration of the multianvil press. Because the sample is a polycrystalline specimen, this value of K S0 represents an upper limit to the Reuss bound (conditions of uniform stress) on the elastic modulus of CaSnO3 perovskite. If the value of αγT is assumed to be 0.01, the value of K S0 corresponds to K T0=165.5±3.1?GPa. The 10 P-V data obtained by single-crystal diffraction were fit with a third-order Birch–Murnaghan equation-of-state to obtain the parameters V 0=246.059±0.013 Å3, K T0=162.6±1.0?GPa, K ′ T0=5.6±0.3. Because single-crystal measurements under hydrostatic conditions are made under conditions of uniform stress, they yield bulk moduli equivalent to the Reuss bound on a polycrystalline specimen. The results from the X-ray and ultrasonic experiments are therefore consistent. The bulk modulus of CaSnO3 perovskite lies above the linear trend of K 0 with inverse molar volume, previously determined for Ca perovskites. This prevents an estimation of the bulk modulus of CaSiO3 perovskite by extrapolation. However, our value of G 0 for CaSnO3 perovskite combined with values for CaTiO3 and CaGeO3 forms a linear trend of G 0 with octahedral tilt angle. This allows a lower bound of 150?GPa to be placed on the shear modulus of CaSiO3 by extrapolation.  相似文献   

2.
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   

3.
Talc is a layered hydrous silicate mineral that plays a vital role in transporting water into Earth’s interior and is crucial for explaining geophysical observations in subduction zone settings. In this study, we explored the structure, equation of state, and elasticity of both triclinic and monoclinic talc under high pressures up to 18 GPa using first principles simulations based on density functional theory corrected for dispersive forces. Our results indicate that principal components of the full elastic constant tensor C11 and C22, shear components C66, and several off-diagonal components show anomalous pressure dependence. This non-monotonic pressure dependence of elastic constant components is likely related to the structural changes and is often manifested in a polytypic transition from a low-pressure polytype talc-I to a high-pressure polytype talc-II. The polytypic transition of talc occurs at pressures within its thermodynamic stability. However, the bulk and shear elastic moduli show no anomalous softening. Our study also shows that talc has low velocity, extremely high anisotropy, and anomalously high VP/VS ratio, thus making it a potential candidate mineral phase that could readily explain unusually high VP/VS ratio and large shear wave splitting delays as observed from seismological studies in many subduction systems.  相似文献   

4.
We established an equation of state for nanocrystalline forsterite using multi-anvil press and diamond anvil cell. Comparative high-pressure and high-temperature experiments have been performed up to 9.6 GPa and 1,300°C. We found that nanocrystalline forsterite is more compressible than macro-powder forsterite. The bulk modulus of nanocrystalline forsterite is equal to 123.3 (±3.4) GPa whereas the bulk modulus of macro-powder forsterite is equal to 129.6 (±3.2) GPa. This difference is attributed to a weakening of the elastic properties of grain boundary and triple junction and their significant contribution in nanocrystalline sample compare to the bulk counterpart. The bulk modulus at zero pressure of forsterite grain boundary was determined to be 83.5 GPa.  相似文献   

5.
Data on the refractive index, density, and bulk modulus variations of Di64An36 glass, which is used as a model basalt melt, were obtained with a polarization interference microscope and a high-pressure diamond anvil cell at ambient temperature and pressure up to 5.0 GPa. An anomalous decrease in the bulk modulus, K t , was observed in the pressure range 0?C1.0 GPa. The values of the zero-pressure isothermal bulk modulus, K t,0 = 22.2, and variation of the bulk modulus with pressure, ??K t /??P = 11.35, were derived using a linear equation relating K t and P over the pressure range with the normal behavior of the compressibility. A comparison of our results with previous data on other glasses and melts showed that the bulk moduli of silicate glasses are similar to those of corresponding melts. The values of the pressure coefficient of the bulk moduli, ??K t /??P, for glasses derived from linear equations are 2.5 times higher than the pressure derivative of the bulk modulus, K?? T , derived using the Birch-Murnaghan equation for corresponding melts. The difference in ??K t /??P and K?? T has an effect on the compressibility of glasses and melts. The compressibility of glasses up to 5.0 GPa calculated as (d ? d 0)/d is almost two times lower than that of corresponding melts.  相似文献   

