The structure of liquid carbon elucidated by in situ X-ray diffraction

Carbon has a central role in biology and organic chemistry, and its solid allotropes provide the basis of much of our modern technology1. However, the liquid form of carbon remains nearly uncharted2, and the structure of liquid carbon and most of its physical properties are essentially unknown3. But liquid carbon is relevant for modelling planetary interiors4,5 and the atmospheres of white dwarfs6, as an intermediate state for the synthesis of advanced carbon materials7,8, inertial confinement fusion implosions9, hypervelocity impact events on carbon materials10 and our general understanding of structured fluids at extreme conditions11. Here we present a precise structure measurement of liquid carbon at pressures of around 1 million atmospheres obtained by in situ X-ray diffraction at an X-ray free-electron laser. Our results show a complex fluid with transient bonding and approximately four nearest neighbours on average, in agreement with quantum molecular dynamics simulations. The obtained data substantiate the understanding of the liquid state of one of the most abundant elements in the universe and can test models of the melting line. The demonstrated experimental abilities open the path to performing similar studies of the structure of liquids composed of light elements at extreme conditions.

3D carbon crystals: theoretical prediction and experimental preparation

Sp, sp 2 or sp 3 hybridization of carbon atoms results in a linear, triangular or tetrahedral configuration of bonding geometry, respectively. By combining different hybridizations in one structure, a variety of 3D carbon allotropes with periodic crystal structures can be obtained with potential novel properties and applications. With the rapid development of computational capability in recent years, a large number of new 3D carbon structures have been proposed with their properties predicted; the development of new experimental techniques has also led to the successful experimental preparation of several carbon crystals. Observing the rapid advancement of 3D carbons subsequent to the breakthroughs in 2D graphene, this paper reviews the recent progress in constructing carbon crystals by summarizing the structural design and specifically highlighting the preparation using template carbonization, organic synthesis, high-pressure processing and charge injection.

Acoustic shock wave-induced formation of an undefined high-pressure carbon allotrope

Carbon is nothing less than a rock star in the world of research on allotropes which has a tremendous ability to form several simple and complex allotropic structures of various sp, sp2 and sp3 hybridizations, thanks to its flexible chemical structure. By high-pressure experimental and theoretical approaches, new carbon forms were synthesized from known carbon structures. Herein, we report the phase transition from amorphous carbon nanoparticles to a novel thermodynamically stable carbon allotropic structure, denominated as SD carbon (Sivakumar-Dai carbon), obtained through the impact of acoustic shock waves with a transient pressure of 16.5 MPa. The SD carbon exhibits a couple of Raman bands at 482 and 2431 cm-1 with mixed sp2 and sp3 hybridizations belonging to the non-layered structural type and the formation of the SD carbon mechanism has been proposed based on the thermal conductivity driven super-heating approach. The structure will offer platforms that may pave the way for several novel carbon structures at low shock pressures compared to conventional static pressure compression and other techniques.

Accuracy, transferability, and computational efficiency of interatomic potentials for simulations of carbon under extreme conditions

Large-scale atomistic molecular dynamics (MD) simulations provide an exceptional opportunity to advance the fundamental understanding of carbon under extreme conditions of high pressures and temperatures. However, the fidelity of these simulations depends heavily on the accuracy of classical interatomic potentials governing the dynamics of many-atom systems. This study critically assesses several popular empirical potentials for carbon, as well as machine learning interatomic potentials (MLIPs), in their ability to simulate a range of physical properties at high pressures and temperatures, including the diamond equation of state, its melting line, shock Hugoniot, uniaxial compressions, and the structure of liquid carbon. Empirical potentials fail to accurately predict the behavior of carbon under high pressure-temperature conditions. In contrast, MLIPs demonstrate quantum accuracy, with Spectral Neighbor Analysis Potential (SNAP) and atomic cluster expansion (ACE) being the most accurate in reproducing the density functional theory results. ACE displays remarkable transferability despite not being specifically trained for extreme conditions. Furthermore, ACE and SNAP exhibit superior computational performance on graphics processing unit-based systems in billion atom MD simulations, with SNAP emerging as the fastest. In addition to offering practical guidance in selecting an interatomic potential with a fine balance of accuracy, transferability, and computational efficiency, this work also highlights transformative opportunities for groundbreaking scientific discoveries facilitated by quantum-accurate MD simulations with MLIPs on emerging exascale supercomputers.

