Ramp compression of diamond to five terapascals

Extreme Metastability of Diamond and its Transformation to the BC8 Post-Diamond Phase of Carbon

Diamond possesses exceptional physical properties due to its remarkably strong carbon-carbon bonding, leading to significant resilience to structural transformations at very high pressures and temperatures. Despite several experimental attempts, synthesis and recovery of the theoretically predicted post-diamond BC8 phase remains elusive. Through quantum-accurate multimillion atom molecular dynamics (MD) simulations, we have uncovered the extreme metastability of diamond at very high pressures, significantly exceeding its range of thermodynamic stability. We predict the post-diamond BC8 phase to be experimentally accessible only within a narrow high pressure-temperature region of the carbon phase diagram. The diamond to BC8 transformation proceeds through premelting followed by BC8 nucleation and growth in the metastable carbon liquid. We propose a double-shock compression pathway for BC8 synthesis, which is currently being explored in experiments at the National Ignition Facility.

Time-resolved X-ray diffraction diagnostic development for the National Ignition Facility

We present the development of an experimental platform that can collect four frames of x-ray diffraction data along a single line of sight during laser-driven, dynamic-compression experiments at the National Ignition Facility. The platform is comprised of a diagnostic imager built around ultrafast sensors with a 2-ns integration time, a custom target assembly that serves also to shield the imager, and a 10-ns duration, quasi-monochromatic x-ray source produced by laser-generated plasma. We demonstrate the performance with diffraction data for Pb ramp compressed to 150 GPa and illuminated by a Ge x-ray source that produces ∼7 × 1011, 10.25-keV photons/ns at the 400 μm diameter sample.

Extended X-ray absorption fine structure of dynamically-compressed copper up to 1 terapascal

Large laser facilities have recently enabled material characterization at the pressures of Earth and Super-Earth cores. However, the temperature of the compressed materials has been largely unknown, or solely relied on models and simulations, due to lack of diagnostics under these challenging conditions. Here, we report on temperature, density, pressure, and local structure of copper determined from extended x-ray absorption fine structure and velocimetry up to 1 Terapascal. These results nearly double the highest pressure at which extended x-ray absorption fine structure has been reported in any material. In this work, the copper temperature is unexpectedly found to be much higher than predicted when adjacent to diamond layer(s), demonstrating the important influence of the sample environment on the thermal state of materials; this effect may introduce additional temperature uncertainties in some previous experiments using diamond and provides new guidance for future experimental design.

Double-Shock Compression Pathways from Diamond to BC8 Carbon

Carbon is one of the most important elements for both industrial applications and fundamental research, including life, physics, chemistry, materials, and even planetary science. Although theoretical predictions on the transition from diamond to the BC8 (Ia3[over ¯]) carbon were made more than thirty years ago, after tremendous experimental efforts, direct evidence for the existence of BC8 carbon is still lacking. In this study, a machine learning potential was developed for high-pressure carbon fitted from first-principles calculations, which exhibited great capabilities in modeling the melting and Hugoniot line. Using the molecular dynamics based on this machine learning potential, we designed a thermodynamic pathway that is achievable for the double shock compression experiment to obtain the elusive BC8 carbon. Diamond was compressed up to 584 GPa after the first shock at 20.5  km/s. Subsequently, in the second shock compression at 24.8 or 25.0  km/s, diamond was compressed to a supercooled liquid and then solidified to BC8 in around 1 ns. Furthermore, the critical nucleus size and nucleation rate of BC8 were calculated, which are crucial for nano-second x-ray diffraction measurements to observe BC8 carbon during shock compressions. The key to obtaining BC8 carbon lies in the formation of liquid at a sufficient supercooling. Our work provides a feasible pathway by which the long-sought BC8 phase of carbon can be reached in experiments.

Scaling Law for the Onset of Solidification at Extreme Undercooling

Quasi-isentropic compression enables one to study the solidification of metastable liquid states that are inaccessible through other experimental means. The onset of this nonequilibrium solidification is known to depend on the compression rate and material-specific factors, but this complex interdependence has not been well characterized. In this study, we use a combination of experiments, theory, and computational simulations to derive a general scaling law that quantifies this dependence. One of its applications is a novel means to elucidate melt temperatures at high pressures.

Imaging of the electronic bonding of diamond at pressures up to 2 million atmospheres

Diamond shows unprecedented hardness. Because hardness is a measure of resistance of chemical bonds in a material to external indentation, the electronic bonding nature of diamond beyond several million atmospheres is key to understanding the origin of hardness. However, probing the electronic structures of diamond at such extreme pressure has not been experimentally possible. The measurements on the inelastic x-ray scattering spectra for diamond up to 2 million atmospheres provide data on the evolution of its electronic structures under compression. The mapping of the observed electronic density of states allows us to obtain a two-dimensional image of the bonding transitions of diamond undergoing deformation. The spectral change near edge onset is minor beyond a million atmospheres, while its electronic structure displays marked pressure-induced electron delocalization. Such electronic responses indicate that diamond's external rigidity is supported by its ability to reconcile internal stress, providing insights into the origins of hardness in materials.

Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons

We assess the accuracy of common hybrid exchange-correlation (XC) functionals (PBE0, PBE0-1/3, HSE06, HSE03, and B3LYP) within the Kohn-Sham density functional theory for the harmonically perturbed electron gas at parameters relevant for the challenging conditions of the warm dense matter. Generated by laser-induced compression and heating in the laboratory, the warm dense matter is a state of matter that also occurs in white dwarfs and planetary interiors. We consider both weak and strong degrees of density inhomogeneity induced by the external field at various wavenumbers. We perform an error analysis by comparing with the exact quantum Monte Carlo results. In the case of a weak perturbation, we report the static linear density response function and the static XC kernel at a metallic density for both the degenerate ground-state limit and for partial degeneracy at the electronic Fermi temperature. Overall, we observe an improvement in the density response when the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are used, compared with the previously reported results for the PBE, PBEsol, local-density approximation, and AM05 functionals; B3LYP, on the other hand, does not perform well for the considered system. Additionally, the PBE0, PBE0-1/3, HSE06, and HSE03 functionals are more accurate for the density response properties than SCAN in the regime of partial degeneracy.

Hydrodynamic simulation of hypervelocity generation by multidimensional graded impactors: Planarity enhancement study

Hypervelocity impact in the universe can be generated by a three-stage gas gun. Achieving the desirable planarity of the flyer enlarges the experimentally effective area of the flyer under the hypervelocity condition. The multidimensional graded density impactor (MDGDI) enhances the planarity of the flyer. In this investigation, a one-dimensional Lagrange elastoplastic hydrodynamic method and a Euler grid finite difference method were used to examine the relationship between the structure of graded density impactors (GDIs) and the planarity of flyers. MDGDIs lead to a deviation of the stress wave produced by the one-dimensional graded density impactor (1DGDI), which offsets the stress disturbance effect, changes the velocity at each particle, and enhances the planarity of flyers. The proportion of flat areas of the flyer increases from 52.70% to 95.71% by adopting MDGDIs. The proportion of flat areas is linear with the wave impedance of the high-impedance layer for 1DGDIs and the wave impedance near the barrel of the high-impedance layer for MDGDIs. This investigation guides the design of GDIs and expands the application of gas gun technology in the field of hypervelocity impact.

Imaging velocity interferometer system for any reflector (VISAR) diagnostics for high energy density sciences

Two variants of optical imaging velocimetry, specifically the one-dimensional streaked line-imaging and the two-dimensional time-resolved area-imaging versions of the Velocity Interferometer System for Any Reflector (VISAR), have become important diagnostics in high energy density sciences, including inertial confinement fusion and dynamic compression of condensed matter. Here, we give a brief review of the historical development of these techniques, then describe the current implementations at major high energy density (HED) facilities worldwide, including the OMEGA Laser Facility and the National Ignition Facility. We illustrate the versatility and power of these techniques by reviewing diverse applications of imaging VISARs for gas-gun and laser-driven dynamic compression experiments for materials science, shock physics, condensed matter physics, chemical physics, plasma physics, planetary science and astronomy, as well as a broad range of HED experiments and laser-driven inertial confinement fusion research.

Approximate bounds and temperature dependence of adiabatic connection integrands for the uniform electron gas

Thermal density functional theory is commonly used in simulations of warm dense matter, a highly energetic phase characterized by substantial thermal effects and by correlated electrons demanding quantum mechanical treatment. Methods that account for temperature dependence, such as Mermin–Kohn–Sham finite-temperature density functional theory and free energy density functional theory, are now employed with more regularity and available in many standard code packages. However, approximations from zero-temperature density functional theory are still often used in temperature-dependent simulations using thermally weighted electronic densities as an input to exchange–correlation functional approximations, a practice known to miss temperature-dependent effects in the exchange–correlation free energy of these systems. In this work, the temperature-dependent adiabatic connection is demonstrated and analyzed using a well-known parameterization of the uniform electron gas free energy. Useful tools based on this formalism for analyzing and constraining approximations of the exchange–correlation at zero temperature are leveraged for the finite-temperature case. Inspired by the Lieb–Oxford inequality, which provides a lower bound for the ground-state exchange–correlation energy, bounds for the exchange–correlation at finite temperatures are approximated for various degrees of electronic correlation.

