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Based on the modified thermodynamic model, we calculate the density of olivine-pyroxene mixtures at different proportions of molecular masses in minerals at temperatures of 1000–1700 K and pressures up to 17 GPa. The calculated density of the olivine-pyroxene mixtures is compared with the PREM model and the average density patterns of the Asian and Arctic regions estimated from the data on the Rayleigh wave group velocity dispersion in upper mantle conditions. Taking into account the characteristic temperature profiles of different tectonic units in Asia (Tibetan plateau, Khangay dome, Baikal rift and southern Siberian Platform) and the Arctic (Chukotka fold belt, Barents Sea, northern Greenland and Eurasia Basin), we discuss density patterns and features of the mantle composition underneath structures and to depths of 200 km, where the most significant variations in their density patterns are observed. The results obtained suggest some insights into the geodynamic evolution of the lithosphere in the study area. The calculated density characteristics of the components in the upper mantle and the modelling of their composition are compared with average density patterns under the tectonic units, in order to show the possibilities of previously developed equations of state. It has been shown that the composition (0.9(Mg0.9Fe0.1)2SiO4 + 0.1MgSiO3) describes the PREM model well, in addition to the average velocity patterns of the study regions. Variations in mineralogical compositions are revealed between stable structures and the areas with high levels of tectonic and seismic activity. The present paper could be of interest to geophysicists and mineralogists as it researches overlapping topics for both sciences, indicating the relationship between seismicity and features of the deep structure of the upper mantle.

The equations of state of different phases in the CaSiO3 system (wollastonite, pseudowollastonite, breyite (walstromite), larnite (Ca2SiO4), titanite-structured CaSi2O5 and CaSiO3-perovskite) are constructed using a thermodynamic model based on the Helmholtz free energy. We used known experimental measurements of heat capacity, enthalpy, and thermal expansion at zero pressure and high temperatures, and volume measurements at different pressures and temperatures for calculation of parameters of equations of state of studied Ca-silicates. The used thermodynamic model has allowed us to calculate a full set of thermodynamic properties (entropy, heat capacity, bulk moduli, thermal expansion, Gibbs energy, etc.) of Ca-silicates in a wide range of pressures and temperatures. The phase diagram of the CaSiO3 system is constructed at pressures up to 20 GPa and temperatures up to 2000 K and clarifies the phase boundaries of Ca-silicates under upper mantle conditions. The calculated wollastonite–breyite equilibrium line corresponds to equation P(GPa) = −4.7 × T(K) + 3.14. The calculated density and adiabatic bulk modulus of CaSiO3-perovskite is compared with the PREM model. The calcium content in the perovskite composition will increase the density of mineral and it good agree with the density according to the PREM model at the lower mantle region.

Modified equations of state (EoS) of forsterite, wadsleyite, ringwoodite, akimotoite, bridgmanite and post-perovskite based on the Helmholtz free energy are described using Microsoft Excel spreadsh...

Pressure–volume–temperature relations have been measured to 29 GPa and 1673 K for CaCO3 aragonite using synchrotron X-ray diffraction with a multianvil apparatus at the ‘SPring-8’ facility. A least-squares fit of the room-temperature compression data to the Vinet-Rydberg equation of state (EOS) yielded KT0 = 65.7 ± 0.8 GPa and KT' = 5.1 ± 0.1, with fixed V0 = 227.11 A3. Further analysis of the high-temperature compression data led to the temperature derivative of the bulk modulus (∂KT/∂T)P = −0.016 ± 0.001 GPa/K and zero-pressure thermal expansion α = a0 + a1T with a0 = 4.98 (22) × 10−5 K−1 and a1 = 2.81(38) × 10−8 K−2. The Mie-Gruneisen-Debye approach revealed the Gruneisen parameter γ0 = 1.39 at a fixed Debye temperature θ0 = 516 K and the parameter q = 1. Analysis of axial compressibility and thermal expansion indicates that the c-axis is two times more compressible than the b-axis and four times more compressible than the a-axis, whereas zero-pressure thermal expansion of the a-axis (a0a = 2.6 × 10−5 K−1 and a1a = 2.3 × 10−8 K−2) is weaker than that of the b-axis axis (a0b = 6.3 × 10−5 K−1 and a1b = 0.1 × 10−8 K−2) and c-axis axis (a0c = 5.2 × 10−5 K−1 and a1c = 9.5 × 10−8 K−2). A full set of thermodynamic parameters (including heat capacity, enthalpy and free energy) for aragonite and updated equations of state for magnesite and siderite was obtained using the Kunc-Einstein approach. The new EOS parameters were used for thermodynamic calculations for aragonite decarbonation reactions. The present thermal EOS provides accurate calculations of aragonite density to deep mantle. Decarbonation of subducting oceanic crust containing 2 wt% aragonite would result in a 0.5% density reduction at 30 GPa and 1273 K. Aragonite becomes denser than magnesite at pressures about 16 GPa along the 1500 K isotherm and at 9 GPa along the 298 K isotherm.

