The insulator–metal transition in liquid hydrogen is an important phenomenon to understand the interiors of gas giants, such as Jupiter and Saturn, as well as the physical and chemical behavior of materials at high pressures and temperatures. Here, the path toward an experimental approach is detailed based on spectrally resolved x-ray scattering, tailored to observe and characterize hydrogen metallization in dynamically compressed hydrocarbons in the regime of carbon–hydrogen phase separation. With the help of time-dependent density functional theory calculations and scattering spectra from undriven carbon samples collected at the European x-ray Free-Electron Laser Facility (EuXFEL), we demonstrate sufficient data quality for observing C–H demixing and investigating the presence of liquid metallic hydrogen in future experiments using the reprated drive laser systems at EuXFEL.
The first confirmed discovery of an exoplanet in 19921 and then the discovery of an exoplanet around a Sun-like star by Mayor and Queloz2 opened the floodgates for the detection of exoplanets, leading to multiple dedicated missions to look for exoplanets across the galaxy. After 30 years and over 5000 confirmed exoplanets,3 it is now increasingly important to understand how planetary systems form and evolve. A large number of discovered exoplanets lie in the range of masses of gas giants like Jupiter and Saturn and ice giants like Uranus and Neptune, with the ice giants dominating the population.4,5 Studying these large bodies in our Solar System continues to enhance our understanding of the formation and evolution of planetary systems in general.
Various probe missions afforded us extensive data and improved our understanding of the planets by exploring the upper layers and space around them. The interiors of these astrophysical bodies can be constrained using the measurements of their physical properties, but establishing the internal structure and their bulk composition requires a better understanding of the behavior of the chemical species at high-pressure and high-temperature conditions. The thermal energies at planetary interior conditions are at the same order of magnitude as the energies stored in the chemical bonds, resulting in expected complex chemical processes including phase transitions, species separation, and demixing.6,7 The chemical composition and potential chemical processes taking place inside these planets are essential for creating better models and understanding their thermal, magnetic, and electrical properties.8
The deep planetary conditions are at the low-temperature end of the warm dense matter (WDM) regime. WDM describes the transition region between cold condensed matter and high-temperature plasmas.9,10 One of the materials with great interest in research at WDM conditions is metallic hydrogen. It was first predicted by Wigner and Huntington11 that solid molecular hydrogen would transform into metal at high pressures. A pressure-induced liquid–liquid phase transition from molecular hydrogen to a metallic phase is relevant to planetary interiors and therefore has been widely researched.12–14 The transition is referred to as plasma phase transition, which, depending on temperature, is predicted to either be an abrupt first-order phase transition or a continuous transition to the metallic state.15–17
Theoretical and experimental studies of metallic hydrogen have significantly contributed to the current understanding of planetary evolution. Jupiter and Saturn are predicted to have an interior dominated by liquid metallic hydrogen, which is in contrast to the properties of the insulating, molecular form present in the outer layers.6 This highly condensed metallic hydrogen in the interior of gas giant planets is expected to be responsible for the strong dynamo that drives their exceptionally strong magnetic fields.18 Uranus and Neptune are most often modeled to be made of three layers: a rocky core consisting of silicates and iron, an “icy” shell that contains a mixture of water, methane, and ammonia, and a gaseous envelope dominated by hydrogen and helium.19–21 In the high-pressure and high-temperature environment of these icy-giant planets, it is predicted that methane will form polymeric hydrocarbon chains8,22 and, deeper toward the core, will dissociate into carbon in the form of diamond and metallic hydrogen.23–26
Transcribing the physics of WDM state requires consideration of highly interacting particles. Coupling and quantum effects are not perturbations in the WDM regime, but are as strong as the thermal energy. The complex interplay of competing forces is a reason that the precise theoretical modeling to adequately portray the physics is very difficult.9,27,28 To test the models, dedicated laboratory experiments need to be performed. The so-far applied experimental methods are mostly based on cryogenic liquid hydrogen as the initial material and include static compression approaches using diamond anvil cells29–32 and various dynamic compression techniques.15,33–36
In addition to the challenges of compressing hydrogen to metallization conditions using the above-mentioned methods, the complexity of cryogenic sample environments to start with high-density hydrogen from the beginning also limits diagnostic capabilities. The measurement of electrical conductivities for liquid H2 and D2 dynamically compressed by high-velocity impactors driven by a gun has provided the first pioneering insight.35 In more recent approaches, the insulator–metal transition of hydrogen has been characterized by determining the surface reflectivity of the compressed sample. While there has been progress using a surface reflectivity method, there are notable discrepancies in the P–T conditions where hydrogen metallization was observed.33,34 Indeed, systematic uncertainties of the approach arise from the fact that the reflecting interface is often in direct contact with a material containing the sample, which may induce additional chemistry and changes in the electronic structure. Therefore, techniques capable of accessing the interior of the sample and probing the bulk volume are preferable but difficult to realize experimentally. The high electronic densities of WDM make it opaque to optical probes, and therefore, hard x-rays of keV energy are required to access the bulk volume.
