Thermal diffusivity of garnets at high temperature

Thermal diffusivity (D) of garnets with diverse chemical compositions was measured using the laser-flash technique, which is accurate (±2%) and isolates the lattice component from direct radiative transfer. Temperatures ranged from ~290 to ~1,600 K (unless limited by melting). Seven synthetic (e.g., YAG, GGG) and 15 natural garnets with two types of ionic substitution [Ca₃(Fe,Al)₂Si₃O₁₂ and (Mg,Fe,Ca)₃Al₂Si₃O₁₂] and varying amounts of OH^- were examined. Cation substitution or hydroxyl incorporation lowers D from end-member values. Thermal diffusivity is constant once the temperature (T) exceeds a critical value (T _sat) of ~1,100 to 1,500 K. From ~290 K to T _sat, the measurements are best represented by 1/D=A+BT+CT ² where A, B, and C are constants. These constants vary little among diverse chemical compositions, suggesting that the oxygen sublattice controls heat transport. Higher order terms are needed only when T _sat is low, such as Ant Hill garnet wherein 1/D=0.049403+0.0032299T−2.3992T ²×10⁻⁶+6.0168T ³×10⁻¹⁰(1/D in s/mm²; T in K). The mean free path (λ, computed from D and sound velocities) is slightly larger than the lattice parameter above T _sat, in accord with phonon–phonon interactions requiring non-localized modes. At most temperatures, λ is nm-sized. Large values of λ are obtained by extrapolation to a few Kelvins, suggesting that boundary scattering can only be important at extremely cold temperatures. The observed behavior with T and chemical composition is consistent with the damped harmonic oscillator model. Phonon transport is best represented by inverse thermal diffusivity wherein 1/D goes as T ⁿ where n is between 1 and 3 up to ~200 K, depends on a quadratic or cubic polynomial at moderate T, but is constant above T _sat. The predicted and observed temperature response of 1/D mimics the well-known form for heat capacity, in that acoustic modes control heat transport near cryogenic temperatures, optic phonons dominate above ambient temperature, and a limit analogous to that of Dulong and Petit is reached at very high temperature, due to full population of discrete phonon states.     

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     

Electrical conductivity of K-feldspar at high temperature and high pressure

Electrical conductivity measurements on dry polycrystalline K-feldspar were performed at 1.0 to 3.0 GPa and 873 to 1,173 K with a multi-anvil high-pressure apparatus and the Solartron-1260 Impedance/Gain Phase Analyzer in the frequency range of 10^?1 to 10⁶ Hz. At each temperature the complex impedance displays a perfect semi-circular arc that represents the grain-interior conduction. Under the experimental conditions, electrical conductivity exponentially increases with increasing temperature and slightly decreases with increasing pressure; however, the effect of pressure on the conductivity is less pronounced than that of temperature. The activation enthalpy decreases slightly from 0.99 to 1.02 eV with increasing pressure, and the activation energy and activation volume for K-feldspar are 0.98 eV and 1.46?±?0.17 cm³/mol, respectively. According to these Arrhenius parameters, ionic conduction is proposed to be the dominant conduction mechanism in K-feldspar at high temperatures and pressures, and potassium ions are the charge carriers transporting by an interstitial mechanism. The diffusion coefficient of potassium at high temperatures was calculated from our conductivity data on K-feldspar using Nernst–Einstein equation, and the results were compared with the previous experimental results.     

Thermal equation of state of synthetic orthoferrosilite at lunar pressures and temperatures

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, (Mg_1?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.     