A new synchrotron X-ray diffraction study of chromium oxide Cr2O3 (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K 0,T0), 206 ± 4 GPa; its pressure derivative K′0,T , 4.4 ± 0.8; (∂K 0,T /∂T) = ‒0.037 ± 0.006 GPa K‒1; a = 2.98 ± 0.14 × 10−5 K−1 and b = 0.47 ± 0.28 × 10‒8 K‒2, where α 0,T = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr2O3 was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α 0,T0 was determined to be 2.95 × 10−5 K−1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α 0 value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Gruneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K 0,T0 = 205 ± 3 GPa, K′0,T = 4.0, Gruneisen parameter (γ 0) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr2O3 undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr2O3 is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with $${\text{d}}P/{\text{d}}T = - 0.014$$ GPa/K) was found to be consistent with experimental data.

The equations of state of forsterite, wadsleyite, ringwoodite, MgSiO3-perovskite, akimotoite, and postperovskite are set up by joint analysis of experimentally measured isobaric heat capacity, bulk moduli, thermal expansion depending on temperature at ambient pressure, and volume at room and higher temperatures. Modified equations of state based on the Helmholtz free energy are used to construct a thermodynamic model. The derived equations of state permit calculation of all thermodynamic functions for the minerals depending on temperature and volume or temperature and pressure. A phase diagram of the system MgSiO3–MgO is constructed based on the Gibbs energy calibrated using the referred experimental points. The seismic boundaries at depths of 410 and 520 km and in the zone D’ are interpreted on the basis of the phase transitions. The global upper/lower mantle discontinuity at a depth of 660 km remains debatable; it is in poor agreement with experimental and computational data on the dissociation of ringwoodite to perovskite and periclase.

The equations of state for solid (with bcc, fcc, and hcp structures) and liquid phases of Fe were defined via simultaneous optimization of the heat capacity, bulk moduli, thermal expansion, and volume at room and higher temperatures. The calculated triple points at the phase diagram have the following parameters: bcc–fcc–hcp is located at 7.3 GPa and 820 K, bcc–fcc–liquid at 5.2 GPa and 1998 K, and fcc–hcp–liquid at 106.5 GPa and 3787 K. At conditions near the fcc–hcp–liquid triple point, the Clapeyron slope of the fcc–liquid curve is dT/dP = 12.8 K/GPa while the slope of the hcp–liquid curve is higher (dT/dP = 13.7 K/GPa). Therefore, the hcp–liquid curve overlaps the metastable fcc–liquid curve at pressures of about 160 GPa. At high-pressure conditions, the metastable bcc–hcp curve is located inside the fcc-Fe or liquid stability field. The density, adiabatic bulk modulus and P-wave velocity of liquid Fe calculated up to 328.9 GPa at adiabatic temperature conditions started from 5882 K (outer/inner core boundary) were compared to the PREM seismological model. We determined the density deficit of hcp-Fe at the inner core boundary (T = 5882 K and P = 328.9 GPa) to be 4.4%.