6.
The adiabatic single-crystal elastic moduli of superhydrous B, Mg10Si3O14(OH)4, have been measured at ambient conditions using Brillouin spectroscopy. This material is the first hydrous phase found to be stable at the extreme conditions of 20 GPa and 1400 °C. The single-crystal moduli, in GPa, are: C 11=280.0±1.5, C 22=307.4±1.6, C 33=293.4±1.4, C 44=90.0±1.1, C 55=99.2±0.8, C 66=89.6±0.6, C 12=66.1±2.2, C 13=105.6±2.6, C 23=81.8±2.6. With aggregate elastic properties of K VRH =154.0±4.2 and μ VRH =97.0±0.7 GPa, superhydrous B is approximately 16% suffer than forsterite and 20% softer than magnesium silicate spinel; it is also considerably more elastically isotropic than forsterite. The single-crystal moduli are compared to those of forsterite, magnesium silicate spinel and periclase, materials that are both structurally and compositionally similar to superhydrous B. The longitudinal moduli of superhydrous B and forsterite follow similar trends and appear to be dominated by the incompressibility and rotation of silicon tetrahedra. The shear and off-diagonal moduli more closely resemble those of periclase and spinel and may reflect the properties inherent to layers of magnesium octahedra.  相似文献   

7.
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   

8.
Lamé modulus (λ) and shear modulus (μ) are among the most important,intrinsic,elastic constants of rocks.Using λ and μ could be much more advantageous than using P- and S-wave velocities (Vp and Vs).He...  相似文献   

9.
The fluoroperovskite phase RbCaF3 has been investigated using high-pressure neutron powder diffraction in the pressure range ~0–7.9 GPa at room temperature. It has been found to undergo a first-order high-pressure structural phase transition at ~2.8 GPa from the cubic aristotype phase to a hettotype phase in the tetragonal space group I4/mcm. This transition, which also occurs at ~200 K at ambient pressure, is characterised by a linear phase boundary and a Clapeyron slope of 2.96 × 10?5 GPa K?1, which is in excellent agreement with earlier, low-pressure EPR investigations. The bulk modulus of the high-pressure phase (49.1 GPa) is very close to that determined for the low-pressure phase (50.0 GPa), and both are comparable with those determined for the aristotype phases of CsCdF3, TlCdF3, RbCdF3, and KCaF3. The evolution of the order parameter with pressure is consistent with recent modifications to Landau theory and, in conjunction with polynomial approximations to the pressure dependence of the lattice parameters, permits the pressure variation of the bond lengths and angles to be predicted. On entering the high-pressure phase, the Rb–F bond lengths decrease from their extrapolated values based on a third-order Birch–Murnaghan fit to the aristotype equation of state. By contrast, the Ca–F bond lengths behave atypically by exhibiting an increase from their extrapolated magnitudes, resulting in the volume and the effective bulk modulus of the CaF6 octahedron being larger than the cubic phase. The bulk moduli for the two component polyhedra in the tetragonal phase are comparable with those determined for the constituent binary fluorides, RbF and CaF2.  相似文献   

10.
The crystal structure and the unit-cell parameters of magnetite have been studied at room temperature up to a pressure of 4.5 GPa using a diamond anvil cell and a four-circle X-ray diffractometer. The isothermal bulk modulus (K T ) and its pressure derivative (K' T ) determined by fitting the pressure-volume data to the Murnaghan equation of state are 181(2) GPa and 5.5(15), respectively. The positional parameter u does not vary significantly over the pressure range of this study. The linear compressibilities of the interatomic distances and the bulk moduli of the polyhedra have been calculated from the pressure dependences of the unit-cell edge a and the u parameter. The Bloch equation has been modified to derive a relationship between the Néel temperature and the parameter u. The modified Bloch equation gives a closer agreement with the experimental results than the Weisz equation.  相似文献   

11.
The single crystal elastic constants of nonmetamict zircons have been measured as a function of pressure to 12 kb at room temperature and also as a function of temperature between 25 and 300° C at atmospheric pressure. The pressure derivatives of the elastic constants are: C 11=10.78, C 33=5.88, C 44=0.99, C 66=?0.31, C 12=3.24, C 13=6.20. The anomalous negative behaviour of C 66 versus pressure could be associated with a high pressure phase transition. The pressure and temperature derivatives of the isotropic elastic wave velocities and elastic moduli for nonmetamict zircon are calculated from the present single crystal data by the Voigt, Ruess, and Hill approximations and compared with the values of some other oxides and silicates. The pressure derivative of the isotropic adiabatic bulk modulus is relatively high (dK S/dP=6.50), and the pressure derivative of the shear modulus is relatively low, (dG/dP=0.78), compared to the corresponding values for some other oxides and silicates. The Debye temperature, ?D, and the high temperature limit of the Grüneisen parameter, γHt, calculated from the elastic constants and their pressure derivatives, agrees well with the Debye temperature and the thermal Grüneisen parameter, γth, calculated from the thermal expansion, heat capacity, and compressibility data.  相似文献   

