Optical Properties of Fluid Hydrogen at the Transition to a Conducting State

Dynamical properties of hydrogen fluid at high pressures

The properties of the hydrogen fluid at high pressures are still of interest to the scientific community. The experimentally unreachable dynamical properties could provide new insights into this field. In 2020 [Cheng et al., Nature 585, 217-220 (2020)], the machine-learned approach allows the calculation of the self-diffusion coefficient in the warm dense hydrogen with higher precision. After that, the work [van de Bund et al., Phys. Rev. Lett. 126(22), 225701 (2021)] reports the ab initio treatment of isotopic effects on diffusion in H2/D2 and a significant increase in its value in the region of the phase transition. Both works indicate the anomalous growth of diffusion, but the reasons for this phenomenon are unclear. In the present work, we reveal the plasma-like behavior of the diffusion growth. We apply the classical molecular dynamics method using a machine learning potential developed on the ab initio modeling for the prediction of diffusion and shear viscosity coefficients. We consider dependencies of the vibrational spectrum, molecule lifetime, diffusion, and shear viscosity coefficients on density along the isotherms in the temperature range from 600 to 1100 K.

Nonmetal-to-metal transition in liquid hydrogen using density functional theory and the Heyd-Scuseria-Ernzerhof exchange-correlation functional

We investigate the first-order liquid-liquid phase transition in fluid hydrogen, which is accompanied by a nonmetal-to-metal transition. We use a combination of density functional theory for the electrons and molecular dynamics simulations for the ions. By employing the nonlocal Heyd-Scuseria-Ernzerhof exchange-correlation functional, we accurately determine the equation of state and the corresponding coexistence line. Additionally, we calculate the electrical conductivity using the Kubo-Greenwood formula and find jumps in the coexisting region, which is characteristic of a first-order transition. Our new predictions are compared with previous theoretical results and available experimental data. Thereby, we find that the strongly constrained and appropriately normed exchange-correlation functional provides an excellent balance between computational cost and accuracy.

Spectroradiometry with sub-microsecond time resolution using multianode photomultiplier tube assemblies

Accurate and precise measurements of spectroradiometric temperature are crucial for many high pressure experiments that use diamond anvil cells or shock waves. In experiments with sub-millisecond timescales, specialized detectors such as streak cameras or photomultiplier tubes are required to measure temperature. High accuracy and precision are difficult to attain, especially at temperatures below 3000 K. Here, we present a new spectroradiometry system based on multianode photomultiplier tube technology and passive readout circuitry that yields a 0.24 µs rise-time for each channel. Temperature is measured using five color spectroradiometry. During high pressure pulsed Joule heating experiments in a diamond anvil cell, we document measurement precision to be ±30 K at temperatures as low as 2000 K during single-shot heating experiments with 0.6 µs time-resolution. Ambient pressure melting tests using pulsed Joule heating indicate that the accuracy is ±80 K in the temperature range 1800-2700 K.

Exciton Nature of Plasma Phase Transition in Warm Dense Fluid Hydrogen: ROKS Simulation

The transition of warm dense fluid hydrogen from an insulator to a conducting state at pressures of about 20-400 GPa and temperatures of 500-5000 K has been the subject of active scientific research over the past few decades. However, various experimental and theoretical methods do not provide consistent results. In this work, we have applied the restricted open-shell Kohn-Sham (ROKS) method for first principles molecular dynamics of dense hydrogen after thermal excitation to the first singlet excited state. The Wannier localization method has allowed us to analyze the exciton dynamics in this system. The model shows that a key mechanism of the transition is associated with the dissociation of electron-hole pairs, which allows explaining several stages of the transition of fluid H₂ from molecular state to plasma. This mechanism is able to give a quantitative description of several experimental results as well as to resolve the discrepancies between experimental studies.