According to the geophysical data, the outer liquid core of the Earth has a deficiency of density and seis� mic velocities of 5–12%, and inner solid core has 3– 5% at the expense of the presence of one or several light elements. The most probable candidates for the role of the light element are H, C, O, S, and Si [1]. The problem of light elements may be solved using detailed thermodynamic description of solid iron and nickel compounds, as well as metal alloys, on the basis of the data on their equations of state and phase transition boundaries. The Fe–C system is of key importance for discussion of the composition of the Earth’s core. The equations of state of iron carbides at 300 K are studied at pressures up to 180 GPa [2, 3].

Pressure–volume–temperature relations have been measured to 33 GPa and 1673 K for natural siderite (Fe0.95Mn0.05CO3) using synchrotron X-ray diffraction with a multianvil apparatus at the ‘SPring-8’ facility. A least-squares fit of the room-temperature compression data to a third-order Birch–Murnaghan equation of state (EOS) yielded K0 = 120 ± 1 GPa and K′ = 3.57 ± 0.09, with fixed V0 = 293.4 ± 0.1 A3. Further analysis of the high-temperature compression data yielded the temperature derivative of the bulk modulus ( ∂ KT/ ∂ T)P = −0.015 ± 0.001 GPa/K and zero-pressure thermal expansion α = a0 + a1T with a0 = 3.57(9) × 10−5 K−1 and a1 = 0.06(14) × 10−8 K−2. The analysis of axial compressibility indicates that the c-axis is more compressible (KTc = 59 ± 1 GPa at K′ = 2.7 ± 0.1) than the a-axis (KTa = 166 ± 2 GPa at K′ = 14.0 ± 0.8). The present thermal EOS enables accurate calculation the density and thermodynamic properties of siderite to the deep mantle conditions.

[1] Resent experimental and theoretical studies suggested preferential stability of Fe3C over Fe7C3 at the condition of the Earth's inner core. Previous studies showed that Fe3C remains in an orthorhombic structure with the space group Pnma to 250 GPa, but it undergoes ferromagnetic (FM) to paramagnetic (PM) and PM to nonmagnetic (NM) phase transitions at 6–8 and 55–60 GPa, respectively. These transitions cause uncertainties in the calculation of the thermoelastic and thermodynamic parameters of Fe3C at core conditions. In this work we determined P-V-T equation of state of Fe3C using the multianvil technique and synchrotron radiation at pressures up to 31 GPa and temperatures up to 1473 K. A fit of our P-V-T data to a Mie-Gruneisen-Debye equation of state produce the following thermoelastic parameters for the PM-phase of Fe3C: V0 = 154.6 (1) A3, KT0 = 192 (3) GPa, KT′ = 4.5 (1), γ0 = 2.09 (4), θ0 = 490 (120) К, and q = −0.1 (3). Optimization of the P-V-T data for the PM phase along with existing reference data for thermal expansion and heat capacity using a Kunc-Einstein equation of state yielded the following parameters: V0 = 2.327 cm3/mol (154.56 A3), KT0 = 190.8 GPa, KT′ = 4.68, ΘE10 = 305 K (which corresponds to θ0 = 407 K), γ0 = 2.10, e0 = 9.2 × 10−5 K−1, m = 4.3, and g = 0.66 with fixed parameters mE1 = 3n = 12, γ∞ = 0, β = 0.3, and a0 = 0. This formulation allows for calculations of any thermodynamic functions of Fe3C versus T and V or versus T and P. Assuming carbon as the sole light element in the inner core, extrapolation of our equation of state of the NM phase of Fe3C suggests that 3.3 ± 0.9 wt % С at 5000 К and 2.3 ± 0.8 wt % С at 7000 К matches the density at the inner core boundary.

