Search

Investigating how solid matter behaves at enormous pressures, such as those found in the deep interiors of giant planets, is a great experimental challenge. Over the past decade, computational predictions have revealed that compression to terapascal pressures may bring about counter-intuitive changes in the structure and bonding of solids as quantum mechanical forces grow in influence1–6. Although this behaviour has been observed at modest pressures in the highly compressible light alkali metals7,8, it has not been established whether it is commonplace among high-pressure solids more broadly. We used shaped laser pulses at the National Ignition Facility to compress elemental Mg up to 1.3 TPa, which is approximately four times the pressure at the Earth’s core. By directly probing the crystal structure using nanosecond-duration X-ray diffraction, we found that Mg changes its crystal structure several times with non-close-packed phases emerging at the highest pressures. Our results demonstrate that phase transformations of extremely condensed matter, previously only accessible through theoretical calculations, can now be experimentally explored.

Pushing a pressure standard A challenge for understanding systems at extreme conditions is knowing the exact pressure at which exotic behaviors occur. This situation is caused by the lack of an absolute pressure-density relationship of standard pressure calibrants. Fratanduono et al. conducted a series of dynamic compression observations on platinum and gold to establish a high-pressure scale for these metals up to terapascal conditions (see the Perpsective by Jeanloz). This work provides a robust calibration when using these standards in high-pressure devices such as diamond anvil cells. Science , abh0364, this issue p. 1063 ; see also abi8015, p. 1037

Equation-of-state (pressure, density, temperature, internal energy) and reflectivity measurements on shock-compressed CO_{2} at and above the insulating-to-conducting transition reveal new insight into the chemistry of simple molecular systems in the warm-dense-matter regime. CO_{2} samples were precompressed in diamond-anvil cells to tune the initial densities from 1.35 g/cm^{3} (liquid) to 1.74 g/cm^{3} (solid) at room temperature and were then shock compressed up to 1 TPa and 93 000 K. Variation in initial density was leveraged to infer thermodynamic derivatives including specific heat and Gruneisen coefficient, exposing a complex bonded and moderately ionized state at the most extreme conditions studied.

Ramp compression along a low-temperature adiabat offers a unique avenue to explore the physical properties of materials at the highest densities of their solid form, a region inaccessible by single shock compression. Using the National Ignition Facility and OMEGA laser facilities, copper samples were ramp compressed to peak pressures of 2.30 TPa and densities of nearly $30\text{ }\text{ }\mathrm{g}/\mathrm{cc}$, providing fundamental information regarding the compressibility and phase of copper at pressures more than 5 times greater than previously explored. Through x-ray diffraction measurements, we find that the ambient face-centered-cubic structure is preserved up to 1.15 TPa. The ramp compression equation-of-state measurements shows that there are no discontinuities in sound velocities up to 2.30 TPa, suggesting this phase is likely stable up to the peak pressures measured, as predicted by first-principal calculations. The high precision of these quasiabsolute measurements enables us to provide essential benchmarks for advanced computational studies on the behavior of dense monoatomic materials under extreme conditions that constitute a stringent test for solid-state quantum theory. We find that both density-functional theory and the stabilized jellium model, which assumes that the ionic structure can be replaced by an ionic charge distribution by constant positive-charge background, reproduces our data well. Further, our data could serve to establish new international secondary scales of pressure in the terapascal range that is becoming experimentally accessible with advanced static and dynamic compression techniques.

Little is known regarding the liquid structure of materials compressed to extreme conditions, and even less is known about liquid structures undergoing rapid compression on nanosecond timescales. Here we report on liquid structure factor and radial distribution function measurements of tin shock compressed to 84(19) GPa. High-quality, femtosecond x-ray diffraction measurements at the Linac Coherent Light Source were used to extract the liquid diffuse scattering signal. From the radial distribution function, we find that the structural evolution of the liquid with increasing pressuremimics the evolution of the solid phase. With increasing pressure we find that the liquid structure evolves from a complex structure, with low coordination number, to a simple liquid structure with a coordination number of ∼ 12.We provide a pathway for future experiments to study liquids at elevated pressures using high-energy lasers to shock compress materials beyond the reach of static diamond anvil cell techniques.

MgO is a major constituent of the ${\text{MgO-FeO-SiO}}_{2}$ system that comprises the Earth's mantle and that of super-Earth exoplanets. Knowledge of its high-pressure behavior is important for modeling the more complex compounds. This paper presents measurements of the principal Hugoniot, sound velocity, and temperature of MgO, shocked to pressures of 710 to 2300 GPa using laser-driven compression. The Hugoniot and temperature measurements compare favorably to previous results constraining the shock response of MgO at extreme conditions. The Gr\"uneisen parameter was calculated from the Hugoniot and sound velocity data and was found to be underpredicted by tabular models. The sound velocity of liquid MgO is overpredicted by models implying that the quantity of partial melt required to match decreased wave speeds in ultralow velocity zones in the lower mantle may be less than previously assumed and experiments at lower-mantle pressures are needed.