12.
 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   

13.
 Physical properties including the equation of state, elasticity, and shear strength of pyrite have been measured by a series of X-ray diffraction in diamond-anvil cells at pressures up to 50 GPa. A Birch–Murnaghan equation of state fit to the quasihydrostatic pressure–volume data obtained from laboratory X-ray source/film techniques yields a quasihydrostatic bulk modulus K 0T =133.5 (±5.2) GPa and bulk modulus first pressure derivative K ′ 0T =5.73 (±0.58). The apparent equation of state is found to be strongly dependent on the stress conditions in the sample. The stress dependency of the high-pressure properties is examined with anisotropic elasticity theory from subsequent measurements of energy-dispersive radial diffraction experiments in the diamond-anvil cell. The calculated values of K 0T depend largely upon the angle ψ between the diffracting plane normal and the maximum stress axis. The uniaxial stress component in the sample, t=σ3−σ1, varies with pressure as t=−3.11+0.43P between 10 and 30 GPa. The pressure derivatives of the elastic moduli dC 11/dP=5.76 (±0.15), dC 12/dP=1.41 (±0.11) and dC 44/dP=1.92 (±0.06) are obtained from the diffraction data assuming previously reported zero-pressure ultrasonic data (C 11=382 GPa, C 12=31 GPa, and C 44=109 GPa). Received: 21 December 2000 / Accepted: 11 July 2001  相似文献   

14.
The elastic properties of two types of aluminosilicate (basaltic and rhyolitic) glasses have been studied using both Brillouin and Raman spectroscopy at ambient conditions. It has been found that the elastic moduli of the basaltic glasses decrease with increasing SiO2 concentration. The shear moduli displayed the least dependence on SiO2 content. The bulk moduli of the basaltic glasses strongly depend on the sum of the Q 3 and Q 4 anionic units. Among the modifiers, iron cations showed the strongest effect on the elastic properties of the rhyolitic glasses. For the elastic moduli of rhyolitic glasses, the major effect of alkaline earth cations is on shear modulus; however, both iron and alkali cations showed stronger effects on bulk modulus and similar relative contribution between bulk and shear moduli (based on the equivalent M+ cation). The dependences of elastic moduli on bulk NBO/T observed in both types of glasses suggest that the elastic modulus of an aluminosilicate glass depends on the concentration of effective modifying cations rather than the apparent concentration of all non-network-forming cations. An analysis of data also indicated that the ideal molar mixing model is failed in prediction of the elastic properties of the present multicomponent glasses by using the known parameters.  相似文献   

15.
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   

16.
We present an ultrasonic and neutron powder diffraction study of crystalline MgSO4·7H2O (synthetic epsomite) and MgSO4·7D2O under pressure up to ~3 GPa near room temperature and up to ~2 GPa at lower temperatures. Both methods provide complementary data on the phase transitions and elasticity of magnesium sulphate heptahydrate, where protonated and deuterated counterparts exhibit very similar behaviour and properties. Under compression in the declared pressure intervals, we observed three different sequences of phase transitions: between 280 and 295 K, phase transitions occurred at approximately 1.4, 1.6, and 2.5 GPa; between 240 and 280 K, only a single phase transition occurred; below 240 K, there were no phase transformations. Overall, we have identified four new phase fields at high pressure, in addition to that of the room-pressure orthorhombic structure. Of these, we present neutron powder diffraction data obtained in situ in the three phase fields observed near room temperature. We present evidence that these high-pressure phase fields correspond to regions where MgSO4·7H2O decomposes to a lower hydrate by exsolving water. Upon cooling to liquid nitrogen temperatures, the ratio of shear modulus G to bulk modulus B increases and we observe elastic softening of both moduli with pressure, which may be a precursor to pressure-induced amorphization. These observations may have important consequences for modelling the interiors of icy planetary bodies in which hydrated sulphates are important rock-forming minerals, such as the large icy moons of Jupiter, influencing their internal structure, dynamics, and potential for supporting life.  相似文献   