Based on the modified formalism of Dorogokupets and Oganov (2007), we calculated the equation of state for diamond, MgO, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, and W by simultaneous optimization of the data of shock-wave experiments and ultrasonic, X-ray diffraction, dilatometric, and thermochemical measurements in the temperature range from ~ 100 K to the melting points and pressures of up to several Mbar, depending on the material. The obtained room-temperature isotherms were adjusted with a shift of the R1 luminescence line of ruby, which was measured simultaneously with the unit cell parameters of metals in the helium and argon pressure media. The new ruby scale is expressed as P(GPa) = 1870⋅Δλ / λ0(1 + 6⋅Δλ / λ0). It can be used for correction of room-pressure isotherms of metals, diamond, and periclase. New simultaneous measurements of the volumes of Au, Pt, MgO, and B2-NaCl were used for interrelated test of obtained equations of state and calculation of the room-pressure isotherm for B2-NaCl. Therefore, the constructed equations of state for nine metals, diamond, periclase, and B2-NaCl can be considered self-consistent and consistent with the ruby scale and are close to a thermodynamic equilibrium. The calculated PVT relations can be used as self-consistent pressure scales in the study of the PVT properties of minerals using diamond anvil cell in a wide range of temperatures and pressures.

Endogenous fluid systems play the role of universal energy carriers participating in practically all petrolog� ical processes [1]. Therefore, estimation of their energy parameters is very important. The fluids form a convective heat flux during their upward migration within the geological section and release their heat energy into the environment. The released heat can initiate the processes of metamorphic transformation, granitization, metasomatosis, and rock melting. It is clear that the amount of the transferred heat would depend on many factors, in particular, on the depth of the source, and correspondingly, on the thermody� namic conditions of the fluid system formation, which will reflect first of all in the component composition of the gas mixture. The other, not less important factors are the velocity of ascent (approximation to the adia� bat) and the amount of fluid with respect to the volume of the rocks. Earlier, we studied the energy parameters of individual gases up to the depths of 200 km [2, 3]. It was shown that the maximum energy input to the total heat transport is related to hydrogen and deoxidized gases. The objective of this work is to get a quantitative estimate of the ability of deep fluids to transport heat energy during their ascent from the depths of 1000 km, which corresponds to the conditions of the lower man� tle with account for the variation in the component composition. The solution of this problem is in the calculation of enthalpy for the main fluid components (

A simplest equation within the framework of the Mie-Gruneisen–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-Gruneisen–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 Gruneisen parameter, γ = −(∂lnΘ/∂lnV) T . Pressure as a function of temperature and volume in the Mie-Gruneisen–Einstein approach or the Gao pressure calculator can be used to estimate true pressure at compression x = V/V 0

According to a current concept, copper canisters of thickness 0.05 m will be safe for nuclear waste containment for 100,000 years. We show that more than 1 m copper thickness might be required for 100,000 years durability based on water exposures of copper for 20 h, 7 weeks, 15 years, and 333 years. An observed evolution of hydrogen which involves heterogeneous catalysis of molecular hydrogen, first principles simulations, thermodynamic considerations and corrosion product characterization provide further evidence that water corrodes copper resulting in the formation of a copper hydroxide. These findings cast additional doubt on copper for nuclear waste containment and other important applications.

Semiempirical equations of state (EoS) of Au, Pt, MgO, NaCl-B1, and NaCl-B2 based on expanded Mie–Gruneisen–Debye approach, which are consistent both with the Mie–Gruneisen–Bose–Einstein approach and the thermochemical, X-ray, ultrasonic and shock-wave data in a wide pressure-temperature range, have been constructed. It is shown that to determine the volume dependence of the Gruneisen parameter, not only shock-wave and static compression data, but also experimental information on heat capacity, bulk moduli, volume, and thermal expansion coefficient at zero pressure need to be taken into account. Intrinsic anharmonicity is of great importance at construction of EoS at high temperatures and x=V/V 0>1. Cross-comparison of the current equations of state with independent measurements shows that these EoS may be used as the internally consistent and independent pressure scales in a wide range of temperatures and pressures.

A semiempirical equation of state was derived for magnesite under the thermodynamic conditions of the Earth's mantle. Within experimental uncertainties, it is consistent with thermochemical, ultrasonic, X-ray, and shock-wave data at temperatures from 15 K to the melting point and pressures of up to 100-130 GPa. The fol- lowing values were recommended for the isothermal bulk modulus and its pressure derivative: K T = 111.71 GPa and K ' = 4.08. Thermodynamic analysis showed that magnesite does not decompose to periclase and CO 2 under the thermodynamic conditions of the Earth's lower mantle and outer core.

