Single-crystal hydrostatic compression of synthetic pyrope, almandine, spessartine, grossular and andradite garnets at high pressures

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     

Viscosity of albite melt at high pressure and high temperature

 The viscosity of albite (NaAlSi₃O₈) melt was measured at high pressure by the in situ falling-sphere method using a high-resolution X-ray CCD camera and a large-volume multianvil apparatus installed at SPring-8. This system enabled us to conduct in situ viscosity measurements more accurately than that using the conventional technique at pressures of up to several gigapascals and viscosity in the order of 10⁰ Pa s. The viscosity of albite melt is 5.8 Pa s at 2.6 GPa and 2.2 Pa s at 5.3 GPa and 1973 K. Experiments at 1873 and 1973 K show that the decrease in viscosity continues to 5.3 GPa. The activation energy for viscosity is estimated to be 316(8) kJ mol⁻¹ at 3.3 GPa. Molecular dynamics simulations suggest that a gradual decrease in viscosity of albite melt at high pressure may be explained by structural changes such as an increase in the coordination number of aluminum in the melt. Received: 6 January 2001 / Accepted: 27 August 2001     

Elasticity of CaSnO3 perovskite

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 ų, 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.     

Atomistic simulation of the structure and elastic properties of pyrite (FeS2) as a function of pressure

Interatomic potential parameters have been derived at simulated temperatures of 0 K and 300 K to model pyrite FeS₂. The predicted pyrite structures are within 1% of those determined experimentally, while the calculated bulk modulus is within 7%. The model is also able to simulate the properties of marcasite, even though no data for this phase were included in the fitting procedure. There is almost no difference in results obtained for pyrite using the two potential sets; however, when used to model FeS₂ marcasite, the potential fitted at 0 K performs better. The potentials have also been used to study the high-pressure behaviour of pyrite up to 44 GPa. The calculated equation of state gives good agreement with experiment and shows that the Fe–S bonds shorten more rapidly that the S–S dimer bonds. The behaviour of marcasite at high pressure is found to be similar to that of pyrite.     

高温高压下黄铁矿热力学性质的第一性原理研究

黄铁矿是自然界中分布最为广泛的硫化物矿物,同时也是重要的造矿矿物,在金属矿床、沉积岩、变质岩、花岗岩、基性-超基性岩浆岩、以及地幔岩中都有大量出现。因此,研究黄铁矿在不同温度压力下的热力学性质可以为深入探讨与黄铁矿有关的成岩、成矿、成藏问题提供有用的矿物学依据。本文利用基于密度泛函微扰理论的第一性原理方法,采用准谐近似计算了黄铁矿在高温高压下的热力学性质。我们计算的黄铁矿的晶格常数、零压下的体积模量及其对压力的导数与前人的实验及理论计算结果吻合得很好,零压下等压热容和熵随温度的变化与实验结果有很好的一致性。尤其是,本文计算了直至2500K、100GPa的高温高压下黄铁矿的等温体积模量、热膨胀系数、热容和熵等热力学性质。这为在有硫参与的情况下,人们开展下地壳-岩石圈地幔深度的地球动力学模拟和建立地球物理模型提供了有用的信息。     

Phase transition of synthetic zinc ferrite spinel (ZnFe2O4) at high pressure, from synchrotron X-ray powder diffraction

 Synthetic Zn-ferrite (ideally ZnFe₂O₄; mineral name: franklinite) was studied up to 37 GPa, by X-ray powder diffraction at ESRF (Grenoble, France), on the ID9 beamline; high pressure was achieved by means of a DAC. The P-V equation of state of franklinite was investigated using the Birch-Murnaghan function, and the elastic properties thus inferred [K₀ = 166.4(±3.0) GPa K₀ ^′ = 9.3(±0.6) K₀ ^″ = −0.22 GPa⁻¹] are compared with earlier determinations for MgAl-spinel and magnetite. The structural behaviour of Zn-ferrite as a function of pressure was studied by Rietveld refinements, and interpreted in the light of a phase transition from spinel to either CaTi₂O₄- or MnFe₂O₄-like structure; this transformation occurs above 24 GPa. Received: 15 March 1999 / Accepted: 22 April 2000     

Ab initio elasticity of FeS2 pyrite from 0 to 135 GPa

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.     