X-ray diffraction study of magnesite at high pressure and high temperature

 P–V–T measurements on magnesite MgCO₃ have been carried out at high pressure and high temperature up to 8.6 GPa and 1285 K, using a DIA-type, cubic-anvil apparatus (SAM-85) in conjunction with in situ synchrotron X-ray powder diffraction. Precise volumes are obtained by the use of data collected above 873 K on heating and in the entire cooling cycle to minimize non-hydrostatic stress. From these data, the equation-of-state parameters are derived from various approaches based on the Birch-Murnaghan equation of state and on the relevant thermodynamic relations. With K′₀ fixed at 4, we obtain K₀=103(1) GPa, α(K⁻¹)=3.15(17)×10⁻⁵ +2.32(28)×10⁻⁸ T, (∂K_T/∂T)_P=−0.021(2) GPaK⁻¹, (dα/∂P)_T=−1.81×10⁻⁶ GPa⁻¹K⁻¹ and (∂K_T/∂T)_V= −0.007(1) GPaK⁻¹; whereas the third-order Birch-Murnaghan equation of state with K′₀ as an adjustable parameter yields the following values: K₀=108(3) GPa, K′₀=2.33(94), α(K⁻¹)=3.08(16)×10⁻⁵+2.05(27) ×10⁻⁸ T, (∂K_T/∂T)_P=−0.017(1) GPaK⁻¹, (dα/∂P)_T= −1.41×10⁻⁶ GPa⁻¹K⁻¹ and (∂K_T/∂T)_V=−0.008(1) GPaK⁻¹. Within the investigated P–T range, thermal pressure for magnesite increases linearly with temperature and is pressure (or volume) dependent. The present measurements of room-temperature bulk modulus, of its pressure derivative, and of the extrapolated zero-pressure volumes at high temperatures, are in agreement with previous single-crystal study and ultrasonic measurements, whereas (∂K_T/∂T)_P, (∂α/∂P)_T and (∂K_T/∂T)_V are determined for the first time in this compound. Using this new equation of state, thermodynamic calculations for the reactions (1) magnesite=periclase+CO₂ and (2) magnesite+enstatite=forsterite+CO₂ are consistent with existing experimental phase equilibrium data. Received September 28, 1995/Revised, accepted May 22, 1996     

The Electrical Conductivity of Gabbro at High Temperature and High Pressure

The electric conductivity of gabbro has been measured at 1.0 - 2.0 GPa and 320-700℃, and the conduction mechanism has been analyzed in terms of the impedance spectra.Experimental results indicated that the electric conductivity depends on the frequency of alternative current. Impedance arcs representing the conduction mechanism of grain interiors are displayed in the complex impedance plane, and the mechanism is dominated at high pressure.These arcs occur over the range of 102 - k× 105 Hz (k is the positive integer from 1 to 9). On the basis of our results and previous work, it is concluded that gabbro cannot form any high conductivity layer (HCL) in the middle-lower crust.     

Friction in faulted rock at high temperature and pressure

Two hundred observations of frictional behavior of seven low-porosity silicate rocks were made at temperatures to 700°C and pressures from 2.5 to 6 kbar. For all rocks except one, peridotite, stick-slip occurred at low temperature and gave way to stable sliding at some high temperature, different for each rock. These differences could be related to the presence or absence of minerals such as amphibole, mica, or serpentine. Up to some temperature, depending on rock type, the friction stress was relatively unaffected by temperature. The shear stress decreased at higher temperature, and in some cases such decrease was related to the coincidence of fracture and friction strength. While somewhat dependent on rock type, the friction stress for the seven rocks studied was about the same, within 10–15%. Up to 265°C, water had little effect on the frictional behavior of faulted granite at 3 kbar effective pressure. The frictional stresses measured in the laboratory were significantly higher than estimated for natural faults. This difference could be accounted for by high pore pressure or weak alteration materials in the natural fault zone.     

Thermodynamic properties of San Carlos olivine at high temperature and high pressure

In this study, the thermal expansion and heat capacity of San Carlos olivine under high temperature and high pressure are reported. Combining accurate sound velocity data under different P–T conditions with density and heat capacity data at ambient pressure, the density, adiabatic bulk modulus, shear modulus, and most importantly, thermal expansion and heat capacity, of San Carlos are extracted to 14 GPa by a numerical procedure using classic thermodynamic relationships. These data are in agreement with published findings. To estimate the temperature gradient in the upper mantle, we also report the fitting equations of thermal expansion and heat capacity of San Carlos olivine as a function of both temperature and pressure to the P–T condition of the 410 km discontinuity, which provide the thermodynamic properties with increasing depth in the Earth’s interior.     