The data-driven future of high-energy-density physics

High-energy-density physics is the field of physics concerned with studying matter at extremely high temperatures and densities. Such conditions produce highly nonlinear plasmas, in which several phenomena that can normally be treated independently of one another become strongly coupled. The study of these plasmas is important for our understanding of astrophysics, nuclear fusion and fundamental physics-however, the nonlinearities and strong couplings present in these extreme physical systems makes them very difficult to understand theoretically or to optimize experimentally. Here we argue that machine learning models and data-driven methods are in the process of reshaping our exploration of these extreme systems that have hitherto proved far too nonlinear for human researchers. From a fundamental perspective, our understanding can be improved by the way in which machine learning models can rapidly discover complex interactions in large datasets. From a practical point of view, the newest generation of extreme physics facilities can perform experiments multiple times a second (as opposed to approximately daily), thus moving away from human-based control towards automatic control based on real-time interpretation of diagnostic data and updates of the physics model. To make the most of these emerging opportunities, we suggest proposals for the community in terms of research design, training, best practice and support for synthetic diagnostics and data analysis.

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 core^1-3. Several phases have been predicted to exist in the multi-terapascal regime, which is important for accurate modelling of the interiors of carbon-rich exoplanets^4,5. 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 allotropes^1,2, 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.

Focussing Protons from a Kilojoule Laser for Intense Beam Heating using Proximal Target Structures

Proton beams driven by chirped pulse amplified lasers have multi-picosecond duration and can isochorically and volumetrically heat material samples, potentially providing an approach for creating samples of warm dense matter with conditions not present on Earth. Envisioned on a larger scale, they could heat fusion fuel to achieve ignition. We have shown in an experiment that a kilojoule-class, multi-picosecond short pulse laser is particularly effective for heating materials. The proton beam can be focussed via target design to achieve exceptionally high flux, important for the applications mentioned. The laser irradiated spherically curved diamond-like-carbon targets with intensity 4 × 10¹⁸ W/cm², producing proton beams with 3 MeV slope temperature. A Cu witness foil was positioned behind the curved target, and the gap between was either empty or spanned with a structure. With a structured target, the total emission of Cu Kα fluorescence was increased 18 fold and the emission profile was consistent with a tightly focussed beam. Transverse proton radiography probed the target with ps order temporal and 10 μm spatial resolution, revealing the fast-acting focussing electric field. Complementary particle-in-cell simulations show how the structures funnel protons to the tight focus. The beam of protons and neutralizing electrons induce the bright Kα emission observed and heat the Cu to 100 eV.

Does Pressure Break Mirror-Image Symmetry? A Perspective and New Insights

This paper is aimed at dissecting and discussing the effect of high pressure on chirogenesis, thus unveiling the role of this universal force in astrochemical and primeval Darwinian scenarios. The first part of this contribution revisits the current status and recent experiments, most dealing with crystalline racemates, for which generation of metastable conglomeratic phases would eventually afford spontaneous resolution and hence enantioenriched mixtures. We then provide an in-depth thermodynamic analysis, based on previous studies of non-electrolyte solutions and dense mixtures accounting for the existence of positive excess volume upon mixing, to simulate the mirror symmetry breaking, the evolution of entropy production and dissipation due to enantiomer conversion. Results clearly suggest that mirror symmetry breaking under high pressure may be a genuine phenomenon and that enantioenrichment from initial scalemic mixtures may also take place.

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.

The Magnitude and Waveform of Shock Waves Induced by X-ray Lasers in Water

The high energy densities deposited in materials by focused X-ray laser pulses generate shock waves which travel away from the irradiated region, and can generate complex wave patterns or induce phase changes. We determined the time-pressure histories of shocks induced by X-ray laser pulses in liquid water microdrops, by measuring the surface velocity of the microdrops from images recorded during the reflection of the shock at the surface. Measurements were made with ~30 µm diameter droplets using 10 keV X-rays, for X-ray pulse energies that deposited linear energy densities from 3.5 to 120 mJ/m; measurements were also made with ~60 µm diameter drops for a narrower energy range. At a distance of 15 µm from the X-ray beam, the peak shock pressures ranged from 44 to 472 MPa, and the corresponding time-pressure histories of the shocks had a fast quasi-exponential decay with positive pressure durations estimated to range from 2 to 5 ns. Knowledge of the amplitude and waveform of the shock waves enables accurate modeling of shock propagation and experiment designs that either maximize or minimize the effect of shocks.

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.

