Phase Diagram Of Hydrogen Research Articles

Phase separation in giant planets: inhomogeneous evolution of Saturn

We present the first models of Jupiter and Saturn to couple their evolution to both a radiative-atmosphere grid and to high-pressure phase diagrams of hydrogen with helium and other admixtures. We find that prior calculated phase diagrams in which Saturn's interior reaches a region of predicted helium immiscibility do not allow enough energy release to prolong Saturn's cooling to its known age and effective temperature. We explore modifications to published phase diagrams that would lead to greater energy release, and propose a modified H–He phase diagram that is physically reasonable, leads to the correct extension of Saturn's cooling, and predicts an atmospheric helium mass fraction Y atmos=0.185, in agreement with recent estimates. We also explore the possibility of internal separation of elements heavier than helium, and find that, alternatively, such separation could prolong Saturn's cooling to its known age and effective temperature under a realistic phase diagram and heavy element abundance (in which case Saturn's Y atmos would be solar but heavier elements would be depleted). In none of these scenarios does Jupiter's interior evolve to any region of helium or heavy-element immiscibility: Jupiter evolves homogeneously to the present day. We discuss the implications of our calculations for Saturn's primordial core mass.

Chemical potential and phase diagrams of hydrogen in palladium

The contribution of hydrogen atoms oscillations in Palladium in pair interaction H–H is calculated. The interpolation formula for an electronic chemical potential of a hydrogen subsystem containing only two energy parameter is obtained. It is shown that the approximation of an mean field for the configuration contribution to a chemical potential with renormalized due to oscillations to energy parameters with allowance for of electronic contribution satisfactorily describes an equilibrium of phases in a system a palladium–hydrogen.

First-Principles Surface Phase Diagram for Hydrogen on GaN Surfaces

We discuss the derivation and interpretation of a generalized surface phase diagram, based on first-principles density-functional calculations. Applying the approach to hydrogenated GaN surfaces, we find that the Gibbs free energies of relevant reconstructions strongly depend on temperature and pressure. Choosing chemical potentials as variables results in a phase diagram that provides immediate insight into the relative stability of different structures. A comparison with recent experiments illustrates the power of the approach for interpreting and predicting energetic and structural properties of surfaces under realistic growth conditions.

The status of the low-temperature phase diagram of hydrogen at the turn of the century

Hydrogen is the simplest element in nature. This simplicity in the atomic state is often assumed to hold also for its condensed phases. Nevertheless, experiments carried out during the past 15 years of the XXth century have shown that this picture is not necessarily a faithful one. Several different low-temperature solid phases have been identified, in contrast with the simplicity idea. These exhibit outstanding features like pressure-independent phonon bands, large isotope effects, and strong infrared activity. In this paper I will give an overview of the current understanding of the low-temperature region of the phase diagram of hydrogen, as emerges from a fruitful cooperative action between diamond anvil cell experiments and first-principles theoretical calculations.

Summary

Summary

States of matter in massive planets

This brief article addresses the question: among the very large number of interesting condensed matter physics issues, which are particularly interesting from a planetary perspective? Following some definitions and background, it is argued that we need to understand relevant first-order phase transitions (especially the nature of the hydrogen phase diagram), the behaviour of the entropy (i.e., the Grüneisen parameter), the solubility and partitioning of minor elements (e.g. noble gases mixed with hydrogen), and microscopic transport properties, especially electrical and thermal conductivity. Examples are presented of how these issues influence current interpretations of the observations of Jupiter in particular. In the future, it may be possible to observe spectroscopically the compositions of extra-solar-system planets and brown dwarfs, and thereby learn more about the physics of these bodies.