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.

An Overview of Mechanical Properties of Diamond-like Phases under Tension

Diamond-like phases are materials with crystal lattices very similar to diamond. Recent results suggest that diamond-like phases are superhard and superstrong materials that can be used for tribological applications or as protective coatings. In this work, 14 stable diamond-like phases based on fullerenes, carbon nanotubes, and graphene layers are studied via molecular dynamics simulation. The compliance constants, Young's modulus, and Poisson's ratio were calculated. Deformation behavior under tension is analyzed based on two deformation modes-bond rotation and bond elongation. The results show that some of the considered phases possess very high Young's modulus (E≥1) TPa, even higher than that of diamond. Both Young's modulus and Poisson's ratio exhibit mechanical anisotropy. Half of the studied phases are partial auxetics possessing negative Poisson's ratio with a minimum value of -0.8. The obtained critical values of applied tensile strain confirmed that diamond-like phases are high-strength structures with a promising application prospect. Interestingly, the critical limit is not a fracture but a phase transformation to the short-ordered crystal lattice. Overall, our results suggest that diamond-like phases have extraordinary mechanical properties, making them good materials for protective coatings.

Transonic dislocation propagation in diamond

The motion of line defects (dislocations) has been studied for more than 60 years, but the maximum speed at which they can move is unresolved. Recent models and atomistic simulations predict the existence of a limiting velocity of dislocation motion between the transonic and subsonic ranges at which the self-energy of dislocation diverges, though they do not deny the possibility of the transonic dislocations. We used femtosecond x-ray radiography to track ultrafast dislocation motion in shock-compressed single-crystal diamond. By visualizing stacking faults extending faster than the slowest sound wave speed of diamond, we show the evidence of partial dislocations at their leading edge moving transonically. Understanding the upper limit of dislocation mobility in crystals is essential to accurately model, predict, and control the mechanical properties of materials under extreme conditions.

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.

Dynamic compression of water to conditions in ice giant interiors

Recent discoveries of water-rich Neptune-like exoplanets require a more detailed understanding of the phase diagram of H₂O at pressure–temperature conditions relevant to their planetary interiors. The unusual non-dipolar magnetic fields of ice giant planets, produced by convecting liquid ionic water, are influenced by exotic high-pressure states of H₂O—yet the structure of ice in this state is challenging to determine experimentally. Here we present X-ray diffraction evidence of a body-centered cubic (BCC) structured H₂O ice at 200 GPa and ~ 5000 K, deemed ice XIX, using the X-ray Free Electron Laser of the Linac Coherent Light Source to probe the structure of the oxygen sub-lattice during dynamic compression. Although several cubic or orthorhombic structures have been predicted to be the stable structure at these conditions, we show this BCC ice phase is stable to multi-Mbar pressures and temperatures near the melt boundary. This suggests variable and increased electrical conductivity to greater depths in ice giant planets that may promote the generation of multipolar magnetic fields.

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.

Confirmation of the PPLB Derivative Discontinuity: Exact Chemical Potential at Finite Temperatures of a Model System

The landmark 1982 work of Perdew, Parr, Levy, and Balduz (often called PPLB) laid the foundation for our modern understanding of the role of the derivative discontinuity in density functional theory, which drives much development to account for its effects. A simple model for the chemical potential at vanishing temperature played a crucial role in their argument. We investigate the validity of this model in the simplest nontrivial system to which it can be applied and which can be easily solved exactly, the Hubbard dimer. We find exact agreement in the crucial zero-temperature limit and show the model remains accurate for a significant range of temperatures. We identify how this range depends on the strength of correlations. We extend the model to approximate free energies accounting for the derivative discontinuity, a feature missing in standard semilocal approximations. We provide a correction to this approximation to yield even more accurate free energies. We discuss the relevance of these results for warm dense matter.