Lab in a DAC - high-pressure crystal chemistry in a diamond-anvil cell

The diamond-anvil cell (DAC) was invented 60 years ago, ushering in a new era for material sciences, extending research into the dimension of pressure. Most structural determinations and chemical research have been conducted at ambient pressure, i.e. the atmospheric pressure on Earth. However, modern experimental techniques are capable of generating pressure and temperature higher than those at the centre of Earth. Such extreme conditions can be used for obtaining unprecedented chemical compounds, but, most importantly, all fundamental phenomena can be viewed and understood from a broader perspective. This knowledge, in turn, is necessary for designing new generations of materials and applications, for example in the pharmaceutical industry or for obtaining super-hard materials. The high-pressure chambers in the DAC are already used for a considerable variety of experiments, such as chemical reactions, crystallizations, measurements of electric, dielectric and magnetic properties, transformations of biological materials as well as experiments on living tissue. Undoubtedly, more applications involving elevated pressure will follow. High-pressure methods become increasingly attractive, because they can reduce the sample volume and compress the intermolecular contacts to values unattainable by other methods, many times stronger than at low temperature. The compressed materials reveal new information about intermolecular interactions and new phases of single- and multi-component compounds can be obtained. At the same time, high-pressure techniques, and particularly those of X-ray diffraction using the DAC, have been considerably improved and many innovative developments implemented. Increasingly more equipment of in-house laboratories, as well as the instrumentation of beamlines at synchrotrons and thermal neutron sources are dedicated to high-pressure research.

Heat-release equation of state and thermal conductivity of warm dense carbon by proton differential heating

Warm dense carbon is generated at 0.3-2.0 g/cc and 1-7 eV by proton heating. The release equation of state (EOS) after heating and thermal conductivity of warm dense carbon are studied experimentally in this regime using a Au/C dual-layer target to initiate a temperature gradient and two picosecond time-resolved diagnostics to probe the surface expansion and heat flow. Comparison between the data and simulations using various EOSs and thermal conductivity models is quantified with a statistical χ^{2} analysis. Out of seven EOS tables and five thermal conductivity models, only L9061 with the Lee-More model provides a probability above 50% to match all data.

Deducing density and strength of nanocrystalline Ta and diamond under extreme conditions from X-ray diffraction

In situ X-ray diffraction with advanced X-ray sources offers unique opportunities for investigating materials properties under extreme conditions such as shock-wave loading. Here, Singh's theory for deducing high-pressure density and strength from two-dimensional (2D) diffraction patterns is rigorously examined with large-scale molecular dynamics simulations of isothermal compression and shock-wave compression. Two representative solids are explored: nanocrystalline Ta and diamond. Analysis of simulated 2D X-ray diffraction patterns is compared against direct molecular dynamics simulation results. Singh's method is highly accurate for density measurement (within 1%) and reasonable for strength measurement (within 10%), and can be used for such measurements on nanocrystalline and polycrystalline solids under extreme conditions (e.g. in the megabar regime).

Development of a three-stage gas gun launcher for ultrahigh-pressure Hugoniot measurements

A three-stage gas gun, composed of a two-stage gas gun and the add-on part, has been developed to launch high-Z (tantalum, for example) flyer plates up to 10 km/s for ultrahigh-pressure Hugoniot measurements. Great care has been taken to optimize the add-on part in which a specially designed graded density impactor is employed to quasi-isentropically accelerate the high-Z flyer plate for maximizing its impact velocity. The shock wave in the target generated by the flyer plate is characterized with the flatness of the shock-front better than 1 ns in the concerned area and the uncertainty of the shock-wave velocity less than 2%, thus satisfying the requirements for high-precision Hugoniot measurements. As a demonstration, we measured the ultrahigh-pressure Hugoniot equation of state of tantalum ranging from 0.45 TPa to 0.85 TPa with a symmetric impacting geometry in which the shock-wave velocity and the particle velocity are simultaneously determined. The results obtained are well consistent with data available in the literature, indicating the extended capability of the gas-gun launcher technique.

Magnetized fast isochoric laser heating for efficient creation of ultra-high-energy-density states

Fast isochoric heating of a pre-compressed plasma core with a high-intensity short-pulse laser is an attractive and alternative approach to create ultra-high-energy-density states like those found in inertial confinement fusion (ICF) ignition sparks. Laser-produced relativistic electron beam (REB) deposits a part of kinetic energy in the core, and then the heated region becomes the hot spark to trigger the ignition. However, due to the inherent large angular spread of the produced REB, only a small portion of the REB collides with the core. Here, we demonstrate a factor-of-two enhancement of laser-to-core energy coupling with the magnetized fast isochoric heating. The method employs a magnetic field of hundreds of Tesla that is applied to the transport region from the REB generation zone to the core which results in guiding the REB along the magnetic field lines to the core. This scheme may provide more efficient energy coupling compared to the conventional ICF scheme.

Single crystal toroidal diamond anvils for high pressure experiments beyond 5 megabar

Static compression experiments over 4 Mbar are rare, yet critical for developing accurate fundamental physics and chemistry models, relevant to a range of topics including modeling planetary interiors. Here we show that focused ion beam crafted toroidal single-crystal diamond anvils with ~9.0 μm culets are capable of producing pressures over 5 Mbar. The toroidal surface prevents gasket outflow and provides a means to stabilize the central culet. We have reached a maximum pressure of ~6.15 Mbar using Re as in situ pressure marker, a pressure regime typically accessed only by double-stage diamond anvils and dynamic compression platforms. Optimizing single-crystal diamond anvil design is key for extending the pressure range over which studies can be performed in the diamond anvil cell.

