P–V–T equations of state of MgO and thermodynamics

A simplest equation within the framework of the Mie-Grüneisen–Einstein approach is considered. Pressure estimation values are presented that are derived by conventional arithmetic and algebraic calculations as a function of temperature and volume. The equation under consideration complies with the Mie-Grüneisen–Debye model at high temperature. Different versions of an equation of state (EoS) of MgO proposed by Speziale et al. (J Geophys Res 106B:515–528, 2001) as a pressure standard at high temperatures are subject to analyses. In the literature, at least four versions of Speziale et al. EoS of MgO are discussed; the discrepancy between them reaching a few GPa at T > 2,000 K and P > 100 GPa. Our analyses of these equations suggest that the volume dependence of the Debye temperature is accepted arbitrarily and does not agree with the definition of the Grüneisen parameter, γ = −(∂lnΘ/∂lnV) _T . Pressure as a function of temperature and volume in the Mie-Grüneisen–Einstein approach or the Gao pressure calculator can be used to estimate true pressure at compression x = V/V ₀ < 1 with the Speziale et al. EoS of MgO.     

P–V–T equation of state of Ca3Al2Si3O12 grossular garnet

The thermoelastic parameters of synthetic Ca₃Al₂Si₃O₁₂ grossular garnet were examined in situ at high-pressure and high-temperature by energy dispersive X-ray diffraction, using a Kawai-type multi-anvil press apparatus coupled with synchrotron radiation. Measurements have been conducted at pressures up to 20 GPa and temperatures up to 1,650 K: this P, T range covered the entire high-P, T stability field of grossular garnet. The analysis of room temperature data yielded V _0,300 = 1,664 ± 2 ?³ and K ₀ = 166 ± 3 GPa for K^￠₀ K^{\prime}_{0} fixed to 4.0. Fitting of our P–V–T data by means of the high-temperature third order Birch–Murnaghan or the Mie–Grüneisen–Debye thermal equations of state, gives the thermoelastic parameters: (∂K _0,T /∂T) _P  = −0.019 ± 0.001 GPa K⁻¹ and α _0,T  = 2.62 ± 0.23 × 10⁻⁵ K⁻¹, or γ ₀ = 1.21 for fixed values q ₀ = 1.0 and θ ₀ = 823 (Isaak et al. Phys Chem Min19:106–120, 1992). From the comparison of fits from two different approaches, we propose to constrain the bulk modulus of grossular garnet and its pressure derivative to K _T0 = 166 GPa and K^￠_T0 K^{\prime}_{T0}  = 4.03–4.35. Present results are compared with previously determined thermoelastic properties of grossular-rich garnets.     

Melting of iron–silicon alloy up to the core–mantle boundary pressure: implications to the thermal structure of the Earth’s core

The melting temperature of Fe–18 wt% Si alloy was determined up to 119 GPa based on a change of laser heating efficiency and the texture of the recovered samples in the laser-heated diamond anvil cell experiments. We have also investigated the subsolidus phase relations of Fe–18 wt% Si alloy by the in-situ X-ray diffraction method and confirmed that the bcc phase is stable at least up to 57 GPa and high temperature. The melting curve of the alloy was fitted by the Simon’s equation, P(GPa)/a = (T _m(K)/T ₀) ^c , with parameters, T ₀ = 1,473 K, a = 3.5 ± 1.1 GPa, and c = 4.5 ± 0.4. The melting temperature of bcc Fe–18 wt% Si alloy is comparable with that of pure iron in the pressure range of this work. The melting temperature of Fe–18 wt% Si alloy is estimated to be 3,300–3,500 K at 135 GPa, and 4,000–4,200 K at around 330 GPa, which may provide the lower bound of the temperatures at the core–mantle boundary and the inner core–outer core boundary if the light element in the core is silicon.     

Equations of state of CaSiO3 Perovskite: a molecular dynamics study

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.     