A survey of some outstanding questions in dense hydrogen

Dense hydrogen, sometimes thought of as the simplest condensed matter system, continues to be a cautionary tale against overconfidence in the predictive powers of condensed matter theory. Recent experimental advances using diamond anvil cells (DACs), and single and multi-shock compression all present new challenges to theory, and old questions such as the ground state insulator to metal transition pressure remain almost as unsettled as when originally proposed by Wigner and Huntington 60 years ago. This article gives an overview of efforts to understand two areas of the hydrogen phase diagram: the low to room temperature region probed by DAC experiments and the 0.5–2.0 Mbar pressure, 0.5–3.0 e.v. temperature range now being explored in deuterium using laser-generated shocks. The aim is to provide nonspecialists with a guide to this interesting and active field.

Phase equilibrium of quantum fluids from simulation: Hydrogen and neon

A detailed derivation of a new method for directly computing phase equilibria for quantum fluids is presented. This method is a combination of the path integral formalism with the Gibbs ensemble technique. We use this path integral Gibbs ensemble Monte Carlo method to calculate the vapor-liquid phase diagrams of hydrogen and neon from simulation. Agreement with experimental data is very good. The thermodynamic properties of neon and hydrogen are computed over a wide range of temperatures and pressures. The densities and energies from the simulations are in excellent agreement with literature data. Three different parameter sets for the Lennard-Jones (LJ) neon potential are evaluated by comparing simulation results with experimental data. The Silvera-Goldman potential and Buch LJ potential for hydrogen are evaluated against data on the 100 MPa, 1 GPa, and 2 GPa isobars.

Dissociation and Thermodynamics in Dense Hydrogen Fluid

AbstractThe behavior of matter at high pressures is studied for a better understanding of planetary interiors and the structure and evolution of stars, or for inertial confinement fusion. Especially, the phase diagram of hydrogen and helium as the most abundant elements in the universe has been studied both theoretically and experimentally up to ultra‐high pressures in the Mbar region where metallization is expected to occur. While static high‐pressure experiments in diamond anvil cells give no evidence for metallic conduction in solid hydrogen up to 250 GPa, recent dynamic shock‐wave experiments in fluid hydrogen have demonstrated metallization for the first time at 140 GPa and 3000 K. The equation of state, possible phase transitions, and the structural properties of fluid hydrogen at ultra‐high pressures as well as of hydrogen plasma at elevated temperatures are of special interest. We use here analytical calculations and Monte Carlo simulations to determine the pair distribution functions in partly dissociated hydrogen. The equation of state and the degree of dissociation are calculated. The gradual transition from molecular to atomic hydrogen occurs due to pressure dissociation. Furthermore, we show the influence of dissociation on the proton‐proton pair distribution function.

Thermodynamic properties and phase equilibrium of fluid hydrogen from path integral simulations

The thermodynamic properties of normal and para-hydrogen are computed from multiple time-step path integral hybrid Monte Carlo (PIHMC) simulations. Four different isotropic pair potentials are evaluated by comparing simulation results with experimental data. The Silvera–Goldman potential is found to be the most accurate of the potentials tested for computing the density and internal energy of fluid hydrogen. Using the Silvera–Goldman potential, simulation and experimental data are compared on isobars ranging from 0.1 to 100 MPa and for temperatures from 18 to 300 K. The Gibbs free energy is calculated from the PIHMC simulations by an adaptation of Widom's particle insertion technique to a path integral fluid. A new method is developed for computing phase equilibria for quantum fluids directly by combining PIHMC with the Gibbs ensemble technique. This Gibbs–PIHMC method is used to calculate the vapour–liquid phase diagram of hydrogen from simulations. Agreement with experimental data is good.

The Phase Diagram of Hydrogen in Ultra Thin Films

AbstractIn this paper, we discuss changes in the phase diagram of hydrogen in both bilayer (i.e. 200–2000 Å Nb/ 100 Å Pd on glass) and multilayer configurations. In fact, it is the changes in this phase diagram, in addition to the Pd coating, that makes theses bilayer systems useful for hydrogen gas sensors. Comparison of x-ray diffraction, electrical resistivity and volumetric measurements of the films before and after hydrogen charging indicate that the phase equilibria between a correlated (high concentration) and a dilute phase of hydrogen in Nb is not sensitive to the number of layers in the films. On the other hand, the experimental methods show different behavior for 200 Å thick Nb films and thicker (>400 Å) Nb layers. Diffraction results showing unisotropic lattice expansion will also be discussed..