Shock Response of Full Density Nanopolycrystalline Diamond

Hugoniot of full-dense nanopolycrystalline diamond (NPD) was investigated up to 1600 GPa. The Hugoniot elastic limit of NPD is 208 (±14) GPa, which is more than twice as high as that of single-crystal diamond. The Hugoniot of NPD is stiffer than that of single-crystal diamond up to 500 GPa, while no significant difference is observed at higher pressures where the elastic precursor is overdriven by a following plastic wave. These findings confirm that the grain boundary strengthening effect recognized in static compression experiments is also effective against high strain-rate dynamic compressions.

Atomic and Electronic Structure of Solid-Density Liquid Carbon

A liquid carbon (l-C) sample is generated through constant volume heating exposing an amorphous carbon foil to an intense ultrashort laser pulse. Time-resolved x-ray absorption spectroscopy at the C K edge is used to monitor the dynamics of the melting process revealing a subpicosecond rearrangement of the electronic structure associated with a sudden change of the C bonding hybridization. The obtained l-C sample, resulting from a nonthermal melting mechanism, reaches a transient equilibrium condition with a temperature of about 14 200 K and pressure in the order of 0.5 Mbar in about 0.3 ps, prior to hydrodynamic expansion. A detailed analysis of the atomic and electronic structure in solid-density l-C based on time-resolved x-ray absorption spectroscopy and theoretical simulations is presented. The method can be fruitfully used for extending the experimental investigation of the C phase diagram in a vast unexplored region covering the 10^{3}-10^{4}  K temperature range with pressures up to 1 Mbar.

Single-pulse (100 ps) extended x-ray absorption fine structure capability at the Dynamic Compression Sector

Determining real-time changes in the local atomistic order is important for a mechanistic understanding of shock wave induced structural and chemical changes. However, the single event and short duration (nanosecond times) nature of shock experiments pose challenges in obtaining Extended X-ray Absorption Fine Structure (EXAFS) measurements-typically used for monitoring local order changes. Here, we report on a new single pulse (∼100 ps duration) transmission geometry EXAFS capability for use in laser shock-compression experiments at the Dynamic Compression Sector (DCS), Advanced Photon Source. We used a flat plate of highly oriented pyrolytic graphite (HOPG) as the spectrometer element to energy disperse x rays transmitted through the sample. It provided high efficiency with ∼15% of the x rays incident on the HOPG reaching an x-ray area detector with high quantum efficiency. This combination resulted in a good signal-to-noise ratio (∼10³), an energy resolution of ∼10 eV at 10 keV, EXAFS spectra covering 100 s of eV, and a good pulse to pulse reproducibility of our single pulse measurements. Ambient EXAFS spectra for Cu and Au are compared to the reference spectra, validating our measurement system. Comparison of single pulse EXAFS results for ambient and laser shocked Ge(100) shows large changes in the local structure of the short lived state of shocked Ge. The current DCS EXAFS capability can be used to perform single pulse measurements in laser shocked materials from ∼9 keV to 13 keV. These EXAFS developments will be available to all users of the DCS.