Thermodynamic mixing properties of olivine derived from lattice vibrations

We use a lattice vibrational technique to derive thermophysical and thermochemical properties of fayalite, Fe₂SiO₄. This semi-empirical technique is based on an extension of Kieffer’s model to incorporate details of the phonon spectrum. It includes treatment of intrinsic anharmonicity and electronic effects based on crystal field theory. We extend it to predict thermodynamic mixing properties of olivine (Mg,Fe)₂SiO₄ solid solutions by using results of our previous work on the system MgO–SiO₂. Achieving this requires a relation between phonon frequency and composition and a composition relation for the energy of the static lattice. Directed by experimental Raman spectroscopic data for specific optic modes in magnesium–iron solid solutions of olivine and pyroxene we use an empirical relation for the composition dependence for phonon frequencies. We show that lattice vibrations have a large effect on the excess entropy and that the static lattice contribution and lattice vibrations have a large impact on excess enthalpy and excess Gibbs energy. Our model indicates that compositional effects in electronic and magnetic properties are negligible. The compositional variation the Néel temperature has a large impact on excess heat capacity for temperatures below 100 K.     

Pressure dependence of the lattice dynamics of diaspore, α-AlO(OH), from Raman spectroscopy and density functional perturbation theory

We have measured the pressure-induced change in the lattice dynamics of diaspore, α-AlO(OH), by in situ Raman spectroscopy up to 25 GPa. The spectra are evaluated by density functional perturbation theory-based atomistic model calculations. The assignment of calculated to experimentally observed Raman bands is based on the calculation of Raman intensities. We discuss the accuracy of the approach employed for these calculations and explain the relative magnitudes of mode Grüneisen parameters.     

Deformation of lower-mantle ferropericlase (Mg,Fe)O across the electronic spin transition

Recent high-pressure studies have shown that an electronic spin transition of iron in ferropericlase, an expected major phase of Earth’s lower mantle, results in changes in its properties, including density, incompressibility, radiative thermal conductivity, electrical conductivity, and sound velocities. To understand the rheology of ferropericlase across the spin transition, we have used in situ radial X-ray diffraction techniques to examine ferropericlase, (Mg_0.83,Fe_0.17)O, deformed non-hydrostatically in a diamond cell up to 81 GPa at room temperature. Compared with recent quasi-hydrostatic studies, the range of the spin transition is shifted by approximately 20 GPa as a result of the presence of large differential stress in the sample. We also observed a reduction in incompressibility and in the unit cell volume of 3% across the spin transition. Our radial X-ray diffraction results show that the {0 0 1} texture is the dominant lattice preferred orientation in ferropericlase across the spin transition and in the low-spin state. Viscoplastic self-consistent polycrystal plasticity simulations suggest that this preferred orientation pattern is produced by {1 1 0}<1–10> slip. Analyzing our radial X-ray diffraction patterns using lattice strain theory, we evaluated the lattice d-spacings of ferropericlase and Mo as a function of the ψ angle between the compression direction and the diffracting plane normal. These analyses give the ratio between the uniaxial stress component (t) and the shear modulus (G) under constant stress condition, which represents a proxy for the supported differential stress and elastic strength. This ratio in the mixed-spin and low-spin states is lower than what is expected from previous studies of high-spin ferropericlase, indicating that the spin transition results in a reduced differential stress and elastic strength along with the volume reduction. The influence of the spin transition on the differential stress and strength of ferropericlase is expected to be less dominant across the wide spin transition zone at high pressure–temperature conditions relevant to the lower mantle.     

Evaluation of EDI derived from the exponential evapotranspiration model for monitoring China’s surface drought

Drought has become the most severe natural disaster in many provinces of China. In this paper, evaporative drought index (EDI) has been used to monitor China’s surface dryness conditions based on the exponential evapotranspiration (ET) model and Hargreaves equation from JAXA-MODIS Insolation products, GEWEX, NCEP-2 and MODIS NDVI data. The exponential ET model based on the surface net radiation, vegetation index, mean air temperature and diurnal air temperature range (DTaR) has been developed to estimate surface ET of China and has been independently validated using ground-measured data collected from two sites (Arou and Miyun) in China, indicating that the bias varies from −5.96 to 5.02 W/m². The good agreement between daily estimated and ground-measured ET using ground observation data collected from all 22 sites further supports the validity of the exponential ET model for regional ET estimation. Moreover, EDI is closely correlated to the average soil moisture at 0–10 cm soil depth of the Yongning site with coefficient of determination of R ² = 0.52. The spatio-temporal patterns of monthly ET and EDI from April to September of 2004 over China are explored and the result indicates EDI is accordant with the precipitation by comparing the 15-day smoothed EDI with precipitation over six representative sites. The EDI based on the exponential ET model by integrating energy fluxes in response to soil moisture stress has demonstrated its validity for monitoring China’s surface drought events.     

