Phase Diagram Of Hydrogen Research Articles

Evolution of Jupiter and Saturn with helium rain

The phase separation between hydrogen and helium at high pressures and temperatures leads to the rainout of helium in the deep interiors of Jupiter and Saturn. This process, also known as “helium rain”, affects their long-term evolution. Modeling the evolution and internal structure of Jupiter and Saturn (and giant exoplanets) relies on the phase diagram of hydrogen and helium. In this work, we simulated the evolution of Jupiter and Saturn with helium rain by applying different phase diagrams of hydrogen and helium and we searched for models that reproduce the measured atmospheric helium abundance in the present day. We find that a consistency between Jupiter’s evolution and the Galileo measurement of its atmospheric helium abundance can only be achieved if a shift in temperature is applied to the existing phase diagrams (−1250 K, +350 K or −3850 K depending on the applied phase diagram). Next, we used the shifted phase diagrams to model Saturn’s evolution and we found consistent solutions for both planets. We confirm that de-mixing in Jupiter is modest, whereas in Saturn, the process of helium rain is significant. We find that Saturn has a large helium gradient and a helium ocean. Saturn’s atmospheric helium mass fraction is estimated to be between 0.13 and 0.16. We also investigated how the applied hydrogen-helium equation of state and the atmospheric model affect the planetary evolution, finding that the predicted cooling times can change by several hundred million years. Constraining the level of super-adiabaticity in the helium gradient formed in Jupiter and Saturn remains challenging and should be investigated in detail in future research. We conclude that further explorations of the immiscibility between hydrogen and helium are valuable as this knowledge directly affects the evolution and current structure of Jupiter and Saturn. Finally, we argue that measuring Saturn’s atmospheric helium content is crucial for constraining Saturn’s evolution as well as the hydrogen-helium phase diagram.

Are claims of cheap muon production correct?

Abstract Background Muon catalyzed fusion is a process, whereby isotopes of hydrogen undergo nuclear fusion thanks to a muon replacing an electron bringing the nuclei within fusion distance. The muon is then ejected and can facilitate a next fusion process. ‘Break even’ has not been achieved yet in spite of the optimization of isotope mixtures and initial muon energy. A main limiting factor is the muon lifetime and the cost in energy of accelerator-based muon production. The possibilities would receive an immense boost toward practical applications if a cheap muon source could be constructed. We challenge a recent publication claiming to have constructed a very intense, yet very ‘cheap’ muon source. Main text A recent publication in this journal (Holmlid in Energ Sustain 12:14, 2022, 10.1186/s13705-022-00338-4) promotes the idea that such a source has been constructed and demonstrated. The suggestion is based on a long series of articles by the same author as main investigator. They all center around a spectacular new aggregation state of hydrogen, so called ultra-dense hydrogen (UDH). The claims in the article (Holmlid in Energ Sustain 12:14, 2022, 10.1186/s13705-022-00338-4), as well as in the previous articles, are based on speculations going far beyond the experiments they purport to explain, and on a striking disregard of very well-established facts, both concerning conservation laws, elementary quantum mechanics and the phase diagrams of hydrogen. There are strong arguments why the claimed muon production does not occur and that the suggested evidence for it is a collection of instrumental artefacts. Conclusion The muon source suggested by Holmlid (Energ Sustain 12:14, 2022, 10.1186/s13705-022-00338-4) does not produce any muons.