Thermoelasticity and stability of natural epidote at high pressure and high temperature:Implications for water transport during cold slab subduction

Epidote is a typical hydrous mineral in subduction zones.Here,we report a synchrotron-based single-crystal X-ray diffraction(XRD)study of natural epidote[Ca1.97Al2.15Fe0.84(SiO4)(Si2O7)O(OH)]under simultaneously high pressure-temperature(high P-T)conditions to~17.7 GPa and 700 K.No phase transition occurs over this P-T range.Using the third-order Birch-Murnaghan equation of state(EoS),we fitted the pressure-volume-temperature(P-V-T)data and obtained the zero-pressure bulk modulus K₀=138(2)GPa,its pressure derivative K'₀=3.0(3),the temperature derivative of the bulk modulus((?K/?T)P=-0.004(1)GPa/K),and the thermal expansion coefficient at 300 K(α₀=3.8(5)×10^-5K^-1),as the zero-pressure unit-cell volume V₀was fixed at 465.2(2)?³(obtained by a single-crystal XRD experiment at ambient conditions).This study reveals that the bulk moduli of epidote show nonlinear compositional dependence.By discussing the stabilization of epidote and comparing its density with those of other hydrous minerals,we find that epidote,as a significant water transporter in subduction zones,may maintain a metastable state to~14 GPa along the coldest subducting slab geotherm and promote slab subduction into the upper mantle while favoring slab stagnation above the 410 km discontinuity.Furthermore,the water released from epidote near 410 km may potentially affect the properties of the 410 km seismic discontinuity.     

高温高压下石膏脱水相变的原位拉曼光谱研究

本文运用激光拉曼光谱仪,利用水热金刚石压腔装置对高温高压条件下石膏-水体系中的石膏脱水相变进行拉曼光谱研究.在压力0.1 MPa～837.9 MPa和温度16～200 ℃条件下通过系列实验对相变的过程进行了原位光谱分析.与人们已知的无水条件下石膏分两步脱水的过程不同,高压下石膏在饱和水环境下倾向于一次性的脱去所有结晶水而形成无水石膏,实验中没有观察到半水石膏的出现.通过实验数据得到石膏和无水石膏的转折温度和平衡压力间的关系式为P(MPa)=19.56·T(℃)-2926.5.     

Reaction of forsterite with hydrogen molecules at high pressure and temperature

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

Carrara大理岩高温高压变形实验研究

利用高精度的Paterson高温高压流变仪对Carrara大理岩在高温(873~1173K)高压(~300MPa)以及约10-6~10-3s-1应变速率下进行了三轴压缩变形实验。结果表明,在等应变速率条件下,其强度随着温度的升高而降低;在等温和等压条件下,其强度随着应变速率的增加先快速增加而后缓慢增加。在应变速率对差应力的双对数投图中,我们发现随着温度的升高拟合直线的斜率减小,并且在873K和高应变速率时973K温度下Carrara大理岩的流变本构方程服从指数律变化关系;而在高温(1073K和1173K)和973K低应变速率条件下Carrara大理岩的应力指数n为5.3~7.7,且服从幂次律变化关系。因此,Carrara大理岩在本研究的实验条件下主要有两种变形机制,一种是用指数律表示的高应力变形机制;另一种是用幂次律表示的中等应力变形机制。     

Raman spectroscopy at high pressure and high temperature. Phase transitions and thermodynamic properties of minerals