Water-cooling diamond anvil cells: An approach to temperature-pressure relation in heated experiments

Temperature induced pressure drift in the diamond anvil cell (DAC) is a major issue in high-pressure high-temperature experiments. It is commonly acknowledged that these drifts originate from multiple factors, but no systematic descriptions have been made so far. By introducing an internal water-cooling system in the DAC, we have performed a systematic investigation into temperature induced pressure drifts to reveal the mechanism behind them and to find a proper experimental procedure to achieve minimal pressure variation in DAC's heating experiment. It is revealed in this experiment that pressure variation during heating processes originates from multiple temperature related factors of the DAC. The variation itself can be considered as a rebalancing process of the compression forces on the sample chamber initiated by the disturbance caused by temperature elevation. It is possible to suppress pressure variation by maintaining the temperature of the DAC body at room temperature to ensure the consistency of compression on the sample chamber. At the same time, the best procedure for the heating experiments is to properly pre-heat the sample chamber equipped with the internal water-cooling system before performing the in situ measurements on the temperature-related properties at the pressurized and heated conditions. Our discovery provides a reliable procedure for the sample heating process in the DAC and helps resolve the complex mystery of the influence of the combination of pressure and temperature in high-pressure high-temperature experiments.

Thermodynamic modeling of fluid polyamorphism in hydrogen at extreme conditions

Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid–fluid phase transition (FFPT) in high-pressure hydrogen between insulating and conducting high-density fluids. This transition is induced by the reversible dimerization/dissociation of the molecular and atomistic states of hydrogen. In this work, we present the first attempt to thermodynamically model the FFPT in hydrogen at extreme conditions. Our predictions for the phase coexistence and the reaction equilibrium of the two alternative forms of fluid hydrogen are based on experimental data and supported by the results of simulations. Remarkably, we find that the law of corresponding states can be utilized to construct a unified equation of state combining the available computational results for different models of hydrogen and the experimental data.

Diamond formation kinetics in shock-compressed C─H─O samples recorded by small-angle x-ray scattering and x-ray diffraction

Extreme conditions inside ice giants such as Uranus and Neptune can result in peculiar chemistry and structural transitions, e.g., the precipitation of diamonds or superionic water, as so far experimentally observed only for pure C─H and H2O systems, respectively. Here, we investigate a stoichiometric mixture of C and H2O by shock-compressing polyethylene terephthalate (PET) plastics and performing in situ x-ray probing. We observe diamond formation at pressures between 72 ± 7 and 125 ± 13 GPa at temperatures ranging from ~3500 to ~6000 K. Combining x-ray diffraction and small-angle x-ray scattering, we access the kinetics of this exotic reaction. The observed demixing of C and H2O suggests that diamond precipitation inside the ice giants is enhanced by oxygen, which can lead to isolated water and thus the formation of superionic structures relevant to the planets' magnetic fields. Moreover, our measurements indicate a way of producing nanodiamonds by simple laser-driven shock compression of cheap PET plastics.

Modeling fluid polyamorphism through a maximum-valence approach

We suggest a simple model to describe polyamorphism in single-component fluids using a maximum-valence approach. The model contains three types of interactions: (i) Atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, (ii) atoms may form covalent bonds that induce association, and (iii) atoms with maximal valence attract or repel each other stronger than other atoms, thus generating liquid-liquid separation. As an example, we qualitatively compare this model with the behavior of liquid sulfur and show that condition (iii) generates a liquid-liquid phase transition in addition to the liquid-gas phase transition.

Transport properties of a quasisymmetric binary nitrogen-oxygen mixture in the warm dense regime

Transport properties of mixtures in the warm dense matter (WDM) regime play an important role in natural astrophysics. However, a physical understanding of ionic transport properties in quasisymmetric liquid mixtures has remained elusive. Here, we present extensive ab initio molecular dynamics (AIMD) simulations on the ionic diffusion and viscosity of a quasisymmetric binary nitrogen-oxygen (N-O) mixture in a wide warm dense regime of 8-120 kK and 4.5-8.0 g/cm^{3}. Diffusion and viscosity of N-O mixtures with different compositions are obtained by using the Green-Kubo formula. Unlike asymmetric mixtures, the change of proportions in N-O mixtures slightly affects the viscosity and diffusion in the strong-coupling region. Furthermore, the AIMD results are used to build and verify a global pseudo-ion in jellium (PIJ) model for ionic transport calculations. The PIJ model succeeds in reproducing the transport properties of N-O mixtures where ionization has occurred, and provides a promising alternative approach to obtaining comparable results to AIMD simulations with relatively small computational costs. Our current results highlight the characteristic features of the quasisymmetric binary mixtures and demonstrate the applicability of the PIJ model in the WDM regime.