High temperature superconductivity in the candidate phases of solid hydrogen

As the simplest element in nature, unraveling the phase diagram of hydrogen is a primary task for condensed matter physics. As conjectured many decades ago, in the low-temperature and high-pressure part of the phase diagram, solid hydrogen is expected to become metallic with a high superconducting transition temperature. The metallization may occur via band gap closure in the molecular solid or via a transition to the atomic solid. Recently, a few experimental studies pushed the achievable pressures into the 400–500 GPa range. There are strong indications that at some pressure in this range metallization via either of these mechanisms occurs, although there are disagreements between experimental reports. Furthermore, there are multiple good candidate crystal phases that have emerged from recent computational and experimental studies which may be realized in upcoming experiments. Therefore, it is crucial to determine the superconducting properties of these candidate phases. In a recent study, we reported the superconducting properties of the C2/c-24 phase, which we believe to be a strong candidate for metallization via band gap closure (Dogan et al 2022 Phys. Rev. B 105 L020509). Here, we report the superconducting properties of the Cmca-12, Cmca-4 and I41/amd-2 phases including the anharmonic effects using a Wannier function-based dense k-point and q-point sampling. We find that the Cmca-12 phase has a superconducting transition temperature that rises from 86 K at 400 GPa to 212 K at 500 GPa, whereas the Cmca-4 and I41/amd-2 phases show a less pressure-dependent behavior with their T c in the 74–94 K and 307–343 K ranges, respectively. These properties can be used to distinguish between crystal phases in future experiments. Understanding superconductivity in pure hydrogen is also important in the study of high-T c hydrides.

Manipulation of the crystalline phase diagram of hydrogen through nanoscale confinement effects in porous carbons.

Condensed phases of molecular hydrogen (H2) are highly desired for clean energy applications ranging from hydrogen storage to nuclear fusion and superconductive energy storage. However, in bulk hydrogen, such dense phases typically only form at exceedingly low temperatures or extremely high (typically hundreds of GPa) pressures. Here, confinement of H2 within nanoporous materials is shown to significantly manipulate the hydrogen phase diagram leading to preferential stabilization of unusual crystalline H2 phases. Using pressure and temperature-dependent neutron scattering at pressures between 200-2000 bar (0.02-0.2 GPa) and temperatures between 10-77 K to map out the phase diagram of H2 when confined inside both meso- and microporous carbons, we conclusively demonstrate the preferential stabilisation of face-centred cubic (FCC) solid ortho-H2 in microporous carbons, at temperatures five times higher than would be possible in bulk H2. Through examination of nanoconfined H2 rotational dynamics, preferential adsorption and spin trapping of ortho-H2, as well as the loss of rotational energy and severe restriction of rotational degrees of freedom caused by the unique micropore environments, are shown to result in changes to phase behaviour. This work provides a general strategy for further manipulation of the H2 phase diagram via nanoconfinement effects, and for tuning of anisotropic potential through control of confining material composition and pore size. This approach could potentially provide lower energy routes to the formation and study of more exotic non-equilibrium condensed phases of hydrogen that could be useful for a wide range of energy applications.

Metallic Hydrogen: A Liquid Superconductor?

Metallic hydrogen is expected to exhibit remarkable physics. Of particular interest in this work is the possibility of high-temperature superconductivity. Comparing calculations of the superconducting critical temperatures of the solid phase to melting temperatures over a range of pressures leads to an interesting question: Will the solid, in a superconducting state, melt to a liquid that remains a superconductor? In this work, the possibility of liquid superconductivity in metallic hydrogen is investigated. This is done by first-principles simulations, and using the results of these to solve the Eliashberg equations. These are carried out over the pressure (and temperature) conditions where molecular dissociation is expected to first occur in the solid phase. Over the pressure range $386.8(4)$--$783.7(4)$ GPa, $T_c$ increases from $308(6)$ to $372(2)$ K with a maximum uncertainty of $10$ K; it then decreases to $356(2)$ K at $883.7(3)$ GPa. Comparisons to the solid phase show that the critical temperature is not significantly changed between the two phases, though the physics behind their superconductivity is different. Careful comparisons of these values to recent results in the context of the hydrogen phase diagram show that they are higher than the melting temperatures and that the solid will melt to liquid atomic hydrogen. The results of this work (in this context) therefore suggest that liquid atomic hydrogen will indeed exist in a superconducting state. They also provide the pressure and temperature conditions over which to look for it.

Construction of phase diagrams to estimate phase transitions at high pressures: A critical point at the solid liquid transition for benzene

Phase diagrams are an integral part of the estimation of material properties in the case of high temperature and pressure. The pressure-temperature (P-T) phase diagram is used to determine the state of aggregation (solid, liquid, gaseous) of a substance under given conditions. This article presents a method to reveal new states in the phase diagram, including the possibility of the plasma state. Using the empirical data of benzene, a critical pressure beyond solid-liquid equilibrium was estimated. It is highly probable that beyond these pressures, benzene may ionize and exhibit plasma behavior. The method proposed in this work for benzene could also be applied to create a comprehensive phase diagram of Hydrogen at certain pressure and temperature. Because the complex behavior of hydrogen, as well as the constant discovery of new varieties and the creation of many different phases of hydrogen makes it very difficult to construct a realistic phase diagram.

