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Ultrahigh-pressure transitions in solid hydrogen
Abstract
During the past five years, major progress has been made in the experimental study of solid hydrogen at ultrahigh pressures as a result of developments in diamond-cell technology. Pressures at which metallization has been predicted to occur have been reached (250-300 Gigapascals). Detailed studies of the dynamic, structural, and electronic properties of dense hydrogen reveal a system unexpectedly rich in physical phenomena, exhibiting a variety of transitions at ultrahigh pressures. This colloquium explores the study of dense hydrogen as an archetypal problem in condensed-matter physics.
... Consequently, the C2 phase has a composition of (H2O)H2. This phase has been reported to persist up to 80 GPa [7,9], undergoing structural changes between [35][36][37][38][39][40] GPa and 55-60 GPa, hypothesized to correspond to hydrogen bond symmetrization and the formation of a denser structure, respectively. However, theoretical calculations suggest that the C2 phase is thermodynamically unstable above 19 GPa [10]. ...
... Additional vibron modes (sidebands) correspond to various combinations of H2 molecule vibrations and exhibit higher frequencies than the main H2 vibron mode (cf. Ref. [11]), consistent with similar observations in compressed bulk hydrogen [35]. As in bulk hydrogen [36], these sidebands correspond to different points in the extended vibron band structure, with the total vibron frequency spread reflecting the vibron bandwidth, which is determined by intermolecular coupling. ...
... Notably, the frequency of this mode is higher in both compounds compared to bulk H2. This difference arises because, in bulk hydrogen, the vibron frequency is significantly lowered by strong intermolecular coupling, which leads to a downward shift [35]. ...
Gas hydrates are considered fundamental building blocks of giant icy planets like Neptune and similar exoplanets. The existence of these materials in the interiors of giant icy planets, which are subject to high pressures and temperatures, depends on their stability relative to their constituent components. In this study, we reexamine the structural stability and hydrogen content of hydrogen hydrates, (H2O)(H2)n, up to 104 GPa, focusing on hydrogen-rich materials. Using synchrotron single-crystal X-ray diffraction, Raman spectroscopy, and first-principles theoretical calculations, we find that the C2-filled ice phase undergoes a transformation to C3-filled ice phase over a broad pressure range of 47 - 104 GPa at room temperature. The C3 phase contains twice as much molecular H2 as the C2 phase. Heating the C2-filled ice above approximately 1500 K induces the transition to the C3 phase at pressures as low as 47 GPa. Upon decompression, this phase remains metastable down to 40 GPa. These findings establish new stability limits for hydrates, with implications for hydrogen storage and the interiors of planetary bodies.
... 4 Phase II, so-called Broken Symmetry Phase (BSP), 5 is stable in the region of low temperatures and relatively high pressures up to 160 GPa. 6 Its crystal structure determined in Raman and infrared experiments 1,7,8 is alike P2 1 /c (monoclinic). This structure, as well as some alternative structures of BSP, were studied theoretically by ab initio Density Functional Theory (DFT) and its modifications. ...
... For phase I this fragment had the hcp structure, and for phase II (BSP) we accepted the monoclinic P2 1 /c crystal structure determined by Raman and infrared experimental data. 1,9 In such structure, the axes of all molecules lie in a plane perpendicular to the z axis, forming alternating layers of two types (see Fig. 1). In turn, each layer consists of alternating rows, in each of which equilibrium polar angle θ 0 of molecular axes is close to π/4, changing its sign in each subsequent row of each layer. ...
... Pressure dependences of the phase transition temperature. Comparison of our first and second order theory prediction with existing experimental data: Raman and infrared data1,20 (1), second order (2), first order (3). ...
The temperature dependence of the pressure and volume changes during the phase I–phase II polymorphic transition in solid D2 is evaluated using the non-empirical atom-atom interaction model and the Mayer group expansion method for solids, taking into account quantum corrections. The results are compared with existing experimental data and ab initio predictions.
... Phase I is the solid phase with the lowest pressure, where hydrogen molecules are arranged in a densely packed hexagonal (hcp) lattice with random orientations at hcp lattice positions [32]. As pressure increasing and temperature decreasing structure of hydrogen will transform to phase II from phase I [32]. ...
... Phase I is the solid phase with the lowest pressure, where hydrogen molecules are arranged in a densely packed hexagonal (hcp) lattice with random orientations at hcp lattice positions [32]. As pressure increasing and temperature decreasing structure of hydrogen will transform to phase II from phase I [32]. The characteristic of phase II is that the coupling between molecules is enhanced and the free rotation of molecules on the lattice is restricted, as the results of pressure increasing. ...
... Therefore, phase II of hydrogen is called the broken-symmetry phase (BSP). Because the phase transition boundary of phase II is sensitive to isotopic effects [32], it can be predicted that the transition of hydrogen from phase I to phase II were predicted to be dominated by nuclear quantum effects in addition to pressure and temperature. The concept of quantum phase transition is well demonstrated in ab initio pathintegral molecular dynamics simulation carried out for phase II [3]. ...
Metallic hydrogen, existing in remarkably extreme environments, was predicted to exhibit long-sought room-temperature superconductivity. Although the superconductivity of metallic hydrogen has not been confirmed experimentally, superconductivity of hydrogen in hydrides was recently discovered with remarkably high critical temperature as theoretically predicted. In recent years, theoretical simulations have become a new paradigm for material science, especially exploration of material at extreme pressure. As the typical high-pressure material, metallic hydrogen has been providing a fertile playground for advanced simulations for long time. Simulations not only provide the substitute of experiments for hydrogen at high-pressure, but also encouraged the discovery of almost all the experimentally discovered superconducting hydrides with the record high superconducting transition temperature. This work reviews recent progress in hydrogen and hydrides under extreme pressure, focusing on phase diagram, structures and the long-sought goal of high-temperature superconductivity. In the end, we highlight structural features of hydrides for realization of hydrogen-driven superconducting hydrides near ambient pressure.
... The structure of solid hydrogen under high pressures has been a focus topic in condensed-matter physics. [1][2][3][4] Considerable investigations have been conducted on this subject over the last century, but the structures of solid hydrogen have not been fully determined yet. The great experimental hurdles lie in the application of extremely high pressures as well as technical challenges involving x-ray and neutron diffraction measurements of the light element under extreme conditions. ...
... Despite the difficulties of x-ray and neutron diffraction, the boundaries between the several phases of solid hydrogen have been effectively established by Raman and infrared (IR) measurements. 3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18] Experimentally, based on the changes in Raman and IR spectra, e.g., peak broadening and splitting, phases I, 3 II, 5 III, 6 IV, 7,8 and V 10,11 have been proposed in succession and the boundaries of these phases have also been identified. However, among all observed phases, only the crystalline structure of the low-pressure phase I has been confirmed as an hcp structure with freely rotating molecules at each lattice point. ...
... Despite the difficulties of x-ray and neutron diffraction, the boundaries between the several phases of solid hydrogen have been effectively established by Raman and infrared (IR) measurements. 3,[5][6][7][8][9][10][11][12][13][14][15][16][17][18] Experimentally, based on the changes in Raman and IR spectra, e.g., peak broadening and splitting, phases I, 3 II, 5 III, 6 IV, 7,8 and V 10,11 have been proposed in succession and the boundaries of these phases have also been identified. However, among all observed phases, only the crystalline structure of the low-pressure phase I has been confirmed as an hcp structure with freely rotating molecules at each lattice point. ...
Understanding the structural behavior of solid hydrogen under high pressures is crucial for uncovering its unique properties and potential applications. In this study, starting from the phase I of solid hydrogen—free-rotator hcp structure, we conduct extensive ab initio molecular dynamics calculations to simulate the cooling, heating, and equilibrium processes within a pressure range of 80–260 GPa. Without relying on any structure previously predicted, we identify the high-pressure phase structures of solid hydrogen as P21/c for phase II, P6522 for phase III, and BG1BG2BG3 six-layer structure for phase IV, which are different from those proposed previously using the structure-search method. The reasonability of these structures are validated by Raman spectra and x-ray diffraction patterns by comparison with the experimental results. Our results actually show pronounced changes in the c/a ratio between phases I, III, and IV, which hold no brief for the experimental interpretation of an isostructural hcp transformations for phases I–III–IV.
... The reason that the metallic phase should appear under high pressure from the low-pressure solid molecular hydrogen consists in the increase of inter-molecular coupling at shorter distances between neighboring molecules so that molecules disintegrate and hydrogen gradually becomes an electrical conductor with itinerant electrons, being similar to monoatomic alkali metals. It is remarkable that the hypothetical metallic hydrogen [321][322][323][324][325][326][327][328][329][330][331][332] possibly is the simplest two-component proton (deuteron)-electron plasma in a liquid or solid state; it may become a two-component superconductor or a complex boson superfluid-superconductor high-pressure material [322,333]. Normal or superconducting states of the metallic hydrogen were proposed to exist in the interior of the Jovian planets of the solar system [328,[334][335][336][337][338][339]. ...
... The reason that the metallic phase should appear under high pressure from the low-pressure solid molecular hydrogen consists in the increase of inter-molecular coupling at shorter distances between neighboring molecules so that molecules disintegrate and hydrogen gradually becomes an electrical conductor with itinerant electrons, being similar to monoatomic alkali metals. It is remarkable that the hypothetical metallic hydrogen [321][322][323][324][325][326][327][328][329][330][331][332] possibly is the simplest two-component proton (deuteron)-electron plasma in a liquid or solid state; it may become a two-component superconductor or a complex boson superfluid-superconductor high-pressure material [322,333]. Normal or superconducting states of the metallic hydrogen were proposed to exist in the interior of the Jovian planets of the solar system [328,[334][335][336][337][338][339]. They were also claimed to be achieved in laboratory experiments but without solid confirmation until now [340,341]. ...