Static pressures exceeding 4 million atmospheres are extremely challenging to achieve, but are necessary for the study of matter that exists under these conditions in natural environments. Here, diamonds anvils with a toroidal design are demonstrated to sustain over 6 million atmospheres in a diamond anvil cell.

Toroidal diamond anvil cell for detailed measurements under extreme static pressures

Over the past 60 years, the diamond anvil cell (DAC) has been developed into a widespread high static pressure device. The adaptation of laboratory and synchrotron analytical techniques to DAC enables a detailed exploration in the 100 GPa range. The strain of the anvils under high load explains the 400 GPa limit of the conventional DAC. Here we show a toroidal shape for a diamond anvil tip that enables to extend the DAC use toward the terapascal pressure range. The toroidal-DAC keeps the assets for a complete, reproducible, and accurate characterization of materials, from solids to gases. Raman signal from the diamond anvil or X-ray signal from the rhenium gasket allow measurement of pressure. Here, the equations of state of gold, aluminum, and argon are measured with X-ray diffraction. The data are compared with recent measurements under similar conditions by two other approaches, the double-stage DAC and the dynamic ramp compression.

Extreme static pressures exceeding a million atmospheres exist in a variety of natural environments, but obtaining such pressures in a laboratory is still a challenge. Here, the authors develop a toroidal diamond anvil design that allows for the generation of 600 GPa (6 million atmospheres) in routinely used diamond anvil cells.

Helium-Iron Compounds at Terapascal Pressures

We investigate the binary phase diagram of helium and iron using first-principles calculations. We find that helium, which is a noble gas and inert at ambient conditions, forms stable crystalline compounds with iron at terapascal pressures. A FeHe compound becomes stable above 4 TPa, and a FeHe_{2} compound above 12 TPa. Melting is investigated using molecular dynamics simulations, and a superionic phase with sublattice melting of the helium atoms is predicted. We discuss the implications of our predicted helium-iron phase diagram for interiors of giant (exo)planets and white dwarf stars.

Continuous Sound Velocity Measurements along the Shock Hugoniot Curve of Quartz

We report continuous measurements of the sound velocity along the principal Hugoniot curve of α quartz between 0.25 and 1.45 TPa, as determined from lateral release waves intersecting the shock front as a function of time in decaying-shock experiments. The measured sound velocities are lower than predicted by prior models, based on the properties of stishovite at densities below ∼7  g/cm^{3}, but agree with density functional theory molecular dynamics calculations and an empirical wide-regime equation of state presented here. The Grüneisen parameter calculated from the sound velocity decreases from γ∼1.3 at 0.25 TPa to 0.66 at 1.45 TPa. In combination with evidence for increased (configurational) specific heat and decreased bulk modulus, the values of γ suggest a high thermal expansion coefficient at ∼0.25-0.65  TPa, where SiO_{2} is thought to be a bonded liquid. From our measurements, dissociation of the molecular bonds persists to ∼0.65-1.0  TPa, consistent with estimates by other methods. At higher densities, the sound velocity is close to predictions from previous models, and the Grüneisen parameter approaches the ideal gas value.

Shock drive capabilities of a 30-Joule laser at the matter in extreme conditions hutch of the Linac Coherent Light Source

We measure the shock drive capabilities of a 30 J, nanosecond, 527 nm laser system at the matter in extreme conditions hutch of the Linac Coherent Light Source. Using a velocity interferometer system for any reflector, we ascertain the maximum instantaneous ablation pressure and characterize its dependence on a drive laser spot size, spatial profile, and temporal profile. We also examine the effects of these parameters on shock spatial and temporal uniformity. Our analysis shows the drive laser capable of generating instantaneous ablation pressures exceeding 160 GPa while maintaining a 1D shock profile. We find that slope pulses provide higher instantaneous ablation pressures than plateau pulses. Our results show instantaneous ablation pressures comparable to those measured at the Omega Laser Facility in Rochester, NY under similar optical drive parameters. Finally, we analyze how optical laser ablation pressures are compare with known scaling relations, accounting for variable laser wavelengths.

X-ray source development for EXAFS measurements on the National Ignition Facility

Extended X-ray absorption Fine Structure (EXAFS) measurements require a bright, spectrally smooth, and broad-band x-ray source. In a laser facility, such an x-ray source can be generated by a laser-driven capsule implosion. In order to optimize the x-ray emission, different capsule types and laser irradiations have been tested at the National Ignition Facility (NIF). A crystal spectrometer is used to disperse the x-rays and high efficiency image plate detectors are used to measure the absorption spectra in transmission geometry. EXAFS measurements at the K-edge of iron at ambient conditions have been obtained for the first time on the NIF laser, and the requirements for optimization have been established.

