Order in dense hydrogen at low temperatures

Abstract

By increase in density, impelled by pressure, the electronic energy bands in dense hydrogen attain significant widths. Nevertheless, arguments can be advanced suggesting that a physically consistent description of the general consequences of this electronic structure can still be constructed from interacting but state-dependent multipoles. These reflect, in fact self-consistently, a disorder-induced localization of electron states partially manifesting the effects of proton dynamics; they retain very considerable spatial inhomogeneity (as they certainly do in the molecular limit). This description, which is valid provided that an overall energy gap has not closed, leads at a mean-field level to the expected quadrupolar coupling, but also for certain structures to the eventual emergence of dipolar terms and their coupling when a state of broken charge symmetry is developed. A simple Hamiltonian incorporating these basic features then leads to a high-density, low-temperature phase diagram that appears to be in substantial agreement with experiment. In particular, it accounts for the fact that whereas the phase I-II phase boundary has a significant isotope dependence, the phase II-III boundary has very little.A t low temperatures and ordinary pressure, crystalline hydrogen has a mean electronic density that exceeds the valence electron density of all the alkali metals and even the alkaline earths under equivalent conditions. However, it is a ground state insulator retaining this physical characteristic at densities an entire order of magnitude higher than its one atmosphere value. Under these compressions application of band theory for rigorously static lattices shows clearly that the electronic energy bands of hydrogen are appreciably wide, indicating significant overlap between the standard orbitals invoked to describe the low density phases. Yet much of the electronic charge remains well localized in the vicinity of a Bohr radius from the protons, and there is evidence that the currently accessible part of the low temperature, high density phase diagram can still be understood in terms of interactions originating with multipole expansions associated with effectively localized states and a continuing preservation of the strongly inhomogeneous character of the microscopic electron density e (1) (r). The deeper understanding of this notion, and its consequences, constitutes the bulk of what follows, but starting from an elementary observation that a macroscopic neutral quantity of hydrogen is but a dual Fermion assembly of electrons and protons, and that the dynamics of the latter have considerable influence on the former. The Dense Hydrogen ProblemThe quantum mechanics of N(ϳ10 23 ) electrons in a uniform compensating charged continuum of volume V is a well studied problem, though debate still continues on the nature of its low density states (especially in reduced dimensionality). If v c (r) ϭ e 2 ͞r is the fundamental Coulomb interaction, and if e ϭ e(N͞V) is the corresponding rigid continuum charge density, the...

Structural properties of hydrogen isotopes in solid phase in the context of inertial confinement fusion

“…It shows four images: bottom pictures are projections for all the molecules on the YZ plane, where you can observe a much more pronounced phase difference for the 1 GPa test. In that case, (Figure 2, left), projection is a circle, ie the molecules are free rotors, while in the case of 45 GPa (Figure 2, right), there is an alignment of molecules with restricted rotation, according to the image proposed by different authors [7,13]. Top of the figure shows the projections on the XY plane.…”

“…Comparison is possible through the theoretical model and predictions from Toledano et al [13]. Different experimental works discuss the transition from Phase I to Phase II of the hydrogen, that jumps from a configuration with molecules as free rotors (the atoms can describe a sphere), to an order where such rotations are restricted [7,15,16]. Toledano and collaborators predict that such a transition occurs around 110 GPa.…”

“…In phase II (or the broken symmetry phase) the structure is possibly Pa3, and the rotation is hindered but is nevertheless of quite wide angle. In phase III (also called the HA phase) the structure is predicted to be in the orthorhombic class and there is still wide-angle libration [7]. In this work, we would like to raise the attention of the ICF community on this matter.…”

Symmetry Breaking in Dense Solid Hydrogen: Mechanisms for the Transitions to Phase II and Phase III

“…Above 150 GPa, phase III forms [7,8]; it has a distinct vibrational spectrum [5] and remains stable up to at least 320 GPa [9,10]. Numerous first-principles calculations have been performed to describe the structures of phases II and III [11][12][13][14][15][16][17][18][19]. Here we show that symmetry considerations provide important constraints on structural models for the different solid phases.…”

“…II transition and mass independence of the II ! III transition, which relate to the quantum properties of hydrogen and require a microscopic model, as proposed, for example, by Edwards and Ashcroft [17]. By contrast, these properties are reflected in the remaining positional disorder assumed in the structure of phase II, which disappears in phase III.…”