The current situation in high-T c superconductivity of the hydrides H 3 S, LaH 10 , and related compounds has been considered from a methodological viewpoint. Both the physical theoretical and historical backgrounds have been presented and analyzed. The necessity of procedural purity in theory and the experimental protocol compliance has been discussed. It has been shown that it is too early now to fully recognize the sensational results on hydride superconductivity.
... The metallization of solid hydrogen is one of the central problems in physics [1][2][3][4], as well as in astrophysics of Jupiter, Saturn, and exoplanets [5]. The building block, the H 2 molecule, is relatively simple, since the electrons are in the spin-singlet state in the ground state composed mainly of 1s states of atoms. ...
... Those molecular states with the experimental value of bond length R ≈ 1.401a 0 [6] form at ambient pressure a molecular crystal with the lattice constant a ∼ 7a 0 R [7], where a 0 is the Bohr radius. Thus, to achieve atomic structure and metallicity one has to break the molecular bond, e.g., by achieving a more typical atomic solid configuration with a ∼ R, what amounts in practice to applying an enormous pressure, as demonstrated repeatedly over the decades [2,8]. But even then one may not achieve metallicity, as due to the relatively large atomic separation the system may compose a Mott (or Mott-Hubbard) insulator [9,10], as the original interelectronic correlation effects may still be sufficiently strong. ...
We obtain in a direct and rigorous manner a transition from a stable molecular hydrogen single chain to the quasiatomic two-chain 2nH state. We devise an original method composed of an exact diagonalization in the Fock space combined with an ab initio adjustment of the single-particle wave function in the correlated state. In this approach the well-known problem of double-counting the interparticle interaction does not arise at all. The transition is strongly discontinuous, and appears even for relatively short chains possible to tackle, . The signature of the transition as a function of applied force is a discontinuous change of the equilibrium intramolecular distance. The corresponding change of the Hubbard ratio U/W reflects the Mott--Hubbard-transition aspect of the atomization. Universal feature of the transition relation to the Mott criterion for the insulator--metal transition is also noted. The role of the electron correlations is thus shown to be of fundamental significance.
... In principle, the electronic structures of materials under high pressures can be probed by experimental measurements on the quantities such as electrical conductivity, optical conductivity and reflectivity [22,23]. To date, however, measurements on the [22]. ...
... In principle, the electronic structures of materials under high pressures can be probed by experimental measurements on the quantities such as electrical conductivity, optical conductivity and reflectivity [22,23]. To date, however, measurements on the [22]. There lacks the knowledge about the global behavior of electronic structures across a wide range of pressures, in particular, pressures spanning an interval with the width of ~ 100 GPa or larger. ...
Titanium dioxide (TiO2) is a wide band gap semiconducting material which is promising for photocatalysis. Here we present first-principles calculations to study the pressure dependence of structural and electronic properties of two TiO2 phases: the cotunnite-type and the Fe2P-type structure. The band gaps are calculated using density functional theory (DFT) with the generalized gradient approximation (GGA), as well as the many-body perturbation theory with the GW approximation. The band gaps of both phases are found to be unexpectedly robust across a broad range pressures. The corresponding pressure coefficients are significantly smaller than that of diamond and silicon carbide (SiC), whose pressure coefficient is the smallest value ever measured by experiment. The robustness originates from the synchronous change of valence band maximum (VBM) and conduction band minimum (CBM) with nearly identical rates of changes. A step-like jump of band gaps around the phase transition pressure point is expected and understood in light of the difference in crystal structures.
... At low temperature and ambient pressure, hydrogen molecules form a solid, which, similarly to the (H 2 ) 2 dimers, consists of essentially freely rotating molecules. [11][12][13] At finite pressures, the rotational motion is suppressed and well-defined molecular crystals are observed. [14][15][16] Various high-pressure phase transitions occur, notably the II-III phase transition, in which the hydrogen molecules become subject to strong in-plane interactions, forming a layered structure with polarized H 2 units. ...
... Molecular hydrogen condenses on a hcp lattice at low temperature and ambient pressure. [11][12][13] Calculating the lattice energy, we expect the performance of the different approximations to be similar to that found for the isolated dimers. However, at finite pressures (100-300 GPa pressure range), intermolecular distances reduce to 1.5-2.5 Å, and, hence, the description of the repulsive potential wall becomes more relevant. ...
The anisotropic potential energy surface of the (H2)2 dimer represents a challenging problem for many-body methods. Here, we determine the potential energy curves of five different dimer configurations (T, Z, X, H, and L) using the lattice regularized diffusion Monte Carlo method and a number of approximate functionals within density functional theory (DFT), including advanced orbital-dependent functionals based on the random phase approximation (RPA). We assess their performance in describing the potential wells, bond distances, and relative energies. The repulsive potential wall is studied by looking at the relative stability of the different dimer configurations as a function of an applied force acting along the intermolecular axis. It is shown that most functionals within DFT break down at finite compression, even those that give an accurate description around the potential well minima. Only by including exchange within RPA, a qualitatively correct description along the entire potential energy curve is obtained. Finally, we discuss these results in the context of solid molecular hydrogen at finite pressures.
... . Importantly, H 2 exhibits distinct behaviors under high pressure (P) and high temperature (T) conditions. At 300 K, gaseous H 2 can be liquefied at P > 35 MPa and liquid H 2 is stable to ∼5.4 GPa (Mao & Hemley, 1994). Upon further compression, the liquid H 2 transforms to a solid phase I with a hexagonal close-packed (hcp) structure that is reported to be stable to ∼180 GPa (Mao & Hemley, 1994). ...
... At 300 K, gaseous H 2 can be liquefied at P > 35 MPa and liquid H 2 is stable to ∼5.4 GPa (Mao & Hemley, 1994). Upon further compression, the liquid H 2 transforms to a solid phase I with a hexagonal close-packed (hcp) structure that is reported to be stable to ∼180 GPa (Mao & Hemley, 1994). Both liquid and solid phase I are regarded as molecular phases, but are expected to show different thermal conduction capability. ...
Plain Language Summary
Hydrogen is the most abundant element in the universe and is also the major constituent in the giant plants (Jupiter, Saturn, Uranus and Neptune) in the solar system. Although most of the surface temperatures of those giant planets are colder than Earth's, their interior temperatures are actually able to reach several thousand degrees Kelvin. The heat flows within these giant planets are very active, while knowledge of heat conduction and propagation are largely unknown. This study investigates the high‐pressure thermal conductivity of H2 at room temperature and high temperature conditions. Our results show that the liquid H2 exhibits low thermal conductivity, in the range of 0.7–1.1 W m⁻¹ K⁻¹ at high pressures and room temperature. However, appearance of solid H2 will increase thermal conductivity significantly and reach ∼27 W m⁻¹ K⁻¹ at 60.2 gigapascals and room temperature. Based on our model, the low thermal conductivity of liquid H2‐He mixture may suppress the heat loss of the giant planets and explain why their surfaces are cold, but interiors are hot.
... In Fig. (6), we show the pressure-density curves for simulations performed using the S [2] sampling strategy for the E [2], E [2,3], and E [2,3,4] cases, alongside experimental results. 3,67,69,70 The corresponding pressuredensity curves calculated from S [2,3] simulation results are nearly indistinguishable from those shown in the figure. The E [2] curve overestimates the experimental results even at low densities, which means that the twobody interaction on its own is much too repulsive. ...
We present path integral Monte Carlo simulation results for the equation of state of solid parahydrogen between and at K. The simulations are performed using non-additive isotropic ab initio two-body, three-body, and four-body potential energy surfaces (PES). We apply corrections to account for both the finite size simulation errors and the Trotter factorization errors. Simulations that use only the two-body PES during sampling yield an equation of state similar to that of simulations that use both the two-body and three-body PESs during sampling. With the four-body interaction energy, we predict an equilibrium density of , very close to the experimental result of . The inclusion of the four-body interaction energy also brings the simulation results in excellent agreement with the experimental pressure-density data until around , beyond which the simulation results overestimate the pressure. These PESs overestimate the average kinetic energy per molecule at the equilibrium density by about compared to the experimental result. Our findings suggest that, at higher densities, we require five-body and higher-order many-body interactions to quantitatively improve the agreement between the pressure-density curve produced by simulations, and that of experiment. Using the four-body PES during sampling at excessively high densities, where such higher-order many-body interactions are likely to be significant, causes an artificial symmetry breaking in the hcp lattice structure of the solid.
... During a phase transition a material undergoes a transformation between different states of matter (e.g., solid to liquid) or structural phases (e.g., martensitic transformation) due to changes in external conditions such as temperature, pressure, or composition [1][2][3][4]. These phase transitions are broadly classified into first-order and second-order types: first-order transitions involve latent heat and discontinuous changes in order parameters, as seen in melting, while second-order transitions occur continuously without latent heat, as in ferromagnetic to paramagnetic transitions. ...