First principles study of dense and metallic nitric sulfur hydrides

Studies of molecular mixtures containing hydrogen sulfide (H₂S) could open up new routes towards hydrogen-rich high-temperature superconductors under pressure. H₂S and ammonia (NH₃) form hydrogen-bonded molecular mixtures at ambient conditions, but their phase behavior and propensity towards mixing under pressure is not well understood. Here, we show stable phases in the H₂S-NH₃ system under extreme pressure conditions to 4 Mbar from first-principles crystal structure prediction methods. We identify four stable compositions, two of which, (H₂S) (NH₃) and (H₂S) (NH₃)₄, are stable in a sequence of structures to the Mbar regime. A re-entrant stabilization of (H₂S) (NH₃)₄ above 300 GPa is driven by a marked reversal of sulfur-hydrogen chemistry. Several stable phases exhibit metallic character. Electron-phonon coupling calculations predict superconducting temperatures up to 50 K, in the Cmma phase of (H₂S) (NH₃) at 150 GPa. The present findings shed light on how sulfur hydride bonding and superconductivity are affected in molecular mixtures. They also suggest a reservoir for hydrogen sulfide in the upper mantle regions of icy planets in a potentially metallic mixture, which could have implications for their magnetic field formation.

Equation of State of CO_{2} Shock Compressed to 1 TPa

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

Evidence for supercritical behaviour of high-pressure liquid hydrogen

Hydrogen, the simplest and most abundant element in the Universe, develops a remarkably complex behaviour upon compression¹. Since Wigner predicted the dissociation and metallization of solid hydrogen at megabar pressures almost a century ago², several efforts have been made to explain the many unusual properties of dense hydrogen, including a rich and poorly understood solid polymorphism^1,3-5, an anomalous melting line⁶ and the possible transition to a superconducting state⁷. Experiments at such extreme conditions are challenging and often lead to hard-to-interpret and controversial observations, whereas theoretical investigations are constrained by the huge computational cost of sufficiently accurate quantum mechanical calculations. Here we present a theoretical study of the phase diagram of dense hydrogen that uses machine learning to 'learn' potential-energy surfaces and interatomic forces from reference calculations and then predict them at low computational cost, overcoming length- and timescale limitations. We reproduce both the re-entrant melting behaviour and the polymorphism of the solid phase. Simulations using our machine-learning-based potentials provide evidence for a continuous molecular-to-atomic transition in the liquid, with no first-order transition observed above the melting line. This suggests a smooth transition between insulating and metallic layers in giant gas planets, and reconciles existing discrepancies between experiments as a manifestation of supercritical behaviour.

Gated detection of supercontinuum pulses enables optical probing of solid and molten silicates at extreme pressure-temperature conditions

Optical studies of materials at high pressure-temperature (P-T) conditions provide insights into their physical properties that may be inaccessible to direct determination at extreme conditions. Incandescent light sources, however, are insufficiently bright to optically probe samples with radiative temperatures above ∼1000 K. Here we report on a system to perform optical absorption experiments in a laser-heated diamond anvil cell at T up to at least 4000 K. This setup is based on a pulsed supercontinuum (broadband) light probe and a gated CCD detector. Precise and tight synchronization of the detector gates (3 ns) to the bright probe pulses (1 ns) diminishes the recorded thermal background and preserves an excellent probe signal at high temperature. We demonstrate the efficiency of this spectroscopic setup by measuring the optical absorbance of solid and molten (Mg,Fe)SiO₃, an important constituent of planetary mantles, at P ∼30 GPa and T ∼1200 K to 4150 K. Optical absorbance of the hot solid (Mg,Fe)SiO₃ is moderately sensitive to temperature but increases abruptly upon melting and acquires a strong temperature dependence. Our results enable quantitative estimates of the opacity of planetary mantles with implications to their thermal and electrical conductivities, all of which have never been constrained at representative P-T conditions, and call for an optical detection of melting in silicate-bearing systems to resolve the extant ambiguity in their high-pressure melting curves.

Phase diagram of hydrogen at extreme pressures and temperatures; updated through 2019 (Review article)

Hydrogen is expected to display remarkable properties under extreme pressures and temperatures stemming from its low mass and thus propensity to quantum phenomena. Exploring such phenomena remains very challenging even though there was a tremendous technical progress both in experimental and theoretical techniques since the last comprehensive review (McMahon et al.) was published in 2012. Raman and optical spectroscopy experiments including infrared have been extended to cover a broad range of pressures and temperatures (P—T) probing phase stability and optical properties at these conditions. Novel pulsed laser heating and toroidal diamond anvil techniques together with diamond anvil protecting layers drastically improved the capabilities of static compression methods. The electrical conductivity measurements have been also performed to much higher than previously pressures and extended to low temperatures. The dynamic compression techniques have been dramatically improved recently enabling ramp isentropic compression that allows probing a wide range of P–T thermodynamic pathways. In addition, new theoretical methods have been developed beyond a common DFT theory, which make them predictive and in better agreement with experiments. With the development of new theoretical and experimental tools and sample loading methods, the quest for metallic hydrogen accelerated recently delivering a wealth of new data, which are reviewed here.