Usin gt hermodynamic perturbation theory, we derive a simple formalism for treating intrinsic anharmonic effects in solids. In this formalism, the central quantity is the intrinsic anharmonicity parameter a ,w hichcan be derived from vibrational spectroscopy or computer simulation. Advantages of our approach include (1) correct low- and high-temperature behaviour, (2) analyticity of all the thermodynamic functions and (3) the possibility of systematic incorporation of higher-order anharmonic effects. This approach can be used in studying equations of state and thermodynamics of solids in a wide temperature range. Ad etailed comparison with other approaches is given.

A simple numerical model for simultaneous optimization of heat capacity at constant pressure, CP , heat capacity at constant volume, CV , volume, V , thermal expansion coefficient, α, isothermal, KT , and adiabatic, KS , bulk moduli at zero pressure, and PVT data for minerals has been developed. The basic function is the Debye energy, expressed through the Nernst-Lindemann energy function for T > 0.2Θ. Three additional empirical parameters are included in the expression for energy, which take into account anharmonicity, premelting, and other effects for real minerals. The volume vs. energy dependence is calculated on the basis of either the Wachtman et al. (1962) or the Suzuki (1975) model or their linear combination. Volume, V 298, Nernst-Lindemann characteristic temperature, Θ, isothermal bulk modulus, K T 298, its pressure derivative, K′ , Gruneisen parameter, γ, isothermal Anderson-Gruneisen parameter, δ T , and three empirical parameters, a , b , c , which can be equal to zero for Debye-like solids, are fitting parameters of the model. The proposed model enables one to calculate thermodynamic functions of simple substances, oxides, and minerals over a temperature range from 0.2Θ up to the melting temperature with a deviation within the scatter of experimental data. Correlation of the proposed model with PVT data is considered. It is shown that the isothermal equation of state results in an unsatisfactory extrapolation of volume in extreme regions. The Wachtman et al. (1962) and the Suzuki (1975) models of the volume vs. energy are extended to high pressure. The high-pressure Wachtman et al. (1962) and Suzuki (1975) models are versions of the Mie-Gruneisen equation of state and allow temperature dependencies of thermodynamic functions for any isobar to be easily calculated. The model described here and the classical Mie-Gruneisen model are found to be equivalent at q ≈ 1. The model is tested using rock salt, corundum, and lawsonite.

A comprehensive P-V-T dataset for bcc-Mo was obtained at pressures up to 31 GPa and temperatures from 300 to 1673 K using MgO and Au pressure calibrants. The thermodynamic analysis of these data was performed using high-temperature Birch-Murnaghan (HTBM) equations of state (EOS), Mie-Gruneisen-Debye (MGD) relation combined with the room-temperature Vinet EOS, and newly proposed Kunc-Einstein (KE) approach. The analysis of room-temperature compression data with the Vinet EOS yields V0 = 31.14 ± 0.02 A3, KT = 260 ± 1 GPa, and KT′ = 4.21 ± 0.05. The derived thermoelastic parameters for the HTBM include (∂KT/∂T)P = −0.019 ± 0.001 GPa/K and thermal expansion α = a0 + a1T with a0 = 1.55 ( ± 0.05) × 10−5 K−1 and a1 = 0.68 ( ± 0.07) × 10−8 K−2. Fitting to the MGD relation yields γ0 = 2.03 ± 0.02 and q = 0.24 ± 0.02 with the Debye temperature (θ0) fixed at 455-470 K. Two models are proposed for the KE EOS. The model 1 (Mo-1) is the best fit to our P-V-T data, whereas the second model (Mo-2) is derived by including the shock compression and other experimental measurements. Nevertheless, both models provide similar thermoelastic parameters. Parameters used on Mo-1 include two Einstein temperatures ΘE10 = 366 K and ΘE20 = 208 K; Gruneisen parameter at ambient condition γ0 = 1.64 and infinite compression γ∞ = 0.358 with β = 0.323; and additional fitting parameters m = 0.195, e0 = 0.9 × 10−6 K−1, and g = 5.6. Fixed parameters include k = 2 in Kunc EOS, mE1 = mE2 = 1.5 in expression for Einstein temperature, and a0 = 0 (an intrinsic anharmonicity parameter). These parameters are the best representation of the experimental data for Mo and can be used for variety of thermodynamic calculations for Mo and Mo-containing systems including phase diagrams, chemical reactions, and electronic structure.

