Calculated equation of state of al, cu, ta, mo, and W to 1000 GPa

Ab initio quasi-harmonic thermoelasticity of molybdenum at high temperature and pressure

We present the ab initio thermoelastic properties of body-centered cubic molybdenum under extreme conditions obtained within the quasi-harmonic approximation including both the vibrational and electronic thermal excitation contributions to the free energy. The quasi-harmonic temperature-dependent elastic constants are calculated and compared with existing experiments and with the quasi-static approximation. We find that the quasi-harmonic approximation allows for a much better interpretation of the experimental data, confirming the trend found previously in other metals. Using the Voigt-Reuss-Hill average, we predict the compressional and shear sound velocities of polycrystalline molybdenum as a function of pressure for several temperatures, which might be accessible in experiments.

Pressure and temperature dependentab-initioquasi-harmonic thermoelastic properties of tungsten

We present theab-initiotemperature and pressure dependent thermoelastic properties of body-centered cubic tungsten. The temperature dependent quasi-harmonic elastic constants (ECs) are computed at several reference volumes including both the phonon and the electronic excitations contribution to the free energy and interpolated at different temperatures and pressures. Good agreement with the experimental ECs on a single crystal at ambient pressure is found. The pressure and temperature dependence of the shear sound velocity measured on polycrystalline tungsten by Qiet alis also in agreement with theory. Some discrepancies are found instead for the compressional velocity at high temperature and this is attributed to the temperature derivative of the bulk modulus, higher in theory than in experiment. These conclusions are reached both by PBE and by PBEsol functionals. The two give elastic properties with a similar pressure and temperature dependence although the latter is closer to experiment at 0 K.

Molecular Dynamics Study on Hugoniot State and Mie-Grüneisen Equation of State of 316 Stainless Steel for Hydrogen Storage Tank

To promote the popularization and development of hydrogen energy, a micro-simulation approach was developed to determine the Mie-Grüneisen EOS of 316 stainless steel for a hydrogen storage tank in the Hugoniot state. Based on the combination of the multi-scale shock technique (MSST) and molecular dynamics (MD) simulations, a series of shock waves at the velocity of 6-11 km/s were applied to the single-crystal (SC) and polycrystalline (PC) 316 stainless steel model, and the Hugoniot data were obtained. The accuracy of the EAM potential for Fe-Ni-Cr was verified. Furthermore, Hugoniot curve, cold curve, Grüneisen coefficient (γ), and the Mie-Grüneisen EOS were discussed. In the internal pressure energy-specific volume (P-E-V) three-dimensional surfaces, the Mie-Grüneisen EOSs show concave characteristics. The maximum error of the calculation results of SC and PC is about 10%. The results for the calculation deviations of each physical quantity of the SC and PC 316 stainless steel indicate that the grain effect of 316 stainless steel is weak under intense dynamic loads, and the impact of the grains in the cold state increases with the increase in the volume compression ratio.

Unexpected low thermal expansion coefficients of pentadiamond

A new carbon allotrope, pentadiamond, was recently reported in the literature. Herein, we investigate its thermal expansion and thermoelastic properties by first principles. It is observed that the bulk modulus and hardness of pentadiamond are far less than those of diamond, but the thermal expansion of pentadiamond is lower than that of diamond in the range of 0 K to 2000 K, and even negative in the temperature range of 0-190 K. The negative thermal expansion at low temperature originates from the transverse vibrations of the edge-shared atoms in the coplanar double-pentagon. The low thermal expansion at high temperature is contributed by the strong bonds in pentadiamond. Benefiting from the low thermal expansion, the elastic constants of pentadiamond decrease very slowly with respect to temperature compared with those of diamond. The low sensitivity of thermodynamic and thermoelastic properties to temperature makes pentadiamond a promising material for high anti-thermal-shock and accurate electronic device applications.

Different structural transitions of rapidly supercooled tantalum melt under pressure

Molecular dynamics (MD) simulations have been performed to study the effects of pressure (P) on the crystallization of tantalum (Ta) under different pressures from [0, 100] GPa. The average potential energy of atoms in the system, the pair distribution function and largest standard cluster analysis (LSCA) have been employed to analyze the structure evolution. It was found that the solidified state at 100 K changes from the complex crystal (β-Ta) through the body-centered cubic (bcc) crystal (α-Ta) to the hexagonal close-packed (hcp) crystal with increasing pressure. At P ≤ 3 GPa, the favorable state is β-Ta, which is composed of Z12, Z14 and Z15 atoms, and crystallization starts at the same temperature of crystallization (Tc = 1897 K), while there is a stochastic relationship between the crystallinity and pressure. At P ∈ [3, 57.5] GPa, the melt is always crystallized into rather perfect α-Ta, and Tc is nearly linear to pressure. However, when P > 57.5 GPa, a quite perfect bcc crystal is first formed and then transforms to a hcp crystal via a solid-solid (bcc-hcp) phase transition. Moreover, if the new hcp atoms formed in the bcc stage are arranged in regular grains, the bcc-hcp transition would take a multiple-intermediate-state pathway else, a single-intermediate-state pathway is the possibilty. Additionaly, the parameter δs readily reflects the crystallinity of the β-Ta, and smaller the value of δs, higher is the crystallinity of the β-Ta. Finally, during the bcc-hcp transition under high pressure, the volume reduction is due to the rearrangement of atoms rather than the reduction in the atomic radius; a slight increase in the number of nearest neighboring pairs results in a significant increase of the system energy.

