Metals physics at ultrahigh pressure: Aluminum, copper, and lead as prototypes

Density deficit of Earth's core revealed by a multimegabar primary pressure scale

An accurate pressure scale is a fundamental requirement to understand planetary interiors. Here, we establish a primary pressure scale extending to the multimegabar pressures of Earth's core, by combined measurement of the acoustic velocities and the density from a rhenium sample in a diamond anvil cell using inelastic x-ray scattering and x-ray diffraction. Our scale agrees well with previous primary scales and shock Hugoniots in each experimental pressure range and reveals that previous scales have overestimated laboratory pressures by at least 20% at 230 gigapascals. It suggests that the light element content in Earth's inner core (the density deficit relative to iron) is likely to be double what was previously estimated, or Earth's inner core temperature is much higher than expected, or some combination thereof.

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.

What Determines the fcc-bcc Structural Transformation in Shock Compressed Noble Metals?

High pressure structural transformations are typically characterized by the thermodynamic state (pressure-volume-temperature) of the material. We present in situ x-ray diffraction measurements on laser-shock compressed silver and platinum to determine the role of deformation-induced lattice defects on high pressure phase transformations in noble metals. Results for shocked Ag show a copious increase in stacking faults (SFs) before transformation to the body-centered-cubic (bcc) structure at 144-158 GPa. In contrast, shock compressed Pt remains largely free of SFs and retains the fcc structure to over 380 GPa. These findings, along with recent results for shock compressed gold, show that SF formation promotes high pressure structural transformations in shocked noble metals that are not observed under static compression. Potential SF-related mechanisms for fcc-bcc transformations are discussed.

Development of shock-dynamics study with synchrotron-based time-resolved X-ray diffraction using an Nd:glass laser system

The combination of high-power laser and synchrotron X-ray pulses allows us to observe material responses under shock compression and release states at the crystal structure on a nanosecond time scale. A higher-power Nd:glass laser system for laser shock experiments was installed as a shock driving source at the NW14A beamline of PF-AR, KEK, Japan. It had a maximum pulse energy of 16 J, a pulse duration of 12 ns and a flat-top intensity profile on the target position. The shock-induced deformation dynamics of polycrystalline aluminium was investigated using synchrotron-based time-resolved X-ray diffraction (XRD) under laser-induced shock. The shock pressure reached up to about 17 GPa with a strain rate of at least 4.6 × 10⁷ s^-1 and remained there for nanoseconds. The plastic deformation caused by the shock-wave loading led to crystallite fragmentation. The preferred orientation of the polycrystalline aluminium remained essentially unchanged during the shock compression and release processes in this strain rate. The newly established time-resolved XRD experimental system can provide useful information for understanding the complex dynamic compression and release behaviors.

Path integral Monte Carlo simulations of warm dense aluminum

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of 0.1-32.4gcm^{-3} and 10^{4}-10^{8} K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and 〈Z〉 to reveal the evolution of the plasma structure and ionization behavior.

Quantum chemical calculations of thermodynamic and mechanical properties of the intermetallic phases in copper–scandium alloy

To understand how the intermetallic phases of Cu–Sc influence the thermal stability and mechanical strength of Cu–Sc alloys, thermodynamic and mechanical characters of the Cu–Sc alloy have been calculated by first-principles. The lattice parameters of Cu4Sc phase are obtained by calculated and the CuSc phase is found to be the most stable phase based on formation energies. In the binary Cu–Sc alloy, the shear moduli of Cu4Sc and Cu2Sc phases along the [100](001) crystal orientation are easier than those along the [100](010) crystal orientation, respectively. Pure Cu phase acts as the most stiffness phase while [Formula: see text]Sc phase has the lowest stiffness. Cu4Sc phase possesses the best plasticity while CuSc phase possesses the worst plasticity. Cu4Sc phase is the most ductile phase while [Formula: see text]Sc phase is the most brittle phase. From the partial density of states, the valence bands of binary Cu–Sc phases are dominated by the Sc-[Formula: see text] states.

Measurement of Body-Centered-Cubic Aluminum at 475 GPa

Nanosecond in situ x-ray diffraction and simultaneous velocimetry measurements were used to determine the crystal structure and pressure, respectively, of ramp-compressed aluminum at stress states between 111 and 475 GPa. The solid-solid Al phase transformations, fcc-hcp and hcp-bcc, are observed at 216±9 and 321±12  GPa, respectively, with the bcc phase persisting to 475 GPa. The high-pressure crystallographic texture of the hcp and bcc phases suggests close-packed or nearly close-packed lattice planes remain parallel through both transformations.