Study on Al2O3 content and phase stability of aluminous-CaSiO3 perovskite at high pressure and temperature

 In order to clarify Al₂O₃ content and phase stability of aluminous CaSiO₃-perovskite, high-pressure and high-temperature transformations of Ca₃Al₂Si₃O₁₂ garnet (grossular) were studied using a MA8-type high-pressure apparatus combined with synchrotron radiation. Recovered samples were examined by analytical transmission electron microscopy. At pressures of 23–25 GPa and temperatures of 1000–1600 K, grossular garnet decomposed into a mixture of aluminum-bearing Ca-perovskite and corundum, although a metastable perovskite with grossular composition was formed when the heating duration was not long enough at 1000 K. On release of pressure, this aluminum-bearing CaSiO₃-perovskite transformed to the “LiNbO₃-type phase” and/or amorphous phase depending on its Al₂O₃ content. The structure of this LiNbO₃-type phase is very similar to that of LiNbO₃ but is not identical. CaSiO₃-perovskite with 8 to 25 mol% Al₂O₃ was quenched to alternating lamellae of amorphous layer and LiNbO₃-type phase. On the other hand, a quenched product from CaSiO₃-perovskite with less than 6 mol% consisted only of amorphous phase. Most of the inconsistencies amongst previous studies could be explained by the formation of perovskite with grossular composition, amorphous phase, and the LiNbO₃-type phase. Received: 11 April 2001 / Accepted: 5 July 2002     

Hydrogen bonding interactions in phase A [Mg7Si2O8(OH)6] at ambient and high pressure

Neutron powder diffraction data of phase A (Mg₇Si₂O₈(OH)₆) were collected at ambient pressure and 3.2?GPa (calculated from the compressibility of phase A) from the deuterated compound, and the structure was refined using the Rietveld method. The derived crystal structure implies that hydrogen atoms occupy two distinct sites in phase A, both forming hydrogen bonds of different lengths with the same oxygen atom. This picture is supported by IR spectra, which exhibit two absorption bands at 3400 and 3513?cm^?1 corresponding to OH stretching vibrations, and proton NMR spectra, which display two peaks with equal intensities and isotropic chemical shifts of 3.7 and 5?ppm. The D-D distance [D(1)-D(2) distance] at ambient pressure was found to be 2.09?±?0.02?Å from the neutron diffraction data and 2.09?±?0.05?Å from the NMR spectra. At 3.2?GPa, there is no statistically significant increase in the O-D interatomic distance while the hydrogen bonding interaction D···O appears to increase for one of the hydrogen sites, D(1), which has the stronger hydrogen bonding interaction compared with the other hydrogen, D(2), at ambient pressure. The O-D bond valences, determined indirectly from the D···O distances were 0.86 and 0.91 at ambient pressure, and 0.83 and 0.90?at 3.2?GPa, for D(1) and D(2), respectively.     

Clinopyroxene-perovskite phase transition of FeGeO3 under high pressure and room temperature

In order to confirm the possible existence of FeGeO₃ perovskite, we have performed in situ X-ray diffraction measurements of FeGeO₃ clinopyroxene at pressures up to 40 GPa at room temperature. The transition of FeGeO₃ clinopyroxene into orthorhombic perovskite is observed at about 33GPa. The cell parameters of FeGeO₃ perovskite are a=4.93(2) Å, b=5.06(6) Å, c=6.66(3) Å and V=166(3) ų at 40 GPa. On release of pressure, the perovskite phase transformed into lithium niobate structure. The previously reported decomposition process of clino-pyroxene into Fe₂GeO₄ (spinel)+GeO₂ (rutile) or FeO (wüstite) +GeO₂ (rutile) was not observed. This shows that the transition of pyroxene to perovskite is kinetically accessible compared to the decomposition processes under low-temperature pressurization.     

Structural and vibrational behaviour of fluorapatite with pressure. Part II: in situ micro-Raman spectroscopic investigation

 High-pressure Raman investigations were carried out on a synthetic fluorapatite up to about 7 GPa to analyse the behaviour of the phosphate group's internal modes and of its lattice modes. The Raman frequencies of all modes increased with pressure and a trend toward reduced splitting was observed for the PO₄-stretching modes [(ν_3a(A_g) and ν_3b(A_g); ν_3a(E_2g) and ν_3b(E_2g)] and the PO₄ out-of-plane bending modes [ν_4a(A_g) and ν_4b(A_g)]. The pressure coefficients of phosphate modes ranged from 0.0047 to 0.0052 GPa⁻¹ for ν₃, from 0.0025 to 0.0044 GPa⁻¹ for ν₄, from 0.0056 to 0.0086 GPa⁻¹ for ν₂ and 0.0046 for ν₁ GPa⁻¹, while the pressure coefficients of lattice modes ranged from 0.0106 to 0.0278 GPa⁻¹. The corresponding Grüneisen parameters varied from 0.437 to 0.474, 0.428, 0.232 to 0.409 and 0.521 to 0.800 for phosphate modes ν₃, ν₁, ν₄, ν₂, respectively, and from 0.99 to 2.59 for lattice modes. The vibrational behaviour was interpreted in view of the high-pressure structural refinement performed on the same crystal under the same experimental conditions. The reduced splitting may thus be linked to the reduced distortion of the environment around the phosphate tetrahedron rather than to the decrease of the tetrahedral distortion itself. Moreover, the amount of calcium polyhedral compression, which is about three times the compression of phosphate tetrahedra, may explain the different Grüneisen parameters. Received: 25 April 2000 / Accepted: 20 December 2000     