An outline of recent developments in Raman spectroscopy at high pressure, high temperature and combined high pressure and high temperature is presented. The instrumental and technical aspects of Raman spectroscopy, and coupling of diamond anvil cells and miniature furnaces to Raman microspectrometers are discussed. Some potential pitfalls, such as the thermal pressure in laser heated diamond anvil cells or the thermal radiation during high-temperature measurements, are presented. Special emphasis is given on processing of high-temperature Raman data. New recently discovered phase transformations in the SiO₂ system (quartz→ quartz II, pressure-induced amorphization of quartz) and structural changes in SiO₂ glass and melt are used to infer the capability of in-situ Raman spectroscopy for determining the microscopic behaviour of minerals, melts and glasses under extreme pressure and temperature conditions. Finally, it is shown how vibrational mode anharmonicity can be obtained from the pressure- and temperature-induced shifts of Raman modes. This anharmonicity can be introduced into the vibrational modeling of the thermodynamic properties (entropy and equation of state) of minerals. The example of calcite is briefly discussed.     

高温高压下叶蜡石脱水电学性质的阻抗谱分析

在1.0、2 .0GPa和873～12 2 3K的温压条件下,借助于12 6 0阻抗增益相位分析仪测定了叶蜡石的电导率,并用阻抗谱原理分析了其微观导电机制。实验结果表明:样品的电导率对频率具有很强的依赖性;电阻率随着温度的升高而减小,电导率随着温度升高而增大,logσ与1/T之间符合Arrenhius线性关系;叶蜡石在1.0GPa和2 .0GPa的压力下脱水温度分别为10 74K和110 1K。根据本次获得的电导率实验结果并结合前人对滑石族所做的工作,得出了与前人不同的结论:滑石族矿物脱水电导率曲线出现了转折点。     

Adsorption behavior of CO2 in magnesite micro-pores at high temperature and pressure

The fluid inclusions in mantle rocks and melt indicated that a large amount of CO₂fluid exists in the deep earth,which is of great significance for understanding the deep carbon cycle and the composition of mantle.However,it was also suggested that carbonate minerals were likely to be the main host of mantle carbon.At the same time,the distribution and behavior of carbon in the mantle still remain a puzzle.In this paper,the adsorption behavior and occurrence characteristics of supercritical CO₂in magnesite(MgCO3)pores were studied by the Grand Canonical Monte Carlo method(GCMC)under the different conditions of CO₂pressures(0–100 MPa),temperatures(350–1500 K)and the pore sizes(7.5–30?).The simulated results showed that the adsorption of CO₂in magnesite was a physical adsorption,which was mainly controlled by the intermolecular force.The gas adsorption became more stable when the adsorption site shifted from the high energy site to the low energy site with increasing pressure(P)and decreasing temperature(T)and pore size.At the same time,the variations of excess adsorption amounts of CO₂in the pores of magnesite(Nexcess)under the different conditions were quantitatively calculated.It was found that the Nexcess decreased with increasing T,but increased with increasing P and pore size.The results favor understanding the CO₂migration,seismic precursor observations,and heat transfer process in the deep earth.     

Quasi-harmonic computer simulations of the structural behaviour and EOS of pyrope at high pressure and high temperature

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

Barium partitioning between alkali feldspar and silicate liquid at high temperature and pressure

Barium partitioning between alkali feldspar and a natural trachyte liquid, enriched with barium, has been determined as a function of pressure and temperature from 10 to 25 kb and 900°–1100° C. Both long duration experiments and a re-equilibration experiment suggest close approach to equilibrium. Partition coefficients (D _Ba) decrease as both temperature and pressure increase (e.g., D _Ba changes from 8.71 at 10 kb, 900° C to 1.48 at 25 kb, 1100° C). Water activity also controls the barium partitioning with a marked decrease in D _Ba ^af/liq for addition of less than 0.8 wt% H₂O, but with no apparent additional effect for higher water contents in the bulk composition (e.g., from 0.8–4.2 wt% H₂O). The composition of alkali feldspar also has a significant effect on D _Ba ^af/liq , but the data obtained do not allow derivation of a complete D-Or relationship. These new data suggest that Henry's Law is obeyed for most of the barium concentrations examined, and the limit of Henry's Law behaviour for barium in alkali feldspar is as high as 6 wt% BaO in alkali feldspar and 1.2 wt% BaO in the melt, similar to the results of Long (1978). The experimental results broadly overlap with natural data for D _Ba, determined from coexisting alkali feldspar phenocrysts and glass (or groundmass).     