Relation Between Normalized Axial Stress and Failure Strain in Heterogeneous Carbonate Rocks Exhibiting Large Axial Strains

A semi-analytical equation for the modeling of stress–strain relationship for heterogeneous carbonate rocks exhibiting large axial strains (ε_af > 1%) is formulated. The equation is derived by modifying the stress–strain model based on Haldane’s distribution proposed by Palchik (2006) for carbonate rocks exhibiting ε _af ≤ 1%. The developed exponential model is used to relate normalized axial stress (σ _a/σ _c) over the whole pre-failure strain range to current axial strain (ε _a) and failure strain (ε _af). For carbonate rocks exhibiting ε _af > 1%, the value of pre-calculated parameter δ involved in the stress–strain model is not constant, but dependent on the failure strain value (ε _af). The normalized stress–strain model can be used to calculate the failure strain in terms of uniaxial compressive strength and stress–strain measurement at one point only. The advantages of the failure strain model and ways of its use in engineering practice are discussed.     

Age constraints on faulting and fault reactivation: a multi-chronological approach

Movement within the Earth’s upper crust is commonly accommodated by faults or shear zones, ranging in scale from micro-displacements to regional tectonic lineaments. Since faults are active on different time scales and can be repeatedly reactivated, their displacement chronology is difficult to reconstruct. This study represents a multi-geochronological approach to unravel the evolution of an intracontinental fault zone locality along the Danube Fault, central Europe. At the investigated fault locality, ancient motion has produced a cataclastic deformation zone in which the cataclastic material was subjected to hydrothermal alteration and K-feldspar was almost completely replaced by illite and other phyllosilicates. Five different geochronological techniques (zircon Pb-evaporation, K–Ar and Rb–Sr illite, apatite fission track and fluorite (U-Th)/He) have been applied to explore the temporal fault activity. The upper time limit for initiation of faulting is constrained by the crystallization age of the primary rock type (known as “Kristallgranit”) at 325 ± 7 Ma, whereas the K–Ar and Rb–Sr ages of two illite fractions <2 μm (266–255 Ma) are interpreted to date fluid infiltration events during the final stage of the cataclastic deformation period. During this time, the “Kristallgranit” was already at or near the Earth’s surface as indicated by the sedimentary record and thermal modelling results of apatite fission track data. (U–Th)/He thermochronology of two single fluorite grains from a fluorite–quartz vein within the fault zone yield Cretaceous ages that clearly postdate their Late-Variscan mineralization age. We propose that later reactivation of the fault caused loss of helium in the fluorites. This assertion is supported by geological evidence, i.e. offsets of Jurassic and Cretaceous sediments along the fault and apatite fission track thermal modelling results are consistent with the prevalence of elevated temperatures (50–80°C) in the fault zone during the Cretaceous.     

Equation of state and melting point studies of forsterite

We report in this paper results of lattice dynamical calculations of the thermodynamic properties, namely, the equation of state and the melting point of forsterite. The root mean square displacements of atoms and thermal parameters are also evaluated. It is observed from our results, that, a modified Lindemann criterion for melting may be proposed for an ionic ‘molecular’ solid like forsterite. Agreement among various theoretical and experimental results is satisfactory indicating that lattice dynamical studies based on microscopic quasiharmonic formulations help in understanding the macroscopic properties of forsterite, over a wide range of temperature and pressure.     

Fe–Mg partitioning between post-perovskite and ferropericlase in the lowermost mantle

Fe–Mg partitioning between post-perovskite and ferropericlase has been studied using a laser-heated diamond anvil cell at pressures up to 154 GPa and 2,010 K which corresponds to the conditions in the lowermost mantle. The composition of the phases in the recovered samples was determined using analytical transmission electron microscopy. Our results reveal that the Fe–Mg partition coefficient between post-perovskite and ferropericlase (K _D^PPv/Fp) increases with decreasing bulk iron content. The compositional dependence of K _D^PPv/Fp on the bulk iron content explains the inconsistency in previous studies, and the effect of the bulk iron content is the most dominant factor compared to other factors, such as temperature and aluminum content. Iron prefers ferropericlase compared to post-perovskite over a wide compositional range, whereas the iron content of post-perovskite (X _Fe^PPv, the mole fraction) does not exceed a value of 0.10. The iron-rich ferropericlase phase may have significant influence on the physical properties, such as the seismic velocity and electrical conductivity at the core–mantle boundary region.     