Triplet interactions and the c(2×2) overlayer phase diagram

Abstract Square lattice phase diagrams are investigated with the extended Ising model, considering pair and triplet interactions. We determine the stability of the c(2×2) structure as a function of different triplet interactions. A systematical study of the asymmetry of the phase diagram shows that the triplet interactions with two nnn bounds play a major role in producing an asymmetric phase diagram. The experimental phase diagram of hydrogen adsorbed on a Pd (001) surface is discussed within this framework.

Hydrogen on Rh(110): a walk through the phase diagram

Hydrogen adsorption leads to a number of five commensurate phases, namely 1 × 3-H (θ = 0.33), 1 × 2-H (θ = 0.5), 1 × 3−2H (θ = 0.66), 1 × 2−2H (θ = 1) and 1 × 1−2H (θ = 2). Low-energy electron diffraction (LEED) combined with thermal desorption spectroscopy (TDS) were used to investigate the phase diagram of hydrogen on Rh(110) in the temperature range of 35–220 K. To study the growth and disordering of the different commensurate phases we analyzed beam profiles and integral intensities of the fractional order beams as a function of coverage (θ) and temperature ( T). By changing the coverage it was found that homogeneous areas of commensurate phases are separated by coexistence regions indicating a first-order phase transition (1 × 3−H ↔ 1 × 2−H; 1 × 3−2H ↔ 1 × 2−2H). Upon temperature variation at constant coverage reversible order-disorder phase transitions were only observed for the phases 1 × 3−H and 1 × 2−H. For coverages θ > 0.5 critical temperatures lie close to or above the desorption boundary. So thermal desorption is a process competing with the respective order-disorder transition. The phase boundaries of the 1 × 3−H and 1 × 2−H phases were determined by evaluating the coverage-dependent transition temperatures which also yield critical temperatures of T c = 132 ± 5 K (1 × 3−H) and T c = 150 ± 5 K (1 × 2−H). The 1 × 3−H phase undergoes a second-order phase transition to lattice-gas disorder, whereas for the 1 × 2−H phase a commensurate-incommensurate phase transition is observed.

Path-integral simulations of hydrogen and hydrogen plasmas.

Feynman path-integral simulations of a system consisting of protons and distinguishable electrons under periodic boundary conditions are presented with the aim of calculating the phase diagram of hydrogen at various temperatures and densities. For a two-electron--two-proton system, for which Fermi statistics can be ignored, the equations of state and the radial distribution functions are obtained, including the effects of temperature and pressure ionization, for temperatures down to 0.68 eV and densities up to 1 g ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. These results are compared to other models. Systems with more than two distinguishable electrons are found to be thermodynamically unstable, by collapsing into a cluster at low temperature, suggesting that further simulations be used to investigate the stability of Boltzmann matter.

Effective-medium calculations for hydrogen in Ni, Pd, and Pt

The effective-medium theory is applied to a study of the energetics of the hydrides of Ni, Pd, and Pt, stressing the properties of ${\mathrm{PdH}}_{\mathrm{\ensuremath{\theta}}}$ for 0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}1. The calculated heat of solution and the heat of hydride formation for the three systems agree very well with experiment. We determine the favored structure for ${\mathrm{PdH}}_{\mathrm{\ensuremath{\theta}}}$ by calculating the total energy and lattice expansion of different configurations. Vibrational frequencies and diffusion barriers of H in Pd are also treated. A simple and transparent physical picture of the hydrogen-metal interaction is developed. From the calculated energetics we make a model calculation of the phase diagram of hydrogen in palladium in qualitative agreement with experiment. On this basis we propose a new explanation of the peculiarities of the Pd-H system.

Single-crystal x-ray diffraction of n-H2 at high pressure.