As a further development of pioneering experiments using laser-based x-ray sources, the advent of x-ray free-electron lasers has matured enough to provide revolutionary capabilities in the diagnosis of dynamically compressed matter, mainly created by high energy lasers producing compression waves on nanosecond timescales. Methods applied include spectrally resolved x-ray Thomson scattering (XRTS) that can access the electron temperature and density, the ionization state, and plasmon features. The plasmon feature is sensitive to frequency-dependent electron–ion collision processes, which are related to the electrical conductivity.37
In this work, we present high-resolution x-ray scattering measurements obtained in the collective regime from undriven carbon samples in comparison with theoretical predictions using the time-dependent density functional theory (TDDFT).38 Furthermore, the possibility of observing the C–H demixing and hydrogen metallization via plasmon scattering under high pressure and high temperature is investigated with the help of experiments including a rep-rated energetic shock driver.
II. X-RAY THOMSON SCATTERING
The collective and non-collective regimes are distinguished by the scattering parameter , where λS is the plasma screening length: corresponds to the collective scattering regime, and is characteristic for non-collective scattering. As α is dependent on k, different regimes can be accessed by varying the incident x-ray energy E0 and/or the scattering angle θ. Here, the focus is on collective scattering to resolve plasmon oscillations of the electrons.
For an advanced study of the sample properties, dynamic structure factor predictions can be extracted from state-of-the-art ab initio methods. For the study, time-dependent density functional theory (TDDFT) simulations43 were performed. At ambient conditions, the linear-response TDDFT calculations were performed using the full-potential linearized augmented-plane wave code implemented in Elk44 using bootstrap,45 a long-range exchange-correlation (XC) kernel for TDDFT as implemented in the Elk code. The response functions at high-pressure and high-temperature conditions are evaluated using the adiabatic local density approximation for TDDFT in yambo46 applying the Kohn–Sham47 orbitals evaluated by Quantum ESPRESSO.48 The simulations were performed for a system size ranging from 64 to 256 atoms consisting of C, H, CH, CH3, and C3H in a supercell using a 2 × 2 × 2 k-point mesh. The Perdew–Burke–Ernzerhof (PBE)49 XC functional is used in all the calculations.