Predicting solid-solid phase transitions remains a long-standing challenge in materials science. Solid-solid transformations underpin a wide range of functional properties critical to energy conversion, information storage, and thermal management technologies. However, their prediction is computationally intensive due to the need to account for finite-temperature effects. Here, we present an uncertainty-aware machine-learning-guided framework for high-throughput prediction of temperature-induced polymorphic phase transitions in inorganic crystals. By combining density functional theory calculations with graph-based neural networks trained to estimate vibrational free energies, we screened a curated dataset of approximately 50,000 inorganic compounds and identified over 2,000 potential solid-solid transitions within the technologically relevant temperature interval 300-600 K. Among our key findings, we uncover numerous phase transitions exhibiting large entropy changes (> 300 J K kg), many of which occur near room temperature hence offering strong potential for solid-state cooling applications. We also identify 21 compounds that exhibit substantial relative changes in lattice thermal conductivity (20-70%) across a phase transition, highlighting them as promising thermal switching materials. Validation against experimental observations and first-principles calculations supports the robustness and predictive power of our approach. Overall, this work establishes a scalable route to discover functional phase-change materials under realistic thermal conditions, and lays the foundation for future high-throughput studies leveraging generative models and expanding open-access materials databases.
... Optical Raman and infrared spectroscopies have yielded valuable information on molecular bonding and local symmetry and have been used in the past for identification of ultrahigh-pressure hydrogen phases III (ref. 16), IV (refs. 17,18), IV′ (ref. ...
The structural evolution of molecular hydrogen H2 under multi-megabar compression and its relation to atomic metallic hydrogen is a key unsolved problem in condensed-matter physics. Although dozens of crystal structures have been proposed by theory1, 2, 3–4, only one, the simple hexagonal-close-packed (hcp) structure of only spherical disordered H2, has been previously confirmed in experiments⁵. Through advancing nano-focused synchrotron X-ray probes, here we report the observation of the transition from hcp H2 to a post-hcp structure with a six-fold larger supercell at pressures above 212 GPa, indicating the change of spherical H2 to various ordered configurations. Theoretical calculations based on our XRD results found a time-averaged structure model in the space group with alternating layers of spherically disordered H2 and new graphene-like layers consisting of H2 trimers (H6) formed by the association of three H2 molecules. This supercell has not been reported by any previous theoretical study for the post-hcp phase, but is close to a number of theoretical models with mixed-layer structures. The evidence of a structural transition beyond hcp establishes the trend of H2 molecular association towards polymerization at extreme pressures, giving clues about the nature of the molecular-to-atomic transition of metallic hydrogen. Considering the spectroscopic behaviours that show strong vibrational and bending peaks of H2 up to 400 GPa, it would be prudent to speculate the continuation of hydrogen molecular polymerization up to its metallization.
... While some cuprates showed a rise in T C under high pressure (~ 164 K at 30 GPa) [6], none have exhibited a significant enhancement. Notably, despite extensive experimental efforts, the formation of metallic hydrogen has yet to be conclusively demonstrated, although potential signatures of its existence have been reported, even at pressures up to 495 GPa [7][8][9][10]. ...
In this study, we explore lithium-doped stable molecular hydrogen structures by performing first-principles crystal structure searches across varying compositions in the Li-H system under high pressure. Our search reveals a cubic phase of LiH12, which shows promise as a high-temperature superconductor. Our Bader charge analysis suggests that electron transfer from Li to H atoms tunes the intra- and inter-molecular H-H distances, which are critical for the metallization of molecular hydrogen. This modulation alters the interaction between bonding and anti-bonding 1s states of hydrogen molecules. Furthermore, Li ions serve as stabilizers for the distorted H2 molecular network through ionic interactions. Numerical solutions to the fully anisotropic Migdal-Eliashberg equations reveals that this phase could exhibit superconductivity above 300 K at a pressure of 250 GPa, a pressure value that is typically achievable using a diamond anvil cell. Detailed analysis of species-specific phonons and the Eliashberg function shows that low- and intermediate-energy phonons are crucial in promoting strong electron-phonon coupling. Thus, our study establishes lithium doping as a promising approach to induce high-temperature superconductivity in compressed molecular hydrogen without causing molecular dissociation.
... In Fig. 6, we show the pressure-density curves for simulations performed using the S [2] sampling strategy for the E [2], E [2,3], and E[2,3,4] cases, alongside experimental results. 3,67,69,70 The corresponding pressure-density curves calculated from the S[2,3] simulation results are nearly indistinguishable from those shown in the figure. The E [2] curve overestimates the experimental results even at low densities, which means that the two-body interaction on its (2) own is much too repulsive. ...
We present path integral Monte Carlo simulation results for the equation of state of solid parahydrogen between 0.024 and 0.1Å−3 at T = 4.2 K. The simulations are performed using non-additive isotropic ab initio two-body, three-body, and four-body potential energy surfaces (PESs). We apply corrections to account for both the finite size simulation errors and the Trotter factorization errors. Simulations that use only the two-body PES during sampling yield an equation of state similar to that of simulations that use both the two-body and three-body PESs during sampling. With the four-body interaction energy, we predict an equilibrium density of 0.02608Å−3, very close to the experimental result of 0.0261Å−3. The inclusion of the four-body interaction energy also brings the simulation results in excellent agreement with the experimental pressure–density data until around 0.065Å−3, beyond which the simulation results overestimate the pressure. These PESs overestimate the average kinetic energy per molecule at the equilibrium density by about 7% compared to the experimental result. Our findings suggest that, at higher densities, we require five-body and higher-order many-body interactions to quantitatively improve the agreement between the pressure-density curve produced by simulations and that of the experiment. Using the four-body PES during sampling at excessively high densities, where such higher-order many-body interactions are likely to be significant, causes an artificial symmetry breaking in the hcp lattice structure of the solid.
... [1][2][3][4][5] Pressure is one of the fundamental thermodynamic variables, which can allow precisely tuning of the interatomic distance and alter the bonding patterns of materials, leading to phase transformations into high-pressure structures with unusual chemical and physical properties. [6][7][8][9][10][11][12][13][14][15][16][17][18] In recent years, advances in experimental and theoretical techniques have fostered remarkable breakthroughs in highpressure science, as exemplified by the discovery of highpressure superconductors, metal-to-semiconductor transitions, superfluids, etc. [19][20][21][22] It is noteworthy that Zhu et al. employed the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method to make predictions and subsequently succeeded in synthesizing the SrB 3 C 3 compound under a pressure of approximately 50 GPa. [23] Further calculations show that SrB 3 C 3 is a superconductor with a superconducting critical temperature of about 40 K. [24][25][26][27] In addition, the physical properties of various boron-carbon compounds doped with different elements have been investigated under high pressure, such as SrB 2 C 4 , BaB 2 C 4 , Na 2 B 4 C 8 , Li 2 B 4 C 8 and so on. ...
As an extreme physical condition, high pressure serves as a potent means to substantially modify the interatomic distances and bonding patterns within condensed matter, thereby enabling the macroscopic manipulation of material properties. We employed the CALYPSO method to predict the stable structures of RbB2C4 across the pressure range from 0 GPa to 100 GPa and investigated its physical properties through first-principles calculations. Specially, we found four novel structures, namely, P63/mcm-, Amm2-, P1-, and I4/mmm-RbB2C4. Under pressure conditions, electronic structure calculations reveal that all of them exhibit metallic characteristics. The calculation results of formation enthalpy show that the P63/mcm structure can be synthesized within the pressure range of 0–40 GPa. Specially, the Amm2, P1, and I4/mmm structures can be synthesized above 4 GPa, 6 GPa, 10 GPa, respectively. Moreover, the estimated Vickers hardness value of I4/mmm-RbB2C4 compound is 47 GPa, suggesting that it is a superhard material. Interestingly, this study uncovers the continuous transformation of the crystal structure of RbB2C4 from a layered configuration to folded and tubular forms, ultimately attaining a stabilized cage-like structure under the pressure span of 0–100 GPa. The application of pressure offers a formidable impetus for the advancement and innovation in condensed matter physics, facilitating the exploration of novel states and functions of matter.
... Hydrogen (deuterium) molecule is deceptively simple but when many of them arrange themselves into the crystalline state, they unexpectedly create the solid with one of most intricate and complex phase diagram among the elements [1][2][3][4][5][6][7]. As the result both hydrogen and deuterium phase diagrams attract considerable attention and were extensively studied in a wide pressure and temperature range. ...
Utilizing the high-pressure low-temperature Raman and optical transmission/absorption spectroscopies, we have mapped out the phase diagram of H 2 -HD- D 2 alloy with the initial H:D concentration 50:50 up to 350 GPa between 10 and 300 K. We followed the phase lines between all known solid phases [I, II, III, IV, and IV ′ ( IV + V )] of pure H 2 and D 2 constraining their locations in the wide space. We trace the phase boundary separating phases III and IV ( IV ′ )/V demonstrating that this phase line has a steep negative slope ( − 0.95 K/GPa), which becomes shallower at above 250 GPa ( − 0.55 K/GPa). The phase line follows the trend observed in the pure species. Additionally, we find that the band gap of the mixture between 300 and 360 GPa is close to those of the pure species suggesting that alloying one isotope by another would not significantly shift the metallization pressure. These observations imply that hydrogen deuteride (HD) has very similar properties to those exhibited by the pure species.
Published by the American Physical Society 2025
... Dense hydrogen exhibits a diverse range of fascinating physical phenomena [1] despite being composed of the simplest element. At low temperatures, the system adopts a variety of solid-state phases, which have been observed in both experiments [2][3][4][5] and simulations [6,7]. ...