X-ray diffraction from a single crystal of solid $n$-${\mathrm{H}}_{2}$ has been obtained at high pressure in a diamond-anvil cell, and the crystal structure has been determined. Nineteen diffraction maxima, corresponding to the hexagonal-close-packed structure ($\frac{P{6}_{3}}{\mathrm{mmc}}$, $Z=2$), were observed. Unit-cell dimensions at 5.40\ifmmode\pm\else\textpm\fi{}0.03 GPa and 300\ifmmode\pm\else\textpm\fi{}1 K are $a=2.659\ifmmode\pm\else\textpm\fi{}0.002$ \AA{}, $c=4.334\ifmmode\pm\else\textpm\fi{}0.003$ \AA{}, and $V=26.55\ifmmode\pm\else\textpm\fi{}0.05$ ${\mathrm{\AA{}}}^{3}$. The structure determination and volume measurement provide the most accurate checks to date on the equation of state and phase diagram of hydrogen in this pressure range.

On the theory of the interactions and phase transitions of hydrogen in the transition metals

Analytical methods based on the cluster approximation described previously are proposed for calculating the thermodynamic properties and phase diagrams of hydrogen in transition metals (Me). In contrast with the mean field approaches usually adopted, these methods allow quantitatively for the strong short-range correlation effects, including blocking and competitive interaction, which are characteristic of Me-H systems. Detailed calculations of the stress-induced and screened Coulomb H-H interactions for the NbH x and PdH x systems have also been performed. They reveal that the blocking effects in b.c.c. Me-H systems are apparently due to the anharmonicity of the stress-induced interactions at small H-H distances. Applications of the methods developed to the description of the incoherent α-α′ phase transitions in NbH x and PdH x and α⊂α)-β phase transitions in NbH x have shown that the methods have a high accuracy and are well suited to the theory of the Me-H systems. In particular, results have been obtained which suggest that many-body interactions of hydrogen atoms have a noticeable effect on the phase diagrams of b.c.c. MeH x alloys.

Phase diagram of hydrogen adsorbed on Ni(111)

The phase diagram for the H/Ni(111) system is calculated by treating a lattice gas on a honeycomb lattice through the position-space renormalization-group theory with prefacing transformation. The following interparticle interactions are considered: (A) nearest-neighbor exclusion, second-neighbor repulsion, and third-neighbor attraction, which was previously proposed by Domany et al.; (B) nearest-neighbor exclusion, second- and third-neighbor repulsions, and further-neighbor interactions up to the sixth-neighbor one. When the interaction parameters involved are suitably adjusted, both the interactions (A) and (B) lead to the phase diagrams in good agreement with the experimental one by Christmann et al. The change of the isosteric heat of hydrogen adsorption with the adsorbed amount is also calculated. The result obtained from interaction (B) is consistent with experiment, whereas that from interaction (A) is not.

Phase diagram of hydrogen adsorbed on Ni(111)

An explanation for the phase diagram of the H/Ni(111) system is proposed, where the existence of the p(2 × 2) phase is assumed in addition to the (2 × 2) phase. Using the position-space renormalization-group theory with prefacing transformation, a lattice gas on a honeycomb lattice, including up to 6th nearest neighbor interactions, is treated. Another explanation previously put forward by Domany et al. is also examined, where the occurrence of the (2 × 2) ordered phase and the gas + p(2 × 2) coexistence phase is assumed. The phase diagrams thus obtained for these two cases are exhibited and discussed.

Phase diagram of hydrogen adsorbed on Ni(111)

An explanation for the phase diagram of the H/Ni(111) system is proposed, where the existence of the p(2×2) phase is assumed in addition to the (2×2) phase. Using the position-space renormalization-group theory with prefacing transformation, a lattice gas on a honeycom lattice, including up to 6th nearest neighbor interactions, is treated. Another explanation previously put forward by Domany et al. is also examined, where the occurrence of the (2×2) ordered phase and the gas+p(2×2) coexistence phase is assumed. The phase diagrams thus obtained for these two cases are exhibited and discussed.