High-pressure Equation Of State Research Articles

Phase comparison and equation of state for Ta2O5

Tantalum pentoxide (Ta2O5) is among the most technologically useful heavy transition metal oxides. Unfortunately, its crystal structure is the subject of long-standing and unresolved disagreement. Among other consequences, this uncertainty has made it impossible to formulate a robust high pressure equation of state for Ta2O5. Here, we report the results of high pressure x-ray diffraction experiments indexed against a comprehensive list of proposed Ta2O5 phases. Five of the proposed phases produce good matches to experimental observations, and the compressibility parameters for these phases are all consistent within uncertainty. This means that regardless of the particular phase chosen, the Ta2O5 equation of state can be described with bulk modulus K0=138±3.68  GPa and pressure derivative K0′=1.82±0.45 . Combining these experimental results with new density-functional theory calculations allows us to identify the λ phase as the best structural model of Ta2O5 at ambient conditions.

High-pressure equations of state and elastic properties of the hcp-Iron

The present study deals with the elastic properties at different pressure of hcp-iron have been carried out. By exerting pressure on the cubic body of n-th power of edge length, we have used a new equation of state based on Eulerian finite theory. We have computed the bulk modulus and their pressure derivative from this formulated equation of state. The results from the proposed equation of state (EOS) show the better agreement with available experimental data. Thus, the derived expressions are able to predict the elastic properties of hcp-iron under high pressures.

Shock Properties of One Unsaturated Clay and Its Equation of State Up to 30 GPa

The complicated composition of unsaturated clay, e.g., solid mineral particles, water, and air, makes it difficult to get its precise equation of state (EOS) over a wide pressure range. In this paper, the high-pressure EOS of unsaturated clay was discussed at the mesoscale. With the original clay extracted from the southern suburbs of Luoyang city, China, three unsaturated clays with moisture contents of 0%, 8%, and 15%, respectively, were remolded. Their Hugoniot parameters in the pressure range of 0–30 GPa were measured using a one-stage or two-stage light gas gun. With the measured Hugoniot parameters, a high-pressure EOS of the unsaturated clay up to 30 GPa was developed and it is in good agreement with the experimental data.

High-pressure equations of state and elastic properties of the lower mantle of the earth

High-pressure equations of state and elastic properties of the lower mantle of the earth

Shock-compressed silicon: Hugoniot and sound speed up to 2100 GPa

High-pressure equation of state and isentropic sound speed data for fluid silicon to pressures of 2100 GPa (21 Mbar) are reported. Principal Hugoniot measurements were performed using impedance matching techniques with \ensuremath{\alpha}-quartz as the reference. Sound speeds were determined by time correlating imposed shock-velocity perturbations in both the sample (Si) and reference material (\ensuremath{\alpha}-quartz). A change in shock velocity versus particle velocity (${u}_{s}--{u}_{p}$) slope on the fluid silicon principal Hugoniot is observed at 200 GPa. Density functional theory based quantum molecular dynamics simulations suggest that both an increase in ionic coordination and a 50% increase in average ionization are coincident with this experimentally observed change in slope.

Theoretical models and experimental determination methods for equations of state of silicate melts: A review

Silicate melts are very active in the interior of the Earth and other terrestrial planets, and are important carriers for the transport of material and energy. The determination of the equation of state (EOS) for silicate melts and the acquisition of a precise quantitative relationship between molar volume (or density) and temperature, pressure, and composition is essential for simulating the generation, migration, and eruption processes of magmas and the evolution of the magma ocean stage during the early formation of the Earth and other terrestrial planets, for calculating and modeling the phase equilibria involving silicate melts, and for revealing the variation of the microstructure of silicate melts with pressure. However, it is experimentally challenging to determine the volumetric properties of silicate melts and the accumulated density data at high pressure are still very limited due to a series of problems such as: the high liquidus temperature of silicate rocks; proneness for silicate melts to react with sample capsules to change the melt composition; and proneness for melts to flow and leak during the high pressure and high temperature experiments. In recent years, there is rapid progress in the high pressure and high temperature experimental techniques, in terms of not only the extension of temperature and pressure ranges but also the improvement on the accuracy of measurements, and the emergence of new methods for in-situ measurements. Here, we review the widely-used theoretical models of ambient-pressure and high-pressure EOS for silicate melts, and illustrate some problems that need to be solved urgently: (1) the room pressure EOS for iron- and titanium-bearing silicate melts needs to be improved; (2) the partial molar properties of the H2O and CO2 components in silicate melts containing volatile components may vary markedly with the melt composition, which need to be addressed in high-pressure EOS; (3) how the formulation and applicable range of EOS correspond to changes in melt structure and compression mechanism requires further study. We highlight the basic principle and applicable range of various methods for determining the EOS for silicate melts, and compare the advantages and disadvantages of double-bob Archimedes method, fusion curve analysis, shock compression experiments, sink-float method, X-ray absorption, X-ray diffraction and ultrasonic interferometry. Future trends in this field are to develop experimental techniques for in situ measurements on melt density or sound velocity at high temperature and high pressure and to accumulate more experimental data, and on the other hand, to improve the theoretical models of the EOS for silicate melts by a combination of research on the microstructure and compression mechanisms of silicate melts.