Formation of kyanite–quartz veins of the Alpe Sponda,Central Alps,Switzerland: implications for Al transport during regional metamorphism

In this study, we have investigated the formation of quartz–kyanite veins of the Alpe Sponda, Central Alps, Switzerland. We have integrated field observations, fluid inclusion and stable isotope data and combined this with numerical geochemical modeling to constrain the chemical processes of aluminum transport and deposition. The estimated P–T conditions of the quartz–kyanite veins, based on conventional geothermometry (garnet–biotite, white mica solvus and quartz–kyanite oxygen isotope thermometry) and fluid inclusion data, are 550 ± 30°C at 5.0 ± 0.5 kbar. Geochemical modeling involved construction of aqueous species predominance diagrams, calculation of kyanite and quartz solubility, and reaction–path simulations. The results of the modeling demonstrate that (1) for the given chemical composition of the vein-forming fluids mixed Al–Si aqueous species are dominant in transporting Al, and that (2) fluid cooling along a small temperature gradient coupled with a pH decrease is able to explain the precipitation of the quartz–kyanite assemblages in the proportions that are observed in the Alpe Sponda veins. We conclude that sufficient amounts of Al can be transported in typical medium- to high-grade regional metamorphic fluids and that immobile behavior of Al is not very likely in advection–dominanted fluid–rock systems in the upper and middle crust.     

Probabilistic seismic hazard of Pakistan, Azad-Jammu and Kashmir

The seismic hazard study for Pakistan and Azad Jammu and Kashmir has been conducted by using probabilistic approach in terms of peak ground acceleration (PGA) in m/s² and also seismic hazard response spectra for different cities. A new version of Ambraseys et al. (Bull Earthq Eng 3:1–53, 2005) ground acceleration model is used, and parameterization is based on most recent updated earthquake catalogs that consisted of 14,000 events. The threshold magnitude was fixed at M _w 4.8, but seismic zones like northern Pakistan–Tajikistan, Hindukush and northern Afghanistan–Tajikistan border had M _w 5.2. The average normalized ‘a’ and ‘b’ values for all zones are 6.15 and 0.95, respectively. Seismicity of study area was modeled, and ground motion was computed for eight frequencies (0.025, 0.1, 0.2, 0.5, 1.0, 1.5, 2.0, 2.5 s) for different annual exceedance rates of 0.02, 0.01, 0.005, 0.002 and 0.001 (return periods 50, 100, 200, 500 and 1,000 years) for stiff rocks at the gridding of 0.1° × 0.1°. Seismic hazard maps based on computed PGA for 0.02, 0.01 and 0.002 annual exceedance are prepared. These maps indicate the earthquake hazard of Pakistan and surrounding areas in the form of acceleration contour lines, which are in agreement with geological and seismotectonic characteristics of the study area. The maximum seismic hazard values are found at Muzaffarabad, Gilgit and Quetta areas.     

The phase boundary between wadsleyite and ringwoodite in Mg2SiO4 determined by in situ X-ray diffraction