We present quartz and molybdenum single-shock Hugoniot data to 62 Mbar and 120 Mbar, respectively. Quartz and molybdenum are attractive standard materials for Hugoniot equation-of-state impedance-matching studies. Quartz is advantageous because a reflecting shock front is supported above $\ensuremath{\sim}1$ Mbar whose velocity can be tracked in situ to very high accuracy. Molybdenum's relatively high impedance makes it a more appropriate standard for other high-impedance material studies to avoid large departures from the standard principal Hugoniot upon release or reshock into the sample. Extensive measurements already exist for both materials up to about 10 Mbar and 10 eV, but new high-energy-density facilities and techniques have extended the experimentally accessible pressure range to g100 Mbar. The data presented here indicate which modern equation-of-state models can be reliably extended into newly-accessible experimental regimes.

We present laser-driven shock compression experiments on cryogenic liquid deuterium to 550 GPa along the principal Hugoniot and reflected-shock data up to 1 TPa. High-precision interferometric Doppler velocimetry and impedance-matching analysis were used to determine the compression accurately enough to reveal a significant difference as compared to state-of-the-art ab initio calculations and thus, no single equation of state model fully matches the principal Hugoniot of deuterium over the observed pressure range. In the molecular-to-atomic transition pressure range, models based on density functional theory calculations predict the maximum compression accurately. However, beyond 250 GPa along the principal Hugoniot, first-principles models exhibit a stiffer response than the experimental data. Similarly, above 500 GPa the reflected shock data show 5%-7% higher compression than predicted by all current models.

In the canonical ramp compression experiment, a smoothly-increasing load is applied to the surface of the sample, and the particle velocity history is measured at two or more different distances into the sample, at interfaces where the surface of the sample can be probed. The velocity histories are used to deduce a stress-density relation, usually using iterative Lagrangian analysis to account for the perturbing effect of the impedance mismatch at the interface. In that technique, a stress- density relation is assumed in order to correct for the perturbation, and is adjusted until it becomes consistent with the deduced stress-density relation. This process is subject to the usual difficulties of nonlinear optimization, such as the existence of local minima (sensitivity to the initial guess), possible failure to converge, and relatively large computational effort. We show that, by considering the interaction of successive characteristics reaching the interfaces, the stress-density relation can be deduced directly by recursion rather than iteration. This calculation is orders of magnitude faster than iterative analysis, and does not require an initial guess. Direct recursion may be less suitable for very noisy data, but it was robust when applied to trial data. The stress-density relation deduced was identical to the result from iterative Lagrangian analysis.

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.

The equation of state (EOS) of carbon in its high-pressure solid and liquid phases is of interest to planetary astrophysics and inertial confinement fusion. Of particular interest are the high-pressure shock and release responses of diamond as these provide rigorous constraints on important paths through the EOS. This paper presents experimental Hugoniot and release data for both single-crystal diamond (SCD) and nanocrystalline diamond (NCD), which is comprised of nanometer-scale diamond grains and is $\ensuremath{\sim}5%$ less dense than SCD. We find that NCD has a stiffer Hugoniot than SCD that can be attributed to porosity. A Gr\"uneisen parameter of $\ensuremath{\sim}1$ was derived from the data, which suggests increased coordination in the high-pressure fluid carbon compared to ambient diamond.

X-ray free electron laser (XFEL) sources have revolutionized our capability to study ultrafast material behavior. Using an XFEL, we revisit the structural dynamics of shock compressed bismuth, resolving the transition sequence on shock release in unprecedented details. Unlike previous studies that found the phase-transition sequence on shock release to largely adhere to the equilibrium phase diagram (i.e., Bi-V → Bi-III → Bi-II → Bi-I), our results clearly reveal previously unseen, non-equilibrium behavior at these conditions. On pressure release from the Bi-V phase at 5 GPa, the Bi-III phase is not formed but rather a new metastable form of Bi. This new phase transforms into the Bi-II phase which in turn transforms into a phase of Bi which is not observed on compression. We determine this phase to be isostructural with β-Sn and recover it to ambient pressure where it exists for 20 ns before transforming back to the Bi-I phase. The structural relationship between the tetragonal β-Sn phase and the Bi-II phase (from which it forms) is discussed. Our results show the effect that rapid compression rates can have on the phase selection in a transforming material and show great promise for recovering high-pressure polymorphs with novel material properties in the future.

A equation of state (EOS) experimental technique that enables the study of thermodynamic derivatives into the TPa regime is described and applied to boron carbide (${\mathrm{B}}_{4}\mathrm{C}$). Data presented here are principal Hugoniot sound speed measurements reported using a laser-driven shock platform, providing a means to explore the high-pressure off-Hugoniot response of opaque materials. The extended ${\mathrm{B}}_{4}\mathrm{C}$ Hugoniot suggests the presence of a high-pressure phase, as recently predicted by molecular dynamics simulations, adding to the complexity of the existing phase diagram.