The experimental data presented here were obtained at the High-Energy-Density (HED) instrument of the European X-ray Free-Electron Laser Facility (EuXFEL).50 The setup used was typical for in situ x-ray diagnostics of laser-driven shock waves at XFEL facilities combining spectrally resolved x-ray scattering in both forward and backward geometries with x-ray diffraction, and only the drive laser was not yet available. The details of the setup together with an analysis of the backward scattering data have been described by Voigt et al.51 For demonstrating the forward scattering capabilities, 10 μm thick diamond samples were probed by x-ray pulses with a photon energy of ∼6000 eV, focused to <10 μm spot sizes using beryllium compound refractive lenses. A monochromator was used to reduce the energy bandwidth to ∼1 eV, from originally ∼20 eV corresponding to the self-amplified spontaneous-emission (SASE) bandwidth. Both the spectrometers used cylindrically bent Highly Annealed Pyrolytic Graphite (HAPG) crystals with 80 mm radius of curvature, albeit the crystals used in the forward scattering setups had coating thickness of 100 μm compared with 40 um in the backward direction.52 The backward scattering setup had a JUNGFRAU detector53 at 155, to study x-ray Raman spectroscopy from different samples.51 The forward scattering signal was collected on an ePix100 detector54 at 18. Dark images were taken as an average of 1200 frames (corresponding to a 2 min 10 Hz acquisition) per gain mode. The setup also included an ePix100 detector for x-ray diffraction (XRD) and an Andor Zyla 5.5 sCMOS detector along with a bent Si-111 crystal spectrometer downstream of transmitted x-rays to measure the source spectrum.51
For the analysis of the forward spectrometer, pixel values with less than a nominal threshold associated with a clear single photon hit were truncated to zero for reducing the noise. Pixel noise in high gain corresponds to ∼290 eV, allowing us to identify single photon counts with only Poisson noise. Several thousand two-dimensional detector images were, then, summed up to derive a lineout. Figure 1 illustrates the forward scattering spectrum from a 10 μm thick diamond sample. The plasmon feature, in this case collective excitations of valence band electrons, is usually downshifted by ∼30 eV with respect to the elastic peak.55 Using the monochromator allows the plasmon feature and the substructures to be clearly resolved, which would have been smeared out with pure SASE.
The forward scattering angle and the XFEL photon energy result in an absolute value of the scattering vector of ∼0.94 Å−1 applying Eq. (1). This wave number was, then, used as input for generating synthetic spectra from TDDFT simulations. In Fig. 2, the plasmon feature obtained from the experiment is compared with the TDDFT simulations convolved with the experimental instrument function. The synthetic spectrum shows reasonable agreement with the experimental data, reproducing the detailed features, except the surface plasmon feature at ∼25 eV,56 which is not covered by the bulk nature of the simulations. The total energy resolution obtained using the monochromator with 100 μm HAPG crystals is ∼5 eV. As the 100 μm HAPG crystals have more depth broadening than the 40 μm HAPG crystals that were used in the backward scattering setup of the same experiment, by using the 40 μm HAPG crystals in the forward scattering setup could bring down the total spectral resolution to ∼3 eV.52 Solely using the SASE mode results in ∼20 eV, which smears out all substructures of the plasmon feature and results in overlap with the elastic scattering peak. The lower signal due to the monochromator has been compensated by taking a larger number of shots cumulatively.
The obtained results suggest the applicability of the method presented for observing C–H demixing and hydrogen metallization under high-pressure, high-temperature conditions. In previous experiments, polystyrene (CH) samples were dynamically compressed at the Linac Coherent Light Source showing C–H phase separation on nanosecond timescales using in situ x-ray diffraction.24,57 Frydrych et al.58 used a similar experimental setup to determine the degree of species separation in a dynamically compressed polystyrene sample to WDM conditions from spectrally resolved forward and backward x-ray scattering data. At pressures of the order of ∼150 GPa and temperatures around ∼6000 K, the carbon transforms into nanometer-sized diamonds. Measured diffraction lineouts provide indirect evidence for nearly complete C–H separation,69 where the isolated hydrogen would be expected to be in a liquid metallic state. However, as XRD does not provide a signal from the weakly scattering hydrogen, and reflectivity measurements from the compression fronts remain elusive due to the ongoing chemical reaction,59 so far there is no direct evidence for the presence of liquid metallic hydrogen in these experiments. Due to its sensitivity to electronic structure and bulk conductivity, the high-resolution forward scattering method described here can overcome these limitations and clarify the state of hydrogen in dynamically compressed C–H mixtures.