In situ X-ray observations of the decomposition of brucite and the graphite–diamond conversion in aqueous fluid at high pressure and temperature

 An experimental technique to make real-time observations at high pressure and temperature of the diamond-forming process in candidate material of mantle fluids as a catalyst has been established for the first time. In situ X-ray diffraction experiments using synchrotron radiation have been performed upon a mixture of brucite [Mg(OH)₂] and graphite as starting material. Brucite decomposes into periclase (MgO) and H₂O at 3.6 GPa and 1050 °C while no periclase is formed after the decomposition of brucite at 6.2 GPa and 1150 °C, indicating that the solubility of the MgO component in H₂O greatly increases with increasing pressure. The conversion of graphite to diamond in aqueous fluid has been observed at 7.7 GPa and 1835 °C. Time-dependent X-ray diffraction profiles for this transformation have been successfully obtained. Received: 17 July 2001 / Accepted: 18 February 2002     

Equation of state of hexagonal aluminous phase in basaltic composition to 63 GPa at 300 K

A laser-heated diamond-anvil cell that is capable of operating up to a pressure of 63 GPa, with X-ray diffraction facilities using a synchrotron radiation source at the SPring-8, has been developed to observe the compressibility of a hexagonal aluminous phase, [K_0.15Na_1.66Ca_0.11Mg_1.29Fe²⁺ _0.86Al_3.13Ti_0.09Si_1.98] _Σ9.27O₁₂. The hexagonal aluminous phase is a potassium host mineral from the subducted oceanic crust in the Earth's lower mantle. A sample was heated using a YAG laser at each pressure increment to relax the deviatoric stress in the sample. X-ray diffraction measurements were carried out at 300 K using an angle-dispersive technique. Pressure was measured using an internal platinum pressure calibrant. The observed unit-cell volumes were used to obtain a third-order Birch–Murnaghan equation of state: unit-cell volume V _o=185.94(±16) ų, density ρ _o=4.145 g/cm³, and bulk modulus K _o=198(±3) GPa when the first pressure is derivative of the bulk modulus K ^′ _o is fixed to 4. The density of hexagonal aluminous phase is lower than that of coexisting Mg-perovskite in the subducted oceanic crust.     

非饱和土抗剪强度及土压力统一解

基于统一强度理论和非饱和土双应力状态变量抗剪强度,合理考虑中间主应力效应,建立了非饱和土双应力状态变量抗剪强度统一解,并与文献试验结果进行比较,验证了公式的正确性;进而考虑基质吸力的不同分布,得到非饱和土主动土压力和被动土压力统一解,克服了朗肯土压力的不足,并得出中间主应力和基质吸力对土压力的影响特性。研究结果表明,主动土压力随着统一强度理论参数和基质吸力的增大而不断减小,被动土压力则相反;当基质吸力沿深度线性减小时,主动土压力和被动土压力都不像基质吸力沿深度为常数时变化得那么快。该结果为非饱和土抗剪强度和土压力分析提供了理论依据,对工程设计有一定的参考价值。     

卸荷状态下粘性土强度特性试验研究

通过大量的室内抗剪强度试验，提出了卸荷比、临界卸荷比、极限卸荷比和强度残留率概念。用卸荷比来衡量应力水平的变化，以探讨粘性土在卸荷状态下强度变化规律以及估算卸荷影响区的范围和影响区内强度的衰减规律，对基坑等卸荷类工程的设计和施工具有一定的指导意义。     

Plastic deformation of wadsleyite: II. High-pressure deformation in shear

 We have studied the dislocation microstructures that develop in (Mg_0.9Fe_0.1)₂SiO₄ wadsleyite deformed by simple shear at high pressure. The experiments were performed in a multianvil apparatus with the shear assembly designed by Karato and Rubie (1997). The samples were synthesized in a separate experiment from high-purity oxides. The deformation experiments were carried out at 14 GPa and 1300 °C with time durations ranging from 1 to 8 h leading to plastic shear strains of 60 and 73%, respectively. The microstructures investigated by transmission electron microscopy (TEM) show that dislocation glide is activated under these conditions over the whole experimental time. The easy slip systems at 1300 °C involve 1/2<111> dislocations gliding in {101} as well as [100] dislocations gliding in (010) and {011}. Received: 15 July 2002 / Accepted: 14 February 2003 Acknowledgements High-pressure experiments were performed at the Bayerisches Geoinstitut under the EU IHP — Access to Research Infrastructures Programme (Contract no. HPRI-1999-CT-00004 to D.C. Rubie). The quality of the preparation of the TEM specimens by H. Schultze is greatly appreciated.     