Understanding high pressure molecular hydrogen with a hierarchical machine-learned potential

The hydrogen phase diagram has several unusual features which are well reproduced by density functional calculations. Unfortunately, these calculations do not provide good physical insights into why those features occur. Here, we present a fast interatomic potential, which reproduces the molecular hydrogen phases: orientationally disordered Phase I; broken-symmetry Phase II and reentrant melt curve. The H2 vibrational frequency drops at high pressure because of increased coupling between neighbouring molecules, not bond weakening. Liquid H2 is denser than coexisting close-packed solid at high pressure because the favored molecular orientation switches from quadrupole-energy-minimizing to steric-repulsion-minimizing. The latter allows molecules to get closer together, without the atoms getting closer, but cannot be achieved within in a close-packed layer due to frustration. A similar effect causes negative thermal expansion. At high pressure, rotation is hindered in Phase I, such that it cannot be regarded as a molecular rotor phase.

Understanding dense hydrogen at planetary conditions

Materials at high pressures and temperatures are of great interest for planetary science and astrophysics, warm dense-matter physics and inertial confinement fusion research. Planetary structure models rely on an understanding of the behaviour of elements and their mixtures under conditions that do not exist on Earth; at the same time, planets serve as natural laboratories for studying materials at extreme conditions. The topic of dense hydrogen is timely given the recent accurate measurements of the gravitational fields of Jupiter and Saturn, the current and upcoming progress in shock experiments, and the advances in numerical simulations of materials at high pressure. In this Review we discuss the connection between modelling planetary interiors and the high-pressure physics of hydrogen and helium. We summarize key experiments and theoretical approaches for determining the equation of state and phase diagram of hydrogen and helium. We relate this to current knowledge of the internal structures of Jupiter and Saturn, and discuss the importance of high-pressure physics to their characterization. Understanding the behaviour of materials at high pressures and temperatures is of great importance to planetary science and the physics of warm dense matter. This Review addresses the close connection between modelling the interiors of gaseous planets and the high-pressure physics of hydrogen and helium.

Estimating volume fractions of superabundant vacancy phases and their potential roles in low energy nuclear reactions and high conductivity in the palladium – isotopic hydrogen system

The addition of three superabundant vacancy (SAV) phases, γ (Pd7VacD6–8), δ (Pd3VacD4 – octahedral), and δ′ (Pd3VacD4 – tetrahedral) to the palladium – isotopic hydrogen phase diagram was recently reported [1]. Also, in that study, production of excess heat from a nuclear source during electrolysis in heavy water indicated portions of the palladium (Pd) – deuterium (D) specimen were in the ordered δ phase, while a drop in resistance of the Pd during excess heat, with an increase in temperature, indicated portions of the specimen had shifted to the ordered δ′ phase. Both δ and δ′, create intersecting channels along the edges of the unit cells which are in effect long strings of Pd lattice vacancies for fast electron transport or a deuteron resonance condition. At high D/Pd ratio, the Pd-D alloy can be multiphase. An estimate of the volume fraction (fv) of δ phase is made from the amount of nuclear energy measured. An estimate of fv of δ′ is made from the measurement of the change in resistivity of the overall multiphase Pd-D alloy using the rule of mixtures. Both δ and δ′ have low volume fractions with fv(δ) ≈ 0.03% and fv(δ′) ≈ 5%. These experimental measurements suggest that δ is the nuclear active environment (NAE) for low energy nuclear reactions (LENR) while δ′ is likely a high conducting state (phase). Which interstitial site (octahedral or tetrahedral) is occupied by isotopic hydrogen would determine whether the phase is nuclear active or highly conductive. These two phases are distinct and can coexist as minor volumetric components (phases) because they are both of low volume fractions, share the same composition (arrangement of Pd and lattice vacancy sites, and can also share the same D/Pd ratio), and result from hydrogen-induced vacancy formation. Thus, portions of the specimen can be producing nuclear energy (excess heat) while other portions can be highly conductive.