We perform deep variational free energy calculations to investigate the dense hydrogen system at 1200 K and high pressures. In this computational framework, neural networks are used to model the free energy through the proton Boltzmann distribution and the electron wavefunction. By directly minimizing the free energy, our results reveal the emergence of a crystalline order associated with the center of mass of hydrogen molecules at approximately 180 GPa. This transition from atomic liquid to a molecular solid is marked by discontinuities in both the pressure and thermal entropy. Additionally, we discuss the broader implications and limitations of these findings in the context of recent studies of dense hydrogen under similar conditions.
... The rotation of H 2 molecules is also a structural feature of the low-pressure 036103-3 phase I of solid bulk hydrogen that is stable up to pressures of about 110 GPa. [58] Consequently, we calculated the energy barrier according to the rotation of the molecular hydrogen at 0 GPa using the method described in Ref. [59]. The rotational barrier peaks midway through the rotation, which is found to be 0.0203 eV/atom (Table S1). ...
The recent discovery of type-VII boron–carbon clathrates with calculated superconducting transition temperatures approaching ∼100 K has sparked interest in exploring new conventional superconductors that may be stabilized at ambient pressure. The electronic structure of the clathrate is highly tunable based on the ability to substitute different metal atoms within the cages, which may also be large enough to host small molecules. Here we introduce molecular hydrogen (H2) within the clathrate cages and investigate its impact on electron–phonon coupling interactions and the superconducting transition temperature (Tc). Our approach involves combining molecular hydrogen with the new diamond-like covalent framework, resulting in a hydrogen-encapsulated clathrate, (H2)B3C3. A notable characteristic of (H2)B3C3 is the dynamic behavior of the H2 molecules, which exhibit nearly free rotations within the B–C cages, resulting in a dynamic structure that remains cubic on average. The static structure of (H2)B3C3 (a snapshot in its dynamic trajectory) is calculated to be dynamically stable at ambient and low pressures. Topological analysis of the electron density reveals weak van der Waals interactions between molecular hydrogen and the B–C cages, marginally influencing the electronic structure of the material. The electron count and electronic structure calculations indicate that (H2)B3C3 is a hole conductor, in which H2 molecules donate a portion of their valence electron density to the metallic cage framework. Electron–phonon coupling calculation using the Migdal–Eliashberg theory predicts that (H2)B3C3 possesses a Tc of 46 K under ambient pressure. These results indicate potential for additional light-element substitutions within the type-VII clathrate framework and suggest the possibility of molecular hydrogen as a new approach to optimizing the electronic structures of this new class of superconducting materials.
... This limit defines the Mott-Ioffe-Regal minimum metallic conductivity 24 and is given by σ min = e 2 /3ħa, where ħ is the reduced Planck's constant, and a ~ (n i ) -1/3 is the interparticle spacing with n i being the ion density. For metallization in the molecular phase, initially suggested by Weir et al. 12 , one electron per molecular ion contributes to conduction, so at the metallization pressure of 140 GPa, the density from ref 35 is 0.385 mole/cm 3 , corresponding to a molecular number density of 2.318x10 23 while a = 1.628 Å. ...
Liquid metallic hydrogen (LMH) was recently produced under static compression and high temperatures in bench-top experiments. Here, we report a study of the optical reflectance of LMH in the pressure region of 1.4-1.7 Mbar and use the Drude free-electron model to determine its optical conductivity. We find static electrical conductivity of metallic hydrogen to be 11,000-15,000 S/cm. A substantial dissociation fraction is required to best fit the energy dependence of the observed reflectance. LMH at our experimental conditions is largely atomic and degenerate, not primarily molecular. We determine a plasma frequency and the optical conductivity. Properties are used to analyze planetary structure of hydrogen rich planets such as Jupiter.
... Phase I occupies a prominent part of the phase diagram, displaying remarkable pressure stability [5,7]. In phase I, solid hydrogen crystallizes in the hexagonal close-packed (hcp) structure over a broad range of pressures and temperatures [8,9]. ...
Zero-point vibrations of solid hydrogen are investigated by analyzing the molecular mean-squared displacement (MSD) and mean-squared relative displacement functions within the statistical moment method approach in statistical mechanics. Numerical computations of these thermodynamic properties were conducted for solid hydrogen from 0 K to its phase transition temperature using the Wigner-Kirkwood mean-field potential derived from the Buckingham exp-6 potential. We have shown that the quantum-mechanical zero-point vibrations play an important role at low temperature. And these thermodynamic quantities increase with temperature, suggesting that both thermal and quantum effects play a significant role near the liquid-solid phase transition. The favorable consistency between our findings and the recent experimental inelastic neutron scattering measurements of MSD attests to the potential of SMM as a novel approach for determining the atomic vibrations of solid hydrogen. This approach allows us to study these effects including the anharmonicity of lattice vibrations.
... To relate the pressure to the density, the data in Fig. 4 of Ref. [13] were used. In the region "no stable phase" the density is below that of solid molecular hydrogen in the limit of zero pressure [14]. ...
Superconductivity, the amazing phenomenon of lossless transmission of electric current through metallic wires, requires cooling of the wire to low temperatures. Metallic hydrogen is considered as the most likely candidate for superconductivity at very high temperatures, possibly even room temperature. However, as a result of various approximations used, conflicting theoretical predictions exist for the range of temperatures where superconductivity is expected to occur. Here we avoid those approximations and confirm that metallic hydrogen is indeed a superconductor, but this is limited to temperatures far below previous estimates. We exploit the ``jellium'' model proposed in 1966 by De Gennes, where superconductivity is caused by the combination of Coulomb repulsion between the electrons and Coulomb attraction between the protons and the electrons. We find that the superconducting order develops over an energy range far exceeding the characteristic phonon energy, and that the phase of the order parameter flips 180 degrees at the characteristic phonon energy above and below the Fermi energy.
... Measurement of the equation of state (EOS) for matter under extreme conditions is of great significance 1-14 to a variety of research fields of planetary physics, [15][16][17] geophysics, [18][19][20] high-pressure science, [21][22][23] and inertial confinement fusion (ICF). [24][25][26][27][28][29][30] Owing to the advent of high-power laser facilities, the difficulty of generating such a laser-driven extreme state under laboratory conditions has been much relieved 31,32 and laser-driven EOS measurement for the generated matter begins to attract particular interest. ...
The theoretical design for the time profile of radiation temperature plays an important role in indirect laser-driven equation-of-state measurement, which severely relies on a large number of radiation hydrodynamic simulations. In this work, we provide a concise data-driven method for optimizing the radiation temperature profile, which combines a time-varying Volterra model with an improvement achieved by data generation via radiation hydrodynamic simulations utilizing random perturbations in a skew normal distribution as inputs. We find that the time-varying Volterra model can be used to investigate the time-dependent relationship between the radiation temperature and the key physical quantities of interest, such as shock-wave velocity and ablation drive pressure. With this method, we realize the inverse designs of the radiation temperature profiles for planar dynamic shock and ramp compressions according to the desired shock-wave velocity and drive pressure, respectively, which shows the advantage of practical application in experiments.
... In the last several decades, only four solid hydrogen phases have been confirmed, mostly by Raman scattering and IR absorption experiments conducted below or at room temperature. [1,[6][7][8][9][10][11][12][13][14][15][16] A large portion of the phase diagram above room temperature up to the melting curve still remains unknown. Only a few experiments with limited PT data points above 300 K have been tried, and the reported results are far from convincing and not self-consistent. ...
We report a phase diagram mapping for solid hydrogen based on several thousands of Raman spectroscopic data points obtained at simultaneous high-pressure and -temperature (PT) experiments. Information about phase behavior in the range of 300 K up to the melting line and 0–300 GPa for hydrogen has remained almost unknown to date; therefore, revealing it is very desirable. A network analysis of the isothermal and isobaric dependencies for various Raman modes has been used; discontinuities in these dependencies, plus the mode appearance/disappearance provide evidence for phase transitions. These transition data show self-consistency and have been used to outline possible phase boundaries for hydrogen in this PT region. Evidence we found shows hydrogen may experience a gradual molecular dissociation process before its metallization.
... The position of the peak (Raman shift) (v p ) in the parameters of Raman spectrometry reflects the vibrational dynamic properties of the ground state of the electrons in the sample molecules, which is expressed in terms of the difference in the wavelength between the incident and scattered light. The change in the position of the peak (peak shift) is mainly determined by the change in the molecular structure of the material and is closely related to the stress on the material [13][14][15][16]. ...
The build-up and occurrence of earthquakes are due to the accumulation and release of stress in fault zones. When subjected to tectonic extrusion stress, the crystal structure of the minerals within a fault zone will change. In this study, Raman spectroscopy analysis was conducted on the concurrently deposited quartz veins from Shenxigou, along the Yingxiu-Beichuan fault, and from Niyang River mouth, in the southern section of the Milin fault. The test results reveal a 3.29 cm⁻¹ shift in the characteristic 464 cm⁻¹ peak of the quartz in the veins along the fault plane of the Yingxiu-Beichuan fault, which was significantly lower than the shifts in the quartz peaks of the quartz on both sides of the vein. The 464 cm⁻¹ peak shifts of the samples collected 10 m to the NW and 21 m to the SE of the fault plane were approximately 4.40 and 4.62 cm⁻¹. In the veins from the Milin fault, considerable shifts of the 464 cm⁻¹ quartz peaks occurred at the fault plane and to both sides within 5.5 m of the fault plane. No significant change in the 464 cm⁻¹ Raman peak of quartz was observed for the samples 5–28 m to the SE of the fault plane. These results indicate that the tectonic extrusion stress accumulated more easily in proximity to the fault plane, resulting in significant changes in the crystals near the fault plane. We conclude that there is a correlation between the degree of change in the crystal structures of the minerals in thrust fault zones and fault activity, and such a correlation can provide a new method for studying the activity of thrust faults in areas with bedrock.
