Metastability of diamond ramp-compressed to 2 terapascals.

Carbon is the fourth-most prevalent element in the Universe and essential for all known life. In the elemental form it is found in multiple allotropes, including graphite, diamond and fullerenes, and it has long been predicted that even more structures can exist at pressures greater than those at Earth's core1-3. Several phases have been predicted to exist in the multi-terapascal regime, which is important for accurate modelling of the interiors of carbon-rich exoplanets4,5. By compressing solid carbon to 2 terapascals (20 million atmospheres; more than five times the pressure at Earth's core) using ramp-shaped laser pulses and simultaneously measuring nanosecond-duration time-resolved X-ray diffraction, we found that solid carbon retains the diamond structure far beyond its regime of predicted stability. The results confirm predictions that the strength of the tetrahedral molecular orbital bonds in diamond persists under enormous pressure, resulting in large energy barriers that hinder conversion to more-stable high-pressure allotropes1,2, just as graphite formation from metastable diamond is kinetically hindered at atmospheric pressure. This work nearly doubles the highest pressure at which X-ray diffraction has been recorded on any material.

Probing the Solid Phase of Noble Metal Copper at Terapascal Conditions.

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 g/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.

Extreme Hardening of Pb at High Pressure and Strain Rate.

We study the high-pressure strength of Pb and Pb-4wt%Sb at the National Ignition Facility. We measure Rayleigh-Taylor growth of preformed ripples ramp compressed to ∼400 GPa peak pressure, among the highest-pressure strength measurements ever reported on any platform. We find agreement with 2D simulations using the Improved Steinberg-Guinan strength model for body-centered-cubic Pb; the Pb-4wt%Sb alloy behaves similarly within the error bars. The combination of high-rate, pressure-induced hardening and polymorphism yield an average inferred flow stress of ∼3.8 GPa at high pressure, a ∼250-fold increase, changing Pb from soft to extremely strong.

Erratum: Measurement of Body-Centered-Cubic Aluminum at 475 GPa [Phys. Rev. Lett. 119, 175702 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.175702.

Absolute Equation-of-State Measurement for Polystyrene from 25 to 60 Mbar Using a Spherically Converging Shock Wave.

We have developed an experimental platform for the National Ignition Facility that uses spherically converging shock waves for absolute equation-of-state (EOS) measurements along the principal Hugoniot. In this Letter, we present one indirect-drive implosion experiment with a polystyrene sample that employs radiographic compression measurements over a range of shock pressures reaching up to 60 Mbar (6 TPa). This significantly exceeds previously published results obtained on the Nova laser [R. Cauble et al., Phys. Rev. Lett. 80, 1248 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.1248] at a strongly improved precision, allowing us to discriminate between different EOS models. We find excellent agreement with Kohn-Sham density-functional-theory-based molecular dynamics simulations.

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.

X-Ray Diffraction of Solid Tin to 1.2 TPa.

We report direct in situ measurements of the crystal structure of tin between 0.12 and 1.2 TPa, the highest stress at which a crystal structure has ever been observed. Using angle-dispersive powder x-ray diffraction, we find that dynamically compressed Sn transforms to the body-centered-cubic (bcc) structure previously identified by ambient-temperature quasistatic-compression studies and by zero-kelvin density-functional theory predictions between 0.06 and 0.16 TPa. However, we observe no evidence for the hexagonal close-packed (hcp) phase found by those studies to be stable above 0.16 TPa. Instead, our results are consistent with bcc up to 1.2 TPa. We conjecture that at high temperature bcc is stabilized relative to hcp due to differences in vibrational free energy.

Direct Observation of Melting in Shock-Compressed Bismuth With Femtosecond X-ray Diffraction.

The melting of bismuth in response to shock compression has been studied using in situ femtosecond x-ray diffraction at an x-ray free electron laser. Both solid-solid and solid-liquid phase transitions are documented using changes in discrete diffraction peaks and the emergence of broad, liquid scattering upon release from shock pressures up to 14 GPa. The transformation from the solid state to the liquid is found to occur in less than 3 ns, very much faster than previously believed. These results are the first quantitative measurements of a liquid material obtained on shock release using x-ray diffraction, and provide an upper limit for the time scale of melting of bismuth under shock loading.

Solid iron compressed up to 560 GPa.

Dynamic compression by multiple shocks is used to compress iron up to 560 GPa (5.6 Mbar), the highest solid-state pressure yet attained for iron in the laboratory. Extended x-ray absorption fine structure (EXAFS) spectroscopy offers simultaneous density, temperature, and local-structure measurements for the compressed iron. The data show that the close-packed structure of iron is stable up to 560 GPa, the temperature at peak compression is significantly higher than expected from pure compressive work, and the dynamic strength of iron is many times greater than the static strength based on lower pressure data. The results provide the first constraint on the melting line of iron above 400 GPa.

High resolution >40 keV x-ray radiography using an edge-on micro-flag backlighter at NIF-ARC.