Topological Equivalence of the Phase Diagrams of Molybdenum and Tungsten

We demonstrate the topological equivalence of the phase diagrams of molybdenum (Mo) and tungsten (W), Group 6B partners in the periodic table. The phase digram of Mo to 800 GPa from our earlier work is now extended to 2000 GPa. The phase diagram of W to 2500 GPa is obtained using a comprehensive ab initio approach that includes (i) the calculation of the T = 0 free energies (enthalpies) of different solid structures, (ii) the quantum molecular dynamics simulation of the melting curves of different solid structures, (iii) the derivation of the analytic form for the solid–solid phase transition boundary, and (iv) the simulations of the solidification of liquid W into the final solid states on both sides of the solid–solid phase transition boundary in order to confirm the corresponding analytic form. For both Mo and W, there are two solid structures confirmed to be present on their phase diagrams, the ambient body-centered cubic (bcc) and the high-pressure double hexagonal close-packed (dhcp), such that at T = 0 the bcc–dhcp transition occurs at 660 GPa in Mo and 1060 GPa in W. In either case, the transition boundary has a positive slope d T / d P .

Thermal equation of state of Molybdenum determined from in situ synchrotron X-ray diffraction with laser-heated diamond anvil cells

Here we report that the equation of state (EOS) of Mo is obtained by an integrated technique of laser-heated DAC and synchrotron X-ray diffraction. The cold compression and thermal expansion of Mo have been measured up to 80 GPa at 300 K, and 92 GPa at 3470 K, respectively. The P-V-T data have been treated with both thermodynamic and Mie–Grüneisen-Debye methods for the thermal EOS inversion. The results are self-consistent and in agreement with the static multi-anvil compression data of Litasov et al. (J. Appl. Phys. 113, 093507 (2013)) and the theoretical data of Zeng et al. (J. Phys. Chem. B 114, 298 (2010)). These high pressure and high temperature (HPHT) data with high precision firstly complement and close the gap between the resistive heating and the shock compression experiment.

Evidence of scaling in the high pressure phonon dispersion relations of some elemental solids

First principles searches are carried out for the existence of an asymptotic scaling law for the zero temperature phonon dispersion relation of several elemental crystalline solids in the high pressure regime. The solids studied are Cu, Ni, Pd, Au, Al, and Ir in the face-centered-cubic (fcc) geometry and Fe, Re, and Os in the hexagonal-close-packed (hcp) geometry. At higher pressures, the dependence of the scale of frequency on pressure can be fitted well by a power law. Elements with a given crystalline geometry have values of the scaling exponent very close to each other (0.32 for fcc and 0.27 for hcp - with a scatter below five percent of the average).

Pressure-enabled phonon engineering in metals

We present a combined first-principles and experimental study of the electrical resistivity in aluminum and copper samples under pressures up to 2 GPa. The calculations are based on first-principles density functional perturbation theory, whereas the experimental setup uses a solid media piston-cylinder apparatus at room temperature. We find that upon pressurizing each metal, the phonon spectra are blue-shifted and the net electron-phonon interaction is suppressed relative to the unstrained crystal. This reduction in electron-phonon scattering results in a decrease in the electrical resistivity under pressure, which is more pronounced for aluminum than for copper. We show that density functional perturbation theory can be used to accurately predict the pressure response of the electrical resistivity in these metals. This work demonstrates how the phonon spectra in metals can be engineered through pressure to achieve more attractive electrical properties.

A first-principles approach to finite temperature elastic constants

A first-principles approach to calculating the elastic stiffness coefficients at finite temperatures was proposed. It is based on the assumption that the temperature dependence of elastic stiffness coefficients mainly results from volume change as a function of temperature; it combines the first-principles calculations of elastic constants at 0 K and the first-principles phonon theory of thermal expansion. Its applications to elastic constants of Al, Cu, Ni, Mo, Ta, NiAl, and Ni₃Al from 0 K up to their respective melting points show excellent agreement between the predicted values and existing experimental measurements.

Ab initio refinement of the thermal equation of state for bcc tantalum: the effect of bonding on anharmonicity

We report a detailed ab initio study for body-centered-cubic (bcc) Ta within the framework of the quasiharmonic approximation (QHA) to refine its thermal equation of state and thermodynamic properties. Based on the excellent agreement of our calculated phonon dispersion curve with experiment, the accurate thermal equations of state and thermodynamic properties are well reproduced. The thermal equation of state (EOS) and EOS parameters are considerably improved in our work compared with previous results by others. Furthermore, at high temperatures, the excellent agreement of our obtained thermal expansion and Hugoniot curves with experiments greatly verifies the validity of the quasiharmonic approximation at higher temperatures. It is known that pressure suppresses the vibrations of atoms from their equilibrium positions, i.e. the bondings among atoms are strengthened by pressure; for the same temperature, anharmonicity becomes less important at high pressure. Thus the highest valid temperature of the QHA can be reasonably extended to the larger range.