Raman evidence for pressure-induced formation of diamondene

Despite the advanced stage of diamond thin-film technology, with applications ranging from superconductivity to biosensing, the realization of a stable and atomically thick two-dimensional diamond material, named here as diamondene, is still forthcoming. Adding to the outstanding properties of its bulk and thin-film counterparts, diamondene is predicted to be a ferromagnetic semiconductor with spin polarized bands. Here, we provide spectroscopic evidence for the formation of diamondene by performing Raman spectroscopy of double-layer graphene under high pressure. The results are explained in terms of a breakdown in the Kohn anomaly associated with the finite size of the remaining graphene sites surrounded by the diamondene matrix. Ab initio calculations and molecular dynamics simulations are employed to clarify the mechanism of diamondene formation, which requires two or more layers of graphene subjected to high pressures in the presence of specific chemical groups such as hydroxyl groups or hydrogens.The synthesis of two-dimensional diamond is the ultimate goal of diamond thin-film technology. Here, the authors perform Raman spectroscopy of bilayer graphene under pressure, and obtain spectroscopic evidence of formation of diamondene, an atomically thin form of diamond.

First-principles simulations of warm dense lithium fluoride

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 LiF. Our simulations cover a wide density-temperature range of 2.08-15.70gcm^{-3} and 10^{4}-10^{9} K. Since PIMC and DFT-MD accurately treat effects of atomic shell structure, we find a pronounced compression maximum and a shoulder on 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, LEOS, and models. In addition, we compute pair-correlation functions that reveal an evolving plasma structure and ionization process that is driven by thermal and pressure ionization. Finally, we compute electronic density of states of liquid LiF from DFT-MD simulations and find that the electronic gap can remain open with increasing density and temperature to at least 15.7 gcm^{-3}.

High-pressure studies with x-rays using diamond anvil cells

Pressure profoundly alters all states of matter. The symbiotic development of ultrahigh-pressure diamond anvil cells, to compress samples to sustainable multi-megabar pressures; and synchrotron x-ray techniques, to probe materials' properties in situ, has enabled the exploration of rich high-pressure (HP) science. In this article, we first introduce the essential concept of diamond anvil cell technology, together with recent developments and its integration with other extreme environments. We then provide an overview of the latest developments in HP synchrotron techniques, their applications, and current problems, followed by a discussion of HP scientific studies using x-rays in the key multidisciplinary fields. These HP studies include: HP x-ray emission spectroscopy, which provides information on the filled electronic states of HP samples; HP x-ray Raman spectroscopy, which probes the HP chemical bonding changes of light elements; HP electronic inelastic x-ray scattering spectroscopy, which accesses high energy electronic phenomena, including electronic band structure, Fermi surface, excitons, plasmons, and their dispersions; HP resonant inelastic x-ray scattering spectroscopy, which probes shallow core excitations, multiplet structures, and spin-resolved electronic structure; HP nuclear resonant x-ray spectroscopy, which provides phonon densities of state and time-resolved Mössbauer information; HP x-ray imaging, which provides information on hierarchical structures, dynamic processes, and internal strains; HP x-ray diffraction, which determines the fundamental structures and densities of single-crystal, polycrystalline, nanocrystalline, and non-crystalline materials; and HP radial x-ray diffraction, which yields deviatoric, elastic and rheological information. Integrating these tools with hydrostatic or uniaxial pressure media, laser and resistive heating, and cryogenic cooling, has enabled investigations of the structural, vibrational, electronic, and magnetic properties of materials over a wide range of pressure-temperature conditions.

Predicted reentrant melting of dense hydrogen at ultra-high pressures

The phase diagram of hydrogen is one of the most important challenges in high-pressure physics and astrophysics. Especially, the melting of dense hydrogen is complicated by dimer dissociation, metallization and nuclear quantum effect of protons, which together lead to a cold melting of dense hydrogen when above 500 GPa. Nonetheless, the variation of the melting curve at higher pressures is virtually uncharted. Here we report that using ab initio molecular dynamics and path integral simulations based on density functional theory, a new atomic phase is discovered, which gives an uplifting melting curve of dense hydrogen when beyond 2 TPa, and results in a reentrant solid-liquid transition before entering the Wigner crystalline phase of protons. The findings greatly extend the phase diagram of dense hydrogen, and put metallic hydrogen into the group of alkali metals, with its melting curve closely resembling those of lithium and sodium.