Radiography of low-contrast features in high-density materials evolving on a nanosecond timescale requires a bright photon source in the tens of keV range with high temporal and spatial resolution. One application for sources in this category is the study of dynamic material strength in samples compressed to Mbar pressures at the National Ignition Facility, high-resolution measurements of plastic deformation under conditions relevant to meteor impacts, geophysics, armor development, and inertial confinement fusion. We present radiographic data and the modulation transfer function (MTF) analysis of a multi-component test object probed at ∼100 keV effective backlighter energy using a 5 µm-thin dysprosium foil driven by the NIF Advanced Radiographic Capability (ARC) short-pulse laser (∼2 kJ, 10 ps). The thin edge of the foil acts as a bright line-projection source of hard x rays, which images the test object at 13.2× magnification into a filtered and shielded image plate detector stack. The system demonstrates a superior contrast of shallow (5 µm amplitude) sinusoidal ripples on gold samples up to 90 µm thick as well as enhanced spatial and temporal resolution using only a small fraction of the laser energy compared to an existing long-pulse-driven backlighter used routinely at the NIF for dynamic strength experiments.

X-ray diffraction at the National Ignition Facility.

We report details of an experimental platform implemented at the National Ignition Facility to obtain in situ powder diffraction data from solids dynamically compressed to extreme pressures. Thin samples are sandwiched between tamper layers and ramp compressed using a gradual increase in the drive-laser irradiance. Pressure history in the sample is determined using high-precision velocimetry measurements. Up to two independently timed pulses of x rays are produced at or near the time of peak pressure by laser illumination of thin metal foils. The quasi-monochromatic x-ray pulses have a mean wavelength selectable between 0.6 Å and 1.9 Å depending on the foil material. The diffracted signal is recorded on image plates with a typical 2θ x-ray scattering angle uncertainty of about 0.2° and resolution of about 1°. Analytic expressions are reported for systematic corrections to 2θ due to finite pinhole size and sample offset. A new variant of a nonlinear background subtraction algorithm is described, which has been used to observe diffraction lines at signal-to-background ratios as low as a few percent. Variations in system response over the detector area are compensated in order to obtain accurate line intensities; this system response calculation includes a new analytic approximation for image-plate sensitivity as a function of photon energy and incident angle. This experimental platform has been used up to 2 TPa (20 Mbar) to determine the crystal structure, measure the density, and evaluate the strain-induced texturing of a variety of compressed samples spanning periods 2-7 on the periodic table.

X-ray scattering measurements on imploding CH spheres at the National Ignition Facility.

We have performed spectrally resolved x-ray scattering measurements on highly compressed polystyrene at pressures of several tens of TPa (100 Mbar) created by spherically convergent shocks at the National Ignition Facility. Scattering data of line radiation at 9.0 keV were recorded from the dense plasma shortly after shock coalescence. Accounting for spatial gradients, opacity effects, and source broadening, we demonstrate the sensitivity of the elastic scattering component to carbon K-shell ionization while at the same time constraining the temperature of the dense plasma. For six times compressed polystyrene, we find an average temperature of 86 eV and carbon ionization state of 4.9, indicating that widely used ionization models need revision in order to be suitable for the extreme states of matter tested in our experiment.

X-ray continuum emission spectroscopy from hot dense matter at Gbar pressures.

We have measured the time-resolved x-ray continuum emission spectrum of ∼30 times compressed polystyrene created at stagnation of spherically convergent shock waves within the Gbar fundamental science campaign at the National Ignition Facility. From an exponential emission slope between 7.7 keV and 8.1 keV photon energy and using an emission model which accounts for reabsorption, we infer an average electron temperature of 375 ± 21 eV, which is in good agreement with HYDRA-1D simulations.

Femtosecond visualization of lattice dynamics in shock-compressed matter.

The ultrafast evolution of microstructure is key to understanding high-pressure and strain-rate phenomena. However, the visualization of lattice dynamics at scales commensurate with those of atomistic simulations has been challenging. Here, we report femtosecond x-ray diffraction measurements unveiling the response of copper to laser shock-compression at peak normal elastic stresses of ~73 gigapascals (GPa) and strain rates of 10(9) per second. We capture the evolution of the lattice from a one-dimensional (1D) elastic to a 3D plastically relaxed state within a few tens of picoseconds, after reaching shear stresses of 18 GPa. Our in situ high-precision measurement of material strength at spatial (<1 micrometer) and temporal (<50 picoseconds) scales provides a direct comparison with multimillion-atom molecular dynamics simulations.

A Seeman-Bohlin geometry for high-resolution nanosecond x-ray diffraction measurements from shocked polycrystalline and amorphous materials.

We report on a focusing x-ray diffraction geometry capable of high-resolution in situ lattice probing from dynamically loaded polycrystalline and amorphous materials. The Seeman-Bohlin-type camera presented here is ideally suited for time-resolved x-ray diffraction measurements performed on high energy multibeam laser platforms. Diffraction from several lattice planes of ablatively shock-loaded 25 mum thick Cu foils was recorded on a focusing circle of diameter D=100 mm with exceptional angular resolution limited only by the spectral broadening of the x-ray source. Excellent agreement was found between the density measured using x-ray diffraction and that inferred from Doppler velocimetry and the known shock Hugoniot of Cu. In addition, x-ray diffraction signal was captured from an amorphous material under static conditions.

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.

Anomalous elastic response of silicon to uniaxial shock compression on nanosecond time scales.

We have used x-ray diffraction with subnanosecond temporal resolution to measure the lattice parameters of orthogonal planes in shock compressed single crystals of silicon (Si) and copper (Cu). Despite uniaxial compression along the (400) direction of Si reducing the lattice spacing by nearly 11%, no observable changes occur in planes with normals orthogonal to the shock propagation direction. In contrast, shocked Cu shows prompt hydrostaticlike compression. These results are consistent with simple estimates of plastic strain rates based on dislocation velocity data.