The phase boundary between wadsleyite and ringwoodite in Mg₂SiO₄ has been determined in situ using a multi-anvil apparatus and synchrotron X-rays radiation at SPring-8. In spite of the similar X-ray diffraction profiles of these high-pressure phases with closely related structures, we were able to identify the occurrence of the mutual phase transformations based on the change in the difference profile by utilizing a newly introduced press-oscillation system. The boundary was located at ~18.9 GPa and 1,400°C when we used Shim’s gold pressure scale (Shim et al. in Earth Planet Sci Lett 203:729–739, 2002), which was slightly (~0.8 GPa) lower than the pressure as determined from the quench experiments of Katsura and Ito (J Geophys Res 94:15663–15670, 1989). Although it was difficult to constrain the Clapeyron slope based solely on the present data due to the kinetic problem, the phase boundary [P (GPa)=13.1+4.11×10⁻³×T (K)] calculated by a combination of a P–T position well constrained by the present experiment and the calorimetric data of Akaogi et al. (J Geophys Res 94:15671–15685, 1989) reasonably explains all the present data within the experimental error. When we used Anderson’s gold pressure scale (Anderson et al. in J Appl Phys 65:1535–1543, 1989), our phase boundary was located in ~18.1 GPa and 1,400°C, and the extrapolation boundary was consistent with that of Kuroda et al. (Phys Chem Miner 27:523–532, 2000), which was determined at high temperature (1,800–2,000°C) using a calibration based on the same pressure scale. Our new phase boundary is marginally consistent with that of Suzuki et al. (Geophys Res Lett 27:803–806, 2000) based on in situ X-ray experiments at lower temperatures (<1,000°C) using Brown’s and Decker’s NaCl pressure scales.     

Thermal diffusivity of natural and synthetic garnet solid solution series

Knowledge of heat transport properties as a function of mineral- and rock-composition and temperature is of major relevance to understand and model heat transfer in the Earth’s interior. A systematic study on 13 natural and 4 synthetic garnets was carried out in an attempt to obtain a better systematic understanding of the processes that affect the heat transport in minerals, especially the effect of chemical substitution in solid solution series. It is found that substitution significantly lowers the thermal diffusivity from end-member values for both synthetic and natural garnets with a minimum of thermal diffusivity at an intermediate composition. The thermal diffusivity as a function of the degree of substitution can be described by the approach of Padture and Klemens (J Am Ceram Soc 80 (4):1018–1020, 1997). With increasing temperature the thermal diffusivity decreases due to phonon-phonon-scattering effects. A quantitative analysis of the high-temperature behaviour was carried out by using the model of Roufosse and Klemens (J Geophys Res 79 (5):703–705, 1974), which takes a lower limit of thermal diffusivity at elevated temperatures into account. The model allows for an extrapolation of the deduced room temperature thermal diffusivities to higher temperatures. Furthermore, the model was modified to determine the high temperature limit of the thermal diffusivity for all investigated natural garnets D _min to be 0.64 ± 0.03 mm²/s.     

Electrical conductivity of amphibole-bearing rocks: influence of dehydration

We investigated the electrical conductivity of amphibole-bearing rocks under the conditions of the middle to lower crust. Alternating current measurements were performed in the frequency range of 10–10⁶ Hz in a cubic-anvil high-pressure apparatus at 0.5–1.0 GPa and 373–873 K. The electrical conductivity of these rocks is weakly temperature dependent below ~800 K with modest anisotropy and relatively low conductivity (~5 × 10⁻³ S/m at ~750 K with the activation enthalpy of 64–67 kJ/mol). However, the electrical conductivity starts to increase with temperature more rapidly above ~800 K (activation enthalpy of 320–380 kJ/mol). The infrared spectroscopy observations indicate that dehydration occurs in this high temperature regime. The observed high activation enthalpy and the reproducibility suggest that the enhanced conductivity is not due to the direct effect caused by the generation of conductive fluids. Dehydration of amphibole is associated with the oxidation of iron (from ferrous to ferric), and we suggest that the increased conductivity associated with dehydration is caused by oxidation. This effect may explain high electrical conductivity observed in some regions of the continental crust.     

Compressibility of synthetic glaucophane

The compressibilities of two synthetic glaucophane samples were measured over the range of 0–10 GPa at ambient temperature in a diamond-anvil cell at the Cornell High-Energy Synchrotron Source (CHESS). The pressure–volume data were fitted to the Birch–Murnaghan equation of state taking care to include only data with a minimum of deviatoric stress. When using a second-order truncation, both samples yielded essentially identical values of the bulk modulus K ₀, which had an average value of 91.8 ± 1.3 GPa. Maximum compression was observed approximately along the a* axis as shown by the strain ellipsoid and supported by the a axis showing the highest compressibility. These results agree closely with the earlier study of a natural glaucophane single-crystal by Comodi et al. (Eur J Mineral 3:485–499, 1991), suggesting that the substitution of about 20–30 mol.% of Fe for Mg and Al in the structure may not significantly change its compressibility.