A new embedded-atom method approach based on the pth moment approximation

Large scale atomistic simulations with suitable interatomic potentials are widely employed by scientists or engineers of different areas. The quick generation of high-quality interatomic potentials is urgently needed. This largely relies on the developments of potential construction methods and algorithms in this area. Quantities of interatomic potential models have been proposed and parameterized with various methods, such as the analytic method, the force-matching approach and multi-object optimization method, in order to make the potentials more transferable. Without apparently lowering the precision for describing the target system, potentials of fewer fitting parameters (FPs) are somewhat more physically reasonable. Thus, studying methods to reduce the FP number is helpful in understanding the underlying physics of simulated systems and improving the precision of potential models. In this work, we propose an embedded-atom method (EAM) potential model consisting of a new manybody term based on the pth moment approximation to the tight binding theory and the general transformation invariance of EAM potentials, and an energy modification term represented by pairwise interactions. The pairwise interactions are evaluated by an analytic-numerical scheme without the need to know their functional forms a priori. By constructing three potentials of aluminum and comparing them with a commonly used EAM potential model, several wonderful results are obtained. First, without losing the precision of potentials, our potential of aluminum has fewer potential parameters and a smaller cutoff distance when compared with some constantly-used potentials of aluminum. This is because several physical quantities, usually serving as target quantities to match in other potentials, seem to be uniquely dependent on quantities contained in our basic reference database within the new potential model. Second, a key empirical parameter in the embedding term of the commonly used EAM model is found to be related to the effective order of moments of local density of states. This may provide a way to improve the precision of EAM potentials further through more precise approximations to tight binding theory. In addition, some critical details about construction procedures are discussed.

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).

Effects of interstitial impurities on the high pressure martensitic α to ω structural transformation and grain growth in zirconium

Static high pressure diamond anvil cell experiments were performed on three polycrystalline Zr samples having varying interstitial impurity concentrations. Systematic increase in transition pressure with the increase in the amount of interstitial impurities is observed for the martensitic α →ω structural phase transition in Zr. Significant room temperature crystal grain growth is also observed for the two highest purity samples at the α →ω transition. In the case of the lowest purity sample interstitial impurities obstruct the α →ω transition, while possibly helping impede grain growth-even as the sample is heated to 1279 K.

Equations of state for solids under strong compression

Various approaches for the representation of equation of state data for solids under strong compression are discussed. The theoretical background for reasonable extrapolations to higher pressures and higher as well as lower temperatures is described. The distinction between ideal, regular, and anomalous behaviour allows to gain deeper insight into the electronic changes occurring in various solids under strong compression. The discussion of experimental data for various regular solids leads finally to an estimate of the accuracy obtained in the present realisation of a practical pressure scale based on equation of state measurements.

Applicability of isothermal unrealistic two-parameter equations of state for solids