We combine experiments and theoretical models to characterize warm dense deuterium. A shockwave was driven in a planar target by the OMEGA laser without a standard pusher making the analysis independent of a quartz or aluminium pressure standard. The conditions of the shocked material were diagnosed with VISAR and optical pyrometry which yields the shock velocity (16.9 ± 0.9 km/s) and the temperature (0.57 ± 0.05 eV). We find a self-consistent description of the data when using ab initio simulations (DFT-MD), but not for other equation of state (EOS) models tested. © 2011 Elsevier B.V.

We report on a series of experiments that use high-power lasers to ramp-compress aluminum (Al) up to 475 GPa. Under this quasi-isentropic compression, Al remains in the solid state and two solid–solid phase transformations are observed. In situ x-ray diffraction is performed to detect the crystal structure. A velocimetry diagnostic measures particle velocities in order to infer the pressure in the Al sample. We show that a solid–solid phase transition, consistent with a transformation to a hexagonal close-packed (hcp) structure, occurs at 216 ± 9 GPa. At higher pressures, a transformation to a structure consistent with the body-centered cubic (bcc) structure occurs at 321 ± 12 GPa. These phase transitions are also observed in 6061-O (annealed) Al alloy at 175 ± 9 GPa and 333 ± 11 GPa, respectively. Correlations in the high-pressure crystallographic texture suggests the close-packed face-centered cubic (fcc) (111), hcp (002), and bcc (110) planes remain parallel through the solid–solid fcc–hcp and hcp–bcc transformations.

We developed an iterative forward analysis (IFA) technique with the ability to use hydrocode simulations as a fitting function for analysis of dynamic compression experiments. The IFA method optimizes over parameterized quantities in the hydrocode simulations, breaking the degeneracy of contributions to the measured material response. Velocity profiles from synthetic data generated using a hydrocode simulation are analyzed as a first-order validation of the technique. We also analyze multiple magnetically driven ramp compression experiments on copper and compare with more conventional techniques. Excellent agreement is obtained in both cases.

The sound velocity in a shocked material provides information about its off-Hugoniot behavior of a material at high pressures. This information can be used to extend the knowledge gained in Hugoniot experiments and to model the re-shock and release behavior. Silica is one of the most important materials for equation of state studies because of its prevalence in the earth's interior and the well-defined properties of α-quartz. This article presents the sound velocity measurements of amorphous fused silica over the range 200 to 1100 GPa using laser-driven shocks and an α-quartz standard. These measurements demonstrate the technique proposed by Fratanduono et al. [J. Appl. Phys. 116, 033517 (2014)] to determine the sound velocity from the arrival of acoustic perturbations. The results compare favorably to the SESAME 7386 equation-of-state table. The Gruneisen parameter was calculated from the sound velocity data and found to be Γ=0.66±0.05 at densities above 6 g/cm3, an increase in precision by a factor of t...

Experiments in high-energy-density physics often use optical pyrometry to determine temperatures of dynamically compressed materials. In combination with simultaneous shock-velocity and optical-reflectivity measurements using velocity interferometry, these experiments provide accurate equation-of-state data at extreme pressures (P > 1 Mbar) and temperatures (T > 0.5 eV). This paper reports on the absolute calibration of the streaked optical pyrometer (SOP) at the Omega Laser Facility. The wavelength-dependent system response was determined by measuring the optical emission from a National Institute of Standards and Technology-traceable tungsten-filament lamp through various narrowband (40-nm-wide) filters. The integrated signal over the SOP's ∼250-nm operating range is then related to that of a blackbody radiator using the calibrated response. We present a simple closed-form equation for the brightness temperature as a function of streak-camera signal derived from this calibration. Error estimates indicate that brightness temperature can be inferred to a precision of

The properties of silica are important to geophysical and high-pressure equation-of-state research. Its most-prevalent crystalline form, α-quartz, has been extensively studied to TPa pressures. This article presents Hugoniot measurements on amorphous silica, commonly referred to as fused silica, over a range from 200 to 1600 GPa using laser-driven shocks and an α-quartz standard. These results extend the measured Hugoniot of fused silica to higher pressures. In the 200- to 600-GPa range, the data are in very good agreement with those obtained by Qi et al. [Phys. Plasmas 22, 062706 (2015)] using magnetically driven aluminum impactors and aluminum as a standard material. A new shock velocity/particle velocity relation is derived to fit the experimental data.

The iterative Lagrangian analysis (ILA) applied to free-surface velocity measurements of ramp-compressed samples is an established technique to determine the stress-density response of materials up to 50 Mbar pressures. In this work, we examine the accuracy of the ILA of ramp compression profiles with multiple shock waves present through the analysis of simulated compression profiles. The results presented indicate that ramp-compression data with weak shock waves can be analyzed using the ILA to quantitatively measure the absolute stress and density along the compression path.