Molybdenum at high pressure and temperature: melting from another solid phase

The Gibbs free energies of bcc and fcc Mo are calculated from first principles in the quasiharmonic approximation in the pressure range from 350 to 850 GPa at room temperatures up to 7500 K. It is found that Mo, stable in the bcc phase at low temperatures, has lower free energy in the fcc structure than in the bcc phase at elevated temperatures. Our density-functional-theory-based molecular dynamics simulations demonstrate that fcc melts at higher than bcc temperatures above 1.5 Mbar. Our calculated melting temperatures and bcc-fcc boundary are consistent with the Mo Hugoniot sound speed measurements. We find that melting occurs at temperatures significantly above the bcc-fcc boundary. This suggests an explanation of the recent diamond anvil cell experiments, which find a phase boundary in the vicinity of our extrapolated bcc-fcc boundary.

Toward an internally consistent pressure scale

Our ability to interpret seismic observations including the seismic discontinuities and the density and velocity profiles in the earth's interior is critically dependent on the accuracy of pressure measurements up to 364 GPa at high temperature. Pressure scales based on the reduced shock-wave equations of state alone may predict pressure variations up to 7% in the megabar pressure range at room temperature and even higher percentage at high temperature, leading to large uncertainties in understanding the nature of the seismic discontinuities and chemical composition of the earth's interior. Here, we report compression data of gold (Au), platinum (Pt), the NaCl-B2 phase, and solid neon (Ne) at 300 K and high temperatures up to megabar pressures. Combined with existing experimental data, the compression data were used to establish internally consistent thermal equations of state of Au, Pt, NaCl-B2, and solid Ne. The internally consistent pressure scales provide a tractable, accurate baseline for comparing high pressure-temperature experimental data with theoretical calculations and the seismic observations, thereby advancing our understanding fundamental high-pressure phenomena and the chemistry and physics of the earth's interior.

Structure, metastability, and electron density of Al lattices in light of the model of anions in metallic matrices

This paper reports a theoretical investigation of the structure, stability, and electron charge density of cubic, rhombohedral, hexagonal, and monoclinic Al lattices. The equations of state and the elastic constants are computed from total energy calculations at different volumes and unit cell strains using the density functional theory approximation. The topology of the electron density is analyzed within the crystalline implementation of the atoms in molecules formalism. The results are discussed in light of the so-called anions in metallic matrices model, which permits the interpretation of the chemical bonding and the explanation of the existence of particular symmetries of inorganic crystals. First, the Al sublattices are identified as the reference building blocks of AlX(3) (X = F, Cl, OH) compounds. The calculations reveal that the equilibrium zero-pressure Al-Al shortest distance is around 2.75 A in all of the Al matrixes, similar to the value observed in the stable face centered cubic structure of Al at room conditions. Second, at their zero-pressure equilibrium geometries, the Al sublattices are found to fulfill the mechanical stability criteria or, alternatively, to show mechanical instabilities that are compatible with the distortions observed for the structures in AlX(3) crystals. However, at the equilibrium volumes of the AlX(3) crystals, all of the Al matrices violate the spinodal condition, and the cohesion and stabilization are provided by the nonmetallic X atoms. Third, the structural anisotropy of the Al sublattices seems to be the main factor to discriminate metallic matrices able to host nonmetallic elements. The inhomogeneities of the electron charge density, which favor the arrival of nonmetallic elements and the crystal formation, are notably enhanced in passing from the fcc structure of pure Al to the less isotropic Al matrices observed in AlX(3) compounds.

High-pressure melting of molybdenum

The melting curve of the body-centered cubic (bcc) phase of Mo has been determined for a wide pressure range using both direct ab initio molecular dynamics simulations of melting as well as a phenomenological theory of melting. These two methods show very good agreement. The simulations are based on density functional theory within the generalized gradient approximation. Our calculated equation of state of bcc Mo is in excellent agreement with experimental data. However, our melting curve is substantially higher than the one determined in diamond anvil cell experiments up to a pressure of 100 GPa. An explanation is suggested for this discrepancy.

First principles molecular dynamics of dense plasmas

Ab initio molecular dynamics calculations are performed for the equation of state of aluminum, spanning condensed matter and dense plasma regimes. Electronic exchange and correlation are included with either a zero- or finite-temperature local density approximation potential. Standard methods are extended to above the Fermi temperature by using final state pseudopotentials to describe thermally excited ion cores. The predicted Hugoniot equation of state agrees well with earlier plasma theories and with experiment for temperatures from 0 to 3 x 10(6) K.