... Solid hydrogen at high pressures exhibits a very rich phase diagram with the presence of five different molecular phases, labelled from I to V (refs. [2][3][4] ). Recently, a new phase transition has been observed above 420 GPa into a metallic state by infrared (IR) absorption measurements 5 , namely, phase VI. ...
Hydrogen is the most abundant element in the Universe. However, understanding the properties of dense hydrogen is still an open challenge because—under megabar pressures—the quantum nature of both electrons and protons emerges, producing deviations from the common behaviour of condensed-matter systems. Experiments are challenging and can access only limited observables, and the interplay between electron correlation and nuclear quantum motion makes standard simulations unreliable. Here we present the computed phase diagram of hydrogen and deuterium at low temperatures and high pressures using state-of-the-art methods to describe both many-body electronic correlation and quantum anharmonic motion of protons. Our results show that the long-sought atomic metallic hydrogen phase—predicted to host room-temperature superconductivity—forms at 577(4) GPa. The anharmonic vibrations of nuclei pushes the stability of this phase towards pressures much larger than previous estimates or attained experimental values. Before atomization, molecular hydrogen transforms from a metallic phase (phase III) to another metallic structure that is still molecular (phase VI) at 410(20) GPa. Isotope effects increase the pressures of both transitions by 63 and 32 GPa, respectively. We predict signatures in optical spectroscopy and d.c. conductivity that can be experimentally used to distinguish between the two structural transitions.
... It is evident that the physical and chemical properties of materials are strongly dependent on the crystal structure [22]. Pressure, as a fundamental thermodynamic variable, can directly modify crystal structure influencing atomic sites, interatomic electrostatic interactions, electronic orbitals, and chemical bonding [23][24][25][26], even in the case when the stoichiometry and temperature remain unchanged [27], which implies that thermoelectric transport parameters could be manipulated through applying pressure. Unfortunately, pressure is frequently underestimated and even overlooked in the preparation and performance of materials, despite in-situ high-pressure technology has exhibited fantastic effects on microscopic structure and transport properties in various thermoelectric materials (table 1) [28][29][30][31][32][33][34][35][36]. ...
Pressure is a fundamental thermodynamic variable that can create exotic materials and modulate transport properties, motivating prosperous progress in multiple fields. As for inorganic thermoelectric materials, pressure is an indispensable condition during a preparation process, which is employed to compress raw powders into the specific shape of solid-state materials for performing properties characterization. In addition to this function, the extra influence of pressure on thermoelectric performance is frequently underestimated and even overlooked. In this review, we summarize recent progress and achievements of pressure-induced structure and performance in thermoelectrics, emphatically involving the modulation of pressure on crystal structure, electrical transport properties, microstructure, and thermal conductivity. According to various studies, the modulated mechanism of pressure on these items above has been discussed in detail, and the perspectives and strategies have been proposed with respect to applying pressure to improve thermoelectric performance. Overall, the purpose of the review is supposed to enrich the understanding of the mechanisms in pressure-induced transport properties and provide a guidance to rationally design a structural pattern to improve thermoelectric performance.
... The phase diagram of hydrogen was corrected according to the updated universal diamond scale (see Fig. 4c). The phase diagram is built on experimental data from different groups 9,33,42,43 with the primarily goal to locate the area of metallic hydrogen. According to the current conception hydrogen transforms from dielectric and semiconducting state into a semimetal at ∼300 GPa 11 (see Fig. 4c). ...
The recent progress in generating static pressures up to terapascal values opens opportunities for studying novel materials with unusual properties, such as metallization of hydrogen and high-temperature superconductivity. However, an evaluation of pressure above ~0.3 terapascal is a challenge. We report a universal high-pressure scale up to ~0.5 terapascal, which is based on the shift of the Raman edge of stressed diamond anvils correlated with the equation of state of Au and does not require an additional pressure sensor. According to the new scale, the pressure values are substantially lower by 20% at ~0.5 terapascal compared to the extrapolation of the existing scales. We compare the available data of H2 at the highest static pressures. We show that the onset of the proposed metallization of molecular hydrogen reported by different groups is consistent when corrected with the new scale and can be compared with various theoretical predictions.
We present the equation of state (EOS) of solid parahydrogen between and at K, calculated using path-integral Monte Carlo simulations, with ab initio two-body and three-body interaction potentials. We correct for finite size simulation errors using potential tail corrections. Trotter factorization errors are accounted for, either via extrapolation, or by using a suitably small imaginary time step. We incorporate the three-body interaction using two methods; the full inclusion method, where pair and three-body interactions are used in both Monte Carlo sampling and in the energy estimators, and the perturbative method, where three-body interactions are omitted from sampling but are still present in energy estimations. Both treatments of the three-body interaction return very similar total energies and pressures. The presence of three-body interactions has only minor effects on the structural properties of the solid. Whereas the pair interaction, on its own, significantly overestimates the pressure of solid parahydrogen, the additional presence of the three-body interaction causes a severe underestimation of the pressure. Our findings suggest that accurate simulations of solid parahydrogen require four-body and possibly higher-order many-body interactions. It may also be the case that static interaction potentials are entirely unsuitable for simulations of solid parahydrogen at high densities.
Materials science exploits only properties that are available at ambience. Therefore, although high-pressure changes the physical state of all condensed matter, most of the extraordinary properties discovered vanish after decompression and cannot be utilized. Here, we demonstrate sublattice decoupling in a mixed-anion chalcohalide Rb6Re6S8I8 upon compression, in which the [Rb6I2]⁴⁺ framework is soft and plastic, while the [Re6S8I6]⁴⁻ clusters are hard and elastic. This discrepancy in the rigidity allows the applied pressure to selectively amorphize the framework while maintaining the ordered state in the cluster, leading to intriguing photocurrent generation and enhancement upon compression. These high-pressure properties are retained at ambience, permitting scalable synthesis of the decompressed samples using a large-volume press, followed by further fabrication into self-powered broadband photodetectors with a response time of ~ 10² μs and a specific detectivity of ~ 10¹¹ Jones. This study subverts the stereotype that pressure engineering is hardly to be employed for device applications.
Here, we propose a multicenter bond theory that addresses the origin and mechanisms behind the formation of electron-rich multicenter bonds (ERMBs) and electron-deficient multicenter bonds (EDMBs), with special emphasis on...
A hexagonal structure of solid molecular hydrogen with symmetry is calculated to be more stable below about 200 GPa than the monoclinic C2/c structure identified previously as the best candidate for phase III. We find that the effects of nuclear quantum and thermal vibrations play a central role in the stabilization of . The and C2/c structures are very similar and their Raman and infra-red data are in good agreement with experiment. However, our calculations show that the hexagonal structure provides better agreement with the available x-ray diffraction data than the C2/c structure at pressures below about 200 GPa. We suggest that two phase-III-like structures may be formed at high pressures, hexagonal below about 200 GPa and monoclinic C2/c at higher pressures.
We examine the molecular-atomic transition in liquid hydrogen as it relates to metallization. Pair potentials are obtained from first principles molecular dynamics and compared with potentials derived from quadratic response. The results provide insight into the nature of covalent bonding under extreme conditions. Based on this analysis, we construct a schematic dissociation-metallization phase diagram and suggest experimental approaches that should significantly reduce the pressures necessary for the realization of the elusive metallic phase of hydrogen.
We present first-principles calculations of metallic atomic hydrogen in the 400-600 GPa pressure range in a tetragonal structure with space group , which is predicted to be its first atomic phase. Our calculations show a band structure close to the free-electron-like limit due to the high electronic kinetic energy induced by pressure. Bands are properly described even in the independent electron approximation fully neglecting the electron-electron interaction. Linear-response harmonic calculations show a dynamically stable phonon spectrum with marked Kohn anomalies. Even if the electron-electron interaction has a minor role in the electronic bands, the inclusion of electronic ex- change and correlation in the density response is essential to obtain a dynamically stable structure. Anharmonic effects, which are calculated within the stochastic self-consistent harmonic approxima- tion, harden high-energy optical modes and soften transverse acoustic modes up to a 20% in energy. Despite a large impact of anharmonicity has been predicted in several high-pressure hydrides, here the superconducting critical temperature is barely affected by anharmonicity, as it is lowered from its harmonic 318 K value only to 300 K at 500 GPa. We atribute the small impact of anharmoncity on superconductivity to the absence of softened optical modes and the fairly uniform distribution of the electron-phonon coupling among the vibrational modes.
Hydrogen, the first element in the periodic table, is predicted to become metallic at extremely high‐pressure conditions. Solid metallic hydrogen is believed to possess extraordinary physical properties, such as room‐temperature superconductivity and superfluidity, earning it the title of the “holy grail” in high‐pressure research. The pursuit of solid metallic hydrogen has spanned nine decades. Despite numerous fascinating discoveries related to dense hydrogen, metallic hydrogen has yet to be experimentally realized. This article aims to provide an overview of the major progress made in this field and offers an outlook on future developments.