High-temperature ion-thermal behavior from average-atom calculations

Atom-in-jellium calculations of the Einstein frequency were used to calculate the mean displacement of an ion over a wide range of compression and temperature. Expressed as a fraction of the Wigner-Seitz radius, the displacement is a measure of the asymptotic freedom of the ion at high temperature, and thus of the change in heat capacity from six to three quadratic degrees of freedom per atom. A functional form for free energy was proposed based on the Maxwell-Boltzmann distribution as a correction to the Debye free energy, with a single free parameter representing the effective density of potential modes to be saturated. This parameter was investigated using molecular dynamics simulations, and found to be ∼0.2 per atom. In this way, the ion-thermal contribution can be calculated for a wide-range equation of state (EOS) without requiring a large number of molecular dynamics simulations. Example calculations were performed for carbon, including the sensitivity of key EOS loci to ionic freedom.

A spherical crystal diffraction imager for Sandia's Z Pulsed Power Facility

Sandia's Z Pulsed Power Facility is able to dynamically compress matter to extreme states with exceptional uniformity, duration, and size, which are ideal for investigating fundamental material properties of high energy density conditions. X-ray diffraction (XRD) is a key atomic scale probe since it provides direct observation of the compression and strain of the crystal lattice and is used to detect, identify, and quantify phase transitions. Because of the destructive nature of Z-Dynamic Material Property (DMP) experiments and low signal vs background emission levels of XRD, it is very challenging to detect a diffraction signal close to the Z-DMP load and to recover the data. We have developed a new Spherical Crystal Diffraction Imager (SCDI) diagnostic to relay and image the diffracted x-ray pattern away from the load debris field. The SCDI diagnostic utilizes the Z-Beamlet laser to generate 6.2-keV Mn-He_α x rays to probe a shock-compressed material on the Z-DMP load. A spherically bent crystal composed of highly oriented pyrolytic graphite is used to collect and focus the diffracted x rays into a 1-in. thick tungsten housing, where an image plate is used to record the data.

Ab initio dielectric response function of diamond and other relevant high pressure phases of carbon

The electronic structure and dielectric properties of the diamond, body centered cubic diamond (bc8), and hexagonal diamond (lonsdaleite) phases of carbon are computed using density functional theory and many-body perturbation theory with the emphasis on the excitonic picture of the solid phases relevant in the regimes of high-pressure physics and warm dense matter. We also discuss the capabilities of reproducing the inelastic x-ray scattering spectra in comparison with the existing models in light of recent x-ray scattering experiments on carbon and carbon bearing materials in the Megabar range.

A Short Review of Current Computational Concepts for High-Pressure Phase Transition Studies in Molecular Crystals

High-pressure chemistry of organic compounds is a hot topic of modern chemistry. In this work, basic computational concepts for high-pressure phase transition studies in molecular crystals are described, showing their advantages and disadvantages. The interconnection of experimental and computational methods is highlighted, showing the importance of energy calculations in this field. Based on our deep understanding of methods’ limitations, we suggested the most convenient scheme for the computational study of high-pressure crystal structure changes. Finally, challenges and possible ways for progress in high-pressure phase transitions research of organic compounds are briefly discussed.

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).

Nanosecond Melting and Recrystallization in Shock-Compressed Silicon

In situ, time-resolved, x-ray diffraction and simultaneous continuum measurements were used to examine structural changes in Si shock compressed to 54 GPa. Shock melting was unambiguously established above ∼31-33  GPa, through the vanishing of all sharp crystalline diffraction peaks and the emergence of a single broad diffraction ring. Reshock from the melt boundary results in rapid (nanosecond) recrystallization to the hexagonal-close-packed Si phase and further supports melting. Our results also provide new constraints on the high-temperature, high-pressure Si phase diagram.

New carbon allotropes in sp + sp3 bonding networks consisting of C8 cubes

We identify using ab initio calculations new types of three-dimensional carbon allotrope constructed by inserting acetylenic or diacetylenic bonds into a body-centered cubic C₈ lattice.