Thermal equation of state of iron and Fe0.91Si0.09

We have carried out an in situ synchrotron X-ray diffraction study on iron and an iron-silicon alloy Fe_0.91Si_0.09 at simultaneously high pressure and temperature. Unit-cell volumes, measured up to 8.9 GPa and 773 K on the bcc phases of iron and Fe_0.91Si_0.09, are analyzed using the Birch-Murnaghan equation of state and thermal pressure approach of Anderson. Equation of state parameters on iron are found to be in agreement with results of previous studies. For both iron and Fe_0.91Si_0.09, thermal pressures show strong dependence on volume; the (∂K_T/∂T)_V values are considerably larger than those previously reported for other solids. The present results, in combination with our previous results on ɛ-FeSi, suggest a small dependency of the room-temperature bulk modulus upon the silicon content, less than 0.3 GPa for 1 wt.% silicon. We also find that substitution of silicon in iron would not appreciably change the thermoelastic properties of iron-rich Fe−Si alloys. If this behavior persists over large pressure and temperature ranges, the relative density contrast between iron and iron-rich Fe−Si alloys at conditions of the outer core of the Earth could be close to that measured at ambient conditions, i.e., 0.6% for 1 wt.% Si. Received: 13 January 1998 / Revised, accepted: 8 May 1998     

Oxygen isotope salt effects at high pressure and high temperature and the calibration of oxygen isotope geothermometers

The influence of NaCl, CaCl₂, and dissolved minerals on the oxygen isotope fractionation in mineral-water systems at high pressure and high temperature was studied experimentally. The salt effects of NaCl (up to 37 molal) and 5-molal CaCl₂ on the oxygen isotope fractionation between quartz and water and between calcite and water were measured at 5 and 15 kbar at temperatures from 300 to 750°C. CaCl₂ has a larger influence than NaCl on the isotopic fractionation between quartz and water. Although NaCl systematically changes the isotopic fractionation between quartz and water, it has no influence on the isotopic fractionation between calcite and water. This difference in the apparent oxygen isotope salt effects of NaCl must relate to the use of different minerals as reference phases. The term oxygen isotope salt effect is expanded here to encompass the effects of dissolved minerals on the fractionations between minerals and aqueous fluids. The oxygen isotope salt effects of dissolved quartz, calcite, and phlogopite at 15 kbar and 750°C were measured in the three-phase systems quartz-calcite-water and phlogopite-calcite-water. Under these conditions, the oxygen isotope salt effects of the three dissolved minerals range from ∼0.7 to 2.1‰. In both three-phase hydrothermal systems, the equilibrium fractionation factors between the pairs of minerals are the same as those obtained by anhydrous direct exchange between each pair of minerals, proving that the use of carbonate as exchange medium provides correct isotopic fractionations for a mineral pair.When the oxygen isotope salt effects of two minerals are different, the use of water as an indirect exchange medium will give erroneous fractionations between the two minerals. The isotope salt effect of a dissolved mineral is also the main reason for the observation that the experimentally calibrated oxygen isotope fractionations between a mineral and water are systematically 1.5 to 2‰ more positive than the results of theoretical calculations. Dissolved minerals greatly affect the isotopic fractionation in mineral-water systems at high pressure and high temperature. If the presence of a solute changes the solubility of a mineral, the real oxygen isotope salt effect of the solute at high pressure and high temperature cannot be correctly derived by using the mineral as reference phase.