A Spectroscopic Study of the Insulator-Metal Transition in Liquid Hydrogen and Deuterium

The insulator-to-metal transition in dense fluid hydrogen is an essential phenomenon in the study of gas giant planetary interiors and the physical and chemical behavior of highly compressed condensed matter. Using direct fast laser spectroscopy techniques to probe hydrogen and deuterium precompressed in a diamond anvil cell and laser heated on microsecond timescales, an onset of metal-like reflectance is observed in the visible spectral range at P >150 GPa and T ≥ 3000 K. The reflectance increases rapidly with decreasing photon energy indicating free-electron metallic behavior with a plasma edge in the visible spectral range at high temperatures. The reflectance spectra also suggest much longer electronic collision time (≥1 fs) than previously inferred, implying that metallic hydrogen at the conditions studied is not in the regime of saturated conductivity (Mott-Ioffe-Regel limit). The results confirm the existence of a semiconducting intermediate fluid hydrogen state en route to metallization.

Combination of pulsed light heating thermoreflectance and laser-heated diamond anvil cell for in-situ high pressure-temperature thermal diffusivity measurements

By combining thermoreflectance measurements and laser heated diamond anvil cell (LHDAC) techniques, an instrument for the measurement of in situ high pressure-temperature thermal diffusivity of materials was developed. In an LHDAC system, high-power continuous-wave laser beams irradiate both faces of a disk-shaped metal sample loaded into diamond anvil cells (DACs), to maintain a stable high-temperature condition. During the operation of the LHDAC system, temperature of the sample is determined from the thermal radiation spectrum between 640 and 740 nm to fit Planck's law. Subsequently, a pulsed laser beam irradiates the metal disk to induce a temperature gradient inside the sample, and the transient temperature, caused by heat diffusion, is measured by a continuous wave probe laser based on the thermoreflectance phenomenon. We determined the thermal conductivities of Pt and Fe up to approximately 60 GPa and 2000 K using the measured thermal diffusivities and obtained values consistent with previous works. The uncertainties in the pressure and the temperature are estimated to be approximately 10%, and that in the thermal conductivity is estimated to approximately 15%. The system developed in this study enables us to determine thermal transport properties of materials under pressure-temperature conditions of the deep Earth.

Optical properties of high-pressure fluid hydrogen across molecular dissociation

Optical properties of compressed fluid hydrogen in the region where dissociation and metallization is observed are computed by ab initio methods and compared with recent experimental results. We confirm that at T > 3,000 K, both processes are continuous, while at T < 1,500 K, the first-order phase transition is accompanied by a discontinuity of the dc conductivity and the thermal conductivity, while both the reflectivity and absorption coefficient vary rapidly but continuously. Our results support the recent analysis of National Ignition Facility (NIF) experiments [Celliers PM, et al. (2018) Science 361:677-682], which assigned the inception of metallization to pressures where the reflectivity is ∼0.3. Our results also support the conclusion that the temperature plateau seen in laser-heated diamond-anvil cell (DAC) experiments at temperatures higher than 1,500 K corresponds to the onset of optical absorption, not to the phase transition.

Insulator-metal transition in dense fluid deuterium

Dense fluid metallic hydrogen occupies the interiors of Jupiter, Saturn, and many extrasolar planets, where pressures reach millions of atmospheres. Planetary structure models must describe accurately the transition from the outer molecular envelopes to the interior metallic regions. We report optical measurements of dynamically compressed fluid deuterium to 600 gigapascals (GPa) that reveal an increasing refractive index, the onset of absorption of visible light near 150 GPa, and a transition to metal-like reflectivity (exceeding 30%) near 200 GPa, all at temperatures below 2000 kelvin. Our measurements and analysis address existing discrepancies between static and dynamic experiments for the insulator-metal transition in dense fluid hydrogen isotopes. They also provide new benchmarks for the theoretical calculations used to construct planetary models.