Dynamic high pressure induced strong and weak hydrogen bonds enhanced by pre-resonance stimulated Raman scattering in liquid water

355 nm pulsed laser is employed to excite pre-resonance forward stimulated Raman scattering (FSRS) of liquid water at ambient temperature. Due to the shockwave induced dynamic high pressure, the obtained Raman spectra begin to exhibit double peaks distribution at 3318 and 3373 cm^-1 with the input energy of 17 mJ,which correspond with OH stretching vibration with strong and weak hydrogen (H) bonds. With laser energy rising from 17 to 27 mJ, the Stokes line at 3318 cm^-1 shifts to 3255 and 3230 cm^-1 because of the high pressure being enlarged. When the energy is up to 32 mJ, only 3373 cm^-1 peak exists. The strong and weak H bond exhibit quite different energy dependent behaviors.

Computational prediction of a simple cubic carbon allotrope consisting of C12 clusters

We identify by ab initio calculations a new simple cubic carbon phase in Pa3¯ symmetry, which has a 48-atom unit cell in all-sp³ bonding networks, thus termed SC48 carbon. It can be viewed as a crystalline form of C₁₂ clusters or a combined structure of SC24 and BC12 carbon, but it is energetically more stable than the recently reported cubic carbon phases such as BC8, SC24, BC12, and fcc-C₁₂. The structural stability is verified by phonon mode analysis. Electronic band and density of state calculations reveal that SC48 carbon is an insulator with a large direct band gap of 4.40 eV. Moreover, simulated x-ray diffraction patterns provide an excellent match to the distinct diffraction peaks found in milled fullerene soot. These results provide a solid foundation for further exploration of this new carbon allotrope.

A strong diffusive ion mode in dense ionized matter predicted by Langevin dynamics

The state and evolution of planets, brown dwarfs and neutron star crusts is determined by the properties of dense and compressed matter. Due to the inherent difficulties in modelling strongly coupled plasmas, however, current predictions of transport coefficients differ by orders of magnitude. Collective modes are a prominent feature, whose spectra may serve as an important tool to validate theoretical predictions for dense matter. With recent advances in free electron laser technology, X-rays with small enough bandwidth have become available, allowing the investigation of the low-frequency ion modes in dense matter. Here, we present numerical predictions for these ion modes and demonstrate significant changes to their strength and dispersion if dissipative processes are included by Langevin dynamics. Notably, a strong diffusive mode around zero frequency arises, which is not present, or much weaker, in standard simulations. Our results have profound consequences in the interpretation of transport coefficients in dense plasmas.

C 20 - T carbon: a novel superhard sp (3) carbon allotrope with large cavities

Through first-principles calculations, we predict a new superhard carbon allotrope named C 20  -  T, which possesses a cubic T symmetry with space group No.198(P213). This new carbon allotrope has an all-sp (3) hybridized bonding network with 20 atoms in its primitive unit cell. The dynamic, mechanical, and thermal stabilities of this new carbon phase at zero pressure are confirmed by using a variety of state-of-the-art theoretical calculations. Interestingly, despite the fact that C 20  -  T carbon has a porous structure with large cavities, our calculations identify its superhard properties with the Vickers hardness of 72.76 Gpa. The ideal tensile and shear strength of C 20  -  T carbon are calculated to be 71.1 and 55.2 GPa respectively, comparable to that of c-BN. Electronic band calculations reveal that this new carbon allotrope is a transparent insulator with an indirect band gap of 5.44 eV. These results broaden our understanding of superhard carbon allotropes.

Atomic bound state and scattering properties of effective momentum-dependent potentials