17.
High-pressure single-crystal X-ray diffraction measurements of synthetic LiCrSi2O6 clinopyroxene (with space group P21/c) were performed in a diamond-anvil cell up to 7.970 GPa. No phase transition has been observed within the pressure range investigated, but the elastic behavior at lower pressures (up to ~2.5 GPa) is affected by an anomalous softening due to the proximity of the phase transition to the HT-C2/c phase at 330 K and at ambient pressure. A third-order Birch–Murnaghan equation of state fitted to the compression data above 2.5 GPa yields a bulk modulus K T0 = 93(2) GPa and its first derivative K′ = 8.8(6). The structural data measured up to 7.970 GPa confirm that the space group P21/c is maintained throughout the whole pressure range investigated. The atomic parameters, obtained from the integrated diffraction intensities, suggest that the Li coordination polyhedron changes its coordination number from 5 to 6 at 6–7 GPa by means of the approach of the bridging O atom, related to the increased kinking of the B tetrahedral chain. Furthermore, at higher pressures, the structural evolution of LiCrSi2O6 provides evidence in the variation of kinking angles and bond lengths of a potential phase transition above 8 GPa to the HP-C2/c space group. A comparison of the Li-clinopyroxenes (M1 = Cr, Al, Sc, Ga, Mg + Fe) previously investigated and our sample shows that their elastic behavior and structural mechanisms of compression are analogous.  相似文献   

18.
Elasticity of CaTiO3, SrTiO3 and BaTiO3 perovskites has been experimentally investigated as a function of pressure up to 3.0 GPa in a liquid-medium piston cylinder apparatus using a high precision ultrasonic interferometric technique. Specimens used are hot-pressed fine-grained (3–10 μm) polycrystalline aggregates with low porosity (<1.5%). Compressional and shear wave velocities and their pressure derivatives have been measured. The results are compared with previous studies on other perovskites and the role of structural transitions is examined. We find that the role of Ti-O6 polyhedral tilting (such as observed in CaTiO3) is small in the sense that a single well-defined general trend exists in perovskites with a wide range of tilting angles, although there is suggestion that cubic perovskites have slightly higher bulk modulus than orthorhombic perovskites. In contrast, cation-anion displacement that changes crystal symmetry from cubic to tetragonal in BaTiO3 has very large effects on elasticity. This distortion significantly reduces the bulk modulus (but not much the shear modulus) and results in an unusually large pressure derivative of bulk modulus (dK/dP～10). A large change in elasticity in BaTiO3 associated with the structural transition (without a significant volume change) is a clear example of the breakdown of the Birch's law between densities and elastic wave velocities.  相似文献   

19.
P-V-T data of MgSiO3 orthoenstatite have been measured by single-crystal X-ray diffraction at simultaneous high pressures (in excess of 4.5 GPa) and temperatures (up to 1000 K). The new P-V-T data of the orthoenstatite, together with previous compression data and thermal expansion data, are described by a modified Birch-Murnaghan equation of state for diverse temperatures. The fitted thermoelastic parameters for MgSiO3 orthoenstatite are: thermal expansion ?α/?P with values of a=2.86(29)×10-5 K-1 and b=0.72(16)×10-8 K-2; isothermal bulk modulus K T o =102.8(2) GPa; pressure derivative of bulk modulus K′=?K/?P=10.2(1.2); and temperature derivative of bulk modulus K=?K/?T=-0.037(5) GPa/K. The derived thermal Grüneisen parameter is γ th=1.05 for ambient conditions; Anderson-Grüneisen parameter is δ T o =11.6, and the pressure derivative of thermal expansion is ?α/?P=-3.5×10-6K-1 GPa-1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at two constant pressures of 1.5 GPa and 4.0 GPa are calculated. The resulting pressure dependence of thermal expansion is Δα/ΔP=-3.2(1)× 10-6 K-1 GPa-1. The significantly large values of K′, K, δ T and ?α/?P indicate that compression/expansion of MgSiO3 orthoenstatite is very sensitive to changes of pressure and temperature.  相似文献   

20.
The molar volumes and bulk moduli of CaSiO3 perovskite are calculated in the temperature range from 300 to 2,800 K and the pressure range from 0 to 143 GPa using molecular dynamics simulations that employ the breathing shell model for oxygen and the quantum correction in addition to the conventional pairwise interatomic potential models. The performance of five equations of state, i.e., the Keane, the generalized-Rydberg, the Holzapfel, the Stacey–Rydberg, and the third-order Birch–Murnaghan equations of state are examined using these data. The third-order Birch–Murnaghan equation of state is found to have a clear tendency to overestimate the bulk modulus at very high pressures. The Stacey–Rydberg equation of state degrades slightly at very high pressures along the low-temperature isotherms. In comparison, the Keane and the Holzapfel equations of state remain accurate in the whole temperature and pressure range considered in the present study. K 0′ derived from the Holzapfel equation of state also agrees best with that calculated independently from molecular dynamics simulations. The adiabatic bulk moduli of CaSiO3 perovskite along lower mantle geotherms are further calculated using the Keane and the Mie-Grüneisen–Debye equations of state. They are found to be constantly higher than those of the PREM by ~5%, and also very similar to those of the MgSiO3 perovskite. Our results support the view that CaSiO3 perovskite remains invisible in the Earth’s lower mantle.  相似文献   

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