Sound velocities of hexagonal close-packed H2and He under pressure

Abstract

Bulk, shear, and compressional aggregate sound velocities of hydrogen and helium in the closepacked hexagonal structure are calculated over a wide pressure range using two complementary approaches: semi-empirical lattice dynamics based on the many-body intermolecular potentials and density-functional theory in the generalized gradient approximation. The sound velocities are used to calculate pressure dependence of the Debye temperature. The comparison between experiment and first-principle and semi-empirical calculations provide constraints on the density dependence of intermolecular interactions in the zero-temperature limit. 62.20.dj Hydrogen and helium are the simplest and most abundant chemical elements in the Universe. Studies of solid helium and hydrogen at elevated pressures, which started at the end of the 1920s, are of great interest for many branches of science. Hydrogen and helium are major constituents of stars and giant planets and their physical properties are very important for condensed matter physics, planetary science and astrophysics. As such the behavior of these elements under extreme environments of pressure and temperature is central to modeling the interiors of planetary and astrophysical bodies.High-pressure x-ray, Raman and infra-red (IR) studies established three molecular phases of solid hydrogen 1-4 . These phases are related to the orientational ordering of the molecules and structural transitions. In phase I, which is stable at zero temperature up to 110 GPa, hydrogen molecules are quantum rotors arranged in the hexagonal-close-packed (hcp) structure. At the I -II phase transition the molecules go from the quantum rotor state to a strongly anharmonic anisotropic librational state. Above 150 GPa solid hydrogen transforms to phase III. The molecular ordering in this phase can be treated classically. Thus, for this part of the phase diagram the most general picture can be formulated in terms of the concept of quantum versus classical orientational ordering 5 . Although the structures of phases II and III are unknown, x-ray and Raman data suggest that the hydrogen molecules in both phases lie close to the sites of the hcp lattice 6,7 . At low temperatures the molecules are stable to at least 360 GPa; but hydrogen transforms to new phases (e.g., phase IV) with increasing temperature at these pressures [8][9][10][11] .At low pressures and temperatures 4 He crystallizes into the hcp structure. High-pressure x-ray diffraction measurements 12-14 have shown that in a wide temperature (up to 400 K) and pressure (up to 58 GPa) range hcp 4 He is stable with the exception of two narrow segments adjacent to the melting curve (25.9 -30.4 bar, bcc, and 0.1 -11.6 GPa, fcc). The highest volume compression reached in the equation of state (EOS) experiments is V 0 /V = 10.4 at 180 GPa for solid hydrogen 6 (V 0 /V = 7.6 for solid D 2 15 ), and V 0 /V = 8.4 for solid helium 13 . The phonon spectra of hcp hydrogen and helium exhibits a Raman-active optical mode of the E 2g symmetry. The frequency ν(P ) ...

Elastic anisotropy and Poisson's ratio of solid helium under pressure

“…In other words, by calculat- ing v S from the proper Voigt-Reuss-Hill G in the present work we actually improve the GGA-experiment agreement compared to Ref. 17.…”

“…It has a meaning of v S calculated by using the modulus C 44 instead of the averaged shear modulus G, like we did previously in Ref. 17. For an isotropic solid G = C 44 .…”

Poisson's ratio in cryocrystals under pressure

“…The DFT calculations were performed using the FP-LMTO code RSPt, while the SE calculations were done using our own code. The calculation details have been published previously [10]. It is important to notice that the two approaches treat solid hydrogen in fundamentally different ways.…”

“…[19]. We have also included zero-point vibrations in the Debye approximation in our calculations of p(V ) and v B (V ) [10]. Generally, to find sound velocities v P and v S one has to find a complete set of elastic moduli C ij .…”

“…H2 melting curve corresponds to Kechin equation [14]. Debye temperatures were calculated using the many-body potentials: for He and H2 [10,15], for Ne and Ar [16].…”