Linear dependence of surface expansion speed on initial plasma temperature in warm dense matter

Recent progress in laser-driven quasi-monoenergetic ion beams enabled the production of uniformly heated warm dense matter. Matter heated rapidly with this technique is under extreme temperatures and pressures, and promptly expands outward. While the expansion speed of an ideal plasma is known to have a square-root dependence on temperature, computer simulations presented here show a linear dependence of expansion speed on initial plasma temperature in the warm dense matter regime. The expansion of uniformly heated 1–100 eV solid density gold foils was modeled with the RAGE radiation-hydrodynamics code, and the average surface expansion speed was found to increase linearly with temperature. The origin of this linear dependence is explained by comparing predictions from the SESAME equation-of-state tables with those from the ideal gas equation-of-state. These simulations offer useful insight into the expansion of warm dense matter and motivate the application of optical shadowgraphy for temperature measurement.

Dynamic X-ray diffraction observation of shocked solid iron up to 170 GPa

Investigation of the iron phase diagram under high pressure and temperature is crucial for the determination of the composition of the cores of rocky planets and for better understanding the generation of planetary magnetic fields. Here we present X-ray diffraction results from laser-driven shock-compressed single-crystal and polycrystalline iron, indicating the presence of solid hexagonal close-packed iron up to pressure of at least 170 GPa along the principal Hugoniot, corresponding to a temperature of 4,150 K. This is confirmed by the agreement between the pressure obtained from the measurement of the iron volume in the sample and the inferred shock strength from velocimetry deductions. Results presented in this study are of the first importance regarding pure Fe phase diagram probed under dynamic compression and can be applied to study conditions that are relevant to Earth and super-Earth cores.

Free energy model for solid high-pressure phases of carbon

Analytic free energy models for three solid high-pressure phases--diamond, body centered cubic phase with eight atoms in the unit cell (BC8), and simple cubic (SC)--are developed using density functional theory. We explicitly include anharmonic effects by performing molecular dynamics simulations and investigate their density and temperature dependence in detail. Anharmonicity in the nuclear motion shifts the phase transitions significantly compared to the harmonic approximation. Furthermore, we apply a thermodynamically constrained correction that brings the equation of state in accordance with diamond anvil cell experiments. The performance of our thermodynamic functions is validated against Hugoniot experiments.

Uniform heating of materials into the warm dense matter regime with laser-driven quasimonoenergetic ion beams

In a recent experiment at the Trident laser facility, a laser-driven beam of quasimonoenergetic aluminum ions was used to heat solid gold and diamond foils isochorically to 5.5 and 1.7 eV, respectively. Here theoretical calculations are presented that suggest the gold and diamond were heated uniformly by these laser-driven ion beams. According to calculations and SESAME equation-of-state tables, laser-driven aluminum ion beams achievable at Trident, with a finite energy spread of ΔE/E∼20%, are expected to heat the targets more uniformly than a beam of 140-MeV aluminum ions with zero energy spread. The robustness of the expected heating uniformity relative to the changes in the incident ion energy spectra is evaluated, and expected plasma temperatures of various target materials achievable with the current experimental platform are presented.

First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions

Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. With first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ=0.1to100g/cm(3) and T=1000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosions on OMEGA using the FPEOS table of CH have predicted ∼30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ∼5% reduction in implosion velocity that is caused by the ∼10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered light from ICF implosions.

Visualization of expanding warm dense gold and diamond heated rapidly by laser-generated ion beams

With the development of several novel heating sources, scientists can now heat a small sample isochorically above 10,000 K. Although matter at such an extreme state, known as warm dense matter, is commonly found in astrophysics (e.g., in planetary cores) as well as in high energy density physics experiments, its properties are not well understood and are difficult to predict theoretically. This is because the approximations made to describe condensed matter or high-temperature plasmas are invalid in this intermediate regime. A sufficiently large warm dense matter sample that is uniformly heated would be ideal for these studies, but has been unavailable to date. Here we have used a beam of quasi-monoenergetic aluminum ions to heat gold and diamond foils uniformly and isochorically. For the first time, we visualized directly the expanding warm dense gold and diamond with an optical streak camera. Furthermore, we present a new technique to determine the initial temperature of these heated samples from the measured expansion speeds of gold and diamond into vacuum. We anticipate the uniformly heated solid density target will allow for direct quantitative measurements of equation-of-state, conductivity, opacity, and stopping power of warm dense matter, benefiting plasma physics, astrophysics, and nuclear physics.

The electrical conductivity of Al2O3 under shock-compression

Sapphire (Al2O3) crystals are used below 100 GPa as anvils and windows in dynamic-compression experiments because of their transparency and high density. Above 100 GPa shock pressures, sapphire becomes opaque and electrically conducting because of shock-induced defects. Such effects prevent temperature and dc conductivity measurements of materials compressed quasi-isentropically. Opacities and electrical conductivities at ~100 GPa are non-equilibrium, rather than thermodynamic parameters. We have performed electronic structure calculations as a guide in predicting and interpreting shock experiments and possibly to discover a window up to ~200 GPa. Our calculations indicate shocked sapphire does not metallize by band overlap at ~300 GPa, as suggested previously by measured non-equilibrium data. Shock-compressed Al2O3 melts to a metallic liquid at ~500 GPa and 10,000 K and its conductivity increases rapidly to ~2000 Ω(-1)cm(-1) at ~900 GPa. At these high shock temperatures and pressures sapphire is in thermal equilibrium. Calculated conductivity of Al2O3 is similar to those measured for metallic fluid H, N, O, Rb, and Cs. Despite different materials, pressures and temperatures, and compression techniques, both experimental and theoretical, conductivities of all these poor metals reach a common end state typical of strong-scattering disordered materials.