To test the sensitivity with the achieved spectral resolution, TDDFT calculations of the plasmon structures for C, H, and CH at conditions of GPa and K were performed on ionic configurations obtained from density functional molecular dynamics (DFT-MD) simulations performed using VASP.60–63 For consistency, the TDDFT calculations of the dynamic structure factor were performed at the k-vector magnitude of Å−1, i.e., the same as the forward scattering in the experiment. The spectral contributions of all three species were convolved with the experimentally obtained instrument function.51 The results are depicted in Fig. 3 and show a single peak with an almost Gaussian shape for a fully mixed CH sample. For fully demixed CH, a culmination of two distinctly shifted plasmon features from the two separate components is observed, forming a double-peak structure. The peak at higher energy shifts originates from the collective excitations of the diamond valence band, while the peak at lower energy shifts represents the plasmon feature of liquid metallic hydrogen. With the experimentally demonstrated spectral resolution of ∼3 eV possible using the 40 μm HAPG crystals, and a separation between the peaks of ∼6–8 eV, C–H phase separation and hydrogen metallization can be observed using the demonstrated setup in future experiments adding a rep-rated drive laser.
Additional TDDFT dynamic structure factor calculations were performed on pure H and C, as well as other C–H mixtures (CH, CH3, and C3H) at different scattering vectors to obtain the respective plasmon peaks and plasmon dispersion shifts. Figure 4 shows the plasmon energy shifts for varying k-values for each species. The obtained results show that the separation between the features of the fully demixed components as shown in Fig. 3 is larger at smaller scattering vector magnitudes. The quadratic dispersion (shown up to ) from the TDDFT results is weak, especially for carbon.43,55 The remaining results exhibiting a slightly stronger quadratic dispersion are only shown for k = 0.80–1.25 Å−1 highlighting the spectral resolution in the plasmon peaks required for diagnostics. In addition, the dispersion feature obtained using XRTS55 for diamond at ambient conditions is additionally shown for Ref. 55 highlighting the differences expected between ambient and warm dense carbon states. Thus, the corresponding experiments need to aim for small scattering angles and/or low photon energies to optimize the sensitivity for C–H separation and hydrogen metallization via inelastic x-ray scattering.
In conclusion, the described method using collective x-ray Thomson scattering is applicable to characterize liquid metallic hydrogen in the bulk of the sample, which is advantageous over the reflectivity measurements that can only probe the surface (which may be in a non-equilibrium state, e.g., a shock front). We presented how the exemplar scattering spectrum from ambient diamond recorded at the HED instrument of European XFEL agrees well with the TDDFT simulations performed. The existing resolution is capable of distinguishing the expected metallic hydrogen feature after demixing. In our demonstration experiment, ∼18 000 shots were accumulated due to a significant decrease in x-ray flux due to the usage of a monochromator. With the new possibility to use self-seeded x-ray beams providing a spectral resolution comparable to using the monochromator,64 but with approximately 50 times more x-ray photons per pulse, the required number of shots will be significantly reduced. Moreover, the samples applied in the demonstration experiment were notably thinner than those in typical shock-compression experiments at XFEL sources (10 μm vs 50–100 μm). Therefore, it can be expected that an accumulation of approximately 1000 shots or even less is required to obtain the data quality presented here. While high repetition rates place high demands on target design and the target delivery system,65 the corresponding developments are under way at the HED instrument, e.g., by allowing to replace targets without the need to break the vacuum in the interaction chamber.66 Furthermore, plastics as a base target material allow for using tape samples that enable such rep-rated experiments with several 1000s of shots before targets have to be swapped.67 Novel diagnostic tools combined with the new DiPOLE high-energy laser system at the HED instrument of EuXFEL will enable bulk-sensitive measurements of planetary core conditions. It is up to 10 Hz repetition rate, and pulse shaping capabilities68 can be expected to play a crucial role in unlocking the physics behind the planets in the Solar System as well as the evolution of the steadily increasing number of confirmed exoplanets beyond.