Effective classical dynamics provide a potentially powerful avenue for modeling large-scale dynamical quantum systems. We have examined the accuracy of a Hamiltonian-based approach that employs effective momentum-dependent potentials (MDPs) within a molecular-dynamics framework through studies of atomic ground states, excited states, ionization energies, and scattering properties of continuum states. Working exclusively with the Kirschbaum-Wilets (KW) formulation with empirical MDPs [C. L. Kirschbaum and L. Wilets, Phys. Rev. A 21, 834 (1980)0556-279110.1103/PhysRevA.21.834], optimization leads to very accurate ground-state energies for several elements (e.g., N, F, Ne, Al, S, Ar, and Ca) relative to Hartree-Fock values. The KW MDP parameters obtained are found to be correlated, thereby revealing some degree of transferability in the empirically determined parameters. We have studied excited-state orbits of electron-ion pair to analyze the consequences of the MDP on the classical Coulomb catastrophe. From the optimized ground-state energies, we find that the experimental first- and second-ionization energies are fairly well predicted. Finally, electron-ion scattering was examined by comparing the predicted momentum transfer cross section to a semiclassical phase-shift calculation; optimizing the MDP parameters for the scattering process yielded rather poor results, suggesting a limitation of the use of the KW MDPs for plasmas.

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 compression of dense oxide (Gd3Ga5O12) from 0.4 to 2.6 TPa: Universal Hugoniot of fluid metals

Materials at high pressures and temperatures are of great current interest for warm dense matter physics, planetary sciences, and inertial fusion energy research. Shock-compression equation-of-state data and optical reflectivities of the fluid dense oxide, Gd3Ga5O12 (GGG), were measured at extremely high pressures up to 2.6 TPa (26 Mbar) generated by high-power laser irradiation and magnetically-driven hypervelocity impacts. Above 0.75 TPa, the GGG Hugoniot data approach/reach a universal linear line of fluid metals, and the optical reflectivity most likely reaches a constant value indicating that GGG undergoes a crossover from fluid semiconductor to poor metal with minimum metallic conductivity (MMC). These results suggest that most fluid compounds, e.g., strong planetary oxides, reach a common state on the universal Hugoniot of fluid metals (UHFM) with MMC at sufficiently extreme pressures and temperatures. The systematic behaviors of warm dense fluid would be useful benchmarks for developing theoretical equation-of-state and transport models in the warm dense matter regime in determining computational predictions.

Body-Centered Orthorhombic C_{16}: A Novel Topological Node-Line Semimetal

We identify by ab initio calculations a novel topological semimetal carbon phase in all-sp^{2} bonding networks with a 16-atom body-centered orthorhombic unit cell, termed bco-C_{16}. Total-energy calculations show that bco-C_{16} is comparable to solid fcc-C_{60} in energetic stability, and phonon and molecular dynamics simulations confirm its dynamical stability. This all-sp^{2} carbon allotrope can be regarded as a three-dimensional modification of graphite, and its simulated x-ray diffraction (XRD) pattern matches well a previously unexplained diffraction peak in measured XRD spectra of detonation and chimney soot, indicating its presence in the specimen. Electronic band structure calculations reveal that bco-C_{16} is a topological node-line semimetal with a single nodal ring. These findings establish a novel carbon phase with intriguing structural and electronic properties of fundamental significance and practical interest.

Theory of density fluctuations in strongly radiative plasmas

Derivation of the dynamic structure factor, an important parameter linking experimental and theoretical work in dense plasmas, is possible starting from hydrodynamic equations. Here we obtain, by modifying the governing hydrodynamic equations, a new form of the dynamic structure factor which includes radiative terms. The inclusion of such terms has an effect on the structure factor at high temperatures, which suggests that its effect must be taken into consideration in such regimes.

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.

H18 Carbon: A New Metallic Phase with sp2-sp3 Hybridized Bonding Network

Design and synthesis of three-dimensional metallic carbons are currently one of the hot issues in contemporary condensed matter physics because of their fascinating properties. Here, based on first-principles calculations, we discover a novel stable metallic carbon allotrope (termed H₁₈ carbon) in () symmetry with a mixed sp²-sp³ hybridized bonding network. The dynamical stability of H₁₈ carbon is verified by phonon mode analysis and molecular dynamics simulations, and its mechanical stability is analyzed by elastic constants, bulk modulus, and shear modulus. By simulating the x-ray diffraction patterns, we propose that H₁₈ carbon would be one of the unidentified carbon phases observed in recent detonation experiments. The analysis of the band structure and density of states reveal that this new carbon phase has a metallic feature mainly due to the C atoms with sp² hybridization. This novel 3D metallic carbon phase is anticipated to be useful for practical applications such as electronic and mechanical devices.