Helium accumulation and bubble formation in FeCoNiCr alloy under high fluence He+ implantation

Face-centered cubic (FCC) high-entropy alloys (HEA), as emerging alloys with equal-molar or near equal-molar constituents, show a promising radiation damage resistance under heavy ion bombardment, making them potential for structural material application in next-generation nuclear reactors, but the accumulation of light helium ions, a product of nuclear fission reaction, has not been studied. The present work experimentally studied the helium accumulation and bubble formation at implantation temperatures of 523 K, 573 K and 673 K in a homogenized FCC FeCoNiCr HEA, a HEA showing excellent radiation damage resistance under heavy ion irradiation. The size and population density of helium bubbles in FeCoNiCr samples were quantitatively analyzed through transmission electron microscopy (TEM), and the helium content existing in bubbles were estimated from a high-pressure Equation of State (EOS). We found that the helium diffusion in such condition was dominated by the self-interstitial/He replacement mechanism, and the corresponding activation energy in FeCoNiCr is comparable with the vacancy migration energy in Ni and austenitic stainless steel but only 14.3%, 31.4% and 51.4% of the accumulated helium precipitated into helium bubbles at 523 K, 573 K and 673 K, respectively, smaller than the pure Ni case. Importantly, the small bubble size suggested that FeCoNiCr HEA has a high resistance of helium bubble formation compared with Ni and steels.

Pressure-induced phase transitions in HoDyYGdTb high-entropy alloy

The HoDyYGdTb high-entropy alloy (HEA) was synthesized and its structural phase transitions were determined under compression up to 60.1GPa at room temperature. Three transformations following the sequence hexagonal close-packed (hcp)→samarium type (Sm-type)→double hexagonal close-packed (dhcp)→distorted face-center cubic (dfcc) are observed at 4.4, 26.7, and 40.2GPa, respectively. The high pressure equation of state was determined for the HEA according to third-order Birch-Murnaghan equation of state. The results show that the bulk modulus and atomic volume of the alloy obey the “additivity law”.

The Theoretical Study of High Pressure Equation of State and Relative Volume Thermal Expansion of fcc Transition Metals Ni, Pd and Pt Using Mean Field Potential Approach

In the theoretical study of thermophysical properties of materials at high temperature and pressure anharmonic effects are important. In this regard, in the present communication, anharmonic effects are taken into account by coupling recently proposed mean field potential (MFP) in conjunction with local pseudopotential for fcc transition metals Ni, Pd and Pt. Using present approach, we have computed volume variation of binding energy at 0K, vibrational free energy of lattice ions (Fion), Helmholtz free energy and relative volume thermal expansion up to melting temperature of Ni, Pd and Pt. Further, applicability of present coupling scheme has been tested by investigating equation of state (EOS) at 300K which explains the microscopic internal structure of material. Our results are in good agreement with experimental and other theoretical findings which demonstrate the capability of present coupling scheme of MFP with local pseudopotential alongwith its computational simplicity.

Electron-phonon coupling and exchange-correlation effects in superconductingH3Sunder high pressure

We investigate the ${\rm H_3S}$ phase of sulphur hydride under high pressure $\simeq$ 200 GPa by means of {\it ab-initio} calculations within the framework of the density-functional theory (DFT) with the PBE0 hybrid exchange-correlation ($E_{\rm xc}$) approximation. The choice of $E_{\rm xc}$ has the largest effect on the calculated electron-phonon coupling (EPC) matrix elements; the high pressure equation of state and phonon frequencies are only slightly modified. Mode-dependent EPC correction factors are determined from PBE0 using a frozen-phonon supercell approach, while standard density-functional perturbation theory is used to determine the EPC with PBE generalized-gradient approximation $E_{\rm xc}$. Our principle finding is that the calculated PBE0 $T_c$ is enhanced by 25\% compared to PBE. This is similar in magnitude, but in opposite direction, to the proposed suppression of $T_c$ by anharmonic effects [Errea {\em et al., Phys. Rev. Lett.} {\bf 114}, 157004 (2015)]. Our calculations demonstrate the importance of considering exchange-correlation approximations for calculations of superconducting properties for this class of materials.