The aim of the present study, an extension of a recent one (Bose Roy and Bose Roy 2005 J. Phys.: Condens. Matter 17 6193), is to assess and compare the curve-fitting utility of the isothermal unrealistic two-parameter equations of state for solids (EOS), proposed at different stages in the development of the EOS field, for the purposes of smoothing and interpolation of pressure-volume data, and extraction of accurate values of the isothermal bulk modulus and its pressure derivative. To this end, 21 such EOSs are considered, formulated by/labelled as Born-Mie (1920), Born-Mayer (1932), Bardeen (1938), Slater-Morse (1939), Birch-Murnaghan (1947), Pack-Evans-James (1948), Lagrangian (1951), Davydov (1956), Davis and Gordon (1967), Onat and Vaisnys (1967), Grover-Getting-Kennedy (1973), Brennan-Stacey (1979), Walzer-Ullmann-Pan'kov (1979), Rydberg (1981), Dodson (1987), Holzapfel (1991), Parsafar-Mason (1994), Shanker-Kushwah-Kumar (1997), Poirier-Tarantola (1998), Deng-Yan (2002) and Kun-Loa-Syassen (2003). Furthermore, all these EOSs are compared with our three-parameter EOS, as well as its two-parameter counterpart proposed in this work. We have applied all the EOS models, with no constraint on the parameters, to the accurate and model-independent isotherms of nine solids. The applicability has been assessed in terms of an unbiased composite test, comprising fitting accuracy, agreement of the fit parameters with experiment, stability of the fit parameters with variation in the compression/pressure ranges and on the basis of the number of wiggles of the data deviation curves about the fit parameters. Furthermore, a rigorous method is devised to scale the relative adequacy of the EOSs with respect to the test parameters. A number of remarkable findings emerge from the present study. Surprisingly, both the old EOSs, the Born-Mie and the Pack-Evans-James, are significantly better in their curve-fitting capability than the Birch-Murnaghan EOS which has been widely used and continues to be used for curve-fitting purposes as a standard EOS in the literature. The Born-Mayer as well as the Walzer-Ullmann-Pan'kov models also fit isotherms better than the Birch. The performance of the EOS based on the Rydberg potential-that has been rediscovered by Rose et al (1984 Phys. Rev. B 29 2963), and strongly promoted by Vinet et al (1989 J. Phys.: Condens. Matter 1 1941) as the so-called universal equation of state, and is currently used as a standard EOS along with that of the Birch-is very poor, on a comparative scale. Furthermore, the curve-fitting capability of our original three-parameter EOS, and more importantly its two-parameter counterpart, is superior to all the isothermal unrealistic two-parameter EOSs so far proposed in the literature.

Evidence of a fcc-hcp transition in aluminum at multimegabar pressure

The structure phase transition and the equation of state (EOS) of the third-period simple metal Al were investigated at pressure up to 333 GPa by powder x-ray diffraction experiments. The theoretically predicted fcc-hcp transition was observed at the reduced volume V/V0 of 0.509(1), corresponding to the pressure of 217+/-10 GPa. From the obtained pressure-volume data, the pressure derivative of the bulk modulus K0' for the EOS of fcc-Al was determined to be 4.83(3) by fitting to the Vinet formulation with a fixed value 72.7 GPa of K0 obtained from previous ultrasonic experiments.

Equation of state and transport coefficients for dense plasmas

We hereby present a model to describe the thermodynamic and transport properties of dense plasmas. The electronic and ionic structures are determined self-consistently using finite-temperature density functional theory and Gibbs-Bogolyubov inequality. The main thermodynamic quantities, i.e., internal energy, pressure, entropy, and sound speed, are obtained by numerical differentiation of the plasma total Helmholtz free energy. Electronic electrical and thermal conductivities are calculated from the Ziman approach. Ionic transport coefficients are estimated using those of hard-sphere system and the Rosenfeld semiempirical "universal" correspondence between excess entropy and dimensionless transport coefficients of dense fluids. Numerical results and comparisons with experiments are presented and discussed.

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.

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

Calculated Hugoniots and 293-K isotherms at pressures up to 1 TPa (10 Mbar) for the five reference metals Al, Cu, Ta, Mo, and W are reported using the classical mean-field approach where both the cold and the thermal parts of the Helmholtz free energy are derived entirely from the 0-K total energies and electronic density of states calculated with the full-potential linearized augmented plane wave method within the generalized gradient approximation to exchange correlational functional. Our approach permits efficient computation and invokes no empirical parameters. Both the experimental Hugoniots and 293-K isotherms are reproduced excellently.

In situ X-Ray study of thermal expansion and phase transition of iron at multimegabar pressure

The density of varepsilon-iron has been calculated at pressures and temperatures up to 300 GPa and 1300 K, respectively. We observe varepsilon to beta phase transition at pressures between 135 and 300 GPa and temperature above 1350 K; the pattern can be interpreted in terms of double hexagonal close-packed structure. The density calculated at high pressure and temperature (330-360 GPa and 5000-7000 K) closely matches with preliminary reference Earth model density, thereby imposing constraint on the composition of the Earth's inner core.

Ultrahigh-Pressure Melting of Lead: A Multidisciplinary Study

Measurements of the melting temperature of lead, carried out to pressures of 1 megabar (10(11) pascal) and temperatures near 4000 kelvin by means of a laser-heated diamond cell, are in excellent agreement with the results of previous shock-wave experiments. The data are analyzed by means of first principles quantum mechanical calculations, and the agreement documents the reliability of current experimental and theoretical techniques for studies of melting at ultrahigh pressures. These studies have potentially wide-ranging applications, from planetary science to condensed matter physics.