A physical basis for Pauling's definition of bond strength

 The average strength, s, of the bonded interactions comprising a cation containing oxide anion coordination polyhedron and the value of the electron density, ρ(r _c ), at the bond-critical points are inversely correlated with bond length. In each case, the observed bond lengths, R, were modeled with power-law expressions defined in terms of s/r and ρ(r _c )/r, respectively, where r is the Periodic Table row number of the cation involved in the bonded interaction. On the basis of the close connection between bond strength and the value of the electron density at the bond-critical point, we conclude that bond strength is a direct measure of bond type; the greater its value, the greater the localization of electron density in the binding region and the greater the shared–electron covalent character of the bonded interaction. Received: 15 October 2002 / Accepted: 17 February 2003 Present address:G. V. Gibbs in care of M. Spackman Department of Chemistry, University of New England, Armidale 2351, Australia Acknowledgements The NSF is thanked for supporting this study with grant EAR–9627458. The paper was written while GVG was a Visiting NSF Scholar at The University of Arizona. The faculty and graduate students of the Department of Geosciences and Bob Downs and Marelina Stimpf in particular are thanked for making the visit great fun.     

高应力下剪切速率对砂土抗剪强度影响研究

应用DRS-1型高压直剪仪,进行了16组法向应力水平、5种剪切速率条件下福建标准砂的抗剪强度试验,试验结果表明,高应力下砂土的抗剪强度受法向应力和剪切速率的共同影响。法向应力和剪切速率通过影响颗粒破碎和颗粒重排列程度等试样的细观参数,决定了砂土宏观上抗剪强度的发挥。当法向应力较小时,砂土抗剪强度与剪切速率基本无关;但是当法向应力较大时,较快剪切速率条件下的砂土抗剪强度变小,且其摩尔强度包线出现了“下弯-上扬”循环波动,因此不可以忽略剪切速率对砂土抗剪强度的影响。     

Iron-water reaction at high pressure and temperature, and hydrogen transport into the core

We observed a direct reaction of metallic iron with water to form iron hydride and iron oxide, 3Fe + H₂O–>2FeH_x + FeO, at pressures from 6 GPa to 84 GPa and temperatures above 1,000 K in diamond anvil cell (DAC). Iron hydride is dhcpFeH_x or -FeH_x, and iron oxide has the rhombohedral or B1 structure at pressures at least up to 37 GPa. The formation of an assembly composed of dhcpFeH_x and FeO with the B8 structure was observed at 84 GPa. In primordial Earth, water formed by dehydration of the low temperature primitive materials reacts with metallic iron in the high temperature component to form iron hydride FeH_x and iron oxide FeO. The former would be incorporated in the iron forming the core. Thus hydrogen could be an important element of the Earths core. This reaction would be essential for transport of hydrogen into the core in the accretion stage of the Earth.     

Role of pressure and temperature in inclusion-induced shear localization: An analogue experimental approach

Using analogue model experiments this study investigates the effects of lithostatic pressure and temperature in controlling the pattern of shear localization around rigid inclusions. Compression experiments were conducted on polymethylmethaacrylate (PMMA) by varying confining pressure (P = 30–70 MPa), homologous temperature (T_o = 0.67–0.80 corresponding to room temperature – 80 °C) and axial strain (yield – 15%) in a triaxial setup. Mechanical data showed temperature has a greater influence on the bulk yield strength and steady-state flow of the analogue material than confining pressure. Increasing confining pressures multiply the shear bands in number, and their overall pattern becomes progressively more complex, leading to composite band structures. On the other hand, under ambient pressure increasing temperature results in a transition from incipient high-strain zones to shear bands with sharp boundaries. Further increase in temperature switches the mode of shear localization, sharp to diffuse type. We finally show the inclusion-induced shear localization as a two-stage process, and provide a micro-mechanical explanation for the P-T dependent shear band patterns, attributed to three mechanically distinct domains of the inclusion-matrix interface: compression, extensional and shear localization.