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.

Shock Response and Phase Transitions of MgO at Planetary Impact Conditions

The moon-forming impact and the subsequent evolution of the proto-Earth is strongly dependent on the properties of materials at the extreme conditions generated by this violent collision. We examine the high pressure behavior of MgO, one of the dominant constituents in Earth's mantle, using high-precision, plate impact shock compression experiments performed on Sandia National Laboratories' Z Machine and extensive quantum calculations using density functional theory (DFT) and quantum Monte Carlo (QMC) methods. The combined data span from ambient conditions to 1.2 TPa and 42 000 K, showing solid-solid and solid-liquid phase boundaries. Furthermore our results indicate that under impact the solid and liquid phases coexist for more than 100 GPa, pushing complete melting to pressures in excess of 600 GPa. The high pressure required for complete shock melting has implications for a broad range of planetary collision events.

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.

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.

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.

Toward the Ultra-incompressible Carbon Materials. Computational Simulation and Experimental Observation

The common opinion that diamond is the stiffest material is disproved by a number of experimental studies where the fabrication of carbon materials based on polymerized fullerenes with outstanding mechanical stiffness was reported. Here we investigated the nature of this unusual effect. We present a model constituted of compressed polymerized fullerite clusters implemented in a diamond matrix with bulk modulus B0 much higher than that of diamond. The calculated B0 value depends on the sizes of both fullerite grain and diamond environment and shows close correspondence with measured data. Additionally, we provide results of experimental study of atomic structure and mechanical properties of ultrahard carbon material supported the presented model.

Nonlinear acoustics at GHz frequencies in a viscoelastic fragile glass former

Using a picosecond pump-probe ultrasonic technique, we study the propagation of high-amplitude, laser-generated longitudinal coherent acoustic pulses in the viscoelastic fragile glass former DC704. We observe an increase of almost 10% in acoustic pulse propagation speed at the highest optical pump fluence which is a result of the supersonic nature of nonlinear propagation in the viscous medium. From our measurement, we deduce the nonlinear acoustic parameter of the glass former in the gigahertz frequency range across the glass transition temperature.

Graphene and nano-diamond synthesis in expansions of molten liquid carbon

Despite their widespread use in high-pressure experiments, little is known about the physical and chemical properties of carbon-containing materials as they expand and cool to ambient conditions. As a result, interpretation of experiments can rely on use of unconstrained models with poor accuracy for the ensuing equation of state properties and final chemical products. To this end, we use quantum simulations to study the free expansion and cooling of carbon from metallic liquid states achieved during shock compression. Expansions from three different sets of shock conditions yielded of a variety of chain and ring structures. We then quantify the relative amounts of graphite-like and diamond-like particles formed during cooling and equilibration. We observe that for all cases, graphene sheets are the majority product formed with more extreme initial conditions producing increasingly larger amounts of diamond particles. Our results can address key needs for future meso-scale models of experiments, where knowledge of material properties and chemical end products can have a pronounced effect on interpreting experimental observables.

Ramp compression of diamond to five terapascals

The recent discovery of more than a thousand planets outside our Solar System, together with the significant push to achieve inertially confined fusion in the laboratory, has prompted a renewed interest in how dense matter behaves at millions to billions of atmospheres of pressure. The theoretical description of such electron-degenerate matter has matured since the early quantum statistical model of Thomas and Fermi, and now suggests that new complexities can emerge at pressures where core electrons (not only valence electrons) influence the structure and bonding of matter. Recent developments in shock-free dynamic (ramp) compression now allow laboratory access to this dense matter regime. Here we describe ramp-compression measurements for diamond, achieving 3.7-fold compression at a peak pressure of 5 terapascals (equivalent to 50 million atmospheres). These equation-of-state data can now be compared to first-principles density functional calculations and theories long used to describe matter present in the interiors of giant planets, in stars, and in inertial-confinement fusion experiments. Our data also provide new constraints on mass-radius relationships for carbon-rich planets.