Crystallographic evolution of hydrogen under multi-megabar compression is a key problem in condensed-matter physics and unsolved challenge for experimentalists and theoreticians. Although dozens of crystal structures have been proposed by theory, only one, the simple hexagonal-close-packed (hcp) structure, has been previously confirmed in experiments. Utilizing new-generation synchrotron nano-focused X-ray probes developed for micron-sized hydrogen crystals at pressures above 212 GPa, we are able to observe the transition from hcp H2 to a larger hexagonal supercell with lattice parameters expanding to √3✕a and 2✕c of hcp, in which the characteristic hcp peaks (1 0 0), (0 0 2), and (1 0 1) become (1 1 0), (0 0 4), and (1 1 2), respectively, and three new peaks, (1 0 1), (1 0 3), and (2 0 1), of the supercell appear. Theoretical calculations based on our XRD results found a time-averaged structure model in space group P6 ̅2c (190) with alternating layers of spherically disordered H2 molecules and ordered molecules toward a graphene-like atomic H network. Such a hexagonal supercell has not been reported by any previous theoretical study for post-hcp phase, but is close to a number of theoretical models with mixed-layer structures. The clear evidence of a structural transition beyond hcp marks the polymerization nature of molecular-to-atomic hydrogen transition.
Achieving superconductivity at room temperature (RT) is a holy grail in physics. Recent discoveries on high‐Tc superconductivity in binary hydrides H3S and LaH10 at high pressure have directed the search for RT superconductors to compress hydrides with conventional electron–phonon mechanisms. Here, an exceptional family of superhydrides is predicated under high pressures, MH12 (M = Mg, Sc, Zr, Hf, Lu), all exhibiting RT superconductivity with calculated Tcs ranging from 313 to 398 K. In contrast to H3S and LaH10, the hydrogen sublattice in MH12 is arranged as quasi‐atomic H2 units. This unique configuration is closely associated with high Tc, attributed to the high electronic density of states derived from H2 antibonding states at the Fermi level and the strong electron–phonon coupling related to the bending vibration of H2 and H‐M‐H. Notably, MgH12 and ScH12 remain dynamically stable even at pressure below 100 GPa. The findings offer crucial insights into achieving RT superconductivity and pave the way for innovative directions in experimental research.
We study the electronic excitation spectra in solid molecular hydrogen (phase I) at ambient temperature and 5- to 90-GPa pressures using quantum Monte Carlo methods and many-body perturbation theory. In this range, the system changes from a wide-gap molecular insulator to a semiconductor, altering the nature of the excitations from localized to delocalized. Computed gaps and spectra agree with experiments, proving the ability to predict accurately band gaps of many-body systems in the presence of nuclear quantum and thermal effects.
DFT-MD simulations of the CH 4 –H 2 mixture studied under icy-planetary conditions suggest a phase transition from molecular to polymer region with liberation of hydrogen leading to a non-metallic to metallic transition, fulfilling the LMA within 4%.
Hydrogen, the simplest and most abundant element of the universe, has proven to be an enigma for high pressure physics. Its predicted metallization and superconductivity under pressure has motivated numerous experimental and theoretical developments in the field of high pressure physics. This chapter summarizes the present understanding of hydrogen under compression. In many cases, hydrides are perceived to represent a chemically pre-compressed state of hydrogen, giving impetus to their investigations, including search for high pressure superconductivity. Due to its current and intense interest, this topic is covered separately in this chapter.
We study the structural phase transition, originally associated with the highest superconducting critical temperature T c measured in high-pressure sulfur hydride. A quantitative description of its pressure dependence has been elusive for any ab initio theory attempted so far, raising questions on the actual mechanism leading to the maximum of T c . Here, we estimate the critical pressure of the hydrogen bond symmetrization in the Im 3 ¯ m structure, by combining density functional theory and quantum Monte Carlo simulations for electrons with path integral molecular dynamics for quantum nuclei. We find that the T c maximum corresponds to pressures where local dipole moments dynamically form on the hydrogen sites, as precursors of the ferroelectric Im 3 ¯ m-R3m transition, happening at lower pressures. For comparison, we also apply the self-consistent harmonic approximation, whose ferroelectric critical pressure lies in between the ferroelectric transition estimated by path integral molecular dynamics and the local dipole formation. Nuclear quantum effects play a major role in a significant reduction (≈50 GPa) of the classical ferroelectric transition pressure at 200 K and in a large isotope shift (≈25 GPa) upon hydrogen-to-deuterium substitution of the local dipole formation pressure, in agreement with the corresponding change in the T c maximum location.
High pressure mineral physics is a field that has shaped our understanding of deep planetary interiors and revealed new material phenomena occurring at extreme conditions. Comprised of sixteen chapters written by well-established experts, this book covers recent advances in static and dynamic compression techniques and enhanced diagnostic capabilities, including synchrotron X-ray and neutron diffraction, spectroscopic measurements, in situ X-ray diffraction under dynamic loading, and multigrain crystallography at megabar pressures. Applications range from measuring equations of state, elasticity, and deformation of materials at high pressure, to high pressure synthesis, thermochemistry of high pressure phases, and new molecular compounds and superconductivity under extreme conditions. This book also introduces experimental geochemistry in the laser-heated diamond-anvil cell enabled by the focused ion beam technique for sample recovery and quantitative chemical analysis at submicron scale. Each chapter ends with an insightful perspective of future directions, making it an invaluable source for graduate students and researchers.
High pressure mineral physics is a field that has shaped our understanding of deep planetary interiors and revealed new material phenomena occurring at extreme conditions. Comprised of sixteen chapters written by well-established experts, this book covers recent advances in static and dynamic compression techniques and enhanced diagnostic capabilities, including synchrotron X-ray and neutron diffraction, spectroscopic measurements, in situ X-ray diffraction under dynamic loading, and multigrain crystallography at megabar pressures. Applications range from measuring equations of state, elasticity, and deformation of materials at high pressure, to high pressure synthesis, thermochemistry of high pressure phases, and new molecular compounds and superconductivity under extreme conditions. This book also introduces experimental geochemistry in the laser-heated diamond-anvil cell enabled by the focused ion beam technique for sample recovery and quantitative chemical analysis at submicron scale. Each chapter ends with an insightful perspective of future directions, making it an invaluable source for graduate students and researchers.
High pressure mineral physics is a field that has shaped our understanding of deep planetary interiors and revealed new material phenomena occurring at extreme conditions. Comprised of sixteen chapters written by well-established experts, this book covers recent advances in static and dynamic compression techniques and enhanced diagnostic capabilities, including synchrotron X-ray and neutron diffraction, spectroscopic measurements, in situ X-ray diffraction under dynamic loading, and multigrain crystallography at megabar pressures. Applications range from measuring equations of state, elasticity, and deformation of materials at high pressure, to high pressure synthesis, thermochemistry of high pressure phases, and new molecular compounds and superconductivity under extreme conditions. This book also introduces experimental geochemistry in the laser-heated diamond-anvil cell enabled by the focused ion beam technique for sample recovery and quantitative chemical analysis at submicron scale. Each chapter ends with an insightful perspective of future directions, making it an invaluable source for graduate students and researchers.
A method for measuring the pressure and the results of the determination of the adiabatic equation for solid hydrogen up to 150 kbar are presented. The compression was performed by the method of the metallic Z-pinch, the density was measured by x-ray analysis, and the pressure was measured using the equation of state for a reference material.
The molecular hydrogens (H2, D2, HD, etc.) form the simplest of all molecular solids. The combination of the light mass, small moment of inertia, weak interactions, and the quasi-metastable ortho-para species result in a fascinating low-temperature behavior that can be understood to a large extent from considerations of first principles. After discussing single molecule properties and intermolecular interactions we discuss in detail the ortho-para properties, conversion and diffusion. This is followed by a description of the crystal structures and the orientational ordering phenomena. The thermodynamic properties are reviewed. The article is concluded with a discussion of the translational ground state of the solid and the effect of the large zero-point motion on the solid state properties. A large number of data are collected in tables and graphs to provide a reference source.
A semiempirical pair potential for molecular hydrogen and deuterium has been derived by fitting to solid state data. The potential is bounded to conform asymptotically to short‐ and long‐range theoretical results. In the solid, many‐body effects are accounted for by including a spherical form of the nonnegligible Axilrod–Muto–Teller three‐body forces. The potential can be used to successfully describe isotropic properties in the solid and gas phases.
Dynamic equation-of-state data for Dâ and Hâ were measured in the pressure range 2--76 GPa (20--760 kbar) using a two-state light-gas gun. Liquid specimens were shocked from initial states near the saturation curve at 20 K. Maximum compression was sixfold over initial liquid density at a calculated temperature of 7000 K for Dâ. The data is discussed in terms of the theory of Ross et al., which includes an effective intermolecular pair potential, molecular vibration, free molecular rotation, and molecular dissociation.
Sound velocities in fluid and crystalline hydrogen were measured under pressure to 24 gigapascals by Brillouin spectroscopy
in the diamond anvil cell. The results provide constraints on the intermolecular interactions of dense hydrogen and are used
to construct an intermolecular potential consistent with all available data. Fluid perturbation theory calculations with the
potential indicate that sound velocities in hydrogen at conditions of the molecular layer of the Jovian planets are lower
than previously believed. Jovian models consistent with the present results remain discrepant with recent free oscillation
spectra of the planet by 15 percent. The effect of changing interior temperatures, the metallic phase transition depth, and
the fraction of high atomic number material on Jovian oscillation frequencies is also investigated with the Brillouin equation
of state. The present data place strong constraints on sound velocities in the Jovian molecular layer and provide an improved
basis for interpreting possible Jovian oscillations.
Direct optical observations of solid hydrogen to pressures in the 250-gigapascal range at 77 K are reported. Hydrogen samples appear nearly opaque at the maximum pressures. Measurements of absorption and Raman spectra provide evidence that electronic excitations in the visible region begin at about 200 gigapascals. The optical data are consistent with a band-overlap mechanism of metallization.