K.V., N.J.H., O.S.H., A.K.S., and D.K. were supported by the Helmholtz Association under VH-NG-1141, and O.S.H. was supported by the Helmholtz Association under Grant No. ERC-RA-0041. M.S. was supported by the Helmholtz Association under Grant No. VH-NG-1338. K.R. acknowledges funding by the Center for Advanced Systems Understanding (CASUS), which is financed by the German Federal Ministry of Education and Research (BMBF) and by the Saxon Ministry for Science, Culture and Tourism (SMWK) with tax funds on the basis of the budget approved by the Saxon State Parliament. The work of J.L. has been supported by GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt as part of the R&D project GSI-URDK2224 with the University of Rostock. N.J.H. and L.B.F. acknowledge support from the Department of Energy, Office of Science, Office of Fusion Energy Sciences, under FWP 100182, and N.J.H. was supported by the Department of Energy, Laboratory Directed Research, and Development program at SLAC National Accelerator Laboratory, under Contract No. DE-AC02–76SF00515. The work of S.P.H-R. was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DEAC52-07NA27344. Z.H. and C.Q. acknowledge the financial support from the China Scholarship Council. The work of M.H. and A.A. is, in part, supported by the French Centre National de la Recherche Scientifique GoToXFEL program and it has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 670787 D PLANETDIVE). The work of P.T.M. was supported by Deutsche Forschungsgemeinschaft (DFG – German Research Foundation) Project No. 505630685. S.S. was supported by DFG Project No. 495324226. Computations were performed on a Bull Cluster at the Center for Information Services and High-Performance Computing (ZIH) at Technische Universität Dresden and on the cluster Hemera at Helmholtz-Zentrum Dresden-Rossendorf (HZDR).
Conflict of Interest
The authors have no conflicts to disclose.
Divyanshu Ranjan: Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Writing – original draft (equal); Writing – review & editing (equal). Samuel Schumacher: Validation (equal); Writing – review & editing (equal). Philipp Thomas May: Writing – review & editing (equal). Alexis Amouretti: Data curation (equal). Karen Appel: Data curation (equal). Erik Brambrink: Data curation (equal). Valerio Cerantola: Data curation (equal). Deniza Chekrygina: Data curation (equal). Luke Bennett Fletcher: Data curation (equal). Sebastian Göde: Data curation (equal). Marion Harmand: Data curation (equal). Kushal ramakrishna: Data curation (equal); Formal analysis (equal); Investigation (equal); Resources (equal); Validation (equal); Writing – review & editing (equal). Nicholas J. Hartley: Data curation (equal); Writing – review & editing (equal). Stefan P. Hau-Riege: Data curation (equal). Mikako Makita: Data curation (equal). Alexander Pelka: Data curation (equal). Anja Katharina Schuster: Data curation (equal). Michal Šmíd: Data curation (equal). Toma Toncian: Data curation (equal). Min Zhang: Data curation (equal); Resources (equal). Thomas Robert Preston: Data curation (equal); Writing – review & editing (equal). Ulf Zastrau: Data curation (equal). Katja Voigt: Data curation (equal); Methodology (equal); Resources (equal). Jan Vorberger: Formal analysis (equal); Resources (equal); Software (equal); Validation (equal); Writing – review & editing (equal). Dominik Kraus: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Oliver S. Humphries: Data curation (equal); Methodology (equal); Resources (equal); Software (equal); Validation (equal); Writing – review & editing (equal). Benjamin Heuser: Validation (equal); Writing – review & editing (equal). Michael Gareth Stevenson: Supervision (equal); Writing – review & editing (equal). Julian Lütgert: Validation (equal); Writing – review & editing (equal). Zhiyu He: Validation (equal); Writing – review & editing (equal). Chongbing Qu: Validation (equal); Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding authors upon reasonable request.