Ramp compression of diamond to five terapascals

The recent discovery of more than a thousand planets outside our Solar System, together with the significant push to achieve inertially confined fusion in the laboratory, has prompted a renewed interest in how dense matter behaves at millions to billions of atmospheres of pressure. The theoretical description of such electron-degenerate matter has matured since the early quantum statistical model of Thomas and Fermi, and now suggests that new complexities can emerge at pressures where core electrons (not only valence electrons) influence the structure and bonding of matter. Recent developments in shock-free dynamic (ramp) compression now allow laboratory access to this dense matter regime. Here we describe ramp-compression measurements for diamond, achieving 3.7-fold compression at a peak pressure of 5 terapascals (equivalent to 50 million atmospheres). These equation-of-state data can now be compared to first-principles density functional calculations and theories long used to describe matter present in the interiors of giant planets, in stars, and in inertial-confinement fusion experiments. Our data also provide new constraints on mass-radius relationships for carbon-rich planets.

A metallic carbon consisting of helical carbon triangle chains

Carbon is the basis of life on Earth and many technological applications. We computationally report an sp3-hybridization-assembled carbon allotrope constructed by helical triangle chains through the evolutionary structure prediction method. Different from the previous metallic carbon K4, this carbon, called Tri-carbon, is mechanically and dynamically stable at ambient pressure. High ring strain in the carbon triangle blocks forces the C–C bond in Tri-carbon to be a 'bent bond', rather than the common single bond in diamond or the π bond in graphite. Unlike the unstrained sp3-hybridization in semiconductive diamond, valence electrons in the 'bent bond' are recombined to form extremely anisotropic sp3-hybridized bonds, thus conferring metallicity to Tri-carbon. Under nonhydrostatic conditions, Tri-carbon shows significantly anisotropic ideal tensile and compressive strength. Tri-carbon is expected to be achieved through chemical methods, such as the synthesis of cyclopropane derivatives (e.g. triangulane and tetrahedrane). These methods eliminate the restriction of ultra-high pressure to obtain metallic carbons.

Evidence for a glassy state in strongly driven carbon

Here, we report results of an experiment creating a transient, highly correlated carbon state using a combination of optical and x-ray lasers. Scattered x-rays reveal a highly ordered state with an electrostatic energy significantly exceeding the thermal energy of the ions. Strong Coulomb forces are predicted to induce nucleation into a crystalline ion structure within a few picoseconds. However, we observe no evidence of such phase transition after several tens of picoseconds but strong indications for an over-correlated fluid state. The experiment suggests a much slower nucleation and points to an intermediate glassy state where the ions are frozen close to their original positions in the fluid.

Raman spectra from symmetric hydrogen bonds in water by high-intensity laser-induced breakdown

Raman spectra of ice VII and X were investigated using strong plasma shockwave generated by laser-induced breakdown (LIB) in liquid water. Simultaneously, the occurrence of the hydrogen emission lines of 656 nm (Hα), 486 nm (Hβ), 434 nm (Hγ) and 410 nm (Hδ) was observed. At 5 × 10(12) W/cm(2) optical power density, the O-H symmetric stretching, translational and librational modes of ice VII and a single peak at 785 cm(-1) appeared in the spectra. The band was assigned to the Raman-active O-O mode of the monomolecular phase, which was the symmetric hydrogen bond of cuprite ice X. The spectra indicated that ice VII and X structure were formed, as the trajectory of the strong plasma shockwave passes through the stable Pressure-Temperature range of ice VII and X. The shockwave temperature and pressure were calculated by the Grüneisen model.