Electrical conductivities were measured for liquid D2 and H2 shock compressed to pressures of 10-20 GPa (100-200 kbar), molar volumes near 8 cu cm/mol, and calculated temperatures of 2900-4600 K. The semiconducting energy gap derived from the conductivities is 12 eV, in good agreement with recent quasi-particle calculations and with oscillator frequencies measured in diamond-anvil cells.
Direct optical observations of solid hydrogen to pressures in the 250-gigapascal (2.5-megabar) range at 77 K are reported. Hydrogen samples appear nearly opaque at the maximum pressures. Measurements of absorption and Raman spectra provide evidence that electronic excitations in the visible region begin at ∼200 gigapascals. The optical data are consistent with a band-overlap mechanism of metallization.
We show that the reaction +3/\ensuremath{\leftrightarrows}3/2AlOOH+1/2Al proceeds to the right at 300 K and at pressures above 136 GPa, producing the metal aluminum in the process. The system of neighboring particles of coated with aluminum hydroxide oxide and covered with aluminum is a dc conductor and exhibits a resonance in the infrared which appears as a plasma edge. In view of this, claims of production of metallic hydrogen based on reflectivity studies on composite - samples are unwarranted.
We have studied the E2g transverse-optical phonon by means of
Raman scattering in solid molecular hydrogen and deuterium at pressures
up to 230 kbar at 5 K in a diamond anvil cell. With the use of a
self-consistent phonon calculation which incorporates anharmonic
corrections to the self-energy, phonon frequencies were calculated using
an isotropic inter-molecular pair potential. Deviations between theory
and experiment point to deficiencies in the potential. The present
experimental data can be used as a test on the isotropic part of the
intermolecular potential of the solid.
We have studied the Q+1(0) intramolecular
vibrational transition in solid molecular hydrogen and deuterium by
means of Raman scattering for pressures up to 600 kbar and temperatures
down to 5 K in a diamond anvil cell. We present a semiempirical model
developed to describe the pressure dependence of the transition
frequency. The agreement between theory and experiment is surprisingly
good up to about 200 kbar. Deviations at higher pressures cannot be
explained in terms of this simple mean-field model.
Using a five-pass interferometric Brillouin spectrometer, we have measured the pressure dependence of longitudinal- and transverse-acoustic velocities and refractive index of solid n-H2 and n-D2 at room temperature in a diamond-anvil cell up to 200 kbar. The equations of state have been determined (55
We have studied ortho- and para- at pressures up to 540 kbar (54 GPa) and by means of Raman scattering in a diamond anvil cell. A phase transition in which the molecules which are spherically symmetric at low pressure go into an orientationally ordered state has been observed in o- at 278\ifmmode\pm\else\textpm\fi{}5 kbar. Line broadening of the roton bands for p\gtrsim kbar is interpreted as a precursor of this transition.
The hexagonal-to-cubic-to-hexagonal structure changes in hydrogen and deuterium were studied by x-ray diffraction over many cycles of the transitions for orthohydrogen and paradeuterium concentrations up to 95%. Results of the x-ray study can be closely correlated with those of infrared, neutron-diffraction, heat-capacity, nuclear-magnetic-resonance, and volume-change measurements. The structure changes take place by a shifting of the hexagonal nets, which appears to be incomplete after the first transition and may cause intermediate close-packed structures to form. Repeated cylcing through the transition stabilizes the cubic structure, possibly because orientation of the J=0 molecules takes place.
The present status of high-pressure research with the diamond anvil cell (DAC) is reviewed in this article, mainly from an experimental aspect. After a brief description of the different types of DAC's that are currently in vogue, the techniques used in conjunction with the DAC in modern high-pressure research are presented. These include techniques for low- and high-temperature studies, x-ray diffractometry, spectroscopy with the DAC, and other measurements. Results on selected materials, with a view to illustrating the physics behind high-pressure phenomena, are presented and discussed. These include metal-semiconductor transitions, electronic transitions, phonons and high-pressure lattice dynamics, and phase transitions. A whole section is devoted to the behavior of condensed gases, principally H2, D2, O2, N2, and rare-gas solids. The concluding section briefly deals with speculations on ultra-high-pressure research with the DAC in the future.
Application of the BCS theory to the proposed metallic modification of hydrogen suggests that it will be a high-temperature superconductor. This prediction has interesting astrophysical consequences, as well as implications for the possible development of a superconductor for use at elevated temperatures.
Low-temperature NMR studies of solid hydrogen at reduced ortho concentrations X<55% are interpreted in terms of possible quadrupolar glass phases in which the ortho molecules are frozen into random configurations. The quadrupolar glass is an extension of the concept of the dipolar glass of spins introduced by Edwards and Anderson.
Hydrogen becomes a solid at 25°C when subjected to a pressure of 57 kilobars. The high-pressure phase appears as a transparent crystalline mass. The refractive index of the high-pressure phase increases sharply with pressure, indicating a density increase of similar magnitude. At 360 kilobars the calculated density of the high-pressure phase is 0.6 to 0.7 grams per cubic centimeter.
Hartree-Fock calculations using the exact-exchange operator are reported for molecular and metallic solid hydrogen. Both calculations used the same basis set and the same crystal formalism. The calculations indicate a transition to the metallic phase at a pressure of 2.1 Mbar, in agreement with recent experiments.
AT high pressure (> 100 GPa), the valence-conduction band gap in solid hydrogen is predicted to decrease and eventually to close, transforming it from an insulator to a metal 1. Recent experiments at pressures up to approximately 300 GPa suggest a gradual closing of the direct gap at very high pressures whereas closure of the indirect gap may occur at lower pressures, perhaps below 200 GPa (refs 2-6). Measurements of the refractive index, n, and its frequency dependence (the dispersion dn/d-omega) as a function of pressure can provide information on the changes in electronic structure that occur under these conditions 7,8. Here we report refractive-index measurements on solid hydrogen at visible frequencies at pressures up to 170 GPa. Unlike earlier studies 9, we find no evidence for a divergence (dielectric instability) at 150 GPa, close to the low-temperature phase transition observed previously 6 and suggested as being associated with metallization 4,9. Our results are consistent with closure of the indirect gap. A fit of our data to a dielectric model indicates that the onset of visible absorption owing to direct interband transitions should occur above 200 GPa, consistent with previous direct observations 3. Pressure-induced molecular dissociation may occur before closure of the direct gap.
Raman spectra of fluid hydrogen at room temperature include rotational, , and vibrational bands, . The rotational bands become diffuse between 0.2 and 55 kbar, the solidification point at 22\ifmmode^\circ\else\textdegree\fi{}C. Between 55 and 630 kbar, only was resolved. This band increases in frequency to 360 kbar, but the frequency decreases between 360 and 630 kbar. These phenomena are consistent with the softening of the molecular bond at high pressure.
The effect of pressure from 60 to over 400 kbar was measured on the
resistance of Se and I. Selenium exhibits a very rapid drop in resistance between
60 and 128 kbar; at 128 kbar it shows a discontinuous drop. At higher pressures
its behavior is apparently metallic. Iodine shows a rapid drop in resistance
from 60 kbar to the region of 225 to 255 kbar where there is relatively abrnpt
change of slope. At higher pressures the change in resistance with pressure is
much smaller. The optical energy gap of selenium extrapolates to zero at about
130 kbar, while the optical gap for iodine extrapolates to zero at 240 kbar.
(auth)
Neither local modes nor extended phonons precisely describe the excitations of anharmonic solids. A simple model Hamiltonian presented here characterizes the transition from local oscillator to optical phonon which would take place if one could continuously increase the phonon dispersion. The model is used to describe two types of transitions: a phonon-localization transition which is the analog of the Mott transition for electrons, and a spectral transition associated with the appearance of two-phonon bound states. In real materials, a sharp phonon-localization transition is probably not achievable, but striking spectral effects may be observable for some systems which are marginally able to produce two-phonon bound states.
Observations of the Q(J) lines in the Raman spectrum of HD are reported for a range of densities at room temperature. The broadening of the individual components at low densities and the eventual overlap and collapse of the band at high densities is shown to be in agreement with the theory of motional narrowing of Alekseev and Sobel'man. A brief comparison of the broadening and shifting of the Q branch of HD with that for H2 is made.
Any lattice in which the hydrogen atoms would be translationally identical (Bravais lattice) would have metallic properties. In the present paper the energy of a body‐centered lattice of hydrogen is calculated as a function of the lattice constant. This energy is shown to assume its minimum value for a lattice constant which corresponds to a density many times higher than that of the ordinary, molecular lattice of solid hydrogen. This minimum—though negative—is much higher than that of the molecular form. The body‐centered modification of hydrogen cannot be obtained with the present pressures, nor can the other simple metallic lattices. The chances are better, perhaps, for intermediate, layer‐like lattices.
The electrical resistance measurement of metallic conducting materials can be done in situ in a diamond‐window, high‐pressure cell with a four‐lead arrangement designed to avoid contact and lead‐wire resistances. Variants of the general method include designs for long (several cm) and short (less than 1 mm) length of samples material, and for the use of solid and fluid pressure‐transmitting media.