Measuring high pressure equation of state of polystyrene using laser driven shock wave

High precision polystyrene equation of state data were measured using laser-driven shock waves with pressures from 180 GPa to 700 GPa. α quartz was used as standard material, the shock wave trajectory in quartz and polystyrene was measured using the Velocity Interferometer for Any Reflector (VISAR). Instantaneous shock velocity in quartz and polystyrene was obtained when the shock wave pass the interface. This provided ~1% precision in shock velocity measurements.

The high pressure structure and equation of state of 2,6-diamino-3,5-dinitropyrazine-1-oxide (LLM-105) up to 20 GPa: X-ray diffraction measurements and first principles molecular dynamics simulations.

Recent theoretical studies of 2,6-diamino-3,5-dinitropyrazine-1-oxide (C4H4N6O5 Lawrence Livermore Molecule No. 105, LLM-105) report unreacted high pressure equations of state that include several structural phase transitions, between 8 and 50 GPa, while one published experimental study reports equation of state (EOS) data up to a pressure of 6 GPa with no observed transition. Here we report the results of a synchrotron-based X-ray diffraction study and also ambient temperature isobaric-isothermal atomistic molecular dynamics simulations of LLM-105 up to 20 GPa. We find that the ambient pressure phase remains stable up to 20 GPa; there is no indication of a pressure induced phase transition. We do find a prominent decrease in b-axis compressibility starting at approximately 13 GPa and attribute the stiffening to a critical length where inter-sheet distance becomes similar to the intermolecular distance within individual sheets. The ambient temperature isothermal equation of state was determined through refinements of measured X-ray diffraction patterns. The pressure-volume data were fit using various EOS models to yield bulk moduli with corresponding pressure derivatives. We find very good agreement between the experimental and theoretically derived EOS.

High pressure equation of state for molten CaCO3 from first principles simulations

Carbonate melts are important active metasomatic agents and efficient transport agents; their thermodynamic properties at high temperatures and pressures are therefore of considerable interest for various geochemical applications. However, due to the extreme challenges in relevant experiments, current knowledge of even the density of carbonate melts is limited. In this study, we provide high quality volumetric data of CaCO3-melt from first principles at high temperatures and pressures (up to 3,500 K and 60 GPa). The accuracy of these data is demonstrated through comprehensive comparison with available experimental data and a thorough discussion of the predictability of the re-scaling method proposed in this study. Based on the simulations, an equation of state has been established that is critical to relevant highly disputed questions such as the decomposition and solidification boundaries of CaCO3 melts, the latter of which is briefly discussed in this study with a newly derived ab initio melting curve to high pressures.

High pressure equation of state and ideal compressive and tensile strength of MgO single crystal: Ab-initio calculations

Ab-initio total energy calculations have been carried out on MgO single crystal as a function of hydrostatic compression to determine the 0 K isotherm, which is then utilized to derive the 300 K isotherm, isentrope, and Hugoniot of MgO. The theoretical isotherm, isentrope, and Hugoniot compare well with the experimental data. The shock parameters C0 and s obtained from theoretical Hugoniot are 6.74 km/s and 1.23 as compared to the experimental values of 6.87 km/s and 1.24, respectively. Having theoretically reproduced the various experimentally measured physical quantities at ambient conditions, the calculations have been extended to determine the ideal compressive and tensile strength of MgO single crystal subjected to uniaxial compressive and tensile loading along [001] direction under two deformation conditions, namely, “uniaxial strain condition” and “uniaxial stress condition.” Examination of elastic stability conditions suggests that for [001] compressive loading, the MgO single crystal will fail mechanically due to shear instability, whereas for expansion it will fail due to vanishing of tensile modulus. The ideal compressive strength under “uniaxial strain condition” and “uniaxial stress condition” is determined to be −283 GPa and −115 GPa, respectively. However, ideal tensile strength is evaluated to be 20 GPa and 11 GPa, respectively, for two loading conditions. Our results suggest that MgO single crystal will offer higher resistance against failure for compression as well as expansion along [001] direction under “uniaxial strain condition” than that for the “uniaxial stress condition.”