An equation of state has been developed for quartz, a substance with a lambda-type phase transition. It has the properties of the Murnaghan equation of state in the normal region and reflects the fundamental behavior of thermodynamic functions in the anomalous region. The term jT/(i-T)1/2 has been introduced in the temperature dependent equations of isobaric heat capacity and the volume coefficient of thermal expansion, where i and j are fitting coefficients. The i coefficient is numerically close to the temperature of the phase transition Tc and is usually in the 0.1

The solid inner core of the Earth consists mostly of iron. There is accumulating evidence that, at the extreme pressures and temperatures of the deep Earth interior, iron stabilizes in the body-centered-cubic phase. However, experimental study of iron at those conditions is very difficult at best. We demonstrate that our ab initio approach is capable of providing volumetric data on iron in very good agreement with experiment at low temperature and high pressure. Since our approach treats high-temperature effects explicitly, this allows us to count on similar precision also at high temperature and high pressure. We perform ab initio molecular-dynamics simulations at a number of volume-temperature conditions and compute the corresponding pressures. These points are then fitted with an equation of state. A number of parameters are computed and compared with existing data. The obtained equation of state for high pressure and temperature nonmagnetic body-centered-cubic phase allows the computation of properties of iron under extreme conditions of the Earth's inner core.

perature range from 10– 20 K up to the melting temperature and to compression x = V / V0 = 0.5– 0.7. The comparison of the calculated room-temperature isotherms for these metals with quasihydrostatic measurements supports recently proposed ruby pressure scales. We recommend a new ruby pressure scale in the form P = A /0 1+ m /0 with parameters A = 1884 GPa and m = 5.5. The cross check on independent data confirms the obtained PVT equations of state of Ag, Al, Au, Cu, Pt, Ta, W, MgO, and diamond. The equations of state of these materials obtained here provide accurate and versatile means for calibrating pressure at all temperatures below the melting point. Furthermore, they can be used for accurate tabulation of thermodynamic properties heat capacities, entropies of these reference substances in a wide P-T range.

The compression curve of iron is measured up to 205 GPa at 298 K, under quasihydrostatic conditions in a diamond anvil cell. Above 150 GPa, the compression of this metal is significantly higher than previously measured under nonhydrostatic conditions. The same compression curve is also calculated ab initio and the deviation between experiment and theory is clearly established. A formulation of the equation of state of iron over a large pressure and temperature range, based on the current data and existing shock-wave data, is also proposed. Implications for the Earth's core are discussed.

static and ab initio molecular dynamics simulations. The simulations were performed using the projector augmented-wave and pseudopotential methods with different descriptions of the Mg atom ~‘‘small core’’ and ‘‘large core’’ !. The errors of large-core pseudopotentials increase with pressure and are mainly due to the overlap between the Mg semicore ~2p! orbitals and the valence orbitals, both of the same Mg atom and of the neighboring O atoms, rather than core deformation or core-core overlap effects. In agreement with previous works, we find that MgO remains in the B1~‘‘NaCl’’ ! structure at all pressures existing within the Earth, and transforms into the CsCl-type structure at 509 GPa. Direct ab initio calculations avoid the simplifying assumptions inherent to many empirical treatments of thermoelasticity and allowed us to assess some of the common assumptions. We present a detailed qualitative analysis of the effects of intrinsic anharmonicity and analyze the

A comprehensive P-V-T dataset for bcc-tungsten was obtained for pressures up to 33.5 GPa and temperatures 300–1673 K using MgO and Au pressure scales. The thermodynamic analysis of these data was performed using high-temperature (HT) and Mie-Gruneisen-Debye (MGD) relations combined with the Vinet equations of state (EOS) for room-temperature isotherm and the newly proposed Kunc-Einstein (KE) EOS. The KE EOS allowed calibration of W thermodynamic parameters to the pressures of at least 300 GPa and temperatures up to 4000 K with minor uncertainties (