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

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

Quantum phase transition in solid hydrogen at high pressure

Extensive experimental and theoretical studies have been devoted to determining the high-pressure phase diagram of hydrogen. We present evidence of a phase at a higher pressure than phase III and below the pressure of the recently observed phase of metallic hydrogen (495 GPa). This phase was determined from infrared (IR) spectroscopy of hydrogen samples at static pressures above 360 \ifmmode\pm\else\textpm\fi{} 15 GPa in a diamond anvil cell, and has been observed in three separate experiments. Whereas earlier studies found new high-pressure phases that only occurred at elevated temperatures, this phase transition occurs at the lowest temperatures investigated, \ensuremath{\sim}5 K, and the steep phase line indicates that it is a quantum phase transition. This phase is characterized by two distinct IR absorption bands (2950 and $3335\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ at 365 GPa). Above the transition pressure we observe strong darkening of the sample in the visible spectrum as pressure is increased. Observations are compatible with the cmca-12 crystal structure.

A comparative study using state-of-the-art electronic structure theories on solid hydrogen phases under high pressures

Identifying the atomic structure and properties of solid hydrogen under high pressures is a long-standing problem of high-pressure physics with far-reaching significance in planetary and materials science. Determining the pressure-temperature phase diagram of hydrogen is challenging for experiment and theory due to the extreme conditions and the required accuracy in the quantum mechanical treatment of the constituent electrons and nuclei, respectively. Here, we demonstrate explicitly that coupled cluster theory can serve as a computationally efficient theoretical tool to predict solid hydrogen phases with high accuracy. We present a first principles study of solid hydrogen phases at pressures ranging from 100 to 450 GPa. The computed static lattice enthalpies are compared to state-of-the-art diffusion Monte Carlo results and density functional theory calculations. Our coupled cluster theory results for the most stable phases including C2/c-24 and P2{}_{1}/c-24 are in good agreement with those obtained using diffusion Monte Carlo, with the exception of Cmca-4, which is predicted to be significantly less stable. We discuss the scope of the employed methods and how they can contribute as efficient and complementary theoretical tools to solve the long-standing puzzle of understanding solid hydrogen phases at high pressures.

Effect of Additional Hydrogen Alloying on the Structure and the Phase Composition of a VTI-4 Intermetallic Alloy

The formation of the structure and the phase composition of a heat-resistant titanium VTI-4 orthorhombic-intermetallic-based alloy is studied in the course of its alloying with hydrogen to different hydrogen contents. The laws of the changes in the phase composition of the hydrogen-containing alloy upon heating to different temperatures are determined. A portion of the VTI-4 alloy–hydrogen phase diagram under the conditions under study is constructed; it demonstrates the location of phase regions as a function of temperature and hydrogen content.

Deuterium Hugoniot: Pitfalls of thermodynamic sampling beyond density functional theory

Outstanding problems in the high-pressure phase diagram of hydrogen have demonstrated the need for more accurate ab initio methods for thermodynamic sampling. One promising method that has been deployed extensively above 100 GPa is coupled electron-ion Monte Carlo (CEIMC), which treats the electronic structure with quantum Monte Carlo (QMC). However, CEIMC predictions of the deuterium principal Hugoniot disagree significantly with experiment, overshooting the experimentally determined peak compression density by $7%$ and lower temperature gas-gun data by well over $20%$. By deriving an equation relating the predicted Hugoniot density to underlying equation of state errors, we show that QMC and many-body methods can easily spoil the error cancellation properties inherent in the Rankine-Hugoniot relation, and very likely suffer from error addition. By cross validating QMC based on systematically improvable trial functions against post-Hartree-Fock many-body methods, we find that these methods introduce errors of the right sign and magnitude to account for much of the observed discrepancy between CEIMC and experiment. We stress that this is not just a CEIMC problem, but that thermodynamic sampling based on other many-body methods is likely to experience similar difficulties.