Metallization and molecular dissociation of dense fluid nitrogen

Diatomic nitrogen is an archetypal molecular system known for its exceptional stability and complex behavior at high pressures and temperatures, including rich solid polymorphism, formation of energetic states, and an insulator-to-metal transformation coupled to a change in chemical bonding. However, the thermobaric conditions of the fluid molecular–polymer phase boundary and associated metallization have not been experimentally established. Here, by applying dynamic laser heating of compressed nitrogen and using fast optical spectroscopy to study electronic properties, we observe a transformation from insulating (molecular) to conducting dense fluid nitrogen at temperatures that decrease with pressure and establish that metallization, and presumably fluid polymerization, occurs above 125 GPa at 2500 K. Our observations create a better understanding of the interplay between molecular dissociation, melting, and metallization revealing features that are common in simple molecular systems.

Nitrogen is a model system still presenting unknown behaviors at the pressures and temperatures typical of deep planets’ interiors. Here the authors explore, by pulsed laser heating in a diamond anvil cell and optical measurements, the metallization and non-molecular states of nitrogen in a previously unexplored domain above 1 Mbar and at 2000-7000K.

Dynamic conductivity and partial ionization in dense fluid hydrogen

A theoretical description for optical conduction experiments in dense fluid hydrogen is presented. Different quantum statistical approaches are used to describe the mechanism of electronic transport in hydrogen's high-temperature dense phase. We show that at the onset of the metallic transition, optical conduction could be described by a strong rise in atomic polarizability, due to increased ionization, whereas in the highly degenerate limit, the Ziman weak scattering model better accounts for the observed saturation of reflectance. The inclusion of effects of partial ionization in the highly degenerate region provides great agreement with experimental results. Hydrogen's fluid metallic state is revealed to be a partially ionized free-electron plasma. Our results provide some of the first theoretical transport models that are experimentally benchmarked, as well as an important guide for future studies.

Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum Monte Carlo Simulations

Understanding planetary interiors is directly linked to our ability of simulating exotic quantum mechanical systems such as hydrogen (H) and hydrogen-helium (H-He) mixtures at high pressures and temperatures. Equation of state (EOS) tables based on density functional theory are commonly used by planetary scientists, although this method allows only for a qualitative description of the phase diagram. Here we report quantum Monte Carlo (QMC) molecular dynamics simulations of pure H and H-He mixture. We calculate the first QMC EOS at 6000 K for a H-He mixture of a protosolar composition, and show the crucial influence of He on the H metallization pressure. Our results can be used to calibrate other EOS calculations and are very timely given the accurate determination of Jupiter's gravitational field from the NASA Juno mission and the effort to determine its structure.

Melting and High P-T Transitions of Hydrogen up to 300 GPa

High P-T Raman spectra of hydrogen in the vibron and lattice mode regions were measured up to 300 GPa and 900 K using externally heated diamond anvil cell techniques. A new melting line determined from the disappearance of lattice mode excitations was measured directly for the first time above 140 GPa. The results differ from theoretical predictions and extrapolations from lower pressure melting relations. In addition, discontinuities in Raman frequencies are observed as a function of pressure and temperature indicative of phase transition at these conditions. The appearance of a new Raman feature near 2700  cm^{-1} at ∼300  GPa and 370 K indicates the transformation to a new crystalline phase. Theoretical calculations of the spectrum suggest the new phase is the proposed Cmca-4 metallic phase. The transition pressure is close to that of a recently reported transition observed on dynamic compression.

Accelerating ab initio Molecular Dynamics and Probing the Weak Dispersive Forces in Dense Liquid Hydrogen

We propose an ab initio molecular dynamics method, capable of dramatically reducing the autocorrelation time required for the simulation of classical and quantum particles at finite temperatures. The method is based on an efficient implementation of a first order Langevin dynamics modified by means of a suitable, position dependent acceleration matrix S. Here, we apply this technique to both Lennard-Jones models, to demonstrate the accuracy and speeding-up of the sampling, and within a quantum Monte Carlo based wave function approach, for determining the phase diagram of high-pressure hydrogen with simulations much longer than the autocorrelation time. With the proposed method, we are able to equilibrate in a few hundred steps even close to the liquid-liquid phase transition (LLT). Within our approach, we find that the LLT transition is consistent with recent density functionals predicting a much larger transition pressure when the long range dispersive forces are taken into account.