Transport properties and equation of state for HCNO mixtures in and beyond the warm dense matter regime

We present simulations of a four-component mixture of HCNO with orbital free molecular dynamics (OFMD). These simulations were conducted for 5-200 eV with densities ranging between 0.184 and 36.8 g/cm3. We extract the equation of state from the simulations and compare to average atom models. We found that we only need to add a cold curve model to find excellent agreement. Additionally, we studied mass transport properties. We present fits to the self-diffusion and shear viscosity that are able to reproduce the transport properties over the parameter range studied. We compare these OFMD results to models based on the Coulomb coupling parameter and one-component plasmas.

Imaging Shock Waves in Diamond with Both High Temporal and Spatial Resolution at an XFEL

The advent of hard x-ray free-electron lasers (XFELs) has opened up a variety of scientific opportunities in areas as diverse as atomic physics, plasma physics, nonlinear optics in the x-ray range, and protein crystallography. In this article, we access a new field of science by measuring quantitatively the local bulk properties and dynamics of matter under extreme conditions, in this case by using the short XFEL pulse to image an elastic compression wave in diamond. The elastic wave was initiated by an intense optical laser pulse and was imaged at different delay times after the optical pump pulse using magnified x-ray phase-contrast imaging. The temporal evolution of the shock wave can be monitored, yielding detailed information on shock dynamics, such as the shock velocity, the shock front width, and the local compression of the material. The method provides a quantitative perspective on the state of matter in extreme conditions.

Prediction of 10-fold coordinated TiO2 and SiO2 structures at multimegabar pressures

We predict by first-principles methods a phase transition in TiO2 at 6.5 Mbar from the Fe2P-type polymorph to a ten-coordinated structure with space group I4/mmm. This is the first report, to our knowledge, of the pressure-induced phase transition to the I4/mmm structure among all dioxide compounds. The I4/mmm structure was found to be up to 3.3% denser across all pressures investigated. Significant differences were found in the electronic properties of the two structures, and the metallization of TiO2 was calculated to occur concomitantly with the phase transition to I4/mmm. The implications of our findings were extended to SiO2, and an analogous Fe2P-type to I4/mmm transition was found to occur at 10 TPa. This is consistent with the lower-pressure phase transitions of TiO2, which are well-established models for the phase transitions in other AX2 compounds, including SiO2. As in TiO2, the transition to I4/mmm corresponds to the metallization of SiO2. This transformation is in the pressure range reached in the interiors of recently discovered extrasolar planets and calls for a reformulation of the equations of state used to model them.

Single Hit Energy-resolved Laue Diffraction

In situ white light Laue diffraction has been successfully used to interrogate the structure of single crystal materials undergoing rapid (nanosecond) dynamic compression up to megabar pressures. However, information on strain state accessible via this technique is limited, reducing its applicability for a range of applications. We present an extension to the existing Laue diffraction platform in which we record the photon energy of a subset of diffraction peaks. This allows for a measurement of the longitudinal and transverse strains in situ during compression. Consequently, we demonstrate measurement of volumetric compression of the unit cell, in addition to the limited aspect ratio information accessible in conventional white light Laue. We present preliminary results for silicon, where only an elastic strain is observed. VISAR measurements show the presence of a two wave structure and measurements show that material downstream of the second wave does not contribute to the observed diffraction peaks, supporting the idea that this material may be highly disordered, or has undergone large scale rotation.

Metallic icosahedron phase of sodium at terapascal pressures

Alkali metals exhibit unexpected structures and electronic behavior at high pressures. Compression of metallic sodium (Na) to 200 GPa leads to the stability of a wide-band-gap insulator with the double hexagonal hP4 structure. Post-hP4 structures remain unexplored, but they are important for addressing the question of the pressure at which Na reverts to a metal. Here, we report the reentrant metallicity of Na at the very high pressure of 15.5 terapascal (TPa), predicted using first-principles structure searching simulations. Na is therefore insulating over the large pressure range of 0.2-15.5 TPa. Unusually, Na adopts an oP8 structure at pressures of 117-125 GPa and the same oP8 structure at 1.75-15.5 TPa. The metallization of Na occurs on the formation of a stable and striking body-centered cubic cI24 electride structure consisting of Na_{12} icosahedra, each housing at its center about one electron that is not associated with any Na ions.