High-pressure phase diagram of hydrogen and deuterium sulfides from first principles: Structural and vibrational properties including quantum and anharmonic effects

We study the structural and vibrational properties of the high-temperature superconducting sulfur trihydride and trideuteride in the high-pressure $Im\bar{3}m$ and $R3m$ phases by first-principles density-functional-theory calculations. On lowering pressure, the rhombohedral transition $Im\bar{3}m \rightarrow R3m$ is expected, with hydrogen bond desymmetrization and occurrence of trigonal lattice distortion. In hydrostatic conditions we find that, contrary to what suggested in some recent experiments, if the rhombohedral distortion exists it affects mainly the hydrogen-bonds, whereas the resulting cell distortion is minimal. We estimate that the occurrence of a stress anisotropy of approximately $10\%$ could explain this discrepancy. Assuming hydrostatic conditions, we calculate the critical pressure at which the rhombohedral transition occurs. Quantum and anharmonic effects, which are relevant in this system, are included at nonperturbative level with the stochastic self-consistent harmonic approximation (SSCHA). Within this approach, we determine the transition pressure by calculating the free energy Hessian. We find that quantum anharmonic effects are responsible for a strong reduction of the critical pressure with respect to the one obtained with the classical harmonic approach. Moreover, we observe a prominent isotope effect, as we estimate higher pressure transition for D${}_3$S than for H${}_3$S. Finally, within SSCHA we calculate the anharmonic phonon spectral functions in the $Im\bar{3}m$ phase. The strong anharmonicity of the system is confirmed by the occurrence of very large anharmonic broadenings leading to complex non-Lorentzian line shapes. However, for the vibrational spectra at zone center, accessible e.g. by infrared spectroscopy, the broadenings are very small (linewidth at most around 2~meV) and anharmonic phonon quasiparticles are well defined.

Phase Diagram of Hydrogen and a Hydrogen-Helium Mixture at Planetary Conditions by Quantum MonteCarlo Simulations.

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

Hydrogen and its compounds under extreme pressure**This review presents an extension of the talk by the authors for the scientific session of the Physical Sciences Division of the Russian Academy of Sciences, “Old and new ideas in phase transition physics,” which was held on December 21, 2016 (see Phys. Usp. 60 948–957 (2017); Usp. Fiz. Nauk 187 1021 (2017)). (Editor’s

In the last two or three years, significant advances in the study of hydrogen and its compounds under extreme conditions (ultrahigh pressures over a wide temperature range) have notably changed the hydrogen phase diagram, provided a break-through in understanding hydrides’ behavior under pressure (as exemplified by the discovery of high-temperature superconductivity in hydrogen sulfide), and, finally, enabled achieving cold metallization of hydrogen. The situation prior to the 2010s is reviewed in brief and more recent work is examined in detail. While the primary focus is on experimental research, mention is also made of the theoretical and numerical work it stimulates.

Simple thermodynamic model for the hydrogen phase diagram

We describe a classical thermodynamic model that reproduces the main features of the solid hydrogen phase diagram. In particular, we show how the general structure types that are found by electronic structure calculations and the quantum nature of the protons can also be understood from a classical viewpoint. The model provides a picture not only of crystal structure, but also for the anomalous melting curve and insights into isotope effects, liquid metallisation and InfraRed activity. The existence of a classical picture for this most quantum of condensed matter systems provides a surprising extension of the correspondence principle of quantum mechanics, in particular the equivalent effects of classical and quantum uncertainty.

Predicted reentrant melting of dense hydrogen at ultra-high pressures.

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

Quantum Monte Carlo study of the phase diagram of solid molecular hydrogen at extreme pressures.

Establishing the phase diagram of hydrogen is a major challenge for experimental and theoretical physics. Experiment alone cannot establish the atomic structure of solid hydrogen at high pressure, because hydrogen scatters X-rays only weakly. Instead, our understanding of the atomic structure is largely based on density functional theory (DFT). By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase. Unfortunately, DFT predicts a metallic structure to be energetically favoured at a broad range of pressures up to 400 GPa, where it is known experimentally that hydrogen is non-metallic. Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment. This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.