AT ambient pressure and low temperatures, hydrogen crystallizes in an insulating molecular phase. The possibility of a transition to a metallic structure at high pressures has been the subject of research for over fifty years1-6. Moreover, it has been recognized for some time that metallic hydrogen could be a superconductor2, but estimates of its transition temperature vary widely4,7,8. Here we present the first ab initio calculation of the electron-phonon coupling constant λ in a distorted hexagonal high-pressure (~400 GPa) phase of hydrogen; this first-principles approach has successfully predicted superconductivity in compressed silicon9,10. From the calculated value of λ for this structure, and using standard BCS-Eliashberg11-13 theory, the superconducting transition temperature Tc is estimated to be 230±85 K. Thus if metallic hydrogen were to be formed in the laboratory in the structure proposed here or in similar structures, it should be superconducting with the highest Tc yet known.
We report observations of the Raman-active vibrational overtone in normal deuterium at 77K and pressures up to 36.4 GPa (1 GPa = 10(4) bar). We observed a sharp Q2(J) line corresponding to the v = 2 <-- 0, DELTAJ = 0, k = 0, DELTAk = 0 transition and a broad Q1(J)+Q'1(J) band corresponding to v,v' = 1 <-- 0, DELTAJ = 0, k congruent-to -k' transitions. The selection rules for the Q1(J) + Q'1(J) manifold allowed us to measure the joint density of states of the manifold which we compared to a theoretical density of states for the v = 1 vibrational band.
Raman scattering from the transverse optical phonon in the hcp phase of solid H2 and D2 has been observed as a function of the density of the solid. Frequencies have been measured, with an accuracy of 0.3 cm–1, in crystals under pressures up to 5000 bar at the melting line. A linear dependence of ln TO on ln V is found (TO is the phonon frequency and V the molar volume) with mode Grneisen constants of TO = 2.07 0.03 for H2 and TO = 1.95 0.03 for D2. The ratio of the phonon frequencies of H2 and D2 at the same molar volume varies between 1.38 and 1.41 over the whole density range, in contrast to the harmonic ratio of 2 obtained from the mass ratio of 2 between H2 and D2. The results are compared with calculations of the phonon frequencies. A fit is provided so that phonon frequencies can be used as a pressure or density calibration scale.
We devised an apparatus and technique for loading diamond‐anvil cells with gases at high pressure. Cells were filled quickly and conveniently at room temperature with helium and hydrogen isotopes to initial densities exceeding those of the normal liquids. We report preliminary values of 4He and D 2 melting points based on the ruby pressure scale and compare them with extrapolations from our earlier melting curves measured to 20 kbar in a piston‐cylinder device. Our filling procedure now makes it possible to use 4He as a pressure medium in diamond cells. The technique is also useful for loading cells with gaseous mixtures.
In 1949, Mott introduced a monotomic array of hydrogen atoms rigidly fixed to the sites of a cubic lattice as a model system with which to address the many-body physics of the metal-insulator transition. Hydrogen, in nature, does not conform to this model (the monatomic constraint is not met) but nevertheless hydrogen presents a system in which many of the major ideas post-dating Mott's paper are clearly manifested. The pairing of protons implies of protons implies necessarily an even number of electrons per cell in crystalline phases, and hence the possibility of band-overlap metallization at sufficiently high density. However, the protons are highly quantum mechanical in their own right, and they possess non-trivial dynamics both translational and librational (and even rotational). On electronic timescales, the latter lead in the one-electron picture to a site-disorder problem and the possible emergence of localization phenomena. However, it is dynamic localization phenomena. However, it is dynamic localization slaved to proton timescales, and a better view of the problem is one which treats electrons and protons on the same footing, a point of view that leads to the notion of pair localization and de-localization.
We report observations of an intense Raman peak at 240 cm−1 that appears abruptly above 150 GPa at low temperatures (e.g., 77 K) in diamond-cell samples of hydrogen and deuterium. The band disappears above a critical temperature. The spectral changes are interpreted as evidence for a new high-pressure transformation.
This paper presents a simple model for such processes as spin diffusion or conduction in the "impurity band." These processes involve transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites. In this simple model the essential randomness is introduced by requiring the energy to vary randomly from site to site. It is shown that at low enough densities no diffusion at all can take place, and the criteria for transport to occur are given.
Thesis (Ph. D.)--Harvard University, 1990. Includes bibliographical references.
Optical studies on diamond at ultrahigh pressures are described which show that the unique properties of diamonds are affected by such stresses. Spectroscopic measurements show that the optical absorption edge shifts from UV to red with increasing pressures, and Raman scattering measurements how evidence for new structural transitions associated with large macroscopic deformation, beginning at a pressure of about 150 GPa. The changes are reversible and are associated with intense luminescence peaks at 2.0-2.2 eV under 458-514 nm radiation. These results may be related to the onset of bandgap closure in the approach to a new high-pressure phase. These spectral features must also be taken into account when diamond is used as optical windows for ultrahigh-pressure investigations.
We have observed a two-vibron bound-to-unbound transition in solid D2 by Raman scattering at a pressure of 34(2) GPa. We investigated the transition by increasing the vibron bandwidth, through the application of pressure, until it dominated the intramolecular anharmonicity. We present an analysis of a simple Hamiltonian that gives the experimental bivibron binding energy and the critical bandwidth-to-anharmonicity ratio. Our results indicate that while the vibron bandwidth increases markedly with pressure, the anharmonicity remains constant.
Refractive-index measurements on solid hydrogen at visible frequencies at pressures up to 170 GPa are reported. No evidence is found for a divergence at 150 GPa, close to the low-temperature phase transition observed previously and suggested as being associated with metallization. The results are consistent with closure of the indirect gap. A fit of the data to a dielectric model indicates that the onset of visible absorption due to direct interband transition should occur above 200 GPa, consistent with previous direct observations. Pressure-induced molecular dissociation may occur before closure of the direct gap.
Reflectance measurements on solid hydrogen to 177 GPa (1.77 Mbar) have been performed from near-infrared to ultraviolet wavelengths (0.5 to 3 eV). Above 150 GPa characteristic free-electron behavior in the infrared region is observed to increase sharply with increasing pressure. Analysis of volume dependence of the plasma frequency obtained from Drude-model fits to the spectra indicates that the pressure of the insulator-metal transition is 149 (+ or - 10) GPa at 295 K. The measurements are consistent with metallization by closure of an indirect gap in the molecular solid.
It is reported that the transition of condensed hydrogen from an insulating molecular crystal phase to a metallic liquid phase, at zero temperature and high pressure, appears possible. Liquid metallic hydrogen (LMH), comprising interpenetrating proton and electron fluids, would constitute a two-component Fermi liquid with both a very high component-mass ratio and long-range, species-dependent bare interactions. The low-temperature equilibrium properties of LMH are examined by means of a generalization to the case of two components of the phenomenological Landau Fermi-liquid theory, and the low-temperature specific heat, compressibility, thermal expansion coefficient and spin susceptibility are given. It is found that the specific heat and the thermal expansion coefficient are vastly greater in the liquid than in the corresponding solid, due to the presence of proton quasiparticle excitations in the liquid.
We report new phenomena associated with the infrared-active vibrons in hydrogen at megabar pressures. We find a striking 3 order of magnitude increase in vibron absorbance at the 150 GPa phase transition at 85 K. A discontinuity in the frequency of the infrared vibron is observed which is identical to that measured by Raman spectroscopy at the same temperature. The results indicate there is a significant change in electronic properties at the transition. In addition, the infrared measurements provide evidence for a phase transition at 110 GPa at low temperature.
Hydrogen and deuterium have been pressurized under static conditions to 1.47 Mbar, which is higher by a factor of 2 than the static data of Sharma et al. (1980). Measurements of the vibron indicate an initial increase and then a sharp decrease in frequency at pressures above 0.5 Mbar. At 1.14 Mbar the vibron frequency decreased to the zero-pressure value, and at 1.47 Mbar the frequency of the vibron in hydrogen is 90/cm below the value of the vibrational mode of the isolated molecule. This pronounced softening of the vibron suggests strengthened intermolecular interaction.
Raman measurements of solid normal deuterium compressed in a diamond-anvil cell indicate that the material undergoes a structural phase transformation at 190\ifmmode\pm\else\textpm\fi{}20 GPa and 77 K. Spectroscopically, the transition appears analogous to that observed in hydrogen at 145\ifmmode\pm\else\textpm\fi{}5 GPa. The large isotope effect on the transition pressure suggests there is a significant vibrational contribution to the relative stability of the solid phases of hydrogen at very high densities.
Room-temperature mixtures of hydrogen and deuterium in the fluid and solid states have been studied to 60.5 GPa (605 kbar). Raman-scattering measurements performed on these mixtures showed substantial deviations in the pressure dependence of the vibrational stretching frequencies of the molecules as compared with spectra from monomolecular hydrogenic samples. Most notably, the maximum in the vibron-frequency shift occurs at higher pressures. These observations are explained in terms of the coupling interaction between identical molecules, the same interaction that governs the Q1(0) and Q1(1) frequency shifts in ortho-para hydrogen mixtures.
For a simple model whose cohesion is dominated by dispersion forces we show that the expansion of the energy in terms of multicenter interactions is ill conditioned at a low density. This density is physically realizable for systems with highly polarizable atoms, and in these circumstances an alternative expression for the internal energy is required. For polarizable systems the requisite densities are readily achievable with the use of modern high-pressure capabilities and have consequences for the interpretation of equation-of-state data in terms of potential-energy functions.
We have used a diamond-anvil cell loaded with solid H2 as a Fabry-Perot étalon. From the interference patterns of transmitted light in the visible region the dispersion of the index of refraction is determined. This is related by a dielectric model to the optical-absorption threshold energy which is found to decrease with pressure.