High Pressure Equation of State for Nanomaterials

Shanker Equation of State is used to study the volume compression of nanocrystalline materials under different pressure. On comparing with the experimental data it gives good results at low pressure, but for higher compression it deviates from the experimental points. Therefore, the Equation of State is modified empirically to study the pressure-volume relation for nanomaterials, namely, n-Rb3C60, n-CdSe (rocksalt phase), n-TiO2 (anatase and rutile phase), Fe-filled nanotube, and γ-Fe2O3, at high pressure. The results obtained from the empirical Equation of State are found to be in better agreement with the available experimental data.

Equation of state and elastic properties of ACrO3 (A=Pb, Ca, Sr and Ba) perovskites under high pressure

Abstract We employ the spin-polarized generalized gradient approximation within the density functional theory to investigate the equation of state, magnetism and elastic constant of cubic ACrO3 (A=Pb, Ca, Sr, and Ba) perovskite. The antiferromagnetic phase is the most stable state at zero pressure. Under pressure, the ferromagnetic state will transform to the non-magnetic state. Considering the effect of magnetism, the equilibrium lattice constant, the bulk modulus and the high pressure equations of state agree well with the available experiments. By using the energy-strain method, the predicted elastic properties are satisfactory.

Analysis of High-Pressure Equation of State for Solids Based on the Lattice Potential Theory

A two-parameter high-pressure equation of state (EOS) is derived on the basis of the lattice potential theory using the concept of a short-range force constant as introduced by Born and Huang. The application of the EOS to some solids is presented and compared with the Birch–Murnaghan (BM) third-order EOS, the BM fourth-order EOS, and the Vinet EOS. A comparison of the results provides a crucial test for the EOSs used in this article.

HIGHER ORDER THERMOELASTIC PROPERTIES OF THE EARTH LOWER MANTLE AND CORE

We have used some of the most reliable high pressure equations of state (EOS) to determine the thermoelastic Grüneisen parameter and its higher order volume derivatives for the lower mantle, outer core and inner core of the Earth. The cross derivatives of bulk modulus with respect to pressure and temperature have also been obtained for the deep interior of the Earth using the results based on the modified free volume theory for the Grüneisen parameter. We have used five EOS viz. (a) modified Rydberg EOS, (b) modified Poirier–Tarantola EOS, (c) Hama–Suito EOS, (d) Stacey EOS, and (e) Kushwah EOS to determine pressure derivatives of bulk modulus. The results for thermoelastic parameters obtained in the present study show systematic variations with the increase in pressure.

High temperature and high pressure equation of state of gold

High-temperature and high-pressure equation of state (EOS) of Au has been developed using measured data from shock compression up to 240 GPa, volume thermal expansion between 100 and 1300 K and 0 GPa, and temperature dependence of bulk modulus at 0 GPa from ultrasonic measurements. The lattice thermal pressures at high temperatures have been estimated based on the Mie-Grüneisen-Debye type treatment with the Vinet isothermal EOS. The contribution of electronic thermal pressure at high temperatures, which is relatively insignificant for Au, has also been included here. The optimized EOS parameters are K'0T = 6.0 and q = 1.6 with fixed K0T = 167 GPa, γ0 = 2.97, and Θ0 = 170 K from previous investigations. We propose the present EOS to be used as a reliable pressure standard for static experiments up to 3000K and 300 GPa.

Elastic–plastic-hydrodynamic analysis of crater blasting in steel fiber reinforced concrete

This paper presents a numerical analysis of crater blasting in steel fiber reinforced concrete (SFRC). In order to model the nonlinear damage-softening behavior of SFRC, the effective stress and effective plastic strain curve is tabulated and used as input for the material Type10 (MAT_ELASTIC_PLASTIC_HYDRO) available in LS-DYNA. The Gruneisen equation of state (EOS) is used to model the pressure volume relationship. With the two erosion criteria namely tensile cut-off and failure strain incorporated, the crater blasting in SFRC is simulated. Numerical results show that the adopted model and high-pressure EOS can well capture the main characteristics and failure process of SFRC under blast loading, and the related parameters can be determined conveniently. In addition, the volume fraction of fibers exerts a significant